The Biomechanics of Impact Injury

Albert I. King

The Biomechanics

of Impact Injury

Biomechanical Response, Mechanisms

of Injury, Human Tolerance and

Simulation

The Biomechanics of Impact Injury

Albert I. King

The Biomechanics of Impact

Injury

Biomechanical Response, Mechanisms

of Injury, Human Tolerance and Simulation

Albert I. King

Department of Biomedical Engineering

Wayne State University

Detroit, MI, USA

ISBN 978-3-319-49790-7 ISBN 978-3-319-49792-1 (eBook)

DOI 10.1007/978-3-319-49792-1

Library of Congress Control Number: 2016957987

© Springer International Publishing AG 2018

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of

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The registered company is Springer International Publishing AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To the Holy Spirit for inspiring, guiding,

and enabling me to write this book

To Liz, my wife for 56 years, whose patience,

love, and service have enabled me to pursue

my career and goals in injury biomechanics

Deo gratias

Preface

The aim of this book is to summarize the significant principles and research results

in injury biomechanics for graduate students and professionals in the field of

automotive safety. It is based on several decades of injury research and grew out

of a course in computer modeling of impact biomechanics that I developed and

taught for many years. Since modeling requires basic knowledge of the biomechanics

of impact, a lot of material related to impact injury was included in the

course. As a result, this book provides the reader with not only the models available

to simulate impact on the human body but also the fundamental knowledge of

impact biomechanics. It covers injury to the entire body, from head to toe, and it

discusses the four main areas of the field, namely, mechanical response, injury

mechanisms, human tolerance, and simulation of impact to various body regions.

The book is organized by body region with topics of special interest added at the

end. Head injury is emphasized because there is currently no cure for this injury,

and it is hoped that the detailed information provided will lead to effective prevention

of this injury. Topics of interest to the automotive safety engineer include side

impact and car-pedestrian impact. The book concludes with a chapter on sportsrelated

impact (contact) injuries in football and baseball. A significant portion of the

material covered is based on the work done at Wayne State University by myself;

my colleagues Dr. King H. Yang, Dr. John M. Cavanaugh, and Dr. David Viano;

and my former and current graduate students, A. Al-Bsharat, P. Begeman, B. Deng,

A. El-Bohy, N. Hakim, W. Hardy, Y. Huang, A. Irwin, R. Jadischke, K. Krieger,

N. Mital, A. Padgaonkar, P. Prasad, J. Ruan, B. Smith, S. Tennyson, P. Vulcan,

K. Yang, and C. Zhou whose work is referenced in this book. The work of former

students of Dr. King Yang and that of Toyota visiting scholars are also acknowledged.

Dr. Yang’s former students are X. Jin, J. Hu, J. Lee, H. Mao, C. Shah,

K. Wang, and L. Zhang, and the Toyota visiting scholars are S. Hayashi,

M. Iwamoto, Y. Kitagawa, and A. Tamura. To all of them, I owe a debt of gratitude

as well as to many unnamed individuals who have provided assistance.

Since biomechanics is an interdisciplinary field, some basic understanding of

mechanics (dynamics) as well as human anatomy will be helpful. However, I have

vii

viii

Preface

had biology majors with no background in physics, and mechanical and electrical

engineers with no training in anatomy take and pass my course. A fair amount of

statistics is used to assess the probability of an injury, and, for those who have no

background in statistics, some additional reading on statistics will be helpful. To

fully appreciate the mathematics behind the modeling of impact events, some

knowledge of differential equations is required.

The problems at the end of each chapter take the form of multiple choice

questions to test the student’s ability to grasp the concepts and to determine if the

student can sort out the correct answer from the many facts and figures presented in

the text.

Finally, I urge the reader to keep in mind this mantra: “You cannot prevent an

injury unless you know its cause.” Several examples are cited in the book, and some

of the unsolved problems are due precisely to a lack of understanding or knowledge

of their cause(s).

Detroit, MI, USA

Albert I. King

Acknowledgements

The assistance of many individuals was essential to the completion of this book. In

addition to those people mentioned in the Preface, I would like to thank the

following individuals:

Dawn (Dan) Li, research assistant in the Biomedical Engineering Department, for

compiling the chapters and carefully checking all aspects of the book

Sherry Barclay, librarian of the Wayne State University Libraries, for finding the

many publications referenced in the book

I would also like to express my gratitude to those who donated their bodies for

impact biomechanics research. Without their generosity, crash dummies could not

be made humanlike and computer models could not be validated.

ix

Contents

1 Introduction .......................................... 1

1.1 Injury and Injury Prevention .......................... 2

1.2 Some US and Global Statistics . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Impact Biomechanics ............................... 4

1.4 History of Impact Biomechanics . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 The Role of the Federal Government and Automotive

Safety Standards . . . . . . . . . . . . ....................... 8

1.6 Major Subdivisions of the Field of Impact Biomechanics . .... 9

1.6.1 Injury Mechanisms . . . ........................ 10

1.6.2 Response to Impact . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.6.3 Human Tolerance to Impact . . . ................. 14

1.6.4 Technology Assessment . . . . . . . . . . . . . . . . . . . . . . . 21

Questions for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Answers to Problems by Chapter . . . ......................... 32

References ............................................ 33

2 Basics of the Biomechanics of Brain Injury .................. 35

2.1 Introduction . . .................................... 35

2.2 Anatomy of the Head and Brain . . ..................... 36

2.2.1 Anatomy of the Brain ......................... 38

2.2.2 Histology of Brain Cells . . . . . . . . . . . . . . . . . . . . . . . 42

2.3 Types of Head Injury . . . ............................ 46

2.3.1 Brain Tissue Damage ......................... 47

2.4 Theories of Brain Injury Mechanisms . . . . . . . . . . . . . . . . . . . 49

2.5 Mechanical Response of the Head and Brain .............. 52

2.5.1 Visualization of Brain Response ................. 54

2.5.2 Mechanical Properties of the Pia-Arachnoid

Complex .................................. 59

xi

xii

Contents

2.6 Tolerance of the Head and Brain to Blunt Impact . . . . . ...... 64

2.6.1 Tolerance of the Skull to Fracture . . . ............. 65

2.6.2 Tolerance of the Brain to Blunt Impact . ........... 66



References ............................................ 74

3 Head Injury Research: Experimental Studies ................. 77

3.1 Experimental Research on Head Injury Mechanisms . . . . . .... 78

3.1.1 The Linear Acceleration Mechanism .............. 78

3.1.2 The Angular Acceleration Mechanism . . . . . . . . . . . . 80

3.2 Experimental Research on Head Impact Response . . . . . . . . . . 83

3.2.1 Visualization of Brain Motion during Impact . . . . . . . . 84

3.2.2 Experiments on Diffuse Axonal Injury ............ 89

3.2.3 Experiments on Focal Brain Injuries . ............. 90

3.3 Experimental Research on Human Head Tolerance

to Impact ........................................ 92

3.4 A Hypothesis for the Cause of Acute Subdural Hematoma . . . . 94

3.4.1 The Dura Mater ............................. 95

3.4.2 The Arachnoids . . ........................... 95

3.4.3 Anatomy of Cortical Vessels . . . . . . . . . . . . . . . . . . . 96

3.4.4 Acute Subdural Hematomas . . . . . . . . . . . . . . . . . . . . 97

3.4.5 Epidemiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.4.6 Biomechanical Mechanisms for the Formation of ASDH 98

3.5 Concluding Remarks ................................ 103



References ............................................ 107

4 Head Injury Research: Computer Models of Head Impact ....... 111

4.1 Pre-finite Element Models of Head Impact . . .............. 111

4.2 Finite Element Models of the Brain . . . . . . . . . . . . . . . . . . . . . 113

4.2.1 Brain Model by Ruan et al. (1994) . . . . . . . . . . . . . . . 113

4.2.2 Brain Model by Zhou et al. (1995) . . . . . . . . . . . . . . . 117

4.2.3 Brain Model by Al-Bsharat et al. (1999) ........... 118

4.2.4 Brain Model by Zhang et al. (2001): The Wayne

State University Brain Injury Model (WSUBIM) ..... 125

4.2.5 Other Finite Element Models of Brain Injury . . . . . . . . 129

4.3 Computer Models of Animal Brains . .................... 130

4.3.1 Two-Dimensional Swine Model with an Inhomogeneous

Brain ..................................... 131

4.3.2 Models of Focal Brain Injuries . . . . . . . . . . . . . . . . . . 135



Contents

xiii


References ............................................ 149

5 Measurement of Angular Acceleration ...................... 153

5.1 The Unstable Six-Accelerometer Scheme . . . . . . . . . . . . . . . . . 153

5.2 The Stable Measurement of Angular Acceleration

Using the Wayne State Method . . . . . . . . . . . . . . . . . . . . . . . . 156

5.3 Other Methods of Measuring Angular Acceleration ......... 159

5.3.1 Other Measurement Schemes Using Linear

Accelerometers . . . .......................... 159

5.3.2 Measurement Schemes Using Specially Designed

Angular Accelerometers . . . .................... 160

5.4 Validation of the Wayne State Method ................... 161

5.4.1 Criteria for Validation . . ...................... 161

5.4.2 Validation of the Wayne State Method Using Sled

Impact Data . . . ............................. 163

5.4.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 168

5.5 Miscellaneous Problems in the Measurement of Angular

Acceleration ...................................... 169

5.5.1 Frequency Response of Linear Accelerometers . . . . . . 169

5.5.2 Cross Talk in Linear Accelerometers . . . .......... 169

5.5.3 Methods of Calibrating Accelerometers . . . . . . . . . . . . 170

5.5.4 Low-Frequency Response of Accelerometer ........ 171

5.5.5 Effect of Errors in the Data . . . ................. 172

5.6 Conclusions . ..................................... 174



References ............................................ 178

6 Real-World Brain Injuries ............................... 179

6.1 Tolerance of US Football Players to Mild Concussion ....... 179

6.1.1 Study Methodology . ......................... 180

6.1.2 Discussion of the Results of the NFL Study ......... 188

6.2 Simulation of Real-World Vehicular Crashes . . . . . . . . . . . . . . 189

6.3 Head Injuries Sustained in Indy Racecars . . . . . . . . . . . . . . . . . 193

6.3.1 Some Background Information About Racecar

Safety and Crash Severities . . . . . . . . . . . . . . . . . . . . 194

6.3.2 Use of the WSUHIM to Predict Brain Response

in Indy Car Crashes . . . . . . . . .................. 196




References ............................................ 199

xiv

Contents

7 Impact Biomechanics of Neck Injury ....................... 201

7.1 A Brief Anatomical Review of the Spinal Column . . . . . . . . . . 201

7.2 Impact Injuries of the Cervical Spine .................... 207

7.2.1 Activities that Can Cause Neck Injuries ........... 208

7.2.2 Mechanisms of Cervical Spine Injuries due to Impact . 208

7.3 Experimental Studies on Cervical Spine Injuries ............ 213

7.4 Tolerance of the Cervical Spine ........................ 219

7.4.1 Tolerance of the Cervical Spine to Extension

and Flexion ................................ 219

7.4.2 Tolerance of the Cervical Spine to Compression ..... 221

7.4.3 Tolerance of the Cervical Spine to Tension ......... 222

7.4.4 Tolerance of the Cervical Spine in Shear . . ......... 223

7.5 Computer Models of the Cervical Spine . . . . . . . . . . . . . . . . . . 223

7.5.1 The Three-Dimensional Neck Model

by Yang et al. (1998) . . . . . . . . . . . . . . . . . . . . . . . . . 224




References ............................................ 239

8 The Biomechanics of Whiplash ............................ 243

8.1 Anatomy of the Spinal Cord and Neurophysiology of Pain .... 243

8.1.1 Spinal Cord Anatomy ......................... 244

8.1.2 Neurophysiology of Pain . . . . .................. 244

8.2 Hypotheses for Whiplash Pain . . . . . . . . . . . . . . . . . . . . . . . . . 245

8.2.1 The Hyperextension Hypothesis for Whiplash Pain . . . 246

8.2.2 The Muscle Hypothesis for Whiplash Pain . . . . . . . . . 246

8.2.3 The Muscle Flexion Hypothesis for Whiplash Pain . . . 247

8.2.4 A Pinching Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . 248

8.2.5 The Pressure Hypothesis . ..................... 248

8.2.6 The Shear Hypothesis for Whiplash Pain . . . ........ 249

8.3 Experimental Studies on Whiplash . . . . . . . . . . . . . . . . . . . . . 251

8.3.1 Whiplash Experiments Using Volunteers . . . . . . . . . . . 251

8.3.2 Whiplash Experiments Using Cadavers . . . . . . . . . . . . 253

8.3.3 Whiplash Experiments Using Cadavers

and High-Speed X-ray Cinematography . . . . . . . . . . . 254

8.4 Tolerance of the Neck to Whiplash ..................... 271




References ............................................ 278

9 Impact Injuries of the Thoracolumbar Spine ................. 281

9.1 Brief Anatomical Review of the Thoracolumbar Spine . . . . . . . 281

9.2 Impact Injuries of the Thoracolumbar Spine . . . ............ 283

Contents

xv

9.3 Experimental Studies on Lumbar Spine Injuries

due to +G z Acceleration . . ........................... 288

9.3.1 Early Results ............................... 290

9.3.2 Subsequent Test Results . . . .................... 291

9.3.3 Commentary . . . ............................ 303

9.4 Tolerance of the Thoracolumbar Spine ................... 304

9.5 The Issue of Acute Rupture of the Intervertebral Discs . . . . . . . 308



References ............................................ 315

10 Biomechanics of Facet Loading in the Lumbar Spine ........... 319

10.1 Direct Measurement of Lumbar Facet Loading ............. 319

10.2 The Sequence of Events Occurring During Seat Ejection ..... 328

10.3 Mechanism of Injury to the Thoracolumbar Spine

due to Ejection . . . ................................. 330

10.4 Early Models of the Spine Simulating Vertical Acceleration . . . 331

10.4.1 Lumped Parameter Spinal Models ................ 331

10.4.2 Simple Continuum Models . .................... 333

10.4.3 Discrete Parameter Models . . . .................. 333

10.5 A Two-Dimensional Model of the Thoracolumbar Spine . ..... 333

10.6 Simulation of Combined Vertical and Horizontal

Acceleration . . . ................................... 338

10.6.1 Application of the 2-D Model to the Aircraft

Ditching Problem ............................ 339

10.7 Finite Element Modeling of the Thoracolumbar Spine . . . . . . . 343


Questions for Chapter 10 .................................. 349


References ............................................ 354

11 Impact Biomechanics of the Thorax ........................ 357

11.1 Brief Anatomical Review of the Thorax . . . . . . . . . . . . . . . . . . 357

11.2 Thoracic Injury Mechanisms . . ........................ 362

11.2.1 Flail Chest . . ............................... 363

11.2.2 Lung Contusion . . . .......................... 364

11.2.3 Hemo- and Pneumothorax . .................... 364

11.2.4 Injuries to the Heart and Great Vessels ............ 364

11.3 Thoracic Injury Mechanisms . . ........................ 367

11.4 Experiments on the Thorax: Frontal and Side Impact . . . . . . . . 367

11.4.1 Frontal Impact Experiments . ................... 367

11.4.2 Side Impact Experiments . . . . . . . . . . . . . . . . . . . . . . 373

11.5 Thoracic Response to Frontal and Side Impact ............. 381

11.6 Biomechanics of Aortic Rupture due to Thoracic Impact . . . . . 382

11.7 Tolerance of the Thorax to Impact Loading ............... 388

11.8 Modeling of Thoracic Response . . . .................... 390

xvi

Contents




References ............................................ 405

12 Impact Biomechanics of the Abdomen ...................... 409

12.1 Brief Anatomical Review ............................ 409

12.1.1 Solid Abdominal Organs . . . . .................. 410

12.1.2 Hollow Abdominal Organs . .................... 413

12.2 Abdominal Injuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

12.3 Abdominal Injury Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 414

12.4 Mechanical Response of the Abdomen ................... 414

12.4.1 Abdominal Response to Frontal Impact . . . . . . . . . . . . 414

12.4.2 Abdominal Response to Lateral Impact . . . ......... 420

12.5 Tolerance of the Abdomen to Impact .................... 421

12.6 Mechanical Characterization of Abdominal Organs . . ....... 424

12.6.1 The QLV Theory ............................ 424

12.6.2 Stress–Strain Curves for Solid Abdominal

Organs (Tamura et al. 2002) .................... 427

12.7 Computer Models of the Abdomen . . . . . ................ 431

12.7.1 Model Geometry and Material Properties .......... 431

12.7.2 Material Properties of the Model Elements . . . . . . . . . 434

12.7.3 Model Validation and Predictions ................ 436




References ............................................ 445

13 Impact Biomechanics of the Pelvis ......................... 447

13.1 Anatomy of the Skeletal Pelvis . . . . . . . . . . . . . . . . . . . . . . . . 447

13.2 Pelvic Injuries Due to Impact ......................... 452

13.2.1 Femoral Neck Fractures in the Elderly . . . . . . . . . . . . 456

13.3 Mechanical Response of the Pelvis to Impact .............. 457

13.3.1 Frontal Response of the Pelvis to Impact . . . . . . . . . . . 457

13.3.2 Lateral Response of the Pelvis to Impact ........... 461

13.4 Tolerance of the Pelvis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463




References ............................................ 466

14 Impact Biomechanics of the Lower Extremities ............... 469

14.1 Anatomy of the Thigh and Leg . . . . . . . . . . . . . . . . . . . . . . . . 469

14.2 Injury Mechanisms of the Thigh and Leg . . . .............. 475

14.2.1 Long Bone Fractures Due to Tensile Strains ........ 475

14.2.2 Injury Mechanisms Involving the Knee . . . . . . . . . . . . 477

14.2.3 Injury Mechanisms Involving the Ankle . . . . . . . . . . . 484

Contents

xvii

14.3 Mechanical Response of the Thigh and Leg to Impact . . . . . . . 488

14.3.1 Response of the Femur (Knee) to Frontal Impact ..... 488

14.3.2 Tibial Response to Impact . . . . . . . . . . . . . . . . . . . . . 492

14.4 Tolerance of the Thigh and Leg to Impact . . . . . . . . . . . . . . . . 493

14.4.1 Tolerance of the Thigh (Femur) . . . . . ............ 493

14.5 Tolerance of the Leg . . . ............................. 494

14.6 The Tibia Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

14.7 An Impact Model of the Lower Extremity . . . . ............ 496




References ............................................ 505

15 Impact Biomechanics of the Foot .......................... 509

15.1 Anatomy of the Foot and Ankle ........................ 509

15.2 Injury Mechanisms and Tolerance of the Foot and Ankle . .... 514

15.3 The Lisfranc Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

15.4 A Biomechanical Study of Foot Fracture ................. 523

15.5 Modeling of Foot Impact . . . .......................... 531




References ............................................ 536

16 Side Impact ........................................... 539

16.1 The Kinematics of Side Impact ........................ 539

16.2 Side Impact Injuries and Injury Criteria .................. 541

16.3 A Cadaveric Study of Side Impact—Sled Tests . . . . . . . . . . . . 545

16.4 A Cadaveric Study of Side Impact—Pendulum Impacts . . . . . . 548

16.5 Models of Side Impact . . ............................ 551

16.5.1 Effect of Air Space . ......................... 557

16.5.2 Effect of Padding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

16.5.3 Reduction in Door Velocity . . . . . . . . . . .......... 558

16.5.4 Loss of Shoulder Engagement . . . . . . . . . . . . . . . . . . 558




References ............................................ 566

17 Car-Pedestrian Impact .................................. 569

17.1 Epidemiology of Car-Pedestrian Impact .................. 569

17.2 Car-Pedestrian Impact Experiments . . . . . . . . . . . . . . . . . . . . . 571

17.3 Modeling of Car-Pedestrian Impact . .................... 580




References ............................................ 594

xviii

Contents

18 Biomechanics of Automotive Safety Restraints ................ 597

18.1 Effectiveness of Restraints in Frontal Impact .............. 597

18.2 Effectiveness of Restraints in Side Impact . . . . . ........... 602

18.3 Effectiveness of Restraints in Rear Impact . . . . . . . . . . . . . . . . 603

18.4 Types of Rollovers ................................. 605

18.5 Rollover Crash Injury Statistics . . ...................... 610

18.6 Experimental Simulation of Rollover Crashes . . . . . . . . . . . . . 613

18.7 Modeling of Rollover Crashes ......................... 614




References ............................................ 627

19 Biomechanics of Sports Injuries ........................... 629

19.1 Overview of Sports Injuries . .......................... 629

19.2 Mild Traumatic Brain Injury in American Football . ......... 629

19.2.1 What is Mild Traumatic Brain Injury? . . . . . . . . . .... 629

19.2.2 The American Football Helmet . . . . . . . . . . . . . . . . . . 631

19.3 Acute Subdural Hematoma (ASDH) . . . . . . . . . . . . . . . . . . . . 632

19.4 Sports-Related Catastrophic Neck Injuries ................ 632

19.5 Fatal Arrhythmias in Baseball Impacts . . . . . . . . . . . . . . . . . . . 633

19.6 Ligament Injuries in Football . . . . . . . . . . . . . . . . . . . . . . . . . 637




References ............................................ 646

20 Epilogue ............................................. 649

20.1 We Have Come a Long Way . . . . . . . . . . . . . ............. 649

20.2 What is Next for Impact Biomechanics? . . . . . . . . . . ....... 651

References ............................................ 652

Index ................................................... 653

List of Figures

Fig. 1.1 Fatality rate per 100 million vehicle miles traveled

from 1922 to 2012 in the USA ..................................... 3

Fig. 1.2 Dramatic drop in annual fatality rate between 2005

and 2008 .............................................................. 4

Fig. 1.3 Professor H. R. Lissner (1908–1965) .............................. 6

Fig. 1.4 Dr. E. S. Gurdjian (1900–1985) .................................... 6

Fig. 1.5 The Wayne State Tolerance Curve for head injury .............. 7

Fig. 1.6 The hip joint—Femoral neck fractures (hip fractures)

do not occur when the greater trochanter is impacted,

and they occur in the elderly when they fall to the side.

Thus, neck fracture due to osteoporosis is the cause

of the fall, and the statement that “Grandma fell

and broke her hip” is biomechanically incorrect ................. 11

Fig. 1.7 Example of impact biomechanical response—Chest

force-deflection response due to frontal

impact by a pendulum .............................................. 12

Fig. 1.8 Example of impact biomechanical response—Contact

force-time curves for frontal head impact ........................ 13

Fig. 1.9 Example of impact biomechanical response—Accelerationtime

curve for acceleration of the 4th rib due to lateral

impact to the chest. The dark curve represents the mean,

while the dotted curves form the corridor of data

from multiple cadavers ............................................. 14

Fig. 1.10 A typical logistic plot. This plot is an example

of using logistic regression to obtain the probability

of a chest injury of AIS4 or above as predicted

by using the independent parameter VC max ...................... 16

Fig. 1.11 Logistic curve for the product of strain and strain rate

for mTBI ............................................................. 18

xix

xx

List of Figures

Fig. 1.12

Fig. 1.13

Definition of true and false positives (TP and FP)

and true and false negatives (TN and FN) for an arbitrary

threshold. For the threshold selected, there are no false

negatives or positives ............................................... 19

Receiver operator characteristic (ROC) curve for the product

of strain and strain rate based on data from Fig. 1.11.

The area under the curve is 0.943. It indicates that this

parameter is a good predictor of injury ........................... 20

Fig. 1.14 The first tolerance is for a sensitivity of 1.0

and is a conservative estimate of injury ........................... 20

Fig. 1.15 The second tolerance is for a specificity of 1.0

and is a liberal estimate of injury .................................. 21

Fig. 1.16 Optimal tolerance for which the sum of the sensitivity

and specificity ratios is a maximum ............................... 21

Fig. 1.17 Hypothetical data for chest acceleration, demonstrating

the meaning of a 3-ms clip. In the figure, the cumulative

duration of the acceleration pulse above 60 g exceeds 3 ms

and the pulse in injurious to the chest ............................. 22

Fig. 1.18 Stress-strain curve for mild steel ................................... 23

Fig. 1.19 A lumped parameter model simulating the head and torso

subjected to vertical loading ....................................... 24

Fig. 1.20 Finite element model of a lumbar vertebra ....................... 25

Fig. 1.21

The ATB model developed by Calspan Corp.

The segment numbers are in green and the joint

numbers are in red ................................................... 26

Fig. 2.1 Various causes of traumatic brain injury in 2010 ................ 36

Fig. 2.2 Bones of the skull and face ......................................... 37

Fig. 2.3 The cerebral meninges, the superior sagittal sinus and bridging

veins that bridge the CSF layer and transport the blood

from the brain into the superior sagittal ........................... 38

Fig. 2.4 Details of the three cerebral meninges, based on a study

by Haines (1991) .................................................... 39

Fig. 2.5 The brain. The cerebrum and the hindbrain are visible.

Approximate locations of the lobes of the cerebrum are

identified ............................................................. 40

Fig. 2.6 The approximate location of the center of gravity (cg) of the

head is in the midsagittal plane slightly anterior to the auditory

meatus and about 3 cm above the Frankfort plane which is at the

level of the inferior border of the orbit or eye socket. The

illustration of the skull was taken from Carola et al. (Eds.),

1992, Human Anatomy & Physiology. Republished with

permission of McGraw-Hill Education, from R. Carola, J.P.

Harley, C.R. Noback (eds.), Human Anatomy & Physiology,

2nd edn., 1992; permission conveyed through Copyright

Clearance Center, Inc. .............................................. 40

List of Figures

xxi

Fig. 2.7 Arteries of the human brain ........................................ 41

Fig. 2.8 Various types of neurons. Legend: cb stands for cell body

and ax stands for axon .............................................. 42

Fig. 2.9 A typical neuron and its components .............................. 43

Fig. 2.10 (A–D) Microstructure of a microtubule ........................... 44

Fig. 2.11 The node of Ranvier of a myelinated axon ....................... 44

Fig. 2.12 The four main types of neuroglia which are supporting

cells for the CNS .................................................... 45

Fig. 2.13 The role of astrocytes in the blood-brain barrier. Orthogonal

arrays of particles in the foot process of the astrocytes along

with the tight junctions in the endothelial cell layer may

play a role in the prevention of diffusion of molecules

from the capillaries into the brain ................................. 46

Fig. 2.14 Diffuse axonal injury in the human corpus callosum.

Dark lines are swollen axons, and black circles are retraction

balls, made visible by means of β-APP staining ................. 48

Fig. 2.15 Pressure gradient produces shear stress ........................... 51

Fig. 2.16 In head impacts, linear and angular acceleration usually

increase monotonically ............................................. 52

Fig. 2.17 Intracranial pressure data from a frontal impact

Fig. 2.18

to a cadaver head .................................................... 52

Cadaver head impact data used to design the Hybrid III head.

The data were from cadaveric forehead impacts to a rigid

surface. The letter F adjacent to a data point indicates that there

was skull fracture. The abscissa, V 2 /2g, is an equivalent

free fall drop height ................................................. 53

Fig. 2.19 Side view of a 50th percentile Hybrid III head ................... 54

Fig. 2.20 Photograph of the biplanar X-ray setup ........................... 55

Fig. 2.21 Schematic of a biplanar high-speed X-ray system. The 3-D

imaging area is in light blue (45 30 25 cm). The 3-D

accuracy is 0.1 mm. This system is located on the main

campus of Henry Ford Hospital, Detroit, MI ..................... 56

Fig. 2.22

Fig. 2.23

Fig. 2.24

Fig. 2.25

Neutral density targets made from tin spheres encased in a

plastic tube to reduce its density to approximately that

of the brain. The tin spheres are in the center of the

photograph. On the right are the plastic tubes and

on the left are end caps to keep the sphere in the tube .......... 57

Location of neutral density targets in a cadaveric brain

for a sagittal plane impact. AC stands for anterior column

and PC stands for posterior column ............................... 57

Cadaveric head specimen suspended from a carriage

used to accelerate the head into a Lucite block .................. 58

The brain traces out a figure eight pattern during impact

relative to the center of gravity of the head. The motion

appears to decrease near the skull. The data were derived

from a frontal impact against a Lucite block with a resultant

xxii

List of Figures

deceleration of 62 g and a peak angular acceleration

of 2529 rad/s 2 . AC stands for anterior column and PC

stands for posterior column ........................................ 58

Fig. 2.26 Diagram of the pia-arachnoid complex, showing

a blood vessel in the subarachnoid space ......................... 60

Fig. 2.27 This figure describes the specimen preparation procedure.

(A) The cortex of the brain with the PAC attached.

(B) PAC with the underlying brain removed and the pia

facing up. (C) A polyethylene block (marked P for pia)

was glued to the pia side of the PAC. (D) A second block

(marked A for arachnoid) was glued to the opposite side

of the PAC and the excess tissue was trimmed away ............ 61

Fig. 2.28 Strain rate dependency of the PAC due to normal traction, as

demonstrated by its elastic modulus (A), ultimate stress (B),

and ultimate strain (C) .............................................. 62

Fig. 2.29 Loading fixture to test the PAC in shear .......................... 63

Fig. 2.30 Strain rate dependency of the PAC due to shear loading, as

demonstrated by its shear modulus (A), ultimate stress (B),

and ultimate strain (C) .............................................. 64

Fig. 2.31 Tolerance of the human skull to impact with a rigid

surface in terms of peak impact force ............................. 65

Fig. 2.32 Tolerance of the human skull to impact with a rigid

surface in terms of peak head acceleration ....................... 66

Fig. 2.33 Tolerance of the skull to fracture in terms of acceleration and

pulse duration. Clinically, a simple skull fracture is frequently

associated with a mild concussion. Thus, this curve can be

regarded as a tolerance curve for brain concussion. It is the

forerunner of the Wayne State Tolerance Curve shown in

the next figure. (Note: The units for acceleration along the

ordinate should be g’s instead of ft/s2) ............................ 67

Fig. 2.34 Comparison of HIC of about 1000 for a half-sine wave

with the WSTC ...................................................... 67

Fig. 2.35 Injury risk curve in terms of HIC based on the WSTC .......... 69

Fig. 3.1 Summary of concussion data collected using the fluid

percussion device. The brain was concussed in the absence

of head acceleration ................................................. 80

Fig. 3.2 Photoelastic pattern in milling yellow in a plastic model of a

midsagittal section of the brain. The closeness of the contours

indicates a high shear stress in the brain stem region ............ 81

Fig. 3.3 Tolerance curve for rhesus monkeys subjected to non-contact

head angular acceleration. At 40,000 rad/s 2 , over 99 % of the

animals were concussed ............................................ 82

Fig. 3.4 Neutral density accelerometers (NDA) are triaxial

accelerometers which can measure brain kinematics of a

cadaveric brain ...................................................... 84

List of Figures

xxiii

Fig. 3.5 Comparison of resultant acceleration of the skull with that of the

brain for two impacts, one at 100 g and the other at 40 g. The

NDA was used measure the brain acceleration which is much

lower than that of the skull and is shown as by a dotted and

dashed curve. The solid curves are the skull accelerations.

The inset shows the NDA in the brain which was not lacerated

by it because of its neutral density feature ........................ 85

Fig. 3.6 Comparison of displacement data measured using the NDA and

the high-speed biplanar X-ray method. The NDA acceleration

was integrated twice to yield displacement which matched the

X-ray displacement data perfectly. There are actually four

curves in this graph from two tests. Both were occipital impacts

at 2.7 m/s (Test C480-T1) and 4.2 m/s (Test C480-T2) ......... 85

Fig. 3.7 Calculated brain stretch or strain obtained by

differentiating the displacement data .............................. 86

Fig. 3.8 Brain motion data for a posterior impact causing a peak

linear acceleration of 24 g and a peak angular acceleration

of 1995 rad/s 2 .Thecircled targets are selected for detailed

study .................................................................. 87

Fig. 3.9 Linear and angular acceleration components of the cadaver head

in test C755-T3 ...................................................... 87

Fig. 3.10 The x- and z-displacements of the circled targets shown in

Fig. 3.9. It is seen that linear acceleration caused very little

displacement, while angular acceleration is responsible for most

of the displacement .................................................. 88

Fig. 3.11 Brain motion is due to the lag in brain rotation relative to the skull 88

Fig. 3.12 The Marmarou weight-drop device to produce DAI in the brain

of a rodent ............................................................ 89

Fig. 3.13 The dynamic cortical deformation method of causing

a focal injury to the brain. A negative pressure pulse

is applied through the tube, and the brain is injured

by being sucked up the tube ........................................ 90

Fig. 3.14 Validation of a FE model of CCI developed by Schreiber et al.

(1997) using data produced by the same authors ................. 91

Fig. 3.15 Test setup for a controlled cortical impact on a rat brain.

A coronal section of the brain is shown with the impactor

vertical and normal to the brain .................................... 91

Fig. 3.16 Controlled cortical impact on a rat brain with the 2.5 mm

impactor tip normal to the brain but inclined at 22.5

to the vertical. The velocity of the impactor was 4 m/s

and the penetration was 2 mm. Drawing based

on Chen et al. (2003) ................................................ 92

Fig. 3.17 Setup for a bilateral controlled cortical impact in

which the contralateral craniotomy allowed the brain

the bulge through it during impact. Drawing based

on Meaney et al. (1994) ............................................ 92

xxiv

List of Figures

Fig. 3.18 A modified controlled cortical impact test using an impactor

with a rounded tip (A). The tip in (B) is enlarged to show its

exact shape ........................................................... 93

Fig. 3.19 (A) Bridging cortical artery connected to the dura.

(B) Adherence of cortical arterial knuckle to dura

and arachnoid ........................................................ 97

Fig. 3.20 ASDH formation due to bridging vein rupture is not possible

in the subdural layer, based on principles of fluid mechanics . . 100

Fig. 4.1 Finite element model of the head by Ruan (1994) ............... 114

Fig. 4.2 Comparison of pendulum impact force ........................... 115

Fig. 4.3 Comparison of coup pressure ...................................... 115

Fig. 4.4 Comparison of contrecoup pressure ............................... 116

Fig. 4.5 A parametric study using the model by Ruan et al. (1994).

The left half shows changes in response when pendulum

mass and velocity are decreased by 25 and 50 %.

The effects of impact direction are shown on the right .......... 116

Fig. 4.6 Inhomogeneous brain model by Zhou (1995). The gray

and white matter have different shear moduli based

on their microstructure .............................................. 117

Fig. 4.7 Comparison of predicted head-pendulum contact force

Fig. 4.8

with data provided by Nahum et al. (1977) ....................... 118

Comparison of predicted coup and contrecoup pressures

with data provided by Nahum et al. (1977) ....................... 119

Fig. 4.9 The brain model by Al-Bsharat et al. (1999)

is an improved version of that by Zhou et al. (1995).

It has a three-layered skull and a sliding interface

between the CSF layer and the dura .............................. 120

Fig. 4.10

Fig. 4.11

Fig. 4.12

Fig. 4.13

Fig. 4.14

Fig. 4.15

Fig. 4.16

Fig. 4.17

Validation of the Al-Bsharat model—comparison of contact

force for a single run ............................................... 121

Validation of the Al-Bsharat model—comparison of contact

force for all five runs ............................................... 121

Validation of the Al-Bsharat model—comparison of coup

pressure for all five runs ........................................... 122

Validation of the Al-Bsharat model—comparison

of contrecoup pressure for all five runs .......................... 122


of skull-brain relative displacement for Test No. C731-T3 . . . . 123





The Wayne State University Brain Injury Model (WSUBIM)

developed by Zhang et al. (2001) .................................. 125

List of Figures

xxv

Fig. 4.18 Definition of elasto-plastic characteristics of facial bone,

including fracture behavior. The failure strain is denoted

by ɛ f ................................................................... 126

Fig. 4.19 Validation of the WSUBIM against intracranial and ventricular

pressure ............................................................... 127

Fig. 4.20 Validation of the WSUBIM against brain motion data .......... 128

Fig. 4.21 Validation of the WSUBIM against nasal impact data.

T stands for test data and S for simulation

or model prediction ................................................. 129

Fig. 4.22 Validation of the WSUBIM against maxillary impact

Fig. 4.23

data taken from Allsop et al. (1988) ............................... 129

Hourglass energy to internal energy ratio computed

for a linear acceleration input of 200 g and an angular

acceleration input of 12,000 rad/s 2 , demonstrating stability

of the model under severe impact conditions ..................... 130

Fig. 4.24 (A–C) The three 2-D models by Zhou et al. (1994)

which were the first models to feature an inhomogeneous

brain. When white matter was assumed to be 60 % stiffer

than gray matter to achieve better correspondence

of strain with observed DAI ........................................ 132

Fig. 4.25 Approximate locations of the three 2-D models

by Zhou et al. (1994) ................................................ 133

Fig. 4.26 Kinematic input for the 2-D model by Zhou et al. (1994) . ..... 134

Fig. 4.27 (A–C) Results of the three 2-D simulations by Zhou et al.

(1994). The shear strain magnitudes are shown along with

darkened areas of observed DAI in porcine experiments ........ 136

Fig. 4.28 Finite element model of a rat brain ................................ 137

Fig. 4.29

Fig. 4.30

Fig. 4.31

Fig. 4.32

Fig. 4.33

Validation of the rat model by Mao et al. (2006) using

data from a DCD experiment performed by Shreiber et al.

(1997). The solid circles are the model predictions,

and the histograms represent the experimentally measured

means and standard deviations ..................................... 137

The six different CCI experiments simulated

by Mao et al. (2006) ................................................ 138

Correlation of model predicted brain contusion volume

with that measured experimentally, using a first principal strain

of 30 % as the contusion threshold. The residual variance

was 10 mm 3 . The 45-deg line represents a perfect correlation,

while the error bars represent 1 standard deviation

from the experimentally determined mean contusion volume

for each test series ................................................... 139

Modeling the Igarashi et al. (2007) experiments

using the model by Mao et al. (2006) ............................. 139

Computed maximum principal strains in the superficial

cortex (SC), deep cortex (DC), hippocampus (Hipp), lateral

xxvi

List of Figures

thalamus (Thala), and cerebellar vermin (CBV) for a moderate

injury ................................................................. 140

Fig. 4.34 Correlation of computed maximum principal strain with

observed neuronal loss, for mild, moderate, and severe

injury, in the five regions of the brain monitored

by the model. The error bars are for 1 standard deviation

of the observed neuronal loss (see the caption for Fig. 4.33

above for an explanation of the symbols) ......................... 140

Fig. 4.35 Two-dimensional parasagittal models of the brain,

(A) without blood vessels and (B) with blood vessels ........... 141

Fig. 4.36 Large arteries in a parasagittal section of the human

brain near the midsagittal plane .................................... 142

Fig. 4.37 A typical stress-stretch curve for cerebral arteries.

The modulus used in the model is 15 MPa. It is for stretch

beyond the physiological range but less than that at failure . . . . 142

Fig. 4.38 Comparison of experimental intracranial pressure

data from Nahum et al. (1977) with pressures predicted

by Models I and II ................................................... 143

Fig. 4.39 Comparison of relative brain motion between data from Hardy

et al. (2001) and that predicted by Models I and II .............. 144

Fig. 4.40 Parametric study of Model II in which G o was varied. For

G o ¼ 5 kPa, the strains are lower, implying that blood vessels

enhance brain stiffness. For G o ¼ 1 kPa and for a 40 % lower

rotational input, the strains were comparable to those with

G o ¼ 5 kPa, implying that the use of low values of G o may

require a brain model with a very fine vascular structure. The

brain regions are shown in the figure below the bar charts . . . . . 145

Fig. 5.1 Definition of coordinate systems for the moving rigid body.

The X-Y-Z system is the inertial reference frame while

the x-y-z system is the body-fixed frame .......................... 154

Fig. 5.2 The five accelerometers needed to compute angular

acceleration, using Eq. 5.3a, 5.3b, and 5.3c ...................... 155

Fig. 5.3 Arrangement of the nine accelerometers used in the Wayne

State method of measuring angular acceleration ................. 157

Fig. 5.4 A nine-accelerometer mount used for measuring angular

acceleration in cadavers and animals .............................. 158

Fig. 5.5 The nine accelerometers for measuring the angular

acceleration of a Hybrid III dummy head are built into the head

form, centered around the triaxial accelerometer at its cg ...... 158

Fig. 5.6 Hypothetical data used to test the Bortz (1971) method ......... 162

Fig. 5.7 Angular velocity components for the X-, Y- and Z-sequence

of rotations ........................................................... 163

Fig. 5.8 Computed yaw, pitch, and roll for the hypothetical

data used ............................................................. 163

List of Figures

Fig. 5.9

Fig. 5.10

Fig. 5.11

Fig. 5.12

Fig. 5.13

Fig. 5.14

Fig. 5.15

Fig. 5.16

Fig. 5.17

Fig. 5.18

Fig. 5.19

Fig. 5.20

Fig. 5.21

xxvii

Schematic drawing of the experimental setup for a frontal

sled impact. It shows the cube for measuring the angular

data and the position of the three orthogonally placed

cameras ............................................................... 164

Calibration data of three of the accelerometers used

and of the standard accelerometer. A uni-axial shaker

at 20 Hz was used. The standard was calibrated against

a known NIST standard to calibrate all accelerometers

used in the experiment .............................................. 165

Raw (unfiltered) accelerometer data containing spikes

due to cable problems ............................................... 165

Two channels of filtered accelerometer data

using an FFT filter ................................................... 165

Angular velocity components of the dummy head computed

from the measured angular accelerations using the Wayne State

method. The dummy was restrained by a lap shoulder belt

and was subjected to a 15 g frontal impact ....................... 166

Angular displacements computed from the angular velocity data

shown in Fig. 5.13 are compared with measured 3-D film data.

The computed data at the end of the test also matched the

measured data and show a trend to return to their pre-impact

values ................................................................. 167

Rotation vector computed using the Wayne State method

is compared with the optically measured rotation vector

for the 15 g sled run ................................................. 167

Angular velocity components of the dummy head computed

from the measured angular accelerations using the Wayne State

method. The dummy was restrained by a lap belt and was

subjected to an 18 g frontal impact ................................ 167

Rotation vector computed using the Wayne State method is

compared with the optically measured rotation vector for the

18 g sled run ......................................................... 168

Yaw, pitch, and roll computed from the measured head

accelerations. The 90 shift in yaw and roll is indicative

of the numerical problems that can be encountered

when the Euler angles are not used to define 3-D rotation . . . . . . 168

Typical calibration curve provided by Meggitt (Endevco)

for their Model 7264C accelerometer. Its response is flat

to about 2 kHz and its resonant frequency is about 25 kHz ..... 170

Errors magnify at low frequencies for three different brands

of accelerometers manufactured in the 1980s .................... 171

Error Analysis—Case 1: Velocity components for a

hypothetical case with a 10 % error in the roll velocity

component but with no offset error (baseline shift)............ 172

xxviii

List of Figures

Fig. 5.22 Computed angular displacements as a result of a 10 % error

in ω x (roll axis) without offset (baseline shift) ................... 173

Fig. 5.23 Error Analysis—Case 2: Velocity components for a

hypothetical case with a 5 % error in the roll velocity component

and with a 5 % offset error (baseline shift) ....................... 173


in ω x (roll axis) with a 5 % offset (baseline shift) ................ 173

Fig. 5.25 Error Analysis—Case 3: Velocity components for a

hypothetical case with a 10 % error in the roll velocity

component and with a 10 % offset error (baseline shift) . . . . . . . . 174


in ω x (roll axis) with a 10 % offset (baseline shift) . ............. 174

Fig. 6.1 Drop test device used by Biokinetics, Inc. to reproduce

the on-field impacts recorded on game videos ................... 180

Fig. 6.2 Example of computed ICP in a concussed individual 9 ms

after impact. The peak positive pressure in the left frontal

area was 110 kPa, and the peak pressure in the right occipital

region was a negative 78 kPa ...................................... 182

Fig. 6.3 Comparing strain contours in an injury case

with a non-injury case .............................................. 182

Fig. 6.4 Elements of the brain experiencing principal strain

in excess of 10 % for the injury case on the left and noninjury

case on the right ..................................................... 183

Fig. 6.5 Cross plot of acceleration data from NFL data, obtained

from reconstructions of head impacts using dummies

by Biokinetics, Inc .................................................. 184

Fig. 6.6 Logistic plot of the probability of an mTBI as a function

of the product of strain and strain rate ............................ 185

Fig. 6.7 Logistic plot of the probability of an mTBI as a function

of strain rate ......................................................... 185

Fig. 6.8 Logistic plot of the probability of an mTBI

as a function of HIC ................................................ 186


as a function of linear acceleration ................................ 186


as a function of angular acceleration .............................. 186

Fig. 6.11 Estimation of tolerance levels from a logistic curve ............. 187

Fig. 6.12 The optimal tolerance is at 29 % for a product value

of 23 s 1 . The first and second tolerances are also shown.

See Fig. 1.14 for an explanation of these tolerance values ...... 187

Fig. 6.13 Damage to the two vehicles involved in an intersection

crash that occurred in Australia .................................... 190

List of Figures

Fig. 6.14

Fig. 6.15

Fig. 6.16

Fig. 6.17

Fig. 6.18

Fig. 6.19

Fig. 6.20

Fig. 6.21

Fig. 7.1

Fig. 7.2

Fig. 7.3

Fig. 7.4

Fig. 7.5

Fig. 7.6

Fig. 7.7

Fig. 7.8

xxix

Computed damage to the struck vehicle (sedan) compared

to the actual damage shown on the left side of Fig. 6.13 ........ 190

Strain contours in the brain of the sedan driver as predicted

by the WSUHIM by Zhang et al. (2001). (A) Midsagittal

section and (B) coronal section .................................... 191

Damage to exemplar vehicles used in a crash test to replicate

the intersection accident described by Franklyn et al. (2005).

The target vehicle is on the left and bullet vehicle

is on the right........................................................ 191

Impact of a large sedan with a telephone pole, resulting

in massive intrusion of driver (right) side compartment

and an AIS 5 brain injury to the driver ............................ 192

A left-hand drive vehicle was used as an exemplar

vehicle to recreate the pole impact in a crash test ............... 192

Posttest photographs of the pole tests show that it was a less

severe impact than the actual crash. The pole is seen in the

photograph on the right ............................................. 193

Top and side cutaway views of a typical Indy-type

racecar ................................................................ 194

Example of a vehicular deceleration pulse for a severe rear

impact causing a Delta V of 70 km/h (44 mph) .................. 195

(A–C) The spinal column viewed frontally, laterally,

and posteriorly ....................................................... 202

Top, side, and rear views of a typical vertebra. In this case,

it is a lumbar vertebra ............................................... 203

Annular layers of an intervertebral disc in which the collagen

fibers run at an oblique angle to the axis of the spine

with the angles in alternating layers almost orthogonal

to each other ......................................................... 204

Ligaments of the spine—there are three continuous ligaments

and several shorter ones that run between vertebrae ............. 204

Sketch of the cross section of the spinal cord and a pair

of nerve roots. Unlike the brain, the white matter is in the

periphery of the cord enclosing the gray matter. Each nerve

root has a ventral (anterior) root that is mainly motor

and a dorsal (posterior) root that is mostly sensory .............. 205

The C1 and C2 vertebrae are linked through the odontoid

process which is held by a transverse ligament to C1 . . ......... 206

Lateral view of the cervical spine which shows that

the slope of the facet (zygapophysial) joint tends

to decrease at the lower cervical levels ........................... 207

Jefferson fracture of C1 – Multipart fracture of the anterior

and posterior arch ................................................... 209

xxx

List of Figures

Fig. 7.9 A vertebral “burst” fracture in which the fractured segments

impact the spinal cord during the fracturing process . . . . . . . ..... 209

Fig. 7.10 Three forms of compression-flexion injuries: (A) Wedge

fracture. (B) Burst fracture. (C) Anterior dislocation

with locked facets ................................................... 210

Fig. 7.11 Compression-flexion neck injury sustained by a motorcyclist.

The neck compression is generated by the inertia of the body

following the head and neck ....................................... 210

Fig. 7.12 Examples of tension extension injuries: (A) Chin impact

with an automotive dash. (B) Whiplash hyperextension

with neck tension. (C) Out-of-position occupant injured

by an airbag causing C1/C2 separation ........................... 212

Fig. 7.13 Airbag induced C1/C2 separation in a cadaver ................... 212

Fig. 7.14 Hangman’s fracture at C2 which is separated at the pedicles

causing failure of the spinal cord and death ...................... 213

Fig. 7.15 Test setup for the pre-deployed airbag test. The airbag

and steering column are stationary, and the seated test

subject is on sled that is accelerated into the airbag ............. 215

Fig. 7.16 Neck drop test experiment conducted by Nightingale et al.

(1997) ................................................................. 216

Fig. 7.17 Surface orientations used for neck drop test experiments . . . .... 216

Fig. 7.18 Buckling of the cervical spine was observed during

the impact ............................................................ 217

Fig. 7.19 Effect of end conditions on the deformation of the cervical

spine. When unconstrained, the spine bends easily

and is not able to withstand axial loads. With rotational

constraints, it does not deform as much and can withstand

more axial load. When fully constrained, it is capable

of withstanding large axial loads with little bending

deformation. Injury severity increases with the degree

of constraint .......................................................... 218

Fig. 7.20 Neck loading corridor for extension (rearward bending),

based on Mertz et al. (1973) ....................................... 219

Fig. 7.21 Neck loading corridor for flexion (forward bending),


Fig. 7.22 Neck loading corridor for lateral bending,

based on Patrick and Chou (1976) ................................. 220

Fig. 7.23 Tolerance of the cervical spine as a function

of duration of impact for the mid-size male ...................... 221

Fig. 7.24 Cervical spine tolerance values from Duke and the Medical

College of Wisconsin differ considerably ......................... 222

Fig. 7.25 Tolerance of the cervical spine to tensile loading,


List of Figures

xxxi

Fig. 7.26 The 3-D neck model by Kleinberger (1993) ...................... 224

Fig. 7.27 The 3-D partial cervical spine model

by Yoganandan et al. (1996) ....................................... 225

Fig. 7.28 Human neck geometry obtained from an MRI of a 50th

percentile male ...................................................... 225

Fig. 7.29 Side view of the neck model by Yang et al. (1998) . . . . . . . . . . . . . 226

Fig. 7.30 Detailed view of the C1–C2 vertebrae in the model

by Yang et al. (1998) ............................................... 227

Fig. 7.31 Detailed view of the C3 vertebra and the C2/C3 disc

in the model by Yang et al. (1998) ................................ 227

Fig. 7.32 Validation of the model by Yang et al. (1998) against crown

impact data from Nightingale et al. (1997) ....................... 228

Fig. 7.33 Head kinematics as predicted by the model by

Yang et al. (1998) compared with sled data at time 60 ms . . . . . 229


Yang et al. (1998) compared with sled data at time 100 ms . . . . 229





Fig. 7.37 Horizontal and vertical head acceleration predicted

by the model by Yang et al. (1998) compared with

experimental data .................................................... 231

Fig. 7.38 Predicted facet capsule stretch by the model by Yang et al.

(1998) ................................................................. 232

Fig. 7.39 Interaction of the head with a pre-deployed airbag,

predicted by the model by Yang et al. (1998) .................... 233

Fig. 7.40 Demonstration of the mechanism of injury when the head

interacts with the pre-deployed airbag, as predicted by the

model by Yang et al. (1998) ....................................... 234

Fig. 8.1 Anatomy of the spinal cord ........................................ 244

Fig. 8.2 The process for the perception of pain by the brain . . ........... 245

Fig. 8.3 High acceleration whiplash testing of rhesus monkeys in

forward-facing mode (+G x acceleration) .......................... 246

Fig. 8.4 Muscles of the neck, highlighting the sternocleidomastoid

muscle which is stretched during head hyperextension .......... 247

Fig. 8.5 (A–B) Spinal compression due to shoulder belt loading

on the chest .......................................................... 250

Fig. 8.6 Mini Hyge sled designed for us with the Henry Ford Hospital

high-speed X-ray unit ............................................... 255

Fig. 8.7 Tools used to install radiopaque (tungsten) targets on individual

cervical vertebrae. (1) Tungsten markers. (2) Pin.

(3) Drill bit. (4) Pusher. (5) Guide tube. (6) Guide tube ......... 255

xxxii

Fig. 8.8

Fig. 8.9

Fig. 8.10

Fig. 8.11

Fig. 8.12

Fig. 8.13

Fig. 8.14

Fig. 8.15

Fig. 8.16

Fig. 8.17

Fig. 8.18

Fig. 8.19

Fig. 8.20

List of Figures

Radiograph of a cadaver neck with a pair of tungsten targets

installed in each cervical vertebra. Note that C7 is shielded

by the shoulder ...................................................... 256

Instrumented cadaver seated on a sled in front of a biplanar

high-speed X-ray unit. The strap holding the head upright

was released just prior to the initiation of sled acceleration . . . . 256

A two-dimensional setup of a 0-deg seatback angle test

with head restraint. One X-ray unit and one image

intensifier was used ................................................. 257

Transducer data for HFH19 (0 seatback run). (A) Sled

acceleration and velocity. (B) Seat pan load. (C) Shear

and compressive force at occipital condyles. (D) Upper neck

moment. .............................................................. 259

Cervical vertebrae rotations in HFH19. (A) Absolute rotations

with respect to an inertial reference frame. (B) Relative rotation

of adjacent cervical vertebrae. The upper cervical vertebrae

are in flexion, while the lower vertebrae are in extension ....... 259

Crash extension motion – Pattern of rotational angle

of each vertebra (From the horizontal plane) ..................... 260

Relative displacement of C1 with respect to C2

along the body-fixed x- and z-axes. C1P and C1A

are, respectively, the posterior and anterior targets

on the C1 vertebra ................................................... 260


along the body-fixed x- and z-axes. C2P and C2A

are, respectively, the posterior and anterior targets

on the C2 vertebra ................................................... 261

Relative displacement of C3 with respect to C4 along

the body-fixed x- and z-axes. C3P and C3A are, respectively,

the posterior and anterior targets on the C3 vertebra ............ 261


along the body-fixed x- and z-axes. C4P and C4A are,

respectively, the posterior and anterior targets on

the C4 vertebra ...................................................... 262

Relative displacement of C5 with respect to C6 along

the body-fixed x- and z-axes. C5P and C5A are, respectively,

the posterior and anterior targets on the C5 vertebra ............ 262

Coordinate systems for individual vertebrae based on neck

targets are used to estimate facet capsular strain as a function of

time. Bony landmarks on either side of the facet joint are

identified, and the change in distance between the landmarks

was used to estimate the strain ..................................... 263

(A) Trajectories of facet bony landmarks used to estimate

facet capsular strain shown in (B) for the C4/C5 capsule ....... 263

List of Figures

xxxiii

Fig. 8.21 Transducer data for HFH20 (20 seatback run). (A) Sled

acceleration and velocity. (B) Seat pan load. (C) Shear

and compressive force at occipital condyles. (D) Upper

neck moment ......................................................... 264

Fig. 8.22 Comparison of relative rotations of cervical vertebrae

for the two seatback angles. The rotations for the 0-deg

seatback angle in Run HFH19 (A) are generally larger

than those for the 20-deg seatback angle in Run

HFH20 (B)........................................................... 265

Fig. 8.23 Relative motion of C1 with respect to C2 from all available

tests (Deng et al. 2000) ............................................. 266


tests (Deng et al. 2000) ............................................. 266


tests (Deng et al. 2000) ............................................. 267


tests (Deng et al. 2000) ............................................. 267


tests (Deng et al. 2000) ............................................. 268

Fig. 8.28 Neck injury criteria for a 50th percentile male ................... 271

Fig. 9.1 A typical thoracic vertebra. The articular facet surfaces

are almost vertical, and the ability of the facet to transmit

vertical load is unlikely ............................................. 282

Fig. 9.2 A typical lumbar vertebra. The articular facet is vertical

(normal to the laminae), diagonally oriented to resist

posteroanterior shear, and slightly curved when viewed

from above. The facets are located above the laminae

and act as a load path to transmit vertical loads down

the spine .............................................................. 283

Fig. 9.3 Wedge fracture of L1 ............................................... 284

Fig. 9.4 Examples of lumbar burst fractures ............................... 284

Fig. 9.5 Diagrammatic depiction of a burst fracture, showing the

fragments moving radially outward, impacting (and injuring)

the spinal cord ....................................................... 285

Fig. 9.6 Fracture dislocation with locked facets ........................... 286

Fig. 9.7 Types of Chance fracture according to Denis (1983). It can

involve one vertebra or two vertebrae with fractures through

the posterior aspect of the vertebra and rupture of the

interspinous ligament. The injury can result in splitting

of the intervertebral disc, the vertebral body, or both.......... 287

Fig. 9.8 Thoracic hyperextension injury to T8–T9 ........................ 287

Fig. 9.9 One form of thoracic rotational injury due to compression

and twisting .......................................................... 288

xxxiv

Fig. 9.10

Fig. 9.11

Fig. 9.12

Fig. 9.13

Fig. 9.14

Fig. 9.15

Fig. 9.16

Fig. 9.17

Fig. 9.18

Fig. 9.19

Fig. 9.20

Fig. 9.21

List of Figures

Schematic of the Wayne State University vertical

accelerator ............................................................ 289

Vertical accelerator sled (simulated ejection seat) with an

embalmed cadaver ready for an ejection test. The cadaver

was restrained by a military lap-shoulder harness ............... 290

The intervertebral disc load cell was used to measure

the load borne by the intervertebral disc and the line

of action of the load ................................................. 292

IVLC installed in the lumbar spine of a cadaver

by means of a double-bladed saw. The inferior portion

of a lumbar vertebra was removed to insert the load

cell above the disc ................................................... 293

(A) Measured intervertebral disc load and estimated

total load. (B) The difference between the two loads shown

in (A) is the facet load. It is negative or compressive at the

beginning of the impact and becomes tensile toward the end

of the impact due to spinal flexion. (C) Confirmation of facet

load from strain gages mounted on the posterior surface of the

lamina. The strain was compressive at the start of the impact

pulse but became tensile later on, in conformity with the

direction of the facet load .......................................... 294

(A) Vertical sled acceleration. (B) Estimated total spine load.

(C) Measured intervertebral disc load for the erect and

hyperextended modes. (D) Facet load for the erect and

hyperextended mode. In the erect mode, the facet load

goes from compression to tension, but in the hyperextended

mode, the facet load remains in compression.

(E) Confirmation of facet load based on laminar strain

at L3 and L4......................................................... 294

Reason why the intervertebral disc load can be larger

than the total load ................................................... 295

Schematic of the elements of the servo loop used

to duplicate a vertical accelerator experiment

in a material testing machine ....................................... 296

Lumbar segment in a material testing machine which duplicated

the vertical accelerator test this segment underwent while it was

in the body of the cadaver .......................................... 296

Duplication of a hyperextended run using a materials testing

machine to measure the total load. The facet load was in

compression throughout the run ................................... 297

Duplication of an erect run using a materials testing

machine to measure the total load. The facet load

did go into tension at the end of the run .......................... 297

Vertical accelerator data from erect mode runs with

and without simulated abdominal pressure in a cadaver

(Unpublished data) .................................................. 298

List of Figures

xxxv

Fig. 9.22 Bank of homemade solid-state (impact-resistant) EMG

amplifiers used on board the vertical accelerator ................. 299

Fig. 9.23 Null check of the EMG system. The sled was fired

with the EMG system turned on but no animal on board

to ensure that the electrodes were not picking up spurious

signals ................................................................ 300

Fig. 9.24 Junction box for EMG leads built into the jacket used

to protect the EMG needles from being pulled out

by the animal ........................................................ 301

Fig. 9.25 Anesthetized animal ready for testing after it wakes

up from the anesthesia .............................................. 301

Fig. 9.26 Fully awake beagle in the vertical accelerator sled waiting

for the next test ...................................................... 302

Fig. 9.27 EMG data from the lumbar multifidus muscle. The sled

acceleration is superimposed on the EMG data so that

the delay time can be determined .................................. 302

Fig. 9.28 EMG data from the spinalis cervicis muscle of a dog

subjected to a mild (5-g) vertical acceleration. The parabolically

shaped curve is called the rectified EMG and is said

to be proportional to the force generated in the muscle . . . ...... 303

Fig. 9.29 Human tolerance to vertical acceleration as a function

of impact duration ................................................... 304

Fig. 9.30 Typical burst fracture patterns created by Willen et al. (1984),

using a drop weight impact testing method. There was a sagittal

plane fracture and a couple of frontal plane fractures,

typical of four of the seven specimens tested ..................... 306

Fig. 9.31 Herniated nucleus pulposus exerting pressure on the exiting

nerve root. Back pain comes from the herniation itself but

pressure on the nerve root causes leg pain as well ............... 308

Fig. 9.32 An artificially created disc rupture which occurred after the

intervertebral disc was loaded cyclically for over 7000 times.

The nucleus pulposus is viscous and does not flow

like a liquid .......................................................... 309

Fig. 9.33 The path taken by the nucleus pulposus for it to herniate

from an intervertebral disc. It is not radial, and each layer is

ruptured at a different location, indicating that process

is slow and quite unlike the bursting of a balloon . . ............. 310

Fig. 10.1 Schematic diagram of a facet pressure sensor .................... 320

Fig. 10.2 X-ray of a facet pressure sensor installed in the tip of an inferior

facet just above the lamina ......................................... 321

Fig. 10.3 Schematic diagram of the test setup to measure facet

contact pressure (side view)........................................ 322

Fig. 10.4 Wires simulating muscle action are activated by turnbuckles

and attached to load cells anchored to the floor .................. 323

xxxvi

Fig. 10.5

Fig. 10.6

Fig. 10.7

Fig. 10.8

Fig. 10.9

Fig. 10.10

Fig. 10.11

Fig. 10.12

Fig. 10.13

Fig. 10.14

Fig. 10.15

Fig. 10.16

Fig. 10.17

Fig. 10.18

Fig. 10.19

Fig. 10.20

Fig. 10.21

Fig. 10.22

Fig. 10.23

List of Figures

Photograph of a disc nucleus pressure transducer

made from a 13-gauge spinal needle .............................. 323

Photograph of the test setup for sensing facet contact

pressure with the lamina ............................................ 324

The test protocol was to simulate loading on the lumbar

spine due to body weight and to a weight carried in front

of the chest by hand. Simulation of extensor muscle action

was included ......................................................... 324

Facet pressure and disc pressure changes due to body

weight and an eccentric weight. See Table 10.2

for the testing sequence ............................................. 325

Simulated extensor muscle forces with the sum shown

as the curve at the top of the figure. See Table 10.2

for the testing sequence ............................................. 325

Average facet pressure for two loading cases, body weight

only and body weight plus a 45 N eccentric weight ............. 326

Simulated muscle force for the two loading cases – body

weight only and body weight plus the 45 N eccentric weight.

The average increase was 182 N. (Re-do this plot using data

from El-Bohy’s dissertation, Table 4.2, p. 48) ................... 327

Average nucleus disc pressure for the two loading

cases – body weight only and body weight plus the 45 N

eccentric weight ..................................................... 327

A zero-zero ejection in progress. The payload was a crash

dummy ............................................................... 330

The base-excitation model used to derive the Dynamic

Response Index ...................................................... 331

Generic elements of Prasad’s 2-D spinal model

in which the facets were simulated by a spring

between A’ and B’ .................................................. 334

Comparison of model and experimental results

of a 6 g run in the erect mode ...................................... 335


of an 8 g run in the erect mode .................................... 336


of a 10 g run in the erect mode .................................... 336


of an 6 g run in the hyperextended mode ......................... 337

Comparison of head horizontal displacement between

model results and experimental data .............................. 338

Comparison of head angular displacement between

model results and experimental data .............................. 339

Comparison of head horizontal linear acceleration

between model results and experimental data .................... 339

Comparison of head angular acceleration between model

results and experimental data ...................................... 340

List of Figures

xxxvii

Fig. 10.24 Assumed accelerations experienced by an aircraft ditching

in the ocean. The peak accelerations were either coincident

in time or one peak preceded the other in the three cases

that were modeled using the Tennyson model ................... 341

Fig. 10.25 Computed odontoid displacement for the helmet and

non-helmeted cases. The displacement was 5.2 mm for the

helmeted case for a 10 g pulse. It could exceed 10 mm for

higher inputs and cause a cord concussion which has the

same effect as a cerebral concussion on the pilot. The peaks

of the +G z and the G x accelerations were coincident

for this case .......................................................... 342

Fig. 10.26 Computed spinal cord stretch for the helmeted and

non-helmeted case. The stretch was not increased by much due

to the helmet. The acceleration peaks were simultaneous ....... 342

Fig. 10.27 The computed chin-chest contact force for the helmeted and

non-helmeted cases. The force is not high enough to cause a

cerebral concussion. Again, the acceleration peaks were

simultaneous ......................................................... 342

Fig. 10.28 Finite element model of a single vertebra. Due to limited

computational capabilities in the 1970s, only half a vertebra

could be modeled, but the facets were modeled so that they

could mate with an adjacent vertebra ............................. 343

Fig. 10.29 Comparison of static model-predicted vertebral cortical

strains with those measured in a vertebra. The location

of the strain was the anterior aspect of the vertebral body

at the center of the body ............................................ 344

Fig. 10.30 Comparison of static model-predicted vertebral cortical

strains with those measured in a vertebra. The location

of the strain was the lateral aspect of the vertebral body

near the superior endplate .......................................... 344

Fig. 10.31 Finite element model of a lumbar motion segment with

two vertebrae and a disc ............................................ 345

Fig. 10.32 Validation of the King and Yang (1986) model of a lumbar

functional spinal unit, using intradiscal pressure ................. 346

Fig. 10.33 Finite element model of a lumbar motion segment

subjected to a variety of loads ..................................... 347

Fig. 10.34 Comparison of predicted disc bulge for a normal

and degenerated disc with the pivot at the center

of the disc ............................................................ 348

Fig. 11.1 An anterior view of the rib cage. The lighter segments are the bony

parts of the ribs. The first 10 ribs are attached to the sternum

via the darker cartilaginous segments. Note also the downward

inclination of the rib cage which is reduced with age.

That is, the ribs become more horizontal with age................. 358

Fig. 11.2 Compartments of the heart ......................................... 359

xxxviii

List of Figures

Fig. 11.3 Valves of the heart .................................................. 360

Fig. 11.4 Diagrammatic depiction of the systemic and pulmonary

circulatory systems. Oxygenated blood is in red and oxygen

depleted blood is in blue ............................................ 361

Fig. 11.5 Electrical conduction system of the heart ......................... 362

Fig. 11.6 The cardiac cycle—Correlation of mechanical and electrical

events ................................................................. 363

Fig. 11.7 Fatalities due to aortic rupture as a percentage of all

automotive fatalities from 1947 to 1997 .......................... 366

Fig. 11.8 Traumatic rupture of the aorta occurs frequently in the

peri-isthmic region, just distal to the aortic arch ................. 366

Fig. 11.9 First whole-body cadaveric tests were carried out by Patrick

et al. (1965) at Wayne State University. Embalmed cadavers

were used ............................................................. 368

Fig. 11.10 Thoracic force-deflection curves for a nominal

19.5-kg (43-lb) impactor at various velocities. Data from

12 tests are shown ................................................... 369

Fig. 11.11 Thoracic force-deflection curves for a nominal 23.1-kg (51-lb)

impactor at various velocities. Data from 11 tests

are shown. The corridor envelopes seven tests for impactor

speeds between 6.7 and 7.4 m/s (15 and 16.6 mph) . . ........... 370

Fig. 11.12 Recommended thoracic response corridor for the

development of a biofidelic dummy. The original corridor

for the high speed response is shown as a shaded region ....... 371

Fig. 11.13 Comparison of initial thoracic stiffness data for frontal impact,

taken from cadavers and a volunteer .............................. 372

Fig. 11.14 Comparison of thoracic plateau force data for frontal impact,

taken from cadavers and a volunteer .............................. 373

Fig. 11.15 Diagram of the test set-up for sternal impacts on rabbits using a

pneumatic impactor ................................................. 374

Fig. 11.16 The type of lung injury is dependent on both impactor

displacement and velocity .......................................... 374

Fig. 11.17 Thoracic response to lateral impact—whole-body drop tests

onto a rigid surface .................................................. 375

Fig. 11.18 Photograph of the Heidelberg side impact test set-up ............. 375

Fig. 11.19 The 12-accelerometer thoracic array mandated by the NHTSA

for cadaveric testing funded by the NHTSA ...................... 376

Fig. 11.20 Lateral pendulum impact test at an oblique angle, 30 anterior

to lateral .............................................................. 379

Fig. 11.21 Force-deflection curves from lateral pendulum chest

impacts ............................................................... 380

Fig. 11.22 Analysis of side impact data—Logistic plots for V*C, C

and G sp at T8 with computed Chi square, p and r values . . . . . . . 381

Fig. 11.23 (A) Uncorrected corridor for chest response at 16 mph,

(based on Kroell et al. (1974)). (B) Corrected corridor for chest

List of Figures

xxxix

response at 16 mph with an average curve added, based on

Lobdell et al. (1973). The correction is substantial .............. 382

Fig. 11.24 Thoracic response to lateral pendulum impact (30 from lateral)

at (A) 4.8, (B) 6.8 and (C) 9.7 m/s................................ 383

Fig. 11.25 Comparison of frontal thoracic impact response (A) with lateral

thoracic impact response (B) ....................................... 384

Fig. 11.26 Frontal impact to the chest of an inverted cadaver by a 32-kg

pendulum which shoveled the mediastinal contents towards the

head and the spine. An aortic rupture occurred .................. 386

Fig. 11.27 Side impact to the chest with the arm moved out

of the way, causing an aortic rupture .............................. 386

Fig. 11.28 Submarining test using a seatbelt that was retracted rapidly

by a belt pre-tensioner. The belt used was placed at an

angle to the torso to partially simulate submarining. An aortic

intimal tear resulted from this test ................................. 387

Fig. 11.29 Oblique impact test at the level of the xiphoid process, 30 form

lateral. An intimal tear was found after the test .................. 387

Fig. 11.30 Empirical linear relationship between AIS and chest

deflection ............................................................. 389

Fig. 11.31 Lumped parameter model for frontal chest impact. Human

impact response: measurement and simulation: proceedings by

King, William Frederic; et al. Reproduced with permission of

KLUWER ACADEMIC PUBLISHERS in the format Book via

Copyright Clearance Center ........................................ 390

Fig. 11.32 Lobdell model predictions of Kroell et al. (1971) frontal chest

impacts at two different speeds and using two different

impactors. Human impact response: measurement and

simulation: proceedings by King, William Frederic; et al

Reproduced with permission of KLUWER ACADEMIC

PUBLISHERS in the format Book via Copyright Clearance

Center ................................................................. 391

Fig. 11.33 Frontal oblique view of the thoracic skeleton of the Wang

(1995) model ......................................................... 392

Fig. 11.34 Model of the mediastinum and diaphragm ........................ 393

Fig. 11.35 Stress-strain curve for heart muscle in compression used in the

model (Curve1) compared with quasi-static response obtained

by Yamada (1970). The modulus was increased tenfold . ....... 393

Fig. 11.36 Simulation of side impact tests performed

by Viano et al. (1989) ............................................... 394

Fig. 11.37 Validation of the Wang (1995) model against force-deflection

data from a series of side impact tests performed

by Viano (1989) ..................................................... 394

Fig. 11.38 Validation of the Wang (1995) model against force-time

data from a series of side impact tests performed

by Viano (1989) ............................................................ 395

xl

List of Figures

Fig. 11.39 Computed deformation of the thorax at the level of the lower

sternum for a 4.4 m/s lateral impact, as predicted by the Wang

(1995) model ......................................................... 395

Fig. 11.40 Modified thoracic model by Shah et al. (2001). The model is on

the right. It is compared to thoracic anatomy shown on the left.

SVC stands for superior vena cava. The color of the arrows

matches that of the words below the figure (courtesy of Dr.

Chirag Shah) ......................................................... 396

Fig. 11.41 Model of the thoracic aorta in the thoracic model by Shah et al.

(2001) ................................................................. 397

Fig. 11.42 The Shah (2007) torso model simulating an oblique lateral

pendulum impact to the abdomen, reported by Viano et al.

(1989). (A) Initial set-up. (B) Kinematics at time of peak force 397

Fig. 11.43 Validation of the torso model by Shah (2007) in terms of an

abdominal force deflection curve against data generated by

Viano (1989) ......................................................... 398

Fig. 11.44 Validation of the torso model by Shah (2007) in terms of an

abdominal force-time curve against data generated by Viano

(1989) ................................................................. 398

Fig. 11.45 The Shah (2007) torso model simulating a frontal pendulum

impact to the thorax, reported by Kroell et al. (1974). (A) Initial

set-up. (B) Kinematics at time of peak force ..................... 399

Fig. 11.46 Validation of the torso model by Shah (2007) against the

thoracic force-deflection curves developed by Kroell et al.

(1974) ................................................................. 399

Fig. 12.1 Front view of the organs of the abdomen ......................... 410

Fig. 12.2 Frontal view of organs of the torso to show the relative position

of the abdominal organs in relation to the rib cage and, in

particular, the position of the kidneys with respect to the other

abdominal organs .................................................... 411

Fig. 12.3 Quadrants or regions of the abdomen ............................. 412

Fig. 12.4 Abdominal response to frontal impact by a 2.54-cm diameter

bar (Cavanaugh et al. 1986) ........................................ 417

Fig. 12.5 Abdominal response to frontal impact by the lower portion of a

steering wheel ....................................................... 418

Fig. 12.6 Abdominal force-deflection curves from belt impact at the level

of L4, obtained from 13 of the 25 swine tests conducted by

Miller (1989) ......................................................... 419

Fig. 12.7 Force-deflection curves for abdominal side impact at three

impact severities ..................................................... 420

Fig. 12.8 Logist plots of V*C, compression and spinal acceleration at T12

with the computed values of χ 2 , p, and r (taken from Viano

(1989)) ................................................................ 421

Fig. 12.9 Strain ramp of duration t 0 with a slope ¼ α. ε 0 ¼ αt 0

and ε ¼ αt ............................................................ 425

List of Figures

xli

Fig. 12.10 Photograph of the test setup for performing relaxation tests on

solid abdominal specimens ......................................... 427

Fig. 12.11 The reduced relaxation function G(t) for the liver ............... 429

Fig. 12.12 The reduced relaxation function G(t) for the kidney ............. 429

Fig. 12.13 The reduced relaxation function G(t) for the spleen ............. 429

Fig. 12.14 Stress–strain plots for the liver at different strain rates .......... 430

Fig. 12.15 Stress–strain plots for the kidney at different strain rates . . . . . . . 430

Fig. 12.16 Stress–strain plots for the spleen at different strain rates. Note

the lack of strain rate sensitivity for the spleen .................. 430

Fig. 12.17 Ultimate strain is independent of strain rate at the three rates

used in the experiment .............................................. 430

Fig. 12.18 Skeletal model for the abdominal model .......................... 432

Fig. 12.19 Frontal view of the liver. The top margin of falciform

ligament is attached to the undersurface of the diaphragm.

Together with the coronary ligament, they hold the liver

in the upper abdomen ............................................... 433

Fig. 12.20 Frontal and rear views of the organs and soft tissues of the

abdominal mode ..................................................... 433

Fig. 12.21 An oblique view of the complete Wayne State University

Human Abdominal Model (WSUHAM) .......................... 434

Fig. 12.22 Nonlinear viscoelastic material model used to simulate solid

abdominal organs .................................................... 435

Fig. 12.23 Kinematics of a pendulum side impact at 6.7 m/s, as predicted

by the WSUHAM, simulating impacts conducted by Viano

(1989) ................................................................. 437

Fig. 12.24

Distortion of abdominal organs due to a 6.7-m/s pendulum side

impact as predicted by the WSUHAM. Maximum compression

occurred at about 30 ms ............................................ 438

Fig. 12.25 Stress contours in the liver at 22.5 ms into the impact by a 6.7-

m/s pendulum. The peak stress was 152 kPa (based on Lee and

Yang (2001)) ......................................................... 439

Fig. 12.26

Fig. 12.27

Fig. 12.28

Fig. 12.29

Fig. 12.30

Comparison of model predicted force-time and force-deflection

curves with experimental data, for impacts at 6.7 m/s ........... 439

Simulation of a cadaveric drop test conducted by Walfisch et al.

(1980). The abdomen was targeted to impact a simulated

armrest ................................................................ 439

Comparison of force-time data for abdominal impacts (A) the

1-m drop tests and (B) the 2-m drop tests. The experimental data

taken from Walfisch et al. (1980) .................................. 440

Simulation of frontal impact abdominal tests by a rigid bar at the

level of L3. The impact speeds were 6.2 and 10.4 m/s. The

experimental data were taken from Cavanaugh et al. (1986) . . . 441

Comparison of model predicted force-time curves

with experimental corridor developed by Cavanaugh et al.

(1986). (A) is for low velocity impacts (6.1 m/s) and (B) is for

high velocity impacts (10.4 m/s) ................................... 441

xlii

List of Figures

Fig. 12.31 Comparison of model predicted force-deflection curves with

experimental force-deflection curves obtained by Cavanaugh

et al. (1986). (A) is for low velocity impacts (6.1 m/s) and (B)is

for high velocity impacts (10.4 m/s) ............................... 441

Fig. 13.1 Frontal view of the pelvis .......................................... 448

Fig. 13.2 Lateral view of the right hip bone or pelvis ...................... 448

Fig. 13.3 The acetabulum (hip socket) houses the head of the femur (thigh

bone) .................................................................. 449

Fig. 13.4 Frontal views of the male (top) and female pelvis (bottom). The

female pelvis has evolved to facilitate childbirth ................ 450

Fig. 13.5 A slightly oblique frontal view of the sacrum (taken from Gray’s

Anatomy (1973)) .................................................... 450

Fig. 13.6 Transverse section of the pelvic and sacrum, showing the

sacroiliac joints which have a synovial segment anteriorly. A

large part of the joint is held together by strong interosseous

ligaments ............................................................. 450

Fig. 13.7 Anterior ligaments between the ilium and the sacrum are shown

in this figure along with the sacrotuberous and the sacrospinous

ligaments on the floor of the pelvis ................................ 451

Fig. 13.8 Posterior ligaments between the pelvis and the sacrum ......... 452

Fig. 13.9 Side view of the sacrum and coccyx .............................. 453

Fig. 13.10 Illustration of a rotationally unstable pelvic fracture caused by

internal rotation of the left hipbone. It is called a bucket handle

fracture because the fractured right pubic rami (on the left of the

figure) provides the image of a bucket handle on X-ray) ........ 454

Fig. 13.11

Illustration of a vertically unstable pelvic fracture with

disruption of both the posterior and anterior arches . . ........... 454

Fig. 13.12 A U-shaped fracture of the sacrum ................................ 456

Fig. 13.13 Acetabular fracture patterns as described by Letournel (1980).

The simple patterns are (A) posterior wall, (B) posterior

column, (C) anterior wall, (D) anterior column, and (E)

transverse fractures. The associated patterns are (F) fractures of

the posterior column with a posterior wall, (G) transverse

fracture of the posterior wall, (H) T-style acetabular fracture, (I)

fracture of the anterior column posterior hemitransverse, and (J)

fractures of both columns ........................................... 458

Fig. 13.14

Fig. 13.15

Fig. 13.16

Fig. 13.17

Fig. 13.18

Impact apparatus used impact the knee and fracture the

acetabulum ........................................................... 458

Orientation of the femur with respect to the pelvis viewed from

the top (A) and the side (B). The pelvis was fixed in a clamp . . 459

Loading rates used in the acetabular fracture study by Rupp

et al. (2002) .......................................................... 459

(A) Pelvic force-deflection curves for lateral impact at 5.2 m/s

and (B) at 9.8 m/s (adapted from Viano (1989)) ................. 461

Hypothetical pelvic force data showing that the cumulative

duration of the force in excess of 12 kN is greater than 3 ms. . . 462

List of Figures

xliii

Fig. 13.19 Probability of hip fracture or dislocation as a function of peak

force at the hip. The probability of injury increases with

increased hip flexion and abduction ............................... 463

Fig. 14.1 Anterior (left) and posterior (right) views of the bones of the

right lower extremity. The femur articulates with the pelvis

proximally and the tibia distally. The tibia articulates with the

femur proximally and with the tarsal (ankle) bone distally . . . . . 470

Fig. 14.2 Anterior view of the right femur. The spherical femoral head fits

into the acetabulum of the pelvis while the condyles on the distal

end roll and slide on the two tibial plateaus ...................... 471

Fig. 14.3 Frontal view of the right tibia and fibula. In (A), the proximal

and distal articulations are shown. In (B), the location of the

head of the fibula is seen in detail. It does not articulate with the

femur. Also, in (B), the distal end of the fibula is the lateral

malleolus while the distal end of the tibia is the medial malleolus 472

Fig. 14.4 (A) Frontal view of the patella. (B) Rear view of the patella . . . 473

Fig. 14.5 Side view of the femoro-tibial joint showing the quadriceps and

patella tendons that hold the patella in place ..................... 473

Fig. 14.6 Muscles of the thigh viewed in cross-section. The femur is

among the anterior extensor muscles .............................. 473

Fig. 14.7 Ligaments of the knee - The lateral and medial collateral

ligaments and the cruciate ligaments hold the knee in place. The

patella has been removed and the patellar tendon has been cut 474

Fig. 14.8 Expanded view of the cruciate ligaments of the knee - The ACL

is attached to the anterior aspect of the tibial plateau while the

PCL is attached to its posterior aspect ............................ 474

Fig. 14.9 Torsional load applied to a long bone ............................. 476

Fig. 14.10 Free body diagram of an element of bone at the fracture site. The

shear resultants form a tensile force at 45 deg to the long axis of

the bone, causing a spiral fracture ................................. 476

Fig. 14.11 Example of a greenstick fracture of the ulna and radius in a

3-year-old who fell with his hands outstretched. The bending

load caused the tensile side to be fractured while the

compression side buckled due to softness of the bone ........... 477

Fig. 14.12 Example of a comminuted Pilon fracture caused by a

compressive load applied to the distal end of the tibia by the

talus (ankle bone) ................................................... 478

Fig. 14.13 Cross-section of a 1978 VW Rabbit knee bolster designed to

protect the knee and to avoid PCL rupture ....................... 479

Fig. 14.14 Stellate fracture of the patella due to direct impact against a

rigid surface. A stellate fracture is one with central point of

injury from which radiate numerous fissures ..................... 479

Fig. 14.15 A condylar notch fracture is caused by the rearward motion of

the patella into the knee joint. It is likely to occur if the knee

load is not shared by the femoral condyles surrounding the

patella (Hayashi et al. 1996) ....................................... 480

xliv

List of Figures

Fig. 14.16

Fig. 14.17

Fig. 14.18

Fig. 14.19

Illustration of the effect of padding to distribute the knee load to

the condyles and thus prevent patella and condylar notch

fractures (Hayashi et al. 1996) ..................................... 480

Illustration of large knee loads that develop if the dash is heavily

padded, pocketing the knee. The horizontal and vertical shear

forces in the pocket can fracture the femoral shaft .............. 481

Experimental set-up for knee impacts to validate the hypothesis

that padding affects the type of knee fracture and to determine

the optimal stiffness of the padding to prevent knee injury ..... 481

Finite element model of knee impact simulating the Hayashi

experiments .......................................................... 482

Fig. 14.20 Validation of the knee impact model by Hayashi et al. (1996)—

(A) Comparison of rigid impact response, (B) Comparison of

response for a rigid padding impact (450 psi), (C) Comparison

of response for a 100 psi pad impact, and (D) Comparison of

response for a 50 psi pad impact (Hayashi et al. 1996) .......... 483

Fig. 14.21 Load sharing between the patella and the condyles as predicted

by the Hayashi model—The condyles share 16 % of the load if a

100-psi pad was used ............................................... 484

Fig. 14.22 Experimental set-up to produce a pilon fracture in a cadaver leg 485

Fig. 14.23

Fig. 14.24

The tendon catcher was a modified rope holder with spikes

inside. However, the spikes were not enough to hold the tendon

and surgical suture was used to reinforce the assembly so that it

could resist a load of 2 kN ......................................... 485

The measured tibial force is consistently 2 kN higher than the

impact force, whether the pilon fracture occurred or not ........ 486

Fig. 14.25 The foot and ankle model developed by Beaugonin et al. (1997)

was used to simulate the impact experiments conducted by

Kitagawa et al. (1998) .............................................. 487

Fig. 14.26

Fig. 14.27

Comparison of model predicted forces with experimental data

obtained by Kitagawa et al. (1998) for the simulation of pilon

fractures .............................................................. 487

Calculated first principal stress in the ankle joint. It is seen that

an area of tensile stress concentration is developed in the distal

tibia at the junction of plafond (the articular surface of the distal

end of the tibia) near the inside surface of the medial malleolus,

suggesting that a fracture could originate there and propagate

into the distal end of the femur to result in a pilon fracture ..... 488

Fig. 14.28 The first knee response curves recorded by Patrick et al. (1965).

The data were taken from a whole-body cadaveric sled test in

which both knee impact loads were measured ................... 489

Fig. 14.29

Femoral response curves for axial knee impacts. (A)

Non-fracture response. (B) Fracture response .................... 490

List of Figures

xlv

Fig. 14.30 Estimate of the neutral axis for bending in femoral shaft in

relation to the axis of the femora neck, based on strain gage data.

Apparently, the lateral surface of the femur is in tension ....... 491

Fig. 14.31 (A) Knee impact response to Styrofoam DB impacts. (B) Knee

impact response to aluminum honeycomb impacts at 3.6 m/s

(11.8 ft/s) ............................................................. 491

Fig. 14.32 Knee/femur impact set-up used by Melvin et al. (1975) who

were the first to test unembalmed cadaveric knees with a linear

impactor .............................................................. 493

Fig. 14.33 (A–B) The lower limb model moved into a driving position by

applying a spring load to the leg ................................... 497

Fig. 14.34 Validation of the foot and tibia model simulating a static load

applied to the foot. There were six tests on cadaveric specimens,

one of which was osteoporotic (Test No. 152). The model was

not as stiff as the averaged data but it compared well with data

from other tests performed by Hirsch and White (1965), Huang

et al. (1993) and Ker et al. (1987) ................................. 499

Fig. 14.35 Drawing of the sled test set-up showing a restrained Hybrid III

dummy seated in front of VW knee bolster. The right leg is a

model of the human lower limb (LLMS) ......................... 499

Fig. 14.36 Comparison of whole-body kinematics between sled test and

model (A) and (B). Details of skeletal contact with the knee

bolster are shown in (C) while in (D) details of patella contact

with bolster are shown. These details cannot be easily visualized

in a sled test but the model is capable of showing the interaction 500

Fig. 14.37 Comparison of knee impact force in the sled test using a VW

knee bolster. The peak deceleration was 35 g. (A) isa

comparison of the measured and predicted force in the femur in

the direction of impact. (B) Compares the three components of

force in the femur ................................................... 501

Fig. 15.1 Top view of the right foot showing all the bones of the foot . . . 510

Fig. 15.2 Side (medial) view of the bones of the left foot, showing the

longitudinal arch ..................................................... 511

Fig. 15.3 Definition of dorsiflexion, plantar flexion, inversion, and

eversion of the foot .................................................. 511

Fig. 15.4 (A) Medial muscles of the leg invert the foot. (B) Lateral

muscles of the leg evert the foot ................................... 512

Fig. 15.5 Lateral ligaments and retinacula of the ankle .................... 512

Fig. 15.6 Superficial medial ligaments of the ankle or the deltoid

ligament. The tibiospring ligament is denoted by (1), the

tibionavicular ligament by (9), the superficial tibiotalar ligament

by (10), the tibiocalcaneal ligament by (14). For details, see

Hintermann and Golanó (2014) .................................... 513

Fig. 15.7 Test setup for dorsiflexion testing of the foot and ankle ........ 514

xlvi

Fig. 15.8

Fig. 15.9

Fig. 15.10

Fig. 15.11

Fig. 15.12

Fig. 15.13

Fig. 15.14

Fig. 15.15

Fig. 15.16

Fig. 15.17

Fig. 15.18

Fig. 15.19

Fig. 15.20

Fig. 15.21

Fig. 15.22

Fig. 15.23

List of Figures

The injury status in dorsiflexion changes abruptly at 45 deg of

dorsiflexion, indicating that injury would likely occur at this

angle .................................................................. 515

Instrumentation of the lower leg and foot used to study response

and tolerance of the ankle in dorsiflexion ......................... 516

Test device used to test the ankle in dorsiflexion. The foot was

impacted by a brake pedal at the ball of the foot . . .............. 516

Ankle inversion can result in sprain or rupture of the lateral

ligaments of the ankle .............................................. 517

Drawing of the impact device used to apply inversion and

eversion loads to the foot ........................................... 517

Test apparatus for inversion/eversion tests used by Funk et al.

(2002). The specimen can be subjected to an initial axial

compression as well as dorsiflexion ............................... 520

Test device used by Wei et al. (2010) to determine ankle

tolerance to external rotation ....................................... 521

The Lisfranc ligament spans the medial cuneiform and the

second metatarsal bone (courtesy of Dr. Brian Smith) .......... 522

Classification of Lisfranc fractures, proposed by Hardcastle

et al. (1982), based on injury patterns rather than mechanism of

injury ................................................................. 523

(A–C) The three impact devices used by Smith (2003) to create

Lisfranc foot injuries. Five tendons were preloaded to simulate

braking, including the Achilles tendon ............................ 525

A foot being tested in the plantar flexed configuration,

simulating braking by a short driver using the toes to press on

the brake pedal (courtesy of Dr. Brian Smith) .................... 526

Comparison of impactor load on the foot in the plantar flexed

(A) and plantar nominal (B) configurations. There is effective

load transmission through the metatarsals in the plantar flexed

configuration ......................................................... 526

Logistic plot of probability of injury vs. velocity of impact for

tests in the plantar flexed configuration with simulated muscle

loading (tendons pulled) ............................................ 527

The definition of true and false positives and true and false

negatives applied to a Logistic plot for foot load. Experimental

data were used to demonstrate a special case of no overlap of

injury and non-injury data along the abscissa. This is not usually

the case for most data sets .......................................... 528

Logistic plot of probability of injury vs. foot load for tests in the

plantar flexed configuration with simulated muscle loading

(tendons pulled) ..................................................... 530

Receiver operating characteristics (ROC) curve for foot load

with tendons pulled. The area under the curve is 0.9667. Since

there are two changes in slope of the ROC, the changes

List of Figures

xlvii

represent a threshold value for injury. The first threshold is at

3196 N with an injury probability of 18.5 % and the second is at

4499 N with a probability of 81.3 % .............................. 531

Fig. 16.1 Side impact fatality rates in the USA from 1975 to 2004.

FMVSS 214 was phased into new cars from 1994 to 1997. The

rate remained unchanged in 2004 relative to the rates in

1994–1997 ........................................................... 540

Fig. 16.2 Depiction of a broadside impact ................................... 540

Fig. 16.3 Vehicle kinematics in a side impact .............................. 541

Fig. 16.4 Frequency of vehicular impacts by angle of impact for single

and multiple vehicle accidents. Single vehicle side impacts are

usually with a fixed object, such as a tree or a utility pole ...... 542

Fig. 16.5 Distribution of automotive fatalities by age. Young drivers tend

to impact fixed objects while older drivers are more involved in

intersection crashes .................................................. 543

Fig. 16.6 Motion of the scapular due to a side impact to the torso. (A)

Motion with no rib fracture. (B) Motion with rib fractures . . . . . 548

Fig. 16.7 Force-deflection curves from lateral pendulum abdominal

impacts ............................................................... 549

Fig. 16.8 Force-deflection curves from lateral pendulum pelvic impacts . 550

Fig. 16.9 MADYMO model of a 50th percentile male simulating side

impact. It has 18 rigid body segments. 1 for the head, 3 for the

neck, 4 for the torso, 4 for upper extremities, and 6 for the lower

extremities ........................................................... 552

Fig. 16.10 Mini-models used in the side impact model by Huang (1995) to

calculate the Viscous Criterion and TTI .......................... 552

Fig. 16.11 Validation of the side impact model by Huang et al. (1994a)

against sled test data from Cavanaugh et al. (1990). (A) Pelvic

offset test against a rigid wall. (B) Flat rigid wall (Fig. 16.11B

was taken from Huang (1995)) ..................................... 553


against sled test data from Cavanaugh et al. (1990). (A) Impact

test against soft paper honeycomb padding. (B) Impact test

against Arsan foam padding (Fig. 16.12A was taken from

Huang (1995)) ....................................................... 554


against pendulum impact data from Viano et al. (1989). (A)

Thoracic force-deflection curves. (B) Abdominal forcedeflection

curves (Fig. 16.13A was taken from Huang (1995)) . 555

Fig. 16.14 Side impact door velocity profiles used in a parametric study of

the Huang et al. (1994a) model. (A) The GM velocity profile.

(B) The Deng velocity profile ...................................... 556

Fig. 16.15 Comparison of computed and measured chest deformation

profiles of one of the two sled-to-sled tests carried out by Huang

et al. (1994b) ......................................................... 560

xlviii

Fig. 16.16

Fig. 17.1

Fig. 17.2

Fig. 17.3

Fig. 17.4

Fig. 17.5

Fig. 17.6

Fig. 17.7

Fig. 17.8

Fig. 17.9

Fig. 17.10

List of Figures

US side impact fatalities from 1995 to 2003 stayed constant

despite the promulgation of FMVSS starting in 1994. The total

number of occupant fatalities during this period varied between

33,064 and 34,108 ................................................... 561

Simulation of an actual pedestrian impact by an SUV with a

high hood (1 m) at 27.2 km/h (17 mph). The momentum

imparted to the lower part of the body caused the pedestrian to

cartwheel and strike the ground head first. The pedestrian

sustained a fatal head injury ........................................ 571

Schematic of the test setup for a car-pedestrian experiment

conducted by Krieger et al. (1976) ................................ 572

The pedestrian (cadaver) was tested in the sled area where it was

subjected to a side impact by the front end of passenger vehicle.

Out of five tests conducted, there was one frontal impact (based

on Krieger (1976)) .................................................. 572

This figure shows the cadaver in position for impact. It was held

upright by a harness for a left-sided impact. The left knee was

prevented from buckling by taping a 1-cm diameter wooden

dowel rod across it. Just before impact, the harness was released

and at impact with the bumper, the dowel broke to allow the

knee to flex. Under the impacted leg, a load cell measured the

ground reaction force which was substantial (based on Krieger

(1976)) ................................................................ 573

The vehicle used for pedestrian impact was a 1973 full-size

Chevrolet. The cadaver was impacted by the left side of the

vehicle where the bumper was straight (no curvature, bends)

(based on Kreiger (1976)) .......................................... 574

Instant of cadaveric head/hood impact of a left-sided 24-km/h

(15-mph) car-pedestrian impact (based on Krieger (1976)) . . . . . 575

Sample data from car-pedestrian experiments by Krieger et al.

(1976). (A) Ground force reaction under impacted leg. (B)

Impacted lower leg lateral acceleration from two cadaveric tests

at about the same velocity. (C) Lateral head acceleration for the

same two tests. (D) Cadaver dummy head angular accelerations

are compared, using tests run at the same speed of 24.1 km/h

(15 mph) .............................................................. 575

The six front end profiles used in the car-pedestrian study by

Cavallero et al. (1983). The pedestrian is a 50th percentile

dummy ............................................................... 579

Inverted X-ray cassette with three load cells attached forming an

isosceles triangle. Lead markers were used to identify the

centroid of the triangle, as shown in Fig. 17.10 (based on

Krieger (1976)) ...................................................... 581

Locating the cg of the pelvis in the antero-posterior view. The

cg is at the intersection of the hash marks which is the centroid

of the isosceles triangle formed by the three load cells .......... 582

List of Figures

xlix

Fig. 17.11 The circular object is the trifilar pendulum that is suspended

from the ceiling by three wires. The rectangular frame is used to

hold body segments in a fixed orientation so that inertial

properties can be measured by orthogonal rotations. Both the

pendulum and the rectangular frame are made of light weight

magnesium ........................................................... 582

Fig. 17.12 Test setup for head drop tests on the hood to provide forcedeflection

data for the ATB model. A dummy head is shown

facing the hood which is below it (based on Krieger (1976)) ... 583

Fig. 17.13 Schematic of the test setup for lower leg drop tests on the

bumper to provide force-deflection data for the ATB model. The

impact force was measured by load cells below the bumper and

leg kinematics were recorded on high speed film ................ 583

Fig. 17.14 Dynamic force-deflection curves for lower leg impact with the

bumper at different impact speeds ................................. 584

Fig. 17.15 Validation of single-segment impacts (A) Comparison of the

x-axis (postero-anterior) head acceleration for a cadaveric head

dropped onto the hood of the test vehicle. (B) Comparison of the

predicted and measured pitch of the head in the same drop test 585

Fig. 17.16 Validation of single-segment impacts—Comparison of

predicted and measured roll angle of the lower leg during a leg

drop test onto the bumper of the test vehicle ..................... 586

Fig. 17.17 Validation of the pedestrian model for single-segment

impacts—Comparison of the x-axis (postero-anterior) angular

acceleration of the right lower leg during a leg-bumper impact

(drop test) ............................................................ 586

Fig. 17.18 Validation of the pedestrian model—Comparison of the head

z-axis (superior-to inferior) linear acceleration of a dummy

car-pedestrian impact ............................................... 587

Fig. 17.19 Validation of the pedestrian model—Comparison of the head

x-axis (postero-anterior) linear acceleration for a cadaveric

car-pedestrian impact at 24.1 km/h (15 mph) .................... 587

Fig. 17.20

Validation of the pedestrian model—Comparison of the lower

torso z-axis (superior-to-inferior) linear acceleration for a

cadaveric car-pedestrian impact at 37.3 km/h (23.2 mph) . ..... 588

Fig. 17.21 Validation of the pedestrian model by Ishikawa et al. (1993).

The vehicular impact speed was 39 km/h (24.2 mph) and the

hood height was between 0.85 and 0.875 m (2.79 and 2.87 ft).

The simulation was terminated upon head contact with the

vehicle ................................................................ 588

Fig. 17.22

The eight front end profiles used by Gupta and Yang (2013) to

simulate car-pedestrian impact. According to the Gupta-Yang

model, for SUV profiles, regardless of the shape, there

was secondary head to ground impact at an impact speed

of 40 km/h ........................................................... 589

l

List of Figures

Fig. 18.1 History of the seatbelt from 1885 to 1983 ........................ 598

Fig. 18.2 Four-point belt systems proposed by Rouhana et al. (2003). The

standard three-point belt is shown in (A), the X4 cross-chest belt

is shown in (B) and the V4 belt is shown in (C)................. 601

Fig. 18.3 A drawing of the ES-2re dummy. ES-2 stands for the second

version of the European side impact dummy and the letters re

indicate that the dummy was modified by the addition of a rib

extension in the rear to prevent the spine from catching on the

seat back during a side impact (courtesy of Mr. Michael

Jarouche, Humanetics Innovative Solutions, Inc.) ............... 604

Fig. 18.4 A photograph (A) and an engineering drawing (B) of a SID-IIs

dummy, showing its five ribs and asymmetric chest. The dummy

can only be impacted on one side (left) because the ribs have

been lengthened to reduce lateral chest stiffness and are

anchored to a block on the right side (courtesy of Mr. Michael

Jarouche, Humanetics Innovative Solutions, Inc.) ............... 605

Fig. 18.5 Examples of rollover due to a trip-over. It occurs when the

lateral motion of the vehicle is resisted by an opposing force,

inducing a roll moment. The surface is deformed by the wheels 606

Fig. 18.6 Examples of rollover due to a flip-over. It occurs when the

vehicle mounts a guard rail or steep hillside and rolls back

towards the side of the guardrail or slope from which it came . 607

Fig. 18.7 Example of a rollover due to a turn-over which is caused by

centrifugal forces generated by a sharply turning or rotating

vehicle when resisted by normal surface friction, including

pavement, gravel, grass, or dirt. No furrowing, gouging,

deformation, curb or any physical obstruction of the surface

occurs at the point of the trip as opposed to a trip-over ......... 607

Fig. 18.8 Example of a rollover due to a climb-over. The vehicle climbs

up and over the fixed object which needs to be high enough to

lift the vehicle off the ground. It then rolls over to the opposite

side of the impacted object ......................................... 608

Fig. 18.9 Example of a fall-over in which the vehicle is on a slope steep

enough to cause its cg to fall outside of the wheelbase .......... 608

Fig. 18.10 Example of a bounce-over. The vehicle rebounds off of a fixed

object, such as a guardrail, and overturns, as a result ............ 609

Fig. 18.11 (A–E) Various laboratory test methods to simulate vehicular

rollovers .............................................................. 609

Fig. 18.12 Rollover test data using a Hybrid III dummy in a Chevrolet

Malibu show that the neck load peaked well before the roof

crushed ............................................................... 614

Fig. 18.13 Modeling rollover with a belted Hybrid III dummy occupant

(taken from Hu (2007)) ............................................. 616

Fig. 18.14 (A–D) Tests used to validate the rollover model

by Hu (2007) ......................................................... 616

List of Figures

li

Fig. 18.15 Comparison of predicted and measured loads for the quasi-static

FMVSS 216 test ..................................................... 617

Fig. 18.16 Simulation of an SAE J2114 dolly test—Comparison of model

predictions with test results. The simulated vehicular motion is

shown in (A) while the computed vehicular angular velocity,

lateral acceleration and vertical acceleration are compared with

test data in (B–D), respectively .................................... 618

Fig. 18.17 (A–D) Simulation of a curb trip. Comparison of model predicted

kinematics with experimental data ................................ 619

Fig. 18.18 (A–D) Simulation of a corkscrew rollover with comparison of

model prediction with experimental data ......................... 620

Fig. 18.19 Comparison of measured and predicted dummy head

accelerations in an SAE J2114 dolly rollover test for the nearside

occupant. (A) Lateral acceleration. (B) Vertical

acceleration .......................................................... 621

Fig. 18.20 Comparison of head impact location and timing in an SAE

J2114 dolly rollover test for the near-side occupant ............. 621

Fig. 18.21 Comparison of measured and predicted dummy data in an SAE

J2114 dolly rollover test for the far-side occupant. (A) Vertical

head acceleration. (B) Axial neck force ........................... 621

Fig. 18.22 Comparison of head impact location and timing in an SAE

J2114 dolly rollover test for the far-side occupant ............... 622

Fig. 18.23 Comparison of measured and predicted dummy head

accelerations in a curb-trip rollover test for the near-side

occupant. (A) Lateral acceleration. (B) Vertical acceleration ... 622

Fig. 18.24 Comparison of head impact location and timing in a curb-trip

rollover test for the near-side occupant ........................... 622

Fig. 18.25 Comparison of measured and predicted dummy data in a curbtrip

rollover test for the far-side occupant. (A) Vertical head

acceleration. (B) Axial neck force ................................. 623

Fig. 18.26 Comparison of head impact location and timing in a curb trip

rollover test for the far-side occupant (taken from

Hu (2007)) ........................................................... 623

Fig. 19.1 Acute ventricular fibrillation in a pig due to a non-penetrating

impact by a rubber bullet travelling at an estimated speed 50 m/s

and striking the sternum which was fractured .................... 634

Fig. 19.2 Experimental set-up used by Kroell et al. (1986) to study

porcine thoracic response and injury, including cardiac injuries 636

Fig. 19.3 Posterior view of the left knee. The medial (or tibial) collateral

ligament is subjected to tensile loading when the knee is

impacted laterally on its lateral aspect ............................ 637

Fig. 19.4 (A) Proximal insertion locations of the ACL. (B) Distal

insertion locations of the ACL. PL is the posterior lateral bundle

and AM is the anterior medial bundle ............................. 638

Fig. 19.5 A braced cadaveric knee ready for a lateral impact .............. 640

lii

List of Figures

Fig. 19.6 Medial aspect of a braced knee, showing the MCL which was

stained dark green and targeted with two rows of white targets,

one along the anterior aspect and the other along the posterior

aspect of the MCL (based on Begeman et al. (1987)) ........... 641

Fig. 19.7 Dynamic and static response of the MCL in terms of forcedeflection.

The static data were obtained from Kennedy et al.

(1976) (based on Begeman et al. (1987)) ......................... 642

Fig. 19.8 Dynamic and static response of the MCL in terms of stressstrain.

The static data were obtained from Kennedy et al. (1976)

(based on Begeman et al. (1987)) .................................. 642

Fig. 20.1 A typical Friedlander wave ......................................... 650

List of Tables

Table 1.1 Road users killed in various modes of transport as a

percentage of regional road traffic deaths 2010 (Source: World

Health Organization) .............................................. 5

Table 1.2 The Abbreviated Injury Scale (AIS) ............................. 15

Table 1.3 Predictor variables for mTBI in the NFL (based on King et al.

2003) ............................................................... 17

Table 1.4 Predictors of tolerance for mTBI (based on King et al.

(2003)) .............................................................. 18

Table 2.1 Average impulse (in psi-s) for different degrees of concussion

in dogs for all 72 tests (Gurdjian et al. 1954) .................. 50

Table 2.2 Summary of head kinematics measured during the Hardy

(2007) tests ......................................................... 59

Table 4.1 Material properties of head tissue used in the Ruan et al.

(1994) model of head impact ..................................... 114

Table 4.2 Comparison of computed and measured contact loads for three

occipital head impacts ............................................ 123

Table 4.3 Material properties of gray and white matter used in the

WSUBIM (Zhang et al. 2001) ................................... 126

Table 4.4 Validation against intracranial pressure data of Nahum et al.

(1977) in the WSUBIM by Zhang et al. (2001) ................ 127

Table 4.5 Statistics for the 2-D porcine models (based on Zhou

(1995)) .............................................................. 133

Table 4.6 Material properties of head tissue used in the 2-D porcine

model by Zhou et al. (1994) ...................................... 133

Table 6.1 NFL Data – 53 cases of head impact data reconstructed from

game films and drop testing (based on data supplied by the

NFL) ................................................................ 181

Table 6.2 List of predictor variables for logistic regression .............. 184

liii

liv

List of Tables

Table 6.3 Rank order of mTBI predictors based on logistic regression

(based on King et al. (2003)) ..................................... 185

Table 6.4 Comparison of model-predicted values with field data ........ 187

Table 6.5 Indy car crash data summary and head response (Courtesy

of Dr. L. Zhang) ................................................... 195

Table 6.6 Summary of brain responses as predicted

by the WSUHIM .................................................. 196

Table 7.1 Neck response as a function of end condition restraints—peak

loads, peak deflections, and resulting injuries if the tolerance

of the neck is exceeded (based on

Nightingale et al. (1991)) ......................................... 218

Table 8.1 List of cadavers used in the whiplash tests by Deng et al.

(2000) ............................................................... 258

Table 8.2 Peak relative rotations of cervical vertebrae for the 20-deg

seatback tests ...................................................... 264

Table 8.3 Peak relative rotations of cervical vertebrae for the 0-deg

seatback tests ...................................................... 265

Table 8.4 Peak relative displacements and axial deformations of facet

capsule landmarks of 20-degree seatback tests ................. 269

Table 8.5 Peak relative displacements and axial deformations of facet

capsule landmarks of 0-degree seatback tests .................. 270

Table 9.1 Effect of spinal configuration on g-level for vertebral

fracture ............................................................. 292

Table 9.2 Student’s t-test of fracture data .................................. 292

Table 9.3 Average EMG onset delay ....................................... 303

Table 9.4 Tolerance of the thoracolumbar spine to quasi-static

compression-flexion loading ..................................... 305

Table 9.5 Summary of motion segment test data .......................... 307

Table 10.1 Cadaveric data and test parameters .............................. 325

Table 10.2 Sequence of events in the facet pressure test a (based on

El-Bohy et al. (1989)) ............................................. 326

Table 10.3 Facet capsular strain due to applied extension and flexion

moments (The applied moments were 18 N.m in extension and

24 N.m in flexion) ................................................. 328

Table 10.4 Parametric study of the aircraft ditching scenario .............. 341

Table 10.5 Predicted facet loads and nucleus pressures for the model

shown in Fig. 10.34 for the five loading cases with the pivot at

the center of the disc .............................................. 347

Table 10.6 Predicted facet loads and nucleus pressures for the model

shown in Fig. 10.34 for the five loading cases with the pivot at

the center of the spinal canal ..................................... 347

Table 11.1 Test conditions and results of WSU side impact tests . ........ 377

Table 11.2 Chest injury criteria (date taken from Viano (1989)) (for

AIS 4 and for a 25 % probability of injury) .................. 381

List of Tables

lv

Table 11.3 Linear relationship between chest compression and AIS

(based on Fig. 11.30 above) ...................................... 389

Table 11.4 Model parameters used by Lobdell et al. (1973) ............... 391

Table 12.1 Summary of frontal abdominal tests performed using

Table 12.2

cadaveric and porcine subjects ................................... 415

Characteristics of the cadavers used in the frontal lower

abdominal impact tests conducted by Cavanaugh et al.

(1986) ............................................................... 416

Table 12.3 Impact kinetics—lower abdominal impacts .................... 417

Table 12.4 Abdominal injury criteria (for AIS 4 and for a 25%

probability of injury) .............................................. 421

Table 12.5

Table 12.6

Tolerance of the liver to frontal impact

by a rigid impactor ................................................ 422

Tolerance of the liver to frontal impact by a shoulder belt

(based on 25 tests on porcine subjects) ......................... 422

Table 12.7 Abdominal tolerance to side impact ............................. 422

Table 12.8 Tolerance of the liver (Rouhana 1993) .......................... 423

Table 12.9 Tolerance of the kidney (Rouhana 1993) ....................... 423

Table 12.10 Tolerance of the upper abdomen (Rouhana 1993) ............. 423

Table 12.11 Tolerance of the lower abdomen (Rouhana 1993) ............. 423

Table 12.12 Material constants for reduced relaxation functions ........... 429

Table 12.13 Material constants for elastic response fitted to the

QLV theory ........................................................ 429

Table 12.14 Weight distribution ................................................ 434

Table 12.15 Material properties of tissues used in the abdominal model by

Lee and Yang (2001) ............................................. 435

Table 12.16 Material properties of abdominal solid organs ................. 436

Table 12.17

Comparison of experimental data from Viano (1989) and

predicted results by the WSUHAM for pendulum

side impact ......................................................... 438

Table 12.18 Comparison of experimental data from Walfisch et al. (1980)

and predicted results by the WSUHAM for pendulum side

impact .............................................................. 440

Table 13.1 Classification of pelvic disruption ............................... 455

Table 13.2 Results of KTH testing resulting in many acetabular

fractures ............................................................ 460

Table 14.1 Knee pendulum impact data from Hayashi et al. (1996) . . . . . . 482

Table 14.2 Of the 16 impact tests conducted there were five pilon

fractures ............................................................ 486

Table 14.3 Tolerance of the Tibia for Anteroposterior and Lateromedial

loading for both sexes ............................................. 494


Loading for males only ........................................... 494

lvi

List of Tables


loading for females only .......................................... 495

Table 14.6 List of material properties used to model bone ................. 497

Table 14.7 List of simulations used to validate the lower limb model

by Beillas et al. (2001) ............................................ 498

Table 15.1 Summary of inversion and eversion ankle test data ............ 518

Table 15.2 Ankle injuries due to inversion and eversion ................... 519

Table 15.3 Summary of significant ankle inversion and eversion injury

data ................................................................. 520

Table 15.4 Sensitivity and specificity analysis of foot load data with

tendons pulled ..................................................... 529

Table 15.5 Sensitivity and specificity analysis of impact velocity data

with tendons pulled ............................................... 532

Table 16.1 List of all 17 side impact sled tests performed by Cavanaugh

et al. at Wayne State University ................................. 546

Table 16.2 Model predictions of the effect of air space on the near-side

occupant (based on Huang (1995)) .............................. 557

Table 16.3 Model predictions of the effect of padding on the near-side

occupant (based on Huang (1995)) .............................. 557

Table 16.4 Model predictions of the effect of a reduction in door velocity

on the near-side occupant (based on Huang (1995)) ........... 558

Table 16.5 Model predictions of the effect of loss of shoulder engagement

on the near-side occupant (based on Huang (1995)) ........... 559

Table 18.1 Types of rollover initiation (based on NHTSA (2001)) . . . . . . . 606

Table 18.2 Distribution of rollover crashes by initiation type for MAIS 2

to 6 injuries ........................................................ 610

Table 18.3 Injury distribution for belted occupants by body region ....... 611

Table 18.4 Injury distribution for unbelted occupants by body region

(taken from Hu (2007)) ........................................... 611

Table 18.5 Distribution of head injury by injury type or anatomic

structure ............................................................ 612

Table 18.6 Types of head injuries sustained by occupants

in a rollover ........................................................ 612

Table 18.7 Distribution of chest injuries among rollover occupants ...... 612

Table 18.8 Distribution of neck injuries among rollover occupants ....... 613

Table 18.9 Relationship between head and neck injury among rollover

occupants ........................................................... 613

Table 19.1 Scores for Glasgow Coma Scale (based on Teasdale and

Jennett (1974)) ..................................................... 630

Table 19.2 MCL strains due to lateral impact

(values in percent strain) ......................................... 641

Table 19.3 MCL failure loads, strain rate and stiffness ..................... 641

Table 19.4 Overall strain rate and loading rate for the MCL tests

conducted (based on Begeman et al. (1987)) ................... 642

Chapter 1

Introduction

This book deals with the subject of impact forces acting on the human body and the

injuries resulting therefrom. The motivation for doing research to uncover the

effects of impact on biological systems is to lower the rate of carnage on US

highways and bi-ways that have become unacceptably high. The surprising fact is

that the USA has lost over 3.6 million lives due to traffic crashes since 1899. This

number is larger than that of the lives lost in all the wars it has been involved in

since 1775. In 1966, the National Research Council published a report entitled

Accidental Death and Disability: The Neglected Disease of Modern Society

principally to deal with the issue of the rapidly rising fatality rate from automotive

crashes. It rose from just over 36,000 in 1960 to almost 51,000 in 1966. The

National Highway Traffic Safety Bureau was established in 1966 to set safety

standards for motor vehicles sold in the USA. In 1983, Congress authorized the

US Department of Transportation to initiate a study by the National Academy of

Sciences (NAS) by convening a panel of experts to determine what is known about

injury and what research is needed to prevent or ameliorate it, including the role the

federal government should play to increase the knowledge of injury. A NAS report,

entitled Injury in America: A Continuing Public Health Problem, was published in

1985, and the Centers for Disease Control and Prevention (CDC) was commissioned

to form the Center for Injury Prevention and Control to assist the Department

of Transportation in enabling injury research in the USA. Automotive safety

was high on the list of priorities. At the same time, the automotive industry was

keenly aware of the problem but was resistant to federal intervention which can

result in regulations that add to the cost of building a car. For the rest of

the twentieth century, industry opposition gradually subsided, and the larger

automotive companies became substantive sponsors of automotive safety research

at many US universities and laboratories. As a result, injury research accelerated

through government and industry funding, and the driving public was the principal

beneficiary of this joint effort. The fatality rate in 2013 was 32,719.


A.I. King, The Biomechanics of Impact Injury, DOI 10.1007/978-3-319-49792-1_1

1

2 1 Introduction

1.1 Injury and Injury Prevention

Injury is an insult to the body sustained accidentally or inflicted deliberately to

cause disability or death. Accidental or unintentional injury is by far more

commonplace than intentional injury. The former can be due to motor vehicle

crashes, fires, drownings, and falls, while the latter is the result of the deliberate

use of force or weapons. The expert panel convened by the NAS was of the opinion

that injury was not an insoluble problem. In particular, unintentional injury was

deemed preventable if certain precautionary steps were taken. For the automobile,

crash prevention is the best means of reducing traffic-related deaths and injuries. In

the present-day context, the use of electronics and other high technology methods to

avoid crashes is slowly becoming a reality. This field of study is known as active

safety. However, not all crashes are preventable, and the occupants involved in a

crash need to be protected by mechanical means to minimize injury and reduce the

probability of death. This field of study is known as passive safety.

1.2 Some US and Global Statistics

In 2013, there were 192,945 fatalities due to all injuries for a population of slightly

over 316 million, and the death rate per 100,000 population was 61.30, according to

the Center for Injury Prevention and Control of the CDC (http://webappa.cdc.gov/

sasweb/ncipcmortrate9.html). In 1983, the number of deaths was 141,431 and the

rate was 60.49. Over this 30-year period, the death rate has increased slightly.

However, the change in automotive-related death rate is quite dramatic. The motor

vehicle-related death rate decreased from 44,452 (19.01) to 35,369 (11.19) over the

same period. For occupant fatalities, the rate decreased from 9.73 to 2.73 (22,743 to

8629 deaths), a 3.56-fold decrease.

In terms of hospitalizations due to all injuries, the total number in 2013 was 30.9

million (9771/100,000), 28.6 million (9063/100,000) of which were unintentional

injuries. In 2001, there were 29.7 million (10,432/100,000) injuries from all

causes and 27.6 million (9673/100,000) from unintentional causes. For the automotive

occupant, the number of nonfatal injuries dropped from 3.04 million

(1067/100,000) in 2001 to 2.46 million (779/100,000) in 2013.

It is also important to consider the economic impact of injury on society. The

CDC has also published the societal cost of injury. The total cost of all injuries in

2010 was $189.5 billion and that for unintentional injuries was $113.3 billion. The

cost of nonfatal injuries, including hospitalization and emergency room visits, was

$397.7 billion for all injuries and $354.5 billion for unintentional injuries. For

motor vehicle occupants, the total societal cost for fatalities was $12.4 billion,

while that for nonfatal injuries, including visits to the emergency room, was $48.7

billion. The total societal cost for motor vehicle occupants is $61.1 billion, and for a

population of 308.75 million, the cost to every man, woman, and child in 2010 was

1.2 Some US and Global Statistics 3

$198, just for motor vehicle occupants. It is clear that no man is an island, and it

behooves us all to drive carefully and to wear our restraint system every time we are

in a car. The fact that these are societal cost hits home when we learn that a portion

of the fee for our vehicle registration is kept in a catastrophic fund by some states to

care for the traffic injury victims who do not have the means to pay for their own

treatment. The above costs are in 2010 dollars and include medical cost for

treatment of the victims and cost of work lost.

The National Highway Traffic Safety Administration (NHTSA) also keeps track

of highway death rates, and one of the best indicators of the continuing improvement

in highway and vehicular safety is the estimate of the number of fatalities per

100 million vehicle miles traveled (VMT). Since the annual gasoline consumption

rate and the average corporate fuel economy rating for each car model are known

and so is the number of cars on the road for any given year, this fatality has been and

still is being computed for each year since 1921. It was about 24 fatalities per

100 million VMT in 1921, and it gradually dropped to as low as 1.08 in 2014 (http://

www-fars.nhtsa.dot.gov/Main/index.aspx). A plot of this trend is shown in Fig. 1.1.

These injury data show the effectiveness of technology, injury prevention

research, and motor vehicle safety standards in assisting automotive designers to

improve safety in cars. Impact biomechanics research played a major role in

achieving these stunning results.

30.00

3.5

Estimated Fatalities per 100 Million VMT

25.00

20.00

15.00

10.00

5.00

Estimated Fatalities per 100 Million VMT

Estimated VMT in Trillions

3

2.5

2

1.5

1

0.5

Estimated VMT in Trillions

0.00

1921 1941 1961 1981 2001

Year

0

Fig. 1.1 Fatality rate per 100 million vehicle miles traveled from 1922 to 2012 in the USA (taken

from Wikipedia and created by Dennis Bratland)

4 1 Introduction

44,000

43,000

43,510

42,708

42,000

Road fatalities

41,000

40,000

39,000

38,000

37,000

40,716

41,259

37,261

36,000

35,000

34,000

33,963

33,000

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Year

Fig. 1.2 Dramatic drop in annual fatality rate between 2005 and 2008 (source: NHTSA)

Figure 1.2 shows the dramatic drop in annual fatality rate after 2005. It was at

43,510 for all traffic-related deaths in 2005 and in 2008 it had dropped to 33,963.

The rate in 2013 was 33,804. There are several possible explanations for this

dramatic change in fatality rate. Chief among them are the wide availability of

frontal and side airbags and decrease in commuter travel and in long-distance

leisure travel.

Table 1.1 summarizes the global fatalities as a percentage of regional road traffic

deaths in 2010, for various modes of transport. People with higher income tend to

die in car crashes which claim the largest percentage of fatalities in developed areas

of the world. In developing areas, motorized 2–3 wheelers claim a higher percentage

of lives. Pedestrian fatalities are also higher in developing countries. Overall,

motorized traffic claims just over 50 % of the road fatalities, while pedestrian

fatalities approach a quarter of the casualties.

1.3 Impact Biomechanics

Biomechanics is the study of loads acting on a biological system, such as a human

body, to study its response to such loads. Impact biomechanics is a special branch of

this field of study that is concerned with loads that act on the body for a short period

of time, usually much less than one second. Although impact biomechanics encompasses

many kinds of collisions, such as in contact sports and slips and falls, it is the

1.4 History of Impact Biomechanics 5

Table 1.1 Road users killed in various modes of transport as a percentage of regional road traffic

deaths 2010 (Source: World Health Organization)

World Health

Organization

region

Income

level

Car

occupants

Motorized

2–3 wheelers Cyclists Pedestrians

Other/

un-specified

African LIC 35 11 7 38 9

MIC 51 4 4 37 4

All 43 7 5 38 7

Americas MIC 31 16 3 27 23

HIC 70 13 2 12 3

All 42 15 3 23 17

Eastern MIC 36 14 3 28 19

Mediterranean HIC 63 3 2 27 5

All 37 14 3 28 18

European LIC 32 0 2 26 40

MIC 52 7 3 32 6

HIC 49 19 7 19 6

All 50 12 4 27 7

South-East LIC 25 19 6 34 16

Asia MIC 15 34 4 11 36

All 15 33 4 12 36

Western LIC 12 66 4 12 6

Pacific MIC 22 38 8 24 8

HIC 33 18 10 33 6

All 23 36 8 25 8

World LIC 31 15 6 36 12

MIC 27 25 4 22 22

HIC 56 16 5 18 5

All 31 23 5 22 19

Note: LIC low-income countries (income < US$1005), MIC middle-income countries (income US

$1006 to US$12,275), HIC high-income countries (income > US$12,275)

principal tool used to prevent injury due to motor vehicle crashes. That is, the

principles of mechanics can be used to prevent a crash victim from sustaining

severe injuries.

1.4 History of Impact Biomechanics

Interest in injuries sustained as a result of an impact began with the accident

investigations carried out by Hugh De Haven of Cornell University in the 1940s.

He was a pilot as well as an engineer and was interested in how people survived

falls from great heights. He published his findings on the ability of the human body

to survive falls from 50 to 150 ft in (De Haven 1942) in which he described how

6 1 Introduction

Fig. 1.3 Professor H. R.

Lissner (1908–1965)

Fig. 1.4 Dr. E. S. Gurdjian

(1900–1985)

they almost walked away from these apparently non-survivable heights. Although

he was able to document the injuries sustained by these individuals, he could only

estimate what impact forces or bodily decelerations they sustained. Nevertheless,

this was a start and it took the form of field investigation. Laboratory research in

impact biomechanics was initiated by a couple of professors at Wayne State

University in Detroit; MI. Professor H. R. Lissner, an engineer (Fig. 1.3), and

Dr. E. S. Gurdjian, a neurosurgeon (Fig. 1.4), began an experimental study to try

to understand the causes of skull fracture and brain injury in 1939. Their first

experiment was to study the forces necessary to cause a skull fracture. Dried

human skulls were coated with a brittle lacquer and set at the bottom of an elevator

shaft of a 12-story building on the campus, and they dropped metal balls onto them

from the top floor to look for the fracture patterns of the brittle lacquer, in an attempt

to understand the stress distribution on the surface of the skull during impact. This

first experiment led to head impact tests on anesthetized animals and cadavers,

eventually culminating in the Wayne State Tolerance Curve (WSTC) for head

injury, as shown in Fig. 1.5 (McElhaney et al. 1976). The WSTC formed the

1.4 History of Impact Biomechanics 7

Fig. 1.5 The Wayne State Tolerance Curve for head injury (taken from McElhaney et al. (1976))

basis for the Head Injury Criterion (HIC) that is currently used in Federal Motor

Vehicle Standard 208 (FMVSS) for head injury.

Lissner was a pioneer in biomechanics and accomplished many things in addition

to his head injury research. He did dynamic tests on femurs and pelves, built a

vertical accelerator in an 8-story building to study spinal injuries sustained by jet

pilots ejecting from disabled jet aircraft, and developed an Achilles tendon load cell

for gait research. The most prestigious award of the Bioengineering Division of the

American Society of Mechanical Engineers (ASME) is called the Lissner Medal

which is awarded annually to a deserving senior researcher in Bioengineering.

Gurdjian was a medical pioneer in brain injury research. He discovered the propagation

of pressure or stress waves traversing the brain when the skull received a

blunt impact and sustained a translational or linear acceleration. To avoid impacting

the skull of anesthetized animals, he invented the fluid percussion method of

delivering a pressure pulse to the brain by drilling a hole in the skull and applying

a short pressure pulse to the dura. The pulses varied in duration from about 1 to

38 milliseconds (ms) (Gurdjian et al. 1954) and were able to render the animal

comatose. He hypothesized that linear acceleration or a transient pressure wave was

the mechanism for traumatic brain injury (TBI). Many veterans returning from

combat in Iraq and Afghanistan suffer from a form of mild traumatic brain injury

(mTBI) after being exposed to a blast overpressure wave caused by an improvised

explosive device (IED). The duration of the pressure wave varies from 2 to 10 ms.

Research is being conducted to look for the cause of blast-induced mTBI, but the

injury was described by Gurdjian over a half century ago.

Upon Lissner’s passing, Professor Lawrence Patrick took over the impact

biomechanics research at Wayne State and made substantive contributions to

automotive safety. He designed and built several impact sleds to simulate car

crashes without having to run a car into a wall, and he volunteered to ride the

8 1 Introduction

sleds as well as to be impacted by a heavy pendulum in the chest to provide living

human data for comparison with cadaveric data that were collected by many

laboratories. His justification for volunteering was that he was almost 50th percentile

in weight and height and represented the average American male.

Another notable contributor was Col. John Paul Stapp (USAF) who made

significant contributions to automotive safety while doing research in the Air

Force space program in the 1940s and 1950s. He volunteered to ride a rocketdriven

sled in Alamogordo, NM, in 1954 to test the effect of wind blast when a pilot

ejects from a disabled jet. The sled rode on a long straight track and was powered by

obsoleted military rockets that provided a thrust of about 4 kN or 1000 lb. For that

particular test, it reached a speed of 632 mph with Col. Stapp strapped into a

forward facing seat. Of course, the sled had to be brought to a safe stop at the end

of the run. Scoops hanging off the sides of the sled engaged water in troughs on both

sides of the tracks to decelerate the sled. He experienced a peak deceleration of

about 45 g at his chest and he sustained a detached retina in one eye. He was

remembered for his courageous ride and for the deceleration portion of the test

which would simulate a severe motor vehicle crash. After retiring from the

Air Force, he became a strong advocate for automotive safety, and an annual

conference to discuss the biomechanics of automotive safety was named in his

honor. It is called the Stapp Car Crash Conference and in 2014, it held its 59th

annual meeting. This conference is the most prestigious conference in impact

biomechanics, and the Stapp Car Crash Journal is the repository of much of the

data in impact biomechanics for the last 50 plus years.

The field of impact biomechanics was recognized by the National Academy of

Engineers when the author of this book was inducted into the Academy in 2000. A

second researcher in impact biomechanics became a member of the Academy in

2003. He is Dr. Priya Prasad who led the automotive safety program at Ford Motor

Company for over a quarter century. Other notable researchers in the field include

Ayub Ommaya (brain injury), Jim McElhaney (neck injury biomechanics), Bud

Mertz (automotive safety at GM), Rolf Eppinger (biomechanical research related to

Federal Safety Standards), John Melvin (automotive and racecar safety), David

Viano (automotive safety), King Yang (modeling of impact events), John

Cavanaugh (side impact tolerance and whiplash research), and Barry Myers (neck

injury biomechanics). This is a short list of many excellent researchers in the field,

and the author apologizes for failure to mention prominent researchers in this field.

1.5 The Role of the Federal Government

and Automotive Safety Standards

The history of impact biomechanics would not be complete without a cursory

discussion of the National Highway Traffic Safety Administration which is a part

of the US Department of Transportation. Its predecessor organization was the

1.6 Major Subdivisions of the Field of Impact Biomechanics 9

National Highway Safety Bureau which was established in 1966 as a result of the

Highway Safety Act of 1966. NHTSA came into being in 1970. Its mission is to

reduce deaths, injuries, and economic losses resulting from motor vehicle crashes.

This is accomplished by setting and enforcing Federal Motor Vehicle Safety

Standards (FMVSS) and corporate fuel economy standards, investigating safety

defects in motor vehicles and promoting safe driving behavior as well as the proper

use of automotive restraints. Manufacturers of motor vehicles cannot market them

in the USA unless these vehicles conform to and have been certified that they

conform to the regulations outlined in FMVSS. The 200 series of FMVSS deals

specifically with occupant safety and is of interest to those concerned with the

biomechanics of impact injury.

The 200 series FMVSS presently has 23 standards which are summarized in

http://www.nhtsa.gov/cars. Vehicles sold in the USA are required to comply with

these standards, and the NHTSA has provided detailed descriptions of the laboratory

tests required for certification of compliance (see http://www.nhtsa.gov/Vehi

cle+Safety/Test+Procedures?procedurePage¼2). The two standards of major

interest to biomechanicians are FMVSS 208 for frontal impact and FMVSS

214 for side impact. The injury criteria for frontal impact are for the head, chest,

and femur, while those for side impact are for the head, spine and pelvis for car-tocar

impacts and for the head, thorax, abdomen, and pelvis for car-to-pole impacts.

The numerical values used in the standards were proposed by the NHTSA and

generally agreed to by the automotive manufacturers. There is generally a good

biomechanical basis for the criteria or injury assessment reference values (IARV)

for the 50th percentile male and less so for the 5th percentile female or the 1-, 3-, or

6-year-old child. These IARVs will be discussed in the book as each body region is

considered. The entire family of five dummies is used for frontal impact, while only

two are specified for side impact, the European Side Impact Dummy (ES-2re) for

the 50th percentile male and the SID-2 s for the fifth percentile female. The adult

dummies are tested dynamically, either belted or unbelted, and protected by an

airbag. There is a belted car-to-car frontal barrier test at 48 km/h (30 mph) and a

32–40 km/h (20–25 mph) frontal offset barrier test in FMVSS 208. For FMVSS

214, the test vehicle is either impacted by a 1361 kg (3000 lb) moving dynamic

barrier (MDB) or a rigid pole. For the MDB tests, the MDB is towed into the

stationary test vehicle at 52.9 0.8 km/h (32.6 0.5 mph) with its wheels turned

27 1 deg toward the test vehicle. The direction of impact is perpendicular to the

side of the test vehicle. Rigid pole tests are conducted by towing the test vehicle into

a 254 mm (10 in) rigid pole at 32 km/h (20 mph).

1.6 Major Subdivisions of the Field of Impact

Biomechanics

As the field of impact biomechanics evolved, the results that appeared in the open

literature could be divided into the following four categories (Viano et al. 1989):

10 1 Introduction

(i) Injury mechanisms

(ii) Response to impact

(iii) Human tolerance to impact

(iv) Technology assessment

1.6.1 Injury Mechanisms

Since the purpose of impact biomechanics is to reduce or eliminate injuries

occurring during an impact event, it is critically important that the cause or

mechanism of injury be understood and verified. As the saying goes: You cannot

prevent an injury if you do not know the cause. It should be pointed out at the outset

that injury causation is not a subject taught in medical schools, and although

physicians are qualified to diagnose and treat an injury, they generally do not

have the background or the knowledge of the mechanisms or mechanical factors

that produced the injury. This task is left to the biomechanical engineer who uses

engineering principles to explain how a body region is injured. The simplest

example is bony fracture. It is well known that bone is weak in tension, and when

a bone fractures, the engineer looks for loading that can produce a high tensile stress

in the bone. Generally, such high stresses come from bending loads, and it is no

great mystery how a rib is fractured by an impact to the chest. Tensile stresses are

developed on the inside surface of the rib when it is loaded from the outside. Other

fractures are not as obvious. Among the elderly, especially among elderly females,

they are at risk of sustaining a hip fracture, which is a fracture of the neck of the

femur or thigh bone (see Fig. 1.6). The commonly accepted explanation of this

injury is that “Grandma fell and broke her hip.” However, upon closer examination

of the injury, it was found that those who break their hip fall to side, and yet data

from side impact studies show that when the greater trochanter is impacted by

the car door, hip fractures rarely occur. Instead, one or both of the pubic rami are

fractured, or the acetabular cup (hip socket) is fractured. Thus, the biomechanical

explanation of the injury is a bending fracture of the femoral neck due to muscular

forces acting on an osteoporotic femoral neck, resulting in a fall to the side

(osteoporosis is bone loss due to aging). So why is it important to ascertain the

precise mechanism of injury? Well, if you believe in the theory that the fall caused

the fracture, then elderly women should wear hip pads to protect them when they

fall. However, if the mechanism is a weak femoral neck that fractures when she

makes a misstep or tries to get out of a bathtub, the countermeasure would be to

ensure that osteoporosis sets in as late as possible in her life cycle. Other examples

will be discussed in later chapters. In every case, the injury can only be prevented if

we know the cause or the mechanism.


Fig. 1.6 The hip joint—Femoral neck fractures (hip fractures) do not occur when the greater

trochanter is impacted, and they occur in the elderly when they fall to the side. Thus, neck fracture

due to osteoporosis is the cause of the fall, and the statement that “Grandma fell and broke her

hip” is biomechanically incorrect (taken from Netter (2006)). Republication 2017. Used with

permission of Elsevier

1.6.2 Response to Impact

When a material is loaded, it responds to the load by deforming and breaking up, if

the load is large enough. Engineers have been studying material response for a very

long time but are relatively new at studying the response of biological tissue to impact

loading. The methods used to describe material response are similar to the traditional

methods except the material is not manufactured under controlled conditions and its

response can vary greatly from sample to sample or person to person. When dealing

with human tissue, especially applying loads to living individuals, the response is by

necessity from low loads that do not cause injury. On the other hand, we need to find

loads that cause severe injuries, such as fracture of bones or rupture of ligaments and

organs. In this case, we use cadaveric tissue or anesthetized living animals. The

response from cadavers and animals will not have muscular response, but that is not a

serious problem in impact situations because impacts are of short duration and

muscular response is usually delayed until the impact event is over. There are a

limited number of cases in which muscular response plays a role to affect impact

response. Some of these cases will be discussed in this book.

There are two reasons for obtaining impact response data. First, the data are

needed to design humanlike dummies or anthropomorphic test devices (ATD).

These devices are used by automobile manufacturers to test the safety features in

their vehicles, and the data from these devices are used to predict if the injuries a

human occupant would sustain would be acceptable. Figure 1.7 is an example of

12 1 Introduction

Fig. 1.7 Example of impact biomechanical response—Chest force-deflection response due to

frontal impact by a pendulum (taken from Neathery (1974))

human thoracic response to a frontal impact. It takes the form of a force-deflection

curve generated by a 152 mm (6 inch) diameter steel pendulum impacting a cadaver

chest. The curves represent two sets of impacts at two velocities, 26.8 km/h

(16.5 mph) using a 23.1 kg (51.1 lb) pendulum and 18.7 km/h (11.5 mph) using a

19.6 kg (43.1 lb) pendulum. At the higher speed, the darker solid curve represents

the mean of the data and is within a corridor (shown by the dotted curves) that

encloses most of the data. Similarly, at the lower speed, the less dark curve is the

mean curve for the lighter impact and is within another corridor that encloses a like

set of data points. The work was done by Kroell et al. (1974) using unembalmed

cadavers. However, the curves in Fig. 1.7 were the result of a data analysis effort by

Neathery (1974). These curves form the basis for the design of the current ATD

chest for frontal impact—the Hybrid III dummy. The second reason for acquiring

the data is to use them for the validation of mathematical (computer) models that

simulate the impact event. Such models take less time and are less expensive to

run than cadaveric or dummy tests, but they need to be validated to ensure that

they can indeed predict the experimental results. Once validated, they can be

extended to predict results that are either difficult or impossible to attain


Contact Force (kN)

-8.0 -6.0 -4.0 -2.0 0.0

Model

Test

0.0

2.0 4.0 6.0 8.0 10.0 12.0

Time (ms)

14.0

Fig. 1.8 Example of impact biomechanical response—Contact force-time curves for frontal head

impact (taken from Ruan et al. (1993))

experimentally. For example, only a model can predict the response of the chest if it

were impacted simultaneously by two pendulums from two arbitrary directions.

Response data can also take the form of force-time curves or acceleration-time

curves. If experimental conditions are such that deflection or deformation is hard to

measure, then the force data can be expressed as a function of time. An example of this

response is shown in Fig. 1.8. It shows the contact force generated by a pendulum

impact to the front of the head of a cadaver, expressed as function of time. A computer

model of this event was modeled, and the predicted contact force is also shown (Ruan

et al. 1993). Skull deflections are relatively small and difficult to measure. Thus, the

best way to depict head impact response is to use a force-time curve.

A third example of biomechanical response is an acceleration-time curve.

Oftentimes, even impact forces are difficult to measure, and the alternative is to

mount miniature accelerometers to the body structure and report acceleration as a

function of time. Figure 1.9 is an acceleration-time curve of the fourth rib of a

cadaver undergoing a side impact. The data were used in an FMVSS 214 Standard

for side impact (Morgan et al. 1986). The criteria for this standard have since been

changed.

14 1 Introduction

Fig. 1.9 Example of impact biomechanical response—Acceleration-time curve for acceleration

of the 4th rib due to lateral impact to the chest. The dark curve represents the mean, while the

dotted curves form the corridor of data from multiple cadavers (Morgan et al. (1986))

1.6.3 Human Tolerance to Impact

The key question in the design of motor vehicles is: How many g’s can I take?

Biomechanical engineers like to answer the question with a question: How badly do

you want to get hurt? So, before we can determine the level of human tolerance, we

need to establish a means by which injury severity can be quantified. A numerical

injury scale was proposed by the Association for the Advancement of Automotive

Medicine (www.aaam.org) in 1969 based on input from accident investigators,

orthopedic surgeons, emergency medicine specialists, biomechanical engineers,

and epidemiologists. It is called the Abbreviated Injury Scale (AIS). This scale

has been revised several times and the latest version is known as AIS2008. It comes

in the form of a codebook that provides injury (AIS) scores for each body region for

6 levels of injury severity. It is important to remember that the AIS score is based on

threat to life and not on disability resulting from the injury. The Abbreviated Injury

Scale is provided in Table 1.2 where an AIS of zero means no injury and an AIS of


Table 1.2 The Abbreviated

Injury Scale (AIS)

AIS

Injury severity

0 No injury

1 Mild injury

2 Moderate injury

3 Serious injury

4 Severe injury

5 Critical

6 Maximum

9 Unknown

6 is maximum injury (currently untreatable). Examples of AIS 4 injuries include

depressed skull fracture, multiple brain contusions, fracture/dislocation of the

cervical spine below C3, flail chest, and severe heart contusion. AIS 5 injuries

can include unconsciousness over 24 h, bilateral subdural hematoma, complete cord

syndrome C4 or below, major laceration of the thoracic aorta, lung laceration with

air embolus, and massive liver laceration. AIS 6 injuries are limited to massive

crush of the cranium, complete cord syndrome at C3 or above, cord laceration at C3

or above, and open laceration of the thoracic aorta.

Having defined the injury levels for each body region, it now becomes the task of

the biomechanical engineer to find tolerance values for any given AIS of a specific

body region. This is indeed a daunting task which takes years of research by many

institutions to accomplish. In fact, the job is not done and the search continues. One

confounding variable in the determination of tolerance levels is the large variation

in tolerance among a given population. This variation occurs among a group of

people of the same gender and age, but larger variations are expected between

males and females, between the elderly and the middle-aged adult, and between the

adult and the child. That is, reliable tolerance limits require a large amount of

laboratory-based injury data, preferably from human subjects. Since it is not ethical

to deliberately injure a living human being, the human subjects used for tolerance

testing would be cadavers donated for scientific research. We will not go into the

ethical aspects of cadaveric research suffice it to say that properly donated bodies

can be used for biomechanical research.

A statistical approach is used to take care of the large variations in the tolerance

data. Test data are used to compute the probability of injury of a certain level based

on the experimentally obtained AIS values. Injury data sets are assumed to follow

the logistic statistical distribution for the following reasons:

1. The data we are dealing with are not integer numbers (can be expressed as

decimal numbers) such as acceleration, force, and time.

2. The data are symmetric. That is, the variation from the mean occurs on both

sides of the mean.

3. The data are clustered around a central value.

4. The likelihood of the occurrence of outliers is low, meaning that it is not zero and

not very low.

16 1 Introduction

5. The dependent variable is binary. For example, was there injury or no injury or

did the injury reach or exceed a prespecified injury level (AIS value) for a given

independent variable?

Under these conditions, the logistic distribution should be selected to represent

the data.

In statistics, we look for relationships between a dependent variable, in this case,

injury severity or the AIS score, and a number of independent variables, in this case,

acceleration, force, etc. This approach is called a regression analysis. When we do a

logistic regression for a dependent variable that is binary, the independent variable

takes on an exponential form, as shown in Eq. (1.1):

px ðÞ¼1 ½ þ expðα βxÞ 1 ð1:1Þ

where x is the response variable, such as force or acceleration, α, β are the logistic

coefficients, and p(x) is the probability of an injury occurring

The coefficients, α and β, can be found by using available software on the

Internet, such as SPSS, or on the web—logistic regression calculation by John

C. Pezzullo. For a given data set, Eq. (1.1) takes the form of a sigmoidal curve. An

example of this is shown in Fig. 1.10 which is an attempt to correlate thoracic injury

at the AIS4 level or higher with a parameter called VC max , otherwise known as the

Viscous Criterion, involving the product of chest velocity (V) and the percentage of

chest compression (C). These variables are shown on the left hand ordinate and the

abscissa. The maximum thoracic AIS (MAIS) was determined experimentally with

the values ranging from 0 to 5. The values of VC max range from 0 to about 4.8.

Since injury is binary (0 or 1), we can do a regression analysis on the data by

generating a regression curve from Eq. (1.1). All injury data below AIS 4 are

designated as having a zero probability of injury and all data at AIS 4 or above as

having a 100 % probability of injury. So to draw the logistic curve, using the

ordinate on the right, the data at MAIS 2 are moved to the abscissa (0 % probability

of injury), and all data at MAIS 4 or above are moved to the top of the graph where

Fig. 1.10 A typical logistic

plot. This plot is an example

of using logistic regression

to obtain the probability of a

chest injury of AIS4 or

above as predicted by using

the independent parameter

VC max (based on

Cavanaugh et al. (1990))


Table 1.3 Predictor

variables for mTBI in the

NFL (based on King

et al. 2003)

2 log Likelihood

Rank order Predictor variable χ 2 p

1 ε.dε/dt| max (s 1 ) 41.0 0.0000

2 dε/dt| max (s 1 ) 33.1 0.0000

3 HIC 15 31.5 0.0000

4 SI 31.2 0.0000

5 Linear accel. (m/s 2 ) 28.3 0.0000

6 ε max 28.0 0.0000

7 Max stress 27.3 0.0000

8 Cum. strain at 15 % 26.0 0.0000

9 Angular accel. (rad/s 2 ) 24.9 0.0000

the probability is 100 %. These data are fed into a computer program that calculates

α and β, and Eq. (1.1) is used to plot the sigmoidal curve. It can be seen that at

VC max ¼ 1, the probability of sustaining an AIS4+ injury is approximately 50 %.

To assess whether a given response variable is a good predictor of injury

(goodness of fit), several parameters can be used, including the chi square (χ 2 )

value, the p-value, and the coefficient of determination (R 2 ). Response variables

that are good predictors of injury should have a high χ 2 value, a p-value as close to

zero as possible, and an R 2 value as close to unity as possible.

We will now consider an actual application of logistic regression to determine

the best variable for predicting brain injury. Table 1.3 ranks how well some of the

predictor (independent) variables are able to predict mTBI in American football,

using the values of the computed χ 2 as a measure of the ability of that variable to

predict mTBI. The data came from a rather convoluted method of analyzing actual

concussion data provided by the National Football League (NFL) which is

discussed in Chap. 2 (King et al. 2003). A brain injury model by Zhang et al.

(2001) was used in conjunction with the data to compute the response of the brain in

the form of stress, strain (ε), strain rate (dε/dt) in the brain, and the volume of brain

that exceeded 15 % strain (cumulative strain at 15 %) as a result of the on-field

collisions. The other variables are input variables that were measured experimentally

in simulated helmet-to-helmet collisions. HIC 15 and SI are the head injury

criterion and the severity index that are computed from Eqs. (1.2) and (1.3),

respectively.

HIC ¼ ðt 2 t 1 Þ

SI ¼

ð t2

2:5

ð Þ max ð1:2Þ

aðÞdt= t t 2 t 1

t 1

ð

a 2:5 dt 1000

ð1:3Þ

Table 1.3 shows that the product of strain and strain rate (ε. dε/dt) is the best

predictor and that HIC is ranked amazingly high even though it was based on the

WSTC and very old data obtained from impacts to the heads of cadavers and

18 1 Introduction

Fig. 1.11 Logistic curve

for the product of strain and

strain rate for mTBI (King

et al. 2003)

Table 1.4 Predictors of tolerance for mTBI (based on King et al. (2003))

Tolerance levels for probability of mTBI

Predictor

25 % 50 % 75 %

ε max 0.29 0.40 0.48

dε/dt max 51 65 81

ε.dε/dt max 20 24 27

Linear accel. (g) 63 81 99

Ang. accel. (rad/s 2 ) 4267 5488 6709

SI 178 298 417

HIC 143 249 336

anesthetized animals. There are many proponents of angular acceleration as a major

cause of brain injury, but this theory is not borne out by this set of NFL data. It

should be noted that injury data from living humans with known inputs are rare and

difficult to obtain.

The logistic curve for the product of strain and strain rate is shown in Fig. 1.11.

The probability of concussion can be estimated from this graph. Table 1.4 shows

the 25 %, 50 %, and 75 % probability of a concussion using some of the predictor

variables in Table 1.2. Table 1.4 shows for the first time actual human angular

acceleration tolerance data for concussion since all previously published data were

extrapolated from animal tests, cadaveric data, or some measured human limit

based on isolated impacts. It also interesting to note that a HIC of 250 is the

tolerance for a 50 % probability of an mTBI and that it is set at 700 in FMVSS 208.

It is also possible to determine an optimal tolerance or an optimal probability of

injury from a regression analysis, using a specific independent variable. Let’s return

to our example shown in Fig. 1.11 and re-plot it without the tolerance estimates.

Instead, we set an arbitrary threshold of 20 for ε. dε/dt, as shown by the dotted

vertical line in Fig. 1.12. On the abscissa, the data points indicating 0 % probability

of injury to the left of the threshold constitute the true negatives (TN). The data

points on the abscissa to the right of the threshold constitute the false positives (FP).


Fig. 1.12 Definition of true

and false positives (TP and

FP) and true and false

negatives (TN and FN) for

an arbitrary threshold. For

the threshold selected, there

are no false negatives or

positives (taken from Smith

(2003))

PROBABILITY OF INJURY %

1.00

0.75

0.50

0.25

0.00

FOOT LOAD vs INJURY

FN TP

TN FP

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0

FOOT LOAD N x100

Similarly, at 100 % probability, there are true positives (TP) to the right of the

threshold and false negatives (FN) to the left of the threshold. That is, when we are

dealing with biological data, there is rarely a threshold that would yield only true

negatives and true positives. If we accept this fact, we can define two ratios,

sensitivity and specificity, as shown in Eqs. (1.4) and (1.5) below:

Sensitivity ¼ TP= ðTP þ TNÞ ¼ TPRðTrue positiverateÞ ð1:4Þ

Specificity ¼ TN= ðFP þ TNÞ ¼ FNRðTrue negativerateÞ ð1:5Þ

We can also define a false-positive rate (FPR), given by

FPR ¼ FP= ðFP þ TNÞ ð1:6Þ

It can be seen that FPR ¼ 1FNR ¼ 1Specificity

Now if we draw a graph with FPR on the abscissa and TPR on the ordinate and

calculate the values of TPR and FPR for a range of thresholds, we get a curve that is

known as a receiver operating characteristic (ROC) or an ROC curve. Each point on

the curve is made up of the two calculated values of TPR and FPR for a selected

threshold; Fig. 1.13 is an ROC curve for the data presented in Fig. 1.11. If there was

no overlap of injury and non-injury data or both sensitivity and specificity are

100 %, then the ROC goes to the top left hand corner of Fig. 1.13, and the area under

the ROC curve would be 1. On the other hand, if the chosen parameter has no

correlation with injury, the data would be random, and the ROC curve would be a

45 deg line from 0, 0 to 1.00 in Fig. 1.13, and the area under the curve is 0.5. That is,

the area under the ROC curve is a measure of the reliability of the data, and the

better the data, the closer the area to unity.

20 1 Introduction

Fig. 1.13 Receiver

operator characteristic

(ROC) curve for the product

of strain and strain rate

based on data from

Fig. 1.11. The area under

the curve is 0.943. It

indicates that this parameter

is a good predictor of injury

(based on data from King

et al. (2003))

Sensitivity

ROC Curve (PRODUCT)

1.0

0.8

0.6

0.4

0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0

1-Specificity

Fig. 1.14 The first

tolerance is for a sensitivity

of 1.0 and is a conservative

estimate of injury (based on

data from King et al.

(2003))

In Fig. 1.14 we choose a criterion that would result in no false negatives, the

sensitivity is equal to 1.0, and the tolerance obtained from the intersection of the

vertical line for the criterion with the logistic curve is called the first tolerance, with a

value of 18 s 1 and a probability of about 20 %. This means that any response value

below it will not result in injury. That is, this is a very conservative tolerance value.

On the other hand, if we chose a criterion that would result in no false positives,

then the specificity is equal to 1.0, and the second tolerance is 35 1 s with a

probability of close to 95 %, as shown in Fig. 1.15. That is, at the second tolerance,

any response above it will be injurious and this tolerance is very liberal.

The optimal tolerance is defined as that for which the sum of the sensitivity and

specificity ratios is a maximum. That is, it is optimized for both sensitivity and

specificity. This is shown in Fig. 1.16. The optimal tolerance is 23 s 1 and the

probability is 29 %.

Finally, tolerance is sometimes expressed in terms of a 3-ms clip, as shown in

Fig. 1.17. The hypothetical data of chest acceleration is to be assessed for tolerance

at 60 g. The cumulative duration of the acceleration pulse above 60 g exceeds 3 ms

and the tolerance is exceeded. The parameter can be any physical quantity besides

acceleration, such as force or pressure.


Fig. 1.15 The second

tolerance is for a specificity

of 1.0 and is a liberal

estimate of injury (based

on data from King et al.

(2003))

Fig. 1.16 Optimal

tolerance for which the sum

of the sensitivity and

specificity ratios is a

maximum (based on data

from King et al. (2003))

1.6.4 Technology Assessment

The fourth and final area of impact biomechanics is technology assessment which

develops tools to assess the safety features in a vehicle that was designed using the

knowledge gained in the previous three areas. The first tool that was developed was

the crash dummy, the surrogate used by automobile manufacturers to assess their

safety designs. These dummies need to be as humanlike as possible and come in

different sizes to represent the population of automotive passengers. There are

frontal impact dummies, like the Hybrid III, which is used widely throughout the

industry. There have also many side impact dummies, such as the EuroSid, the SID,

and the WorldSId. A detailed description of these dummies is beyond the scope of

this book, but their biofidelity and responses will be discussed in conjunction with

22 1 Introduction

Fig. 1.17 Hypothetical data for chest acceleration, demonstrating the meaning of a 3-ms clip. In

the figure, the cumulative duration of the acceleration pulse above 60 g exceeds 3 ms and the pulse

in injurious to the chest

the topics related to the biomechanics of injury. A more recent second tool is

mathematical modeling of impact events to simulate car crashes. The availability

of immense computing power in present-day computers has enabled the modeler to

simulate complex crashes that were not possible to simulate only a decade ago. The

use of models is a less costly alternative to crash testing and is much more versatile

in terms of the number of impact scenarios it can simulate. Many such models will

be covered in this book in subsequent chapters. Only an overview is provided here

to introduce the concept of modeling. In a crash event, we need to model the

vehicles involved as well as the occupants within these vehicles. Although reference

will be made to available vehicular models, our principal focus is on the

human occupant which can be a whole-body model of the occupant or a model of a

particular region of the body, such as the head.

1.6.4.1 What Is a Mathematical Model?

A mathematical model is an analytical representation (set of equations) describing a

physical phenomenon or event. It is a virtual experiment mimicking a real-life

event. In its simplest form, one can think of Hooke’s law (Eq. (1.7)) for the response

of materials to load or Ohm’s law (Eq. (1.8)) for current flow in a conductor, as

mathematical models, as shown below:

σ ¼ Eε

ð1:7Þ

where σ is the stress, E is the Young’s modulus, and ε is the strain.


Fig. 1.18 Stress-strain

curve for mild steel

C

D

Stress, lb/in. 2

B

A

Strain

V ¼ iR

ð1:8Þ

where V is the voltage, i is the current, and R is the resistance.

These are very simple models which have limited applications. Figure 1.18

shows the response of mild steel to a tensile load. Eq. (1.7) is only valid for the

linear portion of the curve at very low strain values. It is not valid for strain values

beyond the point A on the graph. This is true for Ohm’s law as well. Eq. (1.8) is

valid for electric current flow in metal conductors at a constant temperature. It does

not work in liquids or in semiconductors. That is, linear models have a limited range

of validity.

Another example of a simple model is Newton’s second law of motion which

can be written as

ΣF ¼ ma

ð1:9Þ

where ΣF is the vector sum of all forces acting on a body, m is the mass of the body,

and a is the acceleration vector.

Note that, in this book, when a quantity is underscored, it is a vector quantity.

This “law” is based on empirical observations by Sir Isaac Newton and is valid

for the motion of rigid bodies and for bodies with a constant mass. When the

velocity of the body approaches the speed of light, its mass changes and Newton’s

2nd is no longer valid. However, in impact biomechanics, the velocities encountered

are well below that of the speed of light, and there are no concerns regarding

its validity.

The use of mathematical or computer models is an accepted tool in engineering

and in many areas of the physical sciences. Models provide an inexpensive

alternative to experimentation and can predict outcomes that may not be attainable

in the laboratory. In mechanics, deterministic models are more common than

statistical or adaptive models. That is, these models are based on established

axioms, and for a given set of input data, there is only one set of unique results.

The models described in this chapter and, for that matter, in the entire book are

deterministic models. In impact biomechanics, modeling is an essential adjunct to

24 1 Introduction

experimentation because of the large number of variables involved and the great

variability in the material properties or constants used in these models. It is far

easier to change the values of these variables and those of the material properties on

the computer than in an experiment. Once validated, the model can also predict

outcomes that are difficult to replicate experimentally, such as modeling a series of

complex crash events, like multiple rearend crashes on a slick highway.

1.6.4.2 History of Biomechanical Models

In the early days of modeling (1940–1970), whole-body models and regional

models of specific body segments were developed. Regional models would be of

the head, spine, or torso. The first models were composed of spring-mass systems

which later evolved into discrete parameter models, followed by continuum models

described by complex differential equations and numerical models using finite

element (FE) analysis.

Figure 1.19 is an example of a spring-mass or lumped parameter model developed

to simulate the response of the head and torso subjected to a caudocephalad

(tail-to-head) or vertical acceleration input. The lack of anatomical similarity to the

human is quite obvious. The spine is between the thorax and the pelvis, whereas in

the human, the spine is inside the thorax. This lack of biofidelity was deemed

acceptable because the calculation of response was much simpler when the mass of

the thorax is “lumped” above the spine. The next improvement is the formulation of

discrete parameter models which consists of an array of lumped parameter models.

These models can simulate an anatomical segment in greater detail than a single

spring-mass model. For example, the vertebrae and disc of the spine can be

simulated by a discrete parameter model made up of individual spring-massdamper

models which are linked together to form a model of the spine. Further

refinement resulted in a continuum model in which the segment is represented by a

continuous material, and the individual elements have been reduced to an infinitesimal

size. An early model of the spine was represented by a straight column

composed of an elastic solid. Equations for these continuum models are complex,

and in dynamic models, they are usually partial differential equations which have

no closed form solution. Numerical methods were developed to solve these

Fig. 1.19 A lumped

parameter model simulating

the head and torso subjected

to vertical loading

Head

Thorax

Pelvis

Early lumped

parameter

models


Fig. 1.20 Finite element model of a lumbar vertebra (taken from Hakim (1976))

equations, and the most popular method of solving them is the finite element

(FE) method. The continuum is divided into small elements, and the stresses and

strains in the structure can be computed using this numerical method. An example

of an early FE model of a spinal vertebra is shown in Fig. 1.20.

The models described above are generally designed to simulate a region of the

body or impact to the whole body in one-dimension. The evolution of threedimensional

whole-body models started with rigid link models in which rigid

bodies are joined together to form a human shape, as shown in Fig. 1.21. They

are known as open chain models because the link does not close up on itself. This

class of models is not as sophisticated as 3-D FE models, but these models are ideal

for a quick calculation of human response. As a result, they are still being used in

the automotive industry. Currently, the most popular model is the MADYMO

model, developed originally in the Netherlands by the Organization for Applied

Scientific Research (TNO). The software is currently being distributed by Tass

International of Helmond, the Netherlands (www.tassinternational.com).

MADYMO is the latest version of a group of such models that was made popular

by McHenry (1963) of Calspan Corp. in Buffalo, NY. The original model had

4 masses and seven degrees of freedom (DOF) and simulated a frontal impact in

two-dimensions. Belt restraints were used to prevent the occupant from contacting

the interior of the vehicle. It was called a crash victim simulator. Over the next

decade, the model was re-named the Articulated Total Body (ATB) model. It was

three-dimensional and able to simulate contact of the body segments with interior

surfaces of the vehicle in addition to restraint use. The number of segments

26 1 Introduction

Fig. 1.21 The ATB model

developed by Calspan Corp.

The segment numbers are

in green and the joint

numbers are in red (taken

from Cheng et al. (1998))

increased to 15 or more with over 40 DOF. Figure 1.21 shows the current ATB

model of a human occupant. To generate contact forces, force-deflection data were

fed into the computer for all possible contacts of body segments with vehicular

surfaces, such the contact of the knee with the dash or the head with the steering

wheel. When contact is sensed by the program, a force is generated on the contacted

segment along with the calculated penetration or deflection of the surface. This

force stops the segment from moving into the surface and is eventually pushed back

out, simulating a real impact.

Whole-body rigid link models were developed with the following assumptions:

1. The body segments form an open chain and do not close up to form a loop.

2. The segments are rigid and contact data are used to calculate external forces

acting on them.

3. The joints between segments are non-extensible.

4. External forces acting on the segments due to contact can be calculated.

5. The joint moments are known quantities.

Under these assumptions, it is possible to solve for the translational and rotational

components of motion of the body segments using Newton’s second law of

motion. A free body diagram is drawn for each body segment, and if the contact

force and joint torques are known quantities, it is possible to calculate the linear and

angular displacement, velocity, or acceleration of that segment. To see how this

works, assume an open chain of k segments, where k is an integer. The unknowns

are the 6 k kinematic unknowns—the three linear and the three angular positions of

the segment at any given moment plus the unknown joint forces and moments, the


kinetic unknowns. For an open chain, there are k-1 joints, resulting in 6 k-6

additional unknown joint forces and moments. However, because of the assumption

that the joints are non-extensible, it is possible to calculate the linear position of all

segments if the orientation of all segments is known as well as the linear coordinates

of one of the segments. Thus, the number of kinematic unknowns becomes 3 k + 3,

and if the joint moments are known, there will only be 3 k3 unknown joint forces.

That is, the total number of unknowns is 3 k + 3 + 3 k3 ¼ 6 k. This number

matches exactly the number of equations that can be written for this system and

all the unknowns can be solved for. The 6 k equations of motion are given by

ΣF ¼ mað3kequationsÞ ð1:9Þ

and

ΣM ¼ Iαð3kequationsÞ ð1:10Þ

where ΣM is the sum of the moments acting on the body segment, I is the mass

moment of inertia of the segment, and α is the angular acceleration of the segment.

Joint moments are calculated from assumed relationships between joint angle

and moment. For the cadaver, there is no resistance to segmental rotation because it

is flaccid. For the dummy or a living subject, a moment-angle curve becomes a part

of the input data. In a more general context, one can state that, for the direct solution

of an open chain problem, with inextensible joints, the total number of excess

unknowns is equal to the number of joint moments.

The rigid body models can also simulate closed chain systems by a modification

that renders them open. For example, the rib cage is a closed chain system. It is

modeled by a series of segments linked together by inextensible joints. To make it

into an open system, one of those joints is replaced by a spring of known stiffness so

that the joint force there can be computed from the stretch in the spring. In the case of

modeling a vehicular occupant involved in a frontal crash and is bracing with both

hands and feet, this is another closed system that can be opened by assuming appropriate

force-deflection curves for each contact of the body segment with the vehicular

interior. The system then basically becomes open. Another use of these models is to

model human locomotion, such as walking, rising from a chair, climbing stairs,

jumping, or running. What needs to be done is to provide the appropriate joint moments

to the model at the appropriate time to get the model moving. However, it is not easy to

generate these joint moments, say at the knee, to make the model walk normally.

Inappropriate moments at inappropriate times will result in an unnatural gait.

1.6.4.3 Model Validation

Since modeling is essentially a virtual experiment in which mathematical equations

are written to represent the event and are solved to provide the result, there is no

28 1 Introduction

assurance that the result is a close approximation to that of an actual event or crash.

There are many factors in the development of a model that can cause it to yield

inaccurate or even outlandish results and computer maxim: “Garbage In, Garbage

Out” applies to all models. Many journals require authors who submit modeling

papers to provide proof that results predicted by the model approximate those

observed in experiments. That is, the authors are required to “validate” their models.

To improve the prediction of the model or to improve its validity, the following

conditions need to be satisfied:

1. The model should have anatomical similarity, Fig. 1.19 being a poor example of

anatomical similarity.

2. The model should have structural similarity. That is, it should have realistic joint

and material properties. In impact modeling, high strain rate properties of

biological tissue are often unavailable, resulting in poor predictions if the tissue

involved is highly strain rate sensitive.

3. Each of the components of the model should be able to simulate the response

accurately. For example, for a head model, the intracranial pressure will be

predicted more accurately if the skull was modeled correctly. If the skull is too

rigid or too soft, the predicted pressures would not be accurate.

The degree of validity of a model is dependent on many parameters. For a perfect

validation, the response of the model matches that of every experiment conducted.

This is not possible for biomechanical models because of the large variation in

response among specimens. The next level of validation is to match model prediction

with results from a specific test in terms of both the peak magnitude and phase for as

many parameters as possible. Slight shifts in phase are generally acceptable. To

match model predictions against results of several repeated tests, it is common

practice to enclose the experimental data with a corridor and try to have the model

results fit inside as much of the corridor as possible. If the tests use specimens that

have widely different material properties, such as young and old cadavers, it is

allowable to change model constants, such as the modulus of elasticity of bone, to

improve the match. However, justification is needed for changing these constants. If a

published paper claims an excellent match of several biomechanical responses, the

results should be regarded with suspicion at the present stage of modeling capability.

Similarly, modeling techniques are not at a stage for determining the material

properties of tissue using model results. Perfectly validated biomechanical models

are rare. Most partially validated models are useful in comparative studies.

Questions for Chapter 1

1.1. The use of cadavers in impact biomechanics is essential for the advancement

of the science of trauma. Their use is valid because:

[ ] (i) They have the proper mass distribution and identical organs as living

humans

Questions for Chapter 1 29

[ ] (ii) Muscular response occurs after the impact is over and is generally not

strong enough to be of significance in a crash simulation

[ ] (iii) They are excellent subjects for studying skeletal injuries because of

anatomical resemblance to the living subject

[ ] (iv) They can be used for brain injury research but are not ideal for that

purpose because of changes in brain properties after death

[ ] (v) All of the above

1.2. When an open chain of rigid body links is used to model occupant motion in a

crash, the total number of kinematic unknowns, for n rigid bodies connected

by inextensible joints, is:

[ ] (i) 3n

[ ] (ii) 6n

[ ] (iii) 3n + 3

[ ] (iv) 3n 3

[ ] (v) 6n + 6

1.3. Assumptions were made in the formulation of rigid body models, such as the

MADYMO model. Select the incorrect answer:

[ ] (i) All joints are inextensible

[ ] (ii) The chain must be an open link

[ ] (iii) Contact forces are calculated based on mutual force-deflection

properties

[ ] (iv) Inertial properties of each body segment must be known

[ ] (v) The number of body segments is limited to 25

1.4. Rigid body rotation can be defined by:

[ ] (i) Euler angles

[ ] (ii) Yaw, pitch, and roll

[ ] (iii) Direction cosines

[ ] (iv) Quaternions


1.5. There are 9 direction cosines and only 3 Euler angles. If both of these

measures can define rigid body rotation, then,

[ ] (i) There is something wrong

[ ] (ii) Not all 9 direction cosines are independent

[ ] (iii) Euler angles are not adequate to define rigid body rotation

[ ] (iv) Direction cosines are not adequate to define rigid body rotation

[ ] (v) None of the above

1.6. Currently, the principal causes of automotive fatalities are:

[ ] (i) Increase in highway speeds and vehicular density

[ ] (ii) Increase in elderly drivers

[ ] (iii) Increase in the number of drunk drivers

30 1 Introduction

[ ] (iv) (i) and (ii)

[ ] (v) (i) and (iii)

1.7. Federal Motor Vehicle Safety Standard 208 requires that

[ ] (i) The head injury criterion (HIC) not to exceed 1500

[ ] (ii) The peak chest acceleration in excess of 70 g does not exceed 3 ms in

total duration

[ ] (iii) The peak knee load does not exceed 12 kN

[ ] (iv) Side airbags be used in all cX


1.8. Impact biomechanics is a study of

[ ] (i) Human response to impact loading

[ ] (ii) Mechanisms of injury

[ ] (iii) Human tolerance to injury

[ ] (iv) Automotive safety technology


1.9. We need to know human response to impact loading because

[ ] (i) We can find out how people are injured

[ ] (ii) We can use the data to develop test dummies and computer models

[ ] (iii) We can use the information to sell cars

[ ] (iv) We need the information to test our new models


1.10. We need to know the various injury mechanisms due to impact loading so

that

[ ] (i) We can design safety features intelligently

[ ] (ii) Prevent injury by knowing the cause of the injury in advance

[ ] (iii) We can prevent all types of injury to automotive occupants

[ ] (iv) (i) and (ii)

[ ] (v) (ii) and (iii)

1.11. We need to know the levels of human tolerance to impact because

[ ] (i) We want to design a car which can prevent life-threatening injuries to

its occupants

[ ] (ii) We can design a reasonably safe car which can limit the number of

fatal injuries

[ ] (iii) We can use the information to design a safe but affordable vehicle

[ ] (iv) We can use the information to design vehicles for different segments

of the population in the future



1.12. We need to have the ability to assess safety technology because

[ ] (i) We want to improve the design of test dummies

[ ] (ii) We want to develop useful and predictive computer models of

occupant impact

[ ] (iii) We want to be able to determine the effectiveness of safety systems

[ ] (iv) We want to ensure that injury potential of the safety systems we

design is minimized


1.13. Human tolerance has many levels. For automotive safety design, we aim for

the following level of injury:

[ ] (i) Minor level at AIS 2 or below

[ ] (ii) Severe level, including life-threatening injuries

[ ] (iii) Severe level but not including life-threatening injuries

[ ] (iv) Severe level at which 50% of the occupants will suffer a fatal injury

[ ] (v) Ouch level so we can all walk away from all crashes

1.14. Computer models of impact can take the form of:

[ ] (i) Whole body models consisting of rigid links and inextensible joints

[ ] (ii) Finite element models of the whole body

[ ] (iii) Finite element models of different regions of the body

[ ] (iv) Simple spring-mass models of various body regions


1.15. There are several advantages of computer modeling over dummy testing. One

of them is

[ ] (i) Computer models do not need to be validated

[ ] (ii) Computer models can simulate impact situations difficult to reproduce

in the lab

[ ] (iii) Computer models do not need accurate input data

[ ] (iv) Computer models need to be run only once for each impact condition

[ ] (v) Computer models can be developed rapidly

1.16. Unintentional injuries due to automotive crashes are best prevented by

[ ] (i) Passing laws requiring use of seatbelts

[ ] (ii) Use of heavy advertising to not drink and drive

[ ] (iii) Show pictures of crashes on bill boards on the side of highways

[ ] (iv) Put crosses on the roadside where a fatality has occurred

[ ] (v) Design safety features into the car to ensure that the occupant is

protected

1.17. Laboratory research in impact biomechanics

[ ] (i) Was initiated Hugh DeHaven in the 1920s

[ ] (ii) Was initiated by Lissner and Gurdjian in the late 1930s

[ ] (iii) Was supported by NHTSA in the early 1950s

32 1 Introduction

[ ] (iv) Was initiated at General Motors in the early 1960s


1.18. Knowledge of how an injury occurs is important because

[ ] (i) We need it to treat the injury

[ ] (ii) We need it to determine the cost of the injury

[ ] (iii) We need it to determine methods of preventing the injury

[ ] (iv) We need it to establish levels of human tolerance


1.19. The manner in which a body region responds to an impact

[ ] (i) Is known as mechanical response to impact

[ ] (ii) Is an important knowledge base for the design of human-like

dummies

[ ] (iii) Is an important knowledge base for the development of computer

models of impact

[ ] (iv) Is highly variable from subject to subject due to biological variation


1.20. Human tolerance to impact has many levels.

[ ] (i) The most useful level in automotive design is the LD50 level

[ ] (ii) The usual level used for automotive design is the “ouch” level

[ ] (iii) The least useful level is one at which occupants sustain severe but

non-life-threatening injuries

[ ] (iv) The usual level used for automotive design is one at which the

occupants sustain moderate injuries


Answers to Problems by Chapter

Prob

Ans

1 (v)

2 (iii)

3 (v)

4 (v)

5 (ii)

6 (iv)

7 (v)

8 (v)

9 (ii)

10 (iv)

11 (v)

12 (v)

(continued)

References 33

Prob

Ans

13 (iii)

14 (v)

15 (ii)

16 (v)

17 (ii)

18 (iii)

19 (v)

20 (v)

References

J.M. Cavanaugh, T.J. Walilko, M. Malhotra, Y. Zhu, A.I. King, Biomechanical response and

injury of the thorax in twelve sled side impacts, in 34th Stapp Car Crash Conference, SAE

Paper No. 902307, Orlando, FL, 1990

H. Cheng, A. Rizer, A. Obergefell, Articulated total body model version V—user manual. USAF

Report No. AFRL-HE-WP-TR-199-0015, 1998

H. De Haven, Mechanical analysis of survival in falls from heights of fifty to one hundred and fifty

feet. War Med. 2, 586–596 (1942) (Also reprinted in 2000 in Injury Prevention, 2006:62–68)

E. Gurdjian, H. Lissner, J. Webster, F. Latimer, B. Haddad, Studies on experimental concussion:

relation of physiologic effect to time duration of intracranial pressure increase at impact.

Neurology 4, 674–681 (1954)

N.S. Hakim, An experimental study and finite element analysis of the mechanical response of a

vertebra. Ph.D. Dissertation, Wayne State University, Detroit, Michigan, 1976

A.I. King, D.C. Viano, W. Hardy, L. Zhang, K.H. Yang, Is head injury caused by linear or angular

acceleration? in 2003 International IRCOBI Conference on the Biomechanics of Impacts,

Lisbon, Portugal, 2003

C. Kroell, D. Schneider, A. Nahum, Impact tolerance and response of the human thorax II, in 18th

Stapp Car Crash Conference, SAE Paper No. 741187, Ann Arbor, MI, 1974

J.H. McElhaney, J.F. Hilyard, V.L. Roberts, Handbook of Human Tolerance, Japan Automobile

Research Institute, Inc., Ibaraki, 1976

R.R. McHenry, Analysis of the dynamics of automobile passenger restraint systems, in 7th Stapp

Car Crash Conference, Los Angeles, CA, 1963, pp. 207–249

R. Morgan, J. Marcus, R. Eppinger, Side impact: the biofidelity of NHTSA’s proposed ATD and

efficacy of TTI, in 30th Stapp Car Crash Conference, SAE Paper No. 861877, San Diego, CA,

1986

R.F. Neathery, Analysis of chest impact response data and scaled performance recommendations,

in 18th Stapp Car Crash Conference. SAE Paper No. 741188, Ann Arbor, MI, 1974

F.H. Netter, Atlas of Human Anatomy, 4th edn. (Saunders, Philadelphia, 2006)

J.S. Ruan, A.I. King, T.B. Khalil, Finite element modeling of direct head impact, in 37th Stapp Car

Crash Conference, San Antonio, TX, 1993

B.R. Smith, A mechanism of injury in the forefoot in car crashes. Ph.D. Dissertation, Wayne State

University, Detroit, Michigan, 2003

D.C. Viano, A.I. King, J.W. Melvin, K. Weber, Injury biomechanics research: an essential element

in the prevention of trauma. J. Biomech. 22(5), 403–417 (1989)

L. Zhang, K.H. Yang, R. Dwarampudi, K. Omori, T. Li, K. Chang, W.N. Hardy, T.B. Khalil,

A.I. King, Recent advances in brain injury research: a new human head model development

and validation. Stapp Car Crash J. 45, 369–394 (2001)

Chapter 2

Basics of the Biomechanics of Brain Injury

2.1 Introduction

Brain injury is a major public health problem and is commonly seen in falls and

automotive crashes as well as in other environments, such as contact sports, military

action, and assaults. Although the brain is protected by the skull, it can be injured in

relatively low-speed impacts, such as in American football. Statistics on traumatic

brain injury (TBI) provided by the National Center for Injury Prevention and

Control reveal that, in 2010, there were over 50,000 deaths due to TBI and that

TBI was diagnosed in more than 280,000 hospitalizations and in 2.2 million

emergency room visits. Falls are the leading cause of TBI, especially among the

youngest and oldest age groups, while motor vehicle crashes were the third leading

cause of TBI (14 %). The various causes are shown in Fig. 2.1.

Because of the fact that effective treatment of TBI, even mild TBI (mTBI), is

generally not available, prevention of TBI should be a top priority, and biomechanics

can play a leading role in this effort. Biomechanical research on TBI has been

carried out in the USA for over 75 years (see Chap. 1), and there is some

information about the response of the brain to impact and its tolerance. However,

there is still a divided opinion on the causes of TBI because it is not clear whether

linear acceleration or angular acceleration/velocity is the principal cause of TBI.

It is more than likely that both forms of acceleration play a role in causing TBI since

in a head impact both forms of acceleration are present and linear acceleration

increases monotonically with angular acceleration.



35

36 2 Basics of the Biomechanics of Brain Injury

Leading Causes of TBI

Assaults,

10.7%

Motor vehicle

traffic, 14.3%

Falls, 40.5%

Struck by/

against,

15.5%

Unknown/

Other, 19.0%

Fig. 2.1 Various causes of traumatic brain injury in 2010 (source: National Center for Injury

Prevention and Control, http://www.cdc.gov/traumaticbraininjury/get_the_facts.html)

2.2 Anatomy of the Head and Brain

No biomechanical discussion is complete without some understanding of the

anatomical structures involved. The focus in this chapter is on the head and brain.

Even though the brain is part of the central nervous system which encompasses the

spinal cord as well, the anatomy of the spinal cord is deferred to a later chapter. For

the head, it is particularly important that reader has some basic information of its

complex anatomy, especially that of the brain. The head consists of the scalp, skull,

face, meninges, and brain.

The scalp is the outer covering of the head and is composed of the hair, skin,

fascia, muscles, and periosteum. Its thickness is from 5 to 7 mm and it moves as a

single layer. An embalmed scalp is thicker because some of the embalming fluid is

retained in it.

The skull is the strong box or vault protecting the brain. It consists of eight bones

that are fused into a single shell in the mature adult. Its thickness varies from 4 to

7 mm, and it is composed of three layers—cortical bone in the inner and outer

layers sandwiching a layer of spongy or trabecular bone in the center. This spongy

2.2 Anatomy of the Head and Brain 37

Fig. 2.2 Bones of the skull and face (taken from Gray (1995)). Reprinted from Gray’s Anatomy:

The Anatomical Basis of Medicine and Surgery, 38th edn. by Gray, (Churchill Livingstone), 1995,

with permission from Elsevier

bone layer is also known as the diploe. The facial bones make up the rest of the skull

and are fused to the skull. There are 14 facial bones, 13 of which are fused or

attached to the skull to form the face which is defined as an area of the head between

the forehead and the mandible or lower jaw. The mandible is free to move and

articulates about the temporal mandibular joint (TMJ) to enable chewing. At the

base of the skull, there is a thick cylindrical bone around the foramen magnum, the

opening for the spinal cord to pass through. Figure 2.2 is a drawing of the skull,

showing all the bones of the skull and some of the bones of the face. The borders

separating the skull bones are called sutures which do not close until about the age

of 30. Younger skulls have some cartilage on either side of the sutures.

Under the skull are three meninges or membranes that cover the brain. The

outermost layer is a double-layered membrane called the dura mater or simply

the dura. It is the thickest and toughest of the three meninges. The outer layer of

the dura is adherent to the inside surface of the skull in the adult, while the inner

layer is mostly fused to the outer layer except down the midline of the skull where

the two layers are separated to form the superior sagittal sinus—a cavity that

collects venous blood from the brain for drainage back into the heart. The meninges

are shown in Fig. 2.3 which also shows the bridging veins that transport the blood

from the brain into the superior sagittal sinus. According to Haines et al. (1994),

below the dura are two thin layers of cells called border cells. The outer layer is

called the dural border cell and the inner layer is called the arachnoid border cell.


Frontal plane

Bridging Vein

Superior

sagittal plane

Skin

Periosteal

layer

Meningeal

layer

Subarachnoid

space

Arachnoid

villus

Falx cerebri

Parietal bone

CRANIAL MENINGES:

Dura mater

Arachnoid mater

Pia mater

Cerebral cortex

Fig. 2.3 The cerebral meninges, the superior sagittal sinus and bridging veins that bridge the CSF

layer and transport the blood from the brain into the superior sagittal (taken from Totora and

Nielsen (2013)). Republished with permission of John Wiley and Sons Inc., from G.J. Tortora,

M.T. Nielsen, Principles of Human Anatomy, 13th edn. Chapter 18, 2013, permission conveyed

through Copyright Clearance Center, Inc.

Under the border cells is the second membrane, the arachnoid, which is a very thin

layer but which contains a basement membrane that is impervious to water. Below

the arachnoid is a layer of cerebral spinal fluid (CSF) in the subarachnoid space

(SAS) which varies in thickness depending on age. There are trabeculae (collagenous

soft tissue) which tether the arachnoid to the pia, the third membranous cover

of the brain. The pia is extremely thin and is almost transparent. So the surface of

the brain is visible through the pia which appears to wrap tightly around the brain,

investing itself into the sulci of the brain. There is also a basement membrane

associated with the pia. The only region that allows the brain to move relative to the

skull is the CSF layer because the border cells between the arachnoid and dura

prevent sliding in those layers. A more detailed diagram depicting the three

meninges is provided by Fig. 2.4.

Another aspect of brain mobility in the CSF region is the role of the trabeculae

within it. Older mathematical models of the brain simulated the CSF as a layer of

fluid with no shear resistance, ignoring the presence of the trabeculae. Jin et al. (2006,

2007) studied the mechanical properties of the pia-arachnoid complex (PAC) and

found that the trabeculae were capable of resisting tension applied in the normal

direction to the membranes and of resisting shear in the plane of the membranes. That

is, the amount of sliding in the CSF is governed by the trabeculae and not by the CSF,

and brain models should simulate the CSF layer as a low shear modulus solid.

2.2.1 Anatomy of the Brain

As mentioned above, the brain is (a major) part of the central nervous system

(CNS). It consists of a network of neurons and supporting tissue that form the


Skull

Arachnoid Dural

Border Border

Cells Cells

Meningeal Periosteal Dura

Dura

Dura Mater

SAS

SAS

Arachnoid Trabeculae

Arachnoid

Collagen

Elastic Fibers

Amorphous Material

Basement Membrane

Gap Junctions

Desmosomes

Tight Junctions

Brain

Pia Mater

Fig. 2.4 Details of the three cerebral meninges, based on a study by Haines (1991). Republished

with permission of John Wiley and Sons Inc., from D.E. Haines, On the question of subdural space,

The Anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology, 1991,

permission conveyed through Copyright Clearance Center, Inc.

control center for the body. Functionally, it is divided into gray and white matter.

The cells of the CNS are neurons which make up the gray matter, and the extension

of the neurons or axons makes up the white matter. The gray matter is found mostly

on the outside of the brain. The main components of the brain are the forebrain or

cerebrum, the midbrain, and the hindbrain. The cerebrum occupies a large volume

of the skull and consists of two hemispheres that are separated by a membrane

called the falx cerebri which is actually an extension of the dura. Each half of the

cerebrum can be divided into four lobes as shown in Fig. 2.5. The frontal lobe is


Fig. 2.5 The brain.

The cerebrum and the

hindbrain are visible.

Approximate locations

of the lobes of the cerebrum

are identified (taken

from Carola et al. (1992)).

Republished with

permission of McGraw-Hill

Education, from R. Carola,

J.P. Harley, C.R. Noback

(eds.), Human Anatomy &

Physiology, 2nd edn., 1992;

permission conveyed

through Copyright

Clearance Center, Inc.

Occipital lobe

of cerebrum

Parietal lobe

of cerebrum

Frontal lobe

of cerebrum

Cerebellum

Temporal lobe of cerebrum

right behind the frontal bone (forehead) and below it is the temporal lobe.

The parietal lobe is behind the frontal lobe, and the occipital lobe is behind the

parietal lobe. The brain weighs about 1.36 kg (3 lb) or constitutes about 2 % of body

weight. It is 165 mm long and 140 mm wide. The center of gravity of the head is

located just above the horizontal Frankfort plane and just anterior to the auditory

meatus. In Fig. 2.6, the x-axis is at the level of the Frankfort plane, and the origin is

at the center of the auditory meatus (ear canal).

There is a cavity in each hemisphere called the lateral ventricle. It is filled with

CSF and communicates with the third and fourth ventricles. The midbrain is

composed of the various parts of the thalamus, including the hypothalamus. The

hindbrain is made up of the cerebellum, pons, and medulla oblongata, the most

caudal part of the brain stem. The cerebellum is covered by a membrane called the

falx cerebelli, a part of the dura that separates it from the occipital lobe. It is

required for fine movement, motor corrections, and reflex modifications. The third

ventricle is a small cavity in the midline of the forebrain beneath the lateral

ventricles. It connects with the fourth ventricle which is located behind the pons.

The walls of the ventricles are lined with ependymal cells that produce CSF which

circulates from the lateral ventricles to the third and fourth ventricles to the CSF

space between the cerebral meninges. The CSF also surrounds the spinal cord,

extending down to the lumbar level.

The brain requires a constant and ample supply of oxygen. As a result, there are

numerous blood vessels in the brain. The blood vessels shown in Fig. 2.7 are the

cerebral arteries without the veins. The preparation was made possible by injecting

Center of Gravity

of the Head

Parietal

bone

Horizontal

Frankfort

Plane

Occipital

bone

Frontal

bone

Sphenoid

bone

Lacrimal

bone

Nasal bone

Temporal

bone

Zygomatic

bone

Zygomatic

arch

Maxilla

Mandible

Fig. 2.6 The approximate location of the center of gravity (cg) of the head is in the midsagittal

plane slightly anterior to the auditory meatus and about 3 cm above the Frankfort plane which is at

the level of the inferior border of the orbit or eye socket. The illustration of the skull was taken

from Carola et al. (Eds.), 1992, Human Anatomy & Physiology. Republished with permission of

McGraw-Hill Education, from R. Carola, J.P. Harley, C.R. Noback (eds.), Human Anatomy &

Physiology, 2nd edn., 1992; permission conveyed through Copyright Clearance Center, Inc.

Fig. 2.7 Arteries of the human brain (taken from McMinn and Hutchings (1977)). Reprinted from

R.M.H. McMinn, R.T. Hutchings, Color Atlas of Human Anatomy (Year Book Medical Publishers),

1977, with permission from Elsevier


a rubberized solution into the cerebral arteries and allowing it to set. After which,

the rest of brain is dissolved in an acid solution. Thus, the vessels shown are slightly

smaller than the actual vessels because the arterial walls have also been dissolved.

The stiffness of the brain is due largely to that of the arteries and veins because

brain material is extremely soft and weak.

2.2.2 Histology of Brain Cells

The CNS is made up of neurons and neuroglia (supporting cells). Neurons or nerve

cells are the functional cells of the CNS with the ability to sense external input as

well as activate muscle cells. They encode information and transmit it rapidly to

other neurons or non-neuronal cells, in some cases, over large distances, using

minute electrochemical signals. There are many types of neurons, as shown in

Fig. 2.8, but they all have in common a soma or cell body containing a nucleus, a

single axon for the transmission of signals, and one or more dendrites that are

neuronal receptors. Figure 2.9 shows a typical neuron and its components.

Fig. 2.8 Various types of

neurons. Legend: cb stands

for cell body and ax stands

for axon


Fig. 2.9 A typical neuron

and its components

A. Cell body and processes B. Neuro-fibrils

Axon

Neurofibrils

Dendrites

Nucleus

Axon hilock

Nucleolus

Nissl

substance

Nucleus

C. Golgi apparatus

Golgi

apparatus

Nucleus

Lipochrome

pigment

Perikaryon

Dendrite

D. Pigments E. Pigments

Melanin

Figure 2.9A refers to Nissl substance or Nissl bodies which are membrane-bound

ribonucleoproteins that are distinctive in shape and abundant in the cell body and

dendrites. Their main function is protein synthesis for the cell. Axons do not contain

Nissl bodies. As shown in Fig. 2.9B, neurofibrils are found in all neurons. They are

delicate threads running in every direction through the cytoplasm of a neuron and

extend into the axon and dendrites. They consist of neurofilament bundles and

neurofibrils. The subunits of neurofibrils are neurofilaments which are 7.5–10 nm

in diameter. There are also neurotubules and microtubules (25 nm in external

diameter) that provide rapid transport of protein molecules synthesized in the

cell body via the dendrites and axon. Figure 2.10 shows the microstructure of

microtubules which are made up of tubulin molecules. Since protein synthesis is

not an axonal function, the axon has no Nissl bodies. The axon is uniformly

cylindrical, and its axoplasm contains many organelles, such as mitochondria,

microtubules, microfilaments (6 nm in diameter), and neurofilaments. The microfilaments

are paired helical chains of actin which can contract, providing a means

for intra-axonal transport of protein molecules. The neurofilaments provide the

axon with mechanical strength and outnumber microtubules by a considerable

amount. Some axons are myelinated, that is, covered by a myelin sheath which is

a lipid protein that wraps around the axon in multiple layers. The sheath is

discontinuous and the area of discontinuity is called the node of Ranvier

(Fig. 2.11). Biomechanically, the node may be a weak spot for the axon where it

may break under tension, resulting in diffuse axonal injury (DAI). This injury will

be discussed in detail later on in the chapter. Dendrites are processes extending


Fig. 2.10 (A–D)

Microstructure of a

microtubule (taken from

Alberts et al. (1994)).

Copyright © 1994 From

Molecular biology of the

cell by B. Alberts, D. Bray,

J. Lewis, M. Raff, K.

Roberts, J.D. Watson,

Reproduced by permission

of Garland Science/Taylor

& Francis Group LLC

Fig. 2.11 The node of Ranvier of a myelinated axon


Cells of pia mater

Oligodendrocyte

Microglial cell

Neuron

Blood capillary

Protoplasmic astrocyte

Node of Ranvier

Myelin sheath

Axon

Oligodendrocyte

Fibrous astrocytes

Protoplasmic astrocyte

Microglial cell

Ependymal cell

Neurons

Microvillus

Cilia

Ventricle

Fig. 2.12 The four main types of neuroglia which are supporting cells for the CNS (taken from

Tortora and Nielsen (2013)). Republished with permission of John Wiley and Sons Inc., from G.J.

Tortora, M.T. Nielsen, Principles of Human Anatomy, 13th edn. Chapter 16, 2013, permission

conveyed through Copyright Clearance Center, Inc.

from the cell bodies to increase its receptive surface area. Thus, dendrites, together

with the soma, can receive excitatory or inhibitory signals from other axons to set

off an action potential for the neuron or prevent it from occurring.

Neuroglia are supporting cells of CNS neurons and are found between these

neurons. The four main types of neuroglia are astrocytes, oligodendroglia,

ependymal cells, and microglia. Figure 2.12 is an illustration of these cells and

how they support the neurons. Astrocytes are branched stellate cells and are the

largest of the neuroglia. They surround the capillaries of the brain and form part of

the blood-brain barrier. The cytoplasm of astrocytes contains glial filaments composed

of glial fibrillary acidic protein (GFAP), the concentration of which increases

if there is a proliferation of astrocytes due to brain injury. Figure 2.13 is a schematic

of the blood-brain barrier and of the role of astrocytes. Oligodendrocytes produce

myelin for the axon, while the ependymal cells produce and monitor the CSF in the

CNS. Microglial cells are small, have little cytoplasm, and have a few processes. In

the presence of lesions or infection, they enlarge, become mobile, and take on the

role of scavenger cells (phagocytes).


Astrocytes

Foot Process

Capillary

lumen

Endothelial

cells

Glycocalyx

Tight

junction

Nucleus

Fig. 2.13 The role of astrocytes in the blood-brain barrier. Orthogonal arrays of particles in the

foot process of the astrocytes along with the tight junctions in the endothelial cell layer may play a

role in the prevention of diffusion of molecules from the capillaries into the brain

2.3 Types of Head Injury

According to Ommaya (1985), there are four main types of head injury:

1. Injuries to the scalp

2. Injuries to the skull

3. Extracerebral bleeding (focal or diffuse)

4. Brain tissue damage (neural and/or vascular)

Scalp lacerations are considered minor injuries, but there can be a lot of bleeding

because the dense subcutaneous tissue of the scalp prevents constriction and

retraction of the arteries. There are many types of skull fractures varying from

linear fractures to penetrating fractures. Gurdjian et al. (1950) described the extensive

research done in the 1940s investigating the mechanism of skull fracture. Since

bone is weak in tension, the fractures are explained by the development of tensile

stresses in the skull as it is being hit. The impacted site bends inward and the outer

table is in compression, while the adjacent areas of the skull bend outward. Thus,

the outer table fractures at some distance from the site of impact in the outbended

2.3 Types of Head Injury 47

skull. During rebound, the impact site bends outward and the outer table is in

tension. The result is that a linear fracture would start at a site remote from the

impact site but would travel toward the impact site at the end of the impact. Higherenergy

impacts cause stellate patterns of fracture as well as depressed fractures and

crushing of the skull. Extracerebral bleeding is due to arterial rupture under the

skull but above the dura. When an artery, such as the middle meningeal artery, is

ruptured under the skull, the epidural hematoma that forms separates the dura from

the skull and rapidly increases intracranial pressure. If not treated promptly, death

will result. Inbending of the skull at the location where the artery is running under it

and above the dura is the suspected cause.

2.3.1 Brain Tissue Damage

Brain tissue damage can be broadly divided into four major categories:

1. Concussion or mild traumatic brain injury (mTBI)

2. Contusion or bruising of the brain

3. Intracerebral hemorrhage or intracranial bleeding

4. Brain laceration or tearing of the brain

2.3.1.1 Concussion

Concussion is sometime defined as a mild form of brain injury (mTBI) characterized

by a temporary loss of brain function. There does not have to be a loss of

consciousness although concussion severity is graded by the length of unconsciousness.

However, in more severe forms of brain injury, concussion is also one of the

leading symptoms. Other measures of concussive severity are post-traumatic amnesia

and confusion. There are many signs and symptoms of concussion which occur

right after the injury. Physical signs include headache, dizziness, vomiting, and

nausea as well as visual disturbances, tinnitus (ringing in the ears), sleep disturbance,

and occasionally seizures. Cognitive symptoms include disorientation,

inability to focus, and slowed reaction time. Psychological symptoms include

irritability, moodiness, memory problems, and lethargy. In mTBI, physical concussive

symptoms generally resolve in a matter of weeks, while other symptoms may

persist.

In most civilian situations, concussion is brought about by rotational motion of

the head, such as a punch in boxing, where the linear acceleration is relatively low,

while the angular acceleration is relatively high. In the military, blast waves from

explosions can cause concussion, and it is suspected that the mTBI is due to the

pressure wave passing through the brain. This mechanism has yet to be confirmed.

In both cases, there is diffuse axonal injury due to the disruption of axons, even in

mTBI. Tensile axonal loads break the axon and the microtubules inside it. The flow


Fig. 2.14 Diffuse axonal injury in the human corpus callosum. Dark lines are swollen axons, and

black circles are retraction balls, made visible by means of β-APP staining (taken from Gentleman

et al. (1993)). Reprinted from S.M. Gentleman, M.J. Nash, C.J. Sweeting, D.I. Graham, G.W.

Roberts, β-Amyloid precursor protein (βAPP) as a marker for axonal injury after head injury.

Neuroscience Letters, 160, 139–144, 1993, with permission from Elsevier

of axonal transport of protein products is stopped. By the use of antibody staining

techniques, the location of the tear can be identified by the bulb of axonal transport

material at the end of the broken axon. This is known as a retraction bulb or ball and

is the hallmark of DAI (Strich 1956). It should be noted that DAI is seen over a large

area of white matter and is also seen in more severe forms of brain injury. Figure 2.14

is a micrograph of DAI found in the corpus callosum of a human brain. Note that DAI

does not appear in the axon immediately after the injury as it takes time for the

retraction balls to form and for the axons to swell. Although it is assumed that this

may take a day or so, there is evidence provided by Hortobagyi et al. (2007)thatDAI

can be seen in brains of trauma victims who survive for 35 min after the injury. This

has been confirmed by Morrison and MacKenzie (2008). It is also obvious that, in the

human, a diagnosis of DAI can only be made after death.

2.3.1.2 Contusion

Bruising of the brain is called a cerebral contusion which is a focal injury. It occurs

under the site of impact (the coup site) as well as on the side opposite to the impact

(the contrecoup site). The capillaries in the cerebral cortex (gray matter) are broken

either by the pressures generated by the impact or by relative motion of the brain

with respect to the uneven surfaces of the interior of the skull, particularly on the

surfaces of the frontal and temporal lobes. The pia is not torn in contusive injuries.

The pressure mechanism is used to explain the coup-contrecoup phenomenon.

Positive pressure at the site of impact and negative pressure on the side opposite to

2.4 Theories of Brain Injury Mechanisms 49

the impact are the mechanisms causing the observed contusive injury. The symptoms

are similar to a concussive injury and their severity is dependent on the extent

of the contusion.

2.3.1.3 Intracerebral Hemorrhage

Intracerebral hemorrhage or intracranial bleeding is due to the rupture of blood

vessels inside the brain. In the absence of impact injury, the most common cause is

a hemorrhagic stroke. In an impact situation, weak blood vessels rupture due to the

impact, resulting in intracerebral hemorrhage. Arterial ruptures can rapidly increase

intracranial pressure and cause death if there is no surgical intervention.

2.3.1.4 Brain Laceration

Brain lacerations occur in severe head impacts which cause the brain to be mechanically

torn apart. Usually, the pia and arachnoid are torn at the injury site and

lacerations can be thought of as severe form of brain contusion. Skull fractures are

commonly associated with this injury, and blood vessels are usually ruptured,

resulting in intracerebral hemorrhage and the risk of increased intracranial pressure.

The collection of blood in the brain or on the surface of the brain is known as a mass

effect or a hematoma. It is detected on computer tomography scans which frequently

show a midline shift of the brain as the hematoma pushes the brain to the opposite side.

2.4 Theories of Brain Injury Mechanisms

Based on the years of research on brain injury, dating back to 1766, the following

mechanisms have been proposed (Pudenz and Shelden 1946):

1. Positive pressure mechanism

2. Negative pressure mechanism

3. Pressure gradient mechanism

4. Rotational mechanism

TheworkofPudenzandShelden(1946) was aimed at demonstrating brain motion

during head impact, but the authors went into a long discussion of the above

mechanisms before describing the brain motion they documented with high-speed

film for impacts to monkey heads that had their skull caps removed and replaced by a

Lucite calvarium (Shelden et al. 1944). The biomechanical explanations provided in

this early paper on brain injury may not be totally accurate because the membranes of

the brain were no longer intact, but it is of historic interest.

Brain injury due to pressure mechanisms is attributed to translational motion of

the brain, i.e., linear acceleration. When there is an impact to the head, the

in-bending of the skull and the acceleration of the head due to the impact both


Table 2.1 Average impulse (in psi-s) for different degrees of concussion in dogs for all 72 tests

(Gurdjian et al. 1954)

No concussion Threshold concussion Mild concussion Severe concussion

0.038 0.153 0.085 1.060

contribute to the development of compression or a positive pressure at the impact

site. This pressure travels as a wave across the brain and is reflected off the skull on

the contrecoup site, creating a negative pressure there. The pressure mechanism of

concussion was demonstrated by Gurdjian et al. (1954) who developed a method of

applying pressure to the brain of an anesthetized animal (dog) without having to

strike it on the head with an impactor. These authors were roundly criticized by the

press for cruelty when Gurdjian was shown in the papers with a dog’s head in one

hand and a hammer in the other. They invented the fluid percussion method which

applied a pressure pulse of air to a small area of the dura using a specially designed

valve or dropping a weight onto a column of water in contact with the dura.

He achieved a range of impact durations of less than 1 ms to as high as 120 ms.

The peak pressures ranged from 4 to 74 psi (27.5 to 509.5 kPa). The severity of the

injury was divided into four groups: no concussion, threshold concussion, mild

concussion, and severe concussion. They found that concussion occurred for

impacts with high pressures and short duration or with low pressures and long

durations. We can take the data and go a step further by defining impulse as the

product of peak pressure and pulse duration and calculating it for all 72 tests

performed by Gurdjian et al. (1954). The averaged results are shown in Table 2.1

for the four conditions. The threshold impulse turned out to be the highest, and if

that is put aside, there is an increase in impulse with injury severity – 0.038 psi-s for

no concussion, 0.085 psi-s for moderate concussion, and 1.060 psi-s for severe

concussion. The passage of pressure waves across the brain has been measured, and

the coup-contrecoup phenomenon causing concussion is accepted by the medical

community. The implication of this hypothesis is that pressure damages the neurons

in some way and causes dysfunction described above in Sect. 2.3.1.1, in the absence

of head rotational motion. Exposure of the head to blast overpressure due to

explosions, such as the detonation of improvised explosive devices (IED), is a

major cause of mTBI sustained by returning US veterans from the Middle East. The

mechanism of injury due to a pressure wave at the cellular level needs to be found

before effective preventative measures can be implemented to protect our soldiers.

When there is a pressure wave moving through the brain, a pressure gradient

exists. In Fig. 2.15, the pressure on the low-pressure side of a small element of the

brain (left side) is p, while that on the high-pressure side is p + Δp. This unbalance

in normal force on the element results in the generation of a shear stress Δτ above

whatever shear stress, τ, that might exist on the faces of the element. This shear

tends to distort the element and cause injury to the brain.

Of course, if the brain undergoes rotational motion, then large shear stresses

develop as a result of the rotation. This is the basis for the rotational mechanism of

brain injury, originally proposed by Holbourn (1943) who developed a simple

2.4 Theories of Brain Injury Mechanisms 51

Fig. 2.15 Pressure gradient

produces shear stress

physical model of the brain, using gel, to explain the rotational mechanism of

injury. Holbourn’s argument that rotation causes the brain to deform in shear and

thus become injured is sound, but the argument that pressure cannot cause injury,

based on the fact that the nerves continue to conduct signals under immense

hydrostatic pressures, is flawed. In an impact, the pressure wave applies the load

at very high rates and acts as a shock to the brain. This shock effect is quite different

from hydrostatic pressure. However, severe rotational motion in the absence of a

direct impact can result in concussion, as shown by Gennarelli and Thibault (1982).

Angular accelerations of the order of 100,000 rad/s 2 were applied to the heads of

rhesus monkeys, causing the development of DAI as well as acute subdural

hematoma in their brains.

Ommaya and Hirsch (1971) proposed a scaling law for head acceleration

between the human and different species of experimental animals. This law is

given by Eq. (2.1) below:

α h =α r ¼ ðm r =m h Þ 2=3 ð2:1Þ

where α h is the human head angular acceleration, α r is the rhesus head angular

acceleration, m h is the human brain mass, and m r is the rhesus brain mass.

Then, for m h ¼ 1360 g (g), α r ¼ 100,000 rad/s 2 , and m r ¼ 70–100 g, the equivalent

human head angular acceleration would be between 13,800 and 17,500 rad/s 2 .

This level of angular acceleration is difficult to achieve in a human for a purely

rotational (non-contact) head impact without some serious injury to the neck or the

head-neck junction. This is not to say that the study was not worthwhile. Instead, it

points to the fact that both linear and angular acceleration are responsible for

concussion. Note that when the head impacts a surface of any kind, such as a

windshield, there is not only linear deceleration but also a very high concomitant

angular acceleration that does not involve whipping of the head or the involvement

of the neck. Figure 2.16 shows the relationship of linear and angular acceleration of

a helmeted dummy head subjected to a frontal impact against a foam-covered rigid

surface (King et al. 2003).


Angular Acceleration (rad/s 2 )

12000

10000

8000

6000

4000

2000

0

MTBI

Non-Injury

0 200 400 600 800 1000 1200 1400

Linear Acceleration (m/s 2 )

Fig. 2.16 In head impacts, linear and angular acceleration usually increase monotonically

Fig. 2.17 Intracranial

pressure data from a frontal

impact to a cadaver head

(Nahum et al. 1977)

2000mmHg

1000

FRONTAL PRESSURE

5 10 15

TIME (ms)

2.5 Mechanical Response of the Head and Brain

Early researchers in head injury measured linear head acceleration to define the

impact response of the head. Accelerometers were relatively light and small and

could be attached conveniently to the skull, either directly to the skull or using a

mount that is held to the skull with bone screws. Pressure sensors were available to

measure intracranial pressure in living animals but were not useful in cadaveric

brains which were embalmed. In unembalmed or fresh cadavers, brain tissue

degrades quickly after death, and the measured pressures would be meaningful

only if the cadavers were tested soon after death. The general rule of thumb is that

the cadaver should be kept in a 4 C cooler while under preparation and tested no

more than two weeks after death and that the total time outside the cooler should be

less than 24 h. Intracranial pressure data were provided by Nahum et al. (1977), as

shown in Fig. 2.17. Attempts were made in the twentieth century to visualize brain

and skull response during impact (Shatsky et al. 1974; Nusholtz et al. 1984), but

2.5 Mechanical Response of the Head and Brain 53

they were largely unsuccessful or provided little useful information on brain

motion. Thus, the response of the head was defined by its acceleration response

to impact. The response is dependent on the stiffness and the geometry of the

surface the head impacts, and a large volume of published information is available.

One of the aims of determining mechanical response is to build a surrogate or

dummy that can be used in the design of automobiles, helmets, and other protective

devices. In this case, data derived from impacts against padded surfaces are not

useful because the stiffness and other characteristics of the padding are difficult to

specify or may change with repeated impacts and the same padding is not necessarily

available to all researchers. For this reason, skull response to impacts against

a rigid surface provides the “standard” data that can be used by all researchers.

Figure 2.18 shows cadaveric head impact data of the forehead against a rigid

surface and the response of the Hybrid III head to a frontal impact (Mertz 1985).

600

500

F

CADAVER DATA

HYBRID III DATA

SKULL FRACTURE

PEAK HEAD ACC. – g

400

300

200

F

F

F

HYBRID III SPECIFICATION

F

F

100

0

200 400 600 800 1000

V 2

2g

− mm

Fig. 2.18 Cadaver head impact data used to design the Hybrid III head. The data were from

cadaveric forehead impacts to a rigid surface. The letter F adjacent to a data point indicates that

there was skull fracture. The abscissa, V 2 /2g, is an equivalent free fall drop height (taken from

Mertz (1985)). Reprinted with permission Copyright © 2017 SAE International. Further distribution

of this material is not permitted without prior permission from SAE


Fig. 2.19 Side view of a

50th percentile Hybrid III

head

The cadaver data were obtained by Hodgson and Thomas (1971, 1975) who

attached cadavers to a pallet that was hinged at the level of the floor and with the

head overhanging the pallet. In this way, when the pallet was dropped from a known

height, the forehead impacted a rigid surface in the form of a steel plate. However,

the velocity of impact was mistakenly assumed to be equal to the square root of the

product of 2gh where g is gravitational acceleration and h is the height of the drop.

It was later discovered that the actual velocity of impact was greater than the

free-fall velocity. Thus, the abscissa in Fig. 2.18 is the corrected free-fall height

in terms of its free-fall velocity. The Hybrid III dummy is currently used as the

human surrogate in the automotive industry. It consists of an aluminum head form

covered by a vinyl “scalp” that was tuned to simulate the response of head impact

against a rigid surface (see Hybrid III specification in Fig. 2.18). A photograph of

the Hybrid III head is shown in Fig. 2.19. It is representative of a 50th percentile

male in both size and weight. It should be noted that, strictly speaking, the Hybrid

III head simulates human response for impacts of its forehead against a rigid

surface. However, Mertz (1985) showed correlation of Hybrid III padded impacts

to cadaver data.

2.5.1 Visualization of Brain Response

As mentioned in Sect. 2.4 above, attempts at direct visualization of brain motion by

optical means during a head impact were made by Pudenz and Shelden (1946) and

subsequently by several others. The use of a Lucite calvarium enabled the visualization

of the motion of the surface of the brain. However, because a portion of the

skull, including the dura, was removed, it is not clear if the observed motions could

have been exaggerated because the normal constraints provided by the meninges no

longer existed and there was air/gas between the brain and the Lucite. It was a

valiant attempt, but the results may not be realistic and no quantitative data were

provided. The use of roentgenography to visualize brain motion was mentioned


Fig. 2.20 Photograph of the biplanar X-ray setup (courtesy of Dr. Warren Hardy)

above in Sect. 2.5. Shatsky et al. (1974) used flash X-ray cinematography to capture

head and brain motion during impact. A pulsed X-ray source with a duration of

30 ns was used to obtain X-ray images of a rhesus monkey head as it impacted a

rigid wall. The images were enhanced by an image intensifier. There was also a

study by Nusholtz et al. (1984) using a “high-speed” X-ray system, but the

resolution was poor and the X-ray was only able to detect motion of blood vessels

filled with a radiopaque dye.

Accurate visualization of brain motion in an intact skull was first reported by

Hardy et al. (2001). A biplanar high-speed X-ray unit was used to obtain threedimensional

motion characteristics of cadaveric brain relative to the skull.

A photograph of the system is shown in Fig. 2.20. The gantries in the foreground

are supporting the image intensifiers. The X-ray sources are in the background and

are hidden by the curtains surrounding the test specimen. On the right, the red tank

contains compressed air that is used to accelerate the head before it hits a rigid

surface. The experimental setup is shown diagrammatically in Fig. 2.21. The X-ray

sources run continuously, and the X-ray images are captured and intensified by

image intensifiers before they are recorded on video cameras. Initially, the recording

speed was 250 frames/s, but eventually it was increased to 1000 frames/s.

Movement of specimens placed in the crosshatched area can be measured in 3-D

with an accuracy of 0.1 mm, using stereophotogrammetric methods. There are

many details in the reduction of the data, such as computation of the motion in 3-D

and correction for parallax, and the reader is referred to Hardy et al. (2001) for these

procedures.


Fig. 2.21 Schematic of a biplanar high-speed X-ray system. The 3-D imaging area is in light blue

(45 30 25 cm). The 3-D accuracy is 0.1 mm. This system is located on the main campus of

Henry Ford Hospital, Detroit, MI

Freshly dead unembalmed cadaveric heads were used. To be able to visualize

brain motion using the X-ray unit, tiny radiopaque targets in the form of tin spheres,

1.9 mm in diameter, were encased in plastic tubing to reduce its density to

approximate that of the brain. Tin was used in place of dense metals such as gold

or lead to reduce the mass of the target without a loss of contrast in the X-ray image.

The targets were called neutral density targets (NDTs), and they did not cut through

the brain material but would instead move with the brain during an impact.

The NDTs are shown in Fig. 2.22. A large spinal needle was used as a guide for

the placement of the targets. It was inserted into the brain through a small hole in the

skull to a known depth, and targets were dropped into the needle and pushed into

the brain at specified intervals to form a column of six or seven targets. In a typical

test series for a sagittal plane impact, two columns of targets were inserted, one

anteriorly, called the anterior column (AC), and the other posteriorly, called the

posterior column (PC), as shown in Fig. 2.23. The head was decapitated at the level

of T4 and was suspended upside down so that any air that might have entered the

cranial cavity could be flushed out with artificial CSF that was used to pressurize

the brain to simulate a living brain. Other instrumentation consisted of a

9-accelerometer package attached to the skull and arranged in 3-2-2-2 configuration

to measure the linear and angular acceleration of the head. A discussion of the

method can be found in Chap. 5. The head assembly was suspended on a carriage

that could slide smoothly on two horizontal rails, as shown in Fig. 2.24 enabling it

to be accelerated by a piston driven by the compressed air. The moving head

and carriage were arrested when the front of the head impacted a block of Lucite.

The head stopped in the zone where the X-ray beams crossed and where it was

possible to compute the 3-D location of the targets, using stereophotogrammetric

methods. That zone is the light blue area shown in Fig. 2.22. Alternately, the


Fig. 2.22 Neutral density targets made from tin spheres encased in a plastic tube to reduce its

density to approximately that of the brain. The tin spheres are in the center of the photograph. On

the right are the plastic tubes and on the left are end caps to keep the sphere in the tube (taken from

Hardy et al. (2001))

Fig. 2.23 Location of

neutral density targets in a

cadaveric brain for a sagittal

plane impact. AC stands for

anterior column and PC

stands for posterior column

(taken from Hardy et al.

(2001))

AC

1 X

2

3

4

5

6

CG

Z

PC

1

2

3

4

5

6

air-driven impactor hit the back of the head directly while it was in the stereoscopic

zone. The approximate location of the center of gravity (cg) of the head, as

described above, was identified, and the motion of the targets relative to this

hypothetical point was computed. These targets moved in a figure eight pattern,

as shown in Fig. 2.25. Reduction of the data from the video cameras attached to the

biplanar X-ray unit to the form shown in Fig. 2.25 is, to say the least, not a simple


Fig. 2.24 Cadaveric head specimen suspended from a carriage used to accelerate the head into a

Lucite block (taken from Hardy et al. (2001))

Fig. 2.25 The brain traces out a figure eight pattern during impact relative to the center of gravity

of the head. The motion appears to decrease near the skull. The data were derived from a frontal

impact against a Lucite block with a resultant deceleration of 62 g and a peak angular acceleration

of 2529 rad/s 2 . AC stands for anterior column and PC stands for posterior column (taken from



Table 2.2 Summary of head

kinematics measured based

on Hardy (2007) tests

Head kinematics

Range

Linear speed (m/s) 3.5 0.3

Linear acceleration (g) 29–190

Resultant acceleration (g) 38–291

HIC 15 87–959

Angular acceleration (rad/s 2 ) 2,370–24,206

Angular speed (rad/s) 20.3 5.7

process. An automated image enhancement and target tracking algorithm were set

up to process the digital video data from two cameras that recorded target motion

obliquely. Distortion of the images needed to be corrected and the field of view was

calibrated using a multi-point calibration cube after each test. Calculations were

performed to transform the target motion data into a set of anatomical coordinates

with the origin located at the presumed cg of the head. Additionally, the target data

were synchronized in time with the measured acceleration data. Details of the

procedure to produce the data as presented were described by Hardy (2007).

Repeated tests were performed on each specimen because of the long preparation

time needed to set up the experiment. Thus, the impact levels were generally kept

low to avoid skull fracture. Table 2.2 is a summary of the head response parameters

for the 30 tests performed on seven cadaveric specimens.

Note that in Fig. 2.25, the crown of the head is toward the bottom of the figure

and that the excursions of the targets closer to the skull appear to decrease in the

direction of the skull. The maximum excursion occurs near the center of the brain

which is limited to 5 mm for a wide range of angular accelerations. Hardy (2007)

also found that during linear acceleration, there is very little brain motion, of the

order of 1 mm or less.

The combination of a biplanar X-ray system and the use of neutral density

radiopaque targets produced unique three-dimensional motion data of the brain

relative to the skull. The motion was largely due to head rotation and tended to

follow a looping pattern with excursions limited to about 5 mm. A lot more data

can be found in Hardy (2007).

2.5.2 Mechanical Properties of the Pia-Arachnoid Complex

Since the cerebral meninges are sandwiched between the skull and the brain, they

are expected to play a significant role in any head impact. In particular, the

pia-arachnoid complex (PAC) constitutes the mobile part of the meninges and

participates in brain-skull interaction during a head impact. The PAC is compressed

at the coup site and stretched or sheared at the contrecoup site. In compression, the

CSF in the PAC is expected to transmit the compressive load to the brain, but, in

tension or shear, the trabeculae take over the role of transmitting the load from the

dura to the brain. For this reason, the properties of the PAC should be quantified


Trabeculae

Dura

Arachnoid

Subarachnoid

space

Blood vessel

Pia

Gray matter

Penetrating

vessel

Fig. 2.26 Diagram of the pia-arachnoid complex, showing a blood vessel in the subarachnoid

space (taken from Alcolado et al. (1988)). Republished with permission of John Wiley and Sons

Inc., from R. Alcolado, R. Weller, E. Parrish, D. Garrod, The cranial arachnoid and pia mater in

man: anatomical and ultrastructural observations. Neuropathology and Applied Neurobiology 14,

1–17, 1988, permission conveyed through Copyright Clearance Center, Inc.

both in terms of its response to normal traction and in shear. Basically, we are

interested in the tensile and shear properties of the trabeculae in the CSF layer.

2.5.2.1 Response of the PAC to Normal Traction

Jin et al. (2007) studied the response of the PAC under normal traction, using fresh

bovine specimens taken from different parts of the brain and at four different strain

rates (0.36–116.3 s 1 ). A diagram of the ultrastructure of the PAC is shown in

Fig. 2.26. The bovine brain was selected for this study because of its relatively large

size and the availability of fresh material from the slaughter house. The brains were

harvested from calves aged 17–20 weeks immediately after they were slaughtered.

Forty specimens, taken from four bovine brains, were tested within 48 h after death.

After the skull was sawed open, the dura was carefully cut open so as not to damage

the underlying structures, and the brain was taken out of the skull. Pieces of PAC

about 20 20 mm in size were dissected from the cortex, with about 2–5 mm of

brain attached, as shown in Fig. 2.27A. The attached brain tissue was carefully

removed from the pia, using a scalpel, and the PAC was placed on a plastic sheet

with the pia facing up (Fig. 2.27B). A cubic polyethylene block, 127 mm in size,

was attached to the pia with cyanoacrylate glue (Elmer’s Krazy Glue), as shown in

Fig. 2.27C. The arachnoid surface was thoroughly washed with an artificial CSF

solution before it was glued to another polyethylene block of the same size and

carefully aligned with the first block. After the glue had set, the excess tissue around

the polyethylene blocks was trimmed off (Fig. 2.27D). This procedure ensured that

there was no glue between the blocks. It was also important to ensure that there was

no air bubble trapped between the blocks and the specimen to ensure that bond

between the specimen and the blocks was stronger than the tensile resistance of the

PAC. Since the blocks were transparent, trapped air bubbles could be spotted easily,


Fig. 2.27 This figure describes the specimen preparation procedure. (A) The cortex of the brain

with the PAC attached. (B) PAC with the underlying brain removed and the pia facing up. (C) A

polyethylene block (marked P for pia) was glued to the pia side of the PAC. (D) A second block

(marked A for arachnoid) was glued to the opposite side of the PAC and the excess tissue was

trimmed away (taken from Jin et al. (2007))

and defectively glued specimens were not tested. The specimen was tested in a

Model 1321 Instron materials testing machine, again using cyanoacrylate glue to

attach one end to the loading head of the machine and the other to its base. Both the

applied tensile force and the loading head displacement were measured. The

specimens were tested at strain rates of 0.36, 2.0, 20.5, and 116.3 s 1 . It was

estimated by King et al. (2003) that the brain can sustain strain rates of 30–80 s 1

in NFL mTBI cases and by Franklyn et al. (2005) in traumatic axonal injury cases in

vehicular crashes. Specimens were taken from the frontal (n ¼ 14), occipital

(n ¼ 15), and parietal (n ¼ 11) regions of the brain in order to determine regional

differences in mechanical properties of PAC, if any. In order to calculate the strain

on the PAC in normal traction, an additional 65 PAC specimens were stained with

hematoxylin, and the thickness of the specimen was measured under a microscope.

Details of the procedure to measure PAC thickness are provided in Jin et al. (2006).

The PAC thickness was 23.6 5.8 μm.

In terms of results, it was found that there was no regional difference in the

response of the PAC for the four regions of the brain. It was also found that the

mechanical response of the PAC was rate sensitive and that its elastic modulus was

significantly higher at 116.3 s 1 than at the other 3 strain rates. Similarly, the

ultimate stress and ultimate strain are rate sensitive. These data are shown in


A

70

B

160

Elastic Modulus (kPa)

60

50

40

30

20

10

0

0.36/s 2.0/s 20.5/s

Strain Rate

Elastic modulus vs. strain-rate

C

3

116.3/s

Ultimate Stress (kPa)

120

80

40

Ultimate Strain

2.5

2

1.5

1

0.5

0

0.36/s 2.0/s 20.5/s 116.3/s

Strain Rate

0

0.36/s

2.0/s 20.5/s 116.3/s

Strain Rate

Ultimate stress vs. strain rate

Ultimate strain vs. strain rate

Fig. 2.28 Strain rate dependency of the PAC due to normal traction, as demonstrated by its elastic

modulus (A), ultimate stress (B), and ultimate strain (C) (taken from Jin et al. (2007))

Fig. 2.28. Note that for most viscoelastic materials, the ultimate strain decreases

with increasing strain rate, but for the PAC, the opposite is true. The PAC may be

responding more like a structure than a single material, and more detailed study is

required to explain this phenomenon.

2.5.2.2 Response of the PAC to Shear

Jin et al. (2011) conducted a similar study of the PAC to elicit its response to shear

loading. This study has important implication with regard to the modeling of the

PAC in finite element models of the brain. The CSF layer obviously cannot be

modeled as a pure fluid because it contains trabeculae which are collagenous in

nature. However, if would be difficult to assign a shear modulus to the PAC because

no data were available. This study was designed to provide these data over a range

of strain rates. The specimens used and the procedure for their preparation are

identical to that described by Jin et al. (2007) with the exception that the blocks

were glued together at the time of testing rather than ahead of time. A mini Instron

materials testing machine was used along with a fixture that was designed to apply a


Fig. 2.29 Loading fixture to test the PAC in shear (taken from Jin et al. (2011)). Reprinted from X.

Jin, K.H. Yang, A.I. King, Mechanical properties of bovine pia–arachnoid complex in shear.

Journal of Biomechanics. 44(3), 467–474, 2011, with permission from Elsevier

pure shear load on the PAC specimen. It is shown in Fig. 2.29. The PAC is glued to

the fixed block, and cyanoacrylate glue is sprayed onto the PAC surface as well as

on the surface of the movable block. Then the movable block is moved by the

micrometer toward the fixed block to glue the movable block to the PAC.

Compression is maintained until the glue sets. At this point, the micrometer is

turned in the opposite direction to relieve the compression before testing begins.

A shear force is applied to the PAC when the loading head of the Instron moves

downward. This shear load and the displacement of the loading head are recorded.

Since the measured displacement is very small, it was necessary to take into

account the deformation of the test fixture to obtain the true displacement experienced

by the PAC. Forty-three PAC specimens from the frontal, parietal, and

occipital regions of the brain were tested at 0.84, 7.3, and 72 s 1 .

In terms of results, there is again no regional difference in shear modulus,

ultimate stress, and ultimate strain for the three groups. The strain rate effect is

again seen in shear. Figure 2.30 shows the increase in modulus, ultimate stress, and

ultimate strain as a function of strain rate. Significant differences at p < 0.05 and

p < 0.001 are identified by asterisk(s) (*). Both the shear modulus and ultimate

stress are rate sensitive. Ultimate strain does not appear to be very sensitive to strain

rate. The takeaway message is that the CSF layer can resist shear and any brain

model that assumes it to be a pure fluid will probably not predict the correct motion

of the brain.


Fig. 2.30 Strain rate dependency of the PAC due to shear loading, as demonstrated by its shear

modulus (A), ultimate stress (B), and ultimate strain (C) (taken from Jin et al. (2011)). Reprinted

from X. Jin, K.H. Yang, A.I. King, Mechanical properties of bovine pia–arachnoid complex in

shear. Journal of Biomechanics. 44(3), 467–474, 2011, with permission from Elsevier

2.6 Tolerance of the Head and Brain to Blunt Impact

Unintentional injuries to the head and brain are usually caused by blunt impacts as

opposed to penetrating impacts that are encountered in intentional injuries. Tolerance

of the head refers to the tolerance of the skull to fracture which has a bearing

on the tolerance of the brain to impact, but skull fracture is not a precise measure of

brain injury. Lissner et al. (1949) initiated brain injury research by studying the

energy required to cause skull fracture because the presence of skull fracture is an

index of the severity of the blow, with a history of unconsciousness and severe brain

damage (Gurdjian et al. 1963). The energy required to fracture a skull is highly

variable, depending on the location of the impact on the skull or its thickness, the

thickness of the scalp, and the shape of the impactor. It can vary from 400 in-lb to

over 1000 in-lb or 58 to over 146 N-m (Lissner et al. 1949). Also, brain damage can

occur with or without skull fracture. Thus, it is necessary to separate the tolerance of

the skull to fracture from the tolerance of the brain to the many forms of brain injury

discussed in Sect. 2.3.1.

2.6 Tolerance of the Head and Brain to Blunt Impact 65

Fig. 2.31 Tolerance of the

human skull to impact with

a rigid surface in terms of

peak impact force (taken

from Prasad et al. (1985))

Peak Uniaxial Force, kN

14

12

10

8

6

4

2

A

B

A: Non – Fracture Force

130 ± 19mm, 4.24 ± 0.58 kN

B: Fracture Force

330 mm, 6.4 ± 0.6 kN

1060 mm, 10.9 ± 1.1 kN

0 200

2.6.1 Tolerance of the Skull to Fracture

400 600 800 1000 1200

Free - Fall Drop Height, mm

Hodgson and Thomas (1971, 1975) dropped embalmed cadaver heads onto a rigid

(steel) surface. The whole cadaver was placed on a pallet hinged at the floor level

with the head extending beyond the top edge of the pallet. The velocity of impact

was originally calculated as the square root of twice the product of the height of the

p ffiffiffiffiffiffiffi

head above the impacted surface (h) and the acceleration due to gravity (g)( 2gh )

(see Prasad et al. 1985, p. 12). It was eventually corrected by measuring the

velocity of the head of a dummy placed on the pallet. The free-fall drop height

was based on the measured velocity. The head acceleration was measured by an

accelerometer placed on the skull on the opposite side of the impact, and the force

of impact was measured by a load cell on the floor. There were frontal, side, and

occipital (rear) impacts. However, there was a large amount of scatter in the data,

and it was not possible to draw regression curves for each direction of impact. If all

the data from the three directions of impact were grouped together, it was possible

to draw rectangles around the data to separate the fractured cases from the

non-fracture cases. The fracture force as a function of the corrected free-fall drop

height is shown in Fig. 2.31. It is seen that the skull can be fractured from a drop

height of 330 mm or approximately 13 in. In terms of head acceleration, the

tolerance of the skull is shown in Fig. 2.32. The lower limit for fracture is in the

200 g range. It should be noted that the embalmed cadaver has a thicker scalp

because it retains embalming fluid and it is reasonable to expect the tolerance to

fracture to be somewhat lower.


Fig. 2.32 Tolerance of the

human skull to impact with

a rigid surface in terms of

peak head acceleration

(taken from Prasad et al.

(1985))

Peak Uniaxial Acceleration, G

350

300

250

200

150

100

50

C

D

C: Non – Fracture Acceleration

130 ± 19mm, 159 ± 42G

D: Fracture Acceleration

330 mm, 230 ± 42G

1060 mm, 293 ± 42G

0 200

400 600 800 1000 1200

Free - Fall Drop Height, mm

2.6.2 Tolerance of the Brain to Blunt Impact

Blunt impacts to the brain can cause a variety of brain injuries at different severities.

If the AIS manual is consulted, there are injuries to the brain from AIS 1 (mild

concussion) to AIS 6 (crushed skull), with a large number of injuries at each AIS

level. If we are to look at brain injury from the viewpoint of automotive safety, the

original standard was set for AIS 4+ injuries because airbags were not available and

seat belt use was not popular. Currently, the tolerance level has been lowered to

reflect the protection afforded by the airbag. In sports, the issue of mTBI is a major

concern because athletes can experience multiple head impacts. Thus, the exposure

level for football players is much lower than that for automotive occupants.

The history of the search for human tolerance to blunt impact goes back to the

work of early researchers. Some of the tolerance data were deduced from the head

accelerations required to cause a skull fracture or to cause blood vessel damage in

cadaveric brains which were perfused with India ink. Other data were based on an

extrapolation of live animal concussion data to the human level.

The process took about two decades of research to result in a head injury

tolerance curve, currently known as the Wayne State Tolerance Curve (WSTC),

which was first published in preliminary form by Lissner et al. (1960) as a fracture

tolerance curve shown in Fig. 2.33. Animal data were added to this curve along with

the single data point from the famous sled ride by Col. Stapp resulted in the original

WSTC. It is a plot of the “effective” acceleration of the head vs. the duration

of impact, as shown in Fig. 1.5. The term “effective acceleration” was not

defined but assumed to be less than the peak acceleration but larger than the

average acceleration. Eventually, effective acceleration became synonymous

with average acceleration. What the WSTC basically says is that the brain


500

90

ACCELERATION (ft./sec. 2 )

400

300

200

100

HEADS without BODY

HEADS with BODY

72

54

36

18

TEMPORAL PRESSURE (lb./in. 2 )

0 0

.001 .003 .005

.01

TIME IN SECONDS

Fig. 2.33 Tolerance of the skull to fracture in terms of acceleration and pulse duration. Clinically, a

simple skull fracture is frequently associated with a mild concussion. Thus, this curve can

be regarded as a tolerance curve for brain concussion. It is the forerunner of the Wayne State

Tolerance Curve shown in the next figure. (Note: The units for acceleration along the ordinate should

be g’s instead of ft/s2) (taken from Lissner et al. (1960)). Reprinted from H. Lissner, M. Lebow, F.

Evans, Experimental studies on the relation between acceleration and intracranial pressure changes

in man. Surgery, Gynecology & Obstetrics 111, 329–338, 1960, with permission from Elsevier

Fig. 2.34 Comparison of

HIC of about 1000 for a

half-sine wave with

the WSTC

can tolerate higher impact accelerations at shorter durations. According to Patrick

et al. (1963), the curve was based on a reversible concussion with no aftereffects,

but it turned out that it marks the boundary for a severe head injury.

In terms of the data, the short-duration data (10 ms or less) were generally

associated with cadaveric skull fracture data, while those between 10 and 40 ms

were from animal data and the asymptote was based on the 42 or 45 g peak chest

acceleration sustained by Col. John Paul Stapp who rode the rocket sled in Alamogordo,

NM, in 1949 and suffered an injury to his right eye. This level was

eventually raised to 80 g because at 42–45 g, a brain injury is not likely.


Gadd (1962) plotted the WSTC on log-log paper and discovered that the curve

approximated a straight line with a slope of 2.5. He proposed a severity index

(SI) which became known as the Gadd Severity Index (GSI) in the form:

GSI ¼

ð

a 2:5 dt 1000

ð2:2Þ

where a(t) is the resultant head acceleration and t is the time

The integration is to extend over the entire duration of the pulse. The rulemakers

at the National Highway Traffic Safety Administration (NHTSA) proposed that

Eq. (2.2) should be used as a head injury criterion for automotive crash safety. It

was a good suggestion in that the measured head acceleration in dummy tests could

be used conveniently to calculate the GSI and used to determine if the head impact

was acceptable. It soon became evident that this criterion was difficult to meet, and

Versace (1971) proposed an alternate criterion which became known as the Head

Injury Criterion or HIC. The equation for HIC is as follows:

ð t2

2:5

HIC ¼ ðt 2 t 1 Þ aðÞdt= t ðt 2 t 1 Þ max ð2:3Þ

t 1

where a(t) is the resultant head acceleration and t 1 and t 2 are the limits of integration

over time selected so as to maximize the value of HIC.

The time interval would obviously have to be within the pulse duration of the

impact. This time interval should not exceed 15 ms because most impact durations

of head contact last 15 ms or less. With this limitation, the calculated HIC is

designated as HIC 15 . Although field accident data indicate that, in the automotive

environment, if there was no head contact with vehicular structures during a crash,

there were no cases of head injury, it would still be possible to calculate a HIC value

for the measured head acceleration (Prasad and Mertz 1985). In this case, the

maximum interval needs to be extended to 36 ms and the calculated HIC is

designated as HIC 36 . The process for determining the value of HIC is embodied

in a software program that selects the time duration t 1 to t 2 that maximizes the value

of HIC, using the interval for numerical integration as 1 ms.

Obviously, HIC is dependent on the pulse shape, and it is not possible to

compare HIC to the WSTC for all pulse shapes. However, if we assume a halfsine

wave for the head acceleration, the calculated HIC values for durations

between 1 and 40 ms were found to be comparable to the WSTC, as shown in

Fig. 2.34. The red curve is for a HIC of 1000, while the HIC values for the WSTC

(green) curve range from 585 to 2498.

Prasad and Mertz (1985) also did a detailed analysis of the human head impact

data collected from a variety of sources. They found that, for the most part, skull

fracture and brain damage (arterial rupture) occurred at comparable HIC values

and decided that since these were cadaveric data, it was more reliable to use

skull fracture data as a basis for brain damage than data related arterial rupture.


Fig. 2.35 Injury risk curve

in terms of HIC based on the

WSTC (based on Prasad

and Mertz (1985))

INJURY RISK CURVE FOR HIC WHEN T 2 – T 1 ≤ 15 MS

99

98

RISK OF LIFE-THREATENING BRAIN INJURY -%

95

90

80

70

60

50

40

30

20

10

5

2

1

0 500 1000

1500

HIC

2000 2500 3000

HIC = 1000 REPRESENTS A 15% RISK OF LIFE-THREATENING

BRAIN INJURY IF (T 2 – T 1) ≤ MS

There were 54 tests with 27 skull fractures. A logistic curve was drawn to determine

the probability of skull fracture (or brain damage) as a function of HIC. Using the

logarithmic scale for injury probability (of AIS 4+), the S-curve becomes a

straight line, as shown in Fig. 2.35. It is seen that at a HIC of 1000, the risk of an

AIS 4 + injury is 15 %. The current US safety standard calls for a limit of HIC 700

or an injury risk of approximately 5 %.

It should be noted that neither the WSTC nor GSI or HIC can provide detailed

information on the damage sustained by the brain. For example, it is not possible to

predict from HIC whether there was DAI, concussion, subdural hematoma, brain

stem injury, or even skull fracture. HIC is useful for assessing the degree of

protection provided by safety features in a car and is thus a suitable criterion for

rulemaking. To study brain injury in greater detail, we need to look into specific

research studies and to use computer models to predict outcome.

Currently, there is no accepted tolerance value for the brain to angular acceleration.

Research involving the use of concussion data derived from on-field helmetto-helmet

impacts revealed that the angular acceleration for a 50 % probability of a

mild concussion is between 5500 and 6400 rad/s 2 (see Table 6.4, Chap. 6).



2.1. Select the statement that is valid, as it relates to brain injury:

[ ] (i) To generate high shear strains in the brain, it is necessary to subject

the head to linear accelerations

[ ] (ii) Mild traumatic brain injury cannot occur unless the victim was

unconscious for a short time

[ ] (iii) A noncontact head impact resulting in a rotational acceleration of

6000 rad/s 2 can cause a severe brain injury

[ ] (iv) Bridging vein ruptures occur as a result of high angular accelerations

in the mid-sagittal plane



[ ] (i) The pia and arachnoid are separated by cerebral spinal fluid and the

two membranes are not connected by any soft tissue

[ ] (ii) The shear resistance between the pia and arachnoid is due solely to

the presence of the cerebral spinal fluid

[ ] (iii) It is valid to model the space between the pia and the arachnoid as a

Newtonian fluid

[ ] (iv) The space between the pia and the arachnoid is devoid of blood

vessels


2.3. Understanding the mechanical response of the pia-arachnoid complex (PAC)

is important for modeling of the brain. Which of the following statements is

true:

[ ] (i) There is no cerebral spinal fluid between the pia and the arachnoid

[ ] (ii) The trabeculae offer no tensile resistance when the arachnoid is pulled

away from the pia

[ ] (iii) The border cells are between the pia and the arachnoid

[ ] (iv) The PAC has been tested in both plane tension and normal traction



[ ] (i) Diffuse axonal injury (DAI) occurs several hours or days after head

impact

[ ] (ii) Brain motion within an intact human skull during an impact is more

sensitive to linear acceleration than to angular acceleration

[ ] (iii) DAI can only occur in the gray matter of the central nervous system

(CNS)

[ ] (iv) The tolerance of the brain to angular acceleration is 16000 rad/s 2

[ ] (v) If HIC is under 1000, there can still be brain injury


2.5. Wearing a helmet helps to prevent or minimize brain injury by

[ ] (i) Decreasing angular acceleration

[ ] (ii) Decreasing linear acceleration

[ ] (iii) Preventing relative brain motion with respect to the skull

[ ] (iv) Causing the skull to deform more



[ ] (i) Diffuse axonal injury (DAI) is actually a breakdown of the microtubules

within axons

[ ] (ii) DAI cannot be produced by pure linear acceleration

[ ] (iii) DAI can only be caused by angular acceleration

[ ] (iv) DAI can be diagnosed from a CT scan of the brain

[ ] (v) DAI severity is not related to the duration of coma

2.7. The diploe of the skull is

[ ] (i) The outer covering of the skull bone

[ ] (ii) The outer layer of bone of the skull

[ ] (iii) The middle layer of bone of the skull

[ ] (iv) The inner layer of bone of the skull

[ ] (v) The inner covering of the skull bone

2.8. Which of the following statements is incorrect:

[ ] (i) The dura is a double-layered covering above the brain surface, next to

the skull

[ ] (ii) The dura is a thick and tough membrane which is attached to the skull

[ ] (iii) The dura forms a sinus in the midline of the skull for drainage of

venous blood

[ ] (iv) The dura is not in contact with the cerebral spinal fluid surrounding

the brain

[ ] (v) The dura is a thin membrane between the arachnoid and the pia

2.9. The following statements relate to normal cerebral spinal fluid (CSF). Which

one is incorrect?

[ ] (i) CSF contains water and proteins

[ ] (ii) CSF has the approximate mass density of water

[ ] (iii) CSF contains a substantial number of red as well as white blood cells

[ ] (iv) CSF is contained within the dural sac of the central nervous system

[ ] (v) CSF is found in the ventricles of the brain

2.10. The central nervous system

[ ] (i) Consists entirely of white matter

[ ] (ii) Consists entirely of gray matter

[ ] (iii) Consists of both neurons and axons


[ ] (iv) Ends at the junction of the head and neck


2.11. Which of the following statements is incorrect?

[ ] (i) The white matter consists mainly of axons

[ ] (ii) The brain of a normal person weighs approximately 6 lb

[ ] (iii) The medulla oblongata is the brain stem

[ ] (iv) The cerebellum is larger than the cerebrum

[ ] (v) All of the above are correct

2.12. There are several types of brain injury due to blunt impact. Which one of the

following is incorrect?

[ ] (i) Focal injuries

[ ] (ii) Mass lesions

[ ] (iii) Lacerative injuries

[ ] (iv) Diffuse injuries


2.13. Diffuse axonal injury

[ ] (i) Can only occur in the gray matter

[ ] (ii) Is not caused at the instant of impact

[ ] (iii) Can only be caused by angular acceleration

[ ] (iv) Can only occur in the white matter

[ ] (v) Is not associated with loss of consciousness

2.14. Several mechanisms for brain injury have been proposed. Which of the

following is not commonly accepted as being valid?

[ ] (i) Positive pressure at the coup site

[ ] (ii) Negative pressure at the contrecoup site

[ ] (iii) Pressure gradients causing development of shear stresses

[ ] (iv) Change in volume of the skull

[ ] (v) Rotational effects causing DAI

2.15. The following statements refer to blunt impact to the head. Which one is

incorrect?

[ ] (i) High-speed X-ray data on brain motion are available

[ ] (ii) High-speed X-ray data on brain motion are available for low severity

impacts

[ ] (iii) High-speed X-ray data on brain motion are not available from living

human subjects

[ ] (iv) High-speed X-ray data on brain motion have not been published

[ ] (v) High speed X-ray data on brain motion can be acquired at

1000 frames/s

Answers to Problems by Chapter 73

2.16. Brain motion within the skull due to a low speed impact (less than 5 m/s):

[ ] (i) Cannot be measured or observed

[ ] (ii) Is very large, exceeding 20 mm in most cases

[ ] (iii) Is more sensitive to linear acceleration than angular acceleration

[ ] (iv) Is relatively small, not exceeding 10 mm in most cases


2.17. The human skull can be fractured at the following levels of impact:

[ ] (i) Drop heights in excess of 0.5 m

[ ] (ii) Force levels in excess of 6 kN

[ ] (iii) Peak accelerations below 100 g

[ ] (iv) (i) and (iii) above

[ ] (v) (i) and (ii) above

2.18. Tolerance of the brain to blunt impact:

[ ] (i) Can be expressed in terms of HIC < 200

[ ] (ii) Is limited in angular acceleration to 5000 rad/s 2

[ ] (iii) Is due entirely to linear acceleration

[ ] (iv) Is due entirely to angular acceleration


2.19. Brain motion relative to the skull is

[ ] (i) Larger than 10 mm at the periphery of the brain

[ ] (ii) Occurs between the dura mater and the skull

[ ] (iii) Higher due to linear acceleration than angular acceleration

[ ] (iv) Limited to 5 mm regardless of the severity of impact


2.20. The following statements relate to normal cerebral spinal fluid (CSF). Which

one is incorrect?

[ ] (i) CSF contains water, blood cells, and proteins

[ ] (ii) CSF has the approximate mass density of water

[ ] (iii) CSF is found in the brain, both between the pia and the arachnoid and

in the ventricles

[ ] (iv) CSF is contained within the dural sac of the central nervous system

[ ] (v) CSF is found in the ventricles of the brain


Prob

Ans

1 (iv)

2 (v)

(continued)


Prob

Ans

3 (iv)

4 (v)

5 (ii)

6 (i)

7 (iii)

8 (v)

9 (iii)

10 (iii)

11 (ii)

12 (v)

13 (iv)

14 (iv)

15 (iv)

16 (iv)

17 (v)

18 (v)

19 (iv)

20 (i)

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within 35 min after head injury to human adults. Neuropathol. Appl. Neurobiol.

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(Japan Automobile Research Institute, Tokyo, 1976)

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primates. J. Biomech. 4(1), 13–21 (1971)

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No. 710881, Coronado, CA, 1971

Chapter 3

Head Injury Research: Experimental Studies

In retrospect, the experimental research carried out in head injury had the biomechanical

objectives that were outlined in Chap. 1 (Sect. 1.6) although they were not

clearly explained until much later. The research began with the work of Gurdjian

and associates in the mid-1950s followed by the work of Ommaya and associates.

The purpose of their work was to try to understand the mechanisms of brain injury.

Suffering from the lack of what we now call modern technology, the researchers

used head acceleration and intracranial pressure as possible parameters that might

be able to explain how the brain is injured. These were the only measurable

parameters available at the time, and they were used to try to explain how brain

injury occurs. Out of that research came the two competing theories of brain

injury—the linear and angular acceleration mechanisms.

Brain motion within the skull during an impact was not measurable for most of

the twentieth century. As a result, impact response was limited to the study of skull

response to impact. The response data did not add any insight into brain response

but did provide important data for the design of a humanlike dummy head—the

head of the Hybrid III dummy. Accurate data on brain response became available

in 2001.

The search for measures that can accurately predict the tolerance of the brain to

impact began with the work done at Wayne State University which published the

so-called Wayne State Tolerance Curve (WSTC). This led to a couple of injury

criteria which are still in use to this day. The history behind the development of

these criteria is discussed in this chapter.

The evaluation of vehicular safety features utilizes crash dummies and computer

models. The research and development of crash dummies are beyond the scope of

this book, and models of the brain are discussed in the next chapter.



77

78 3 Head Injury Research: Experimental Studies

3.1 Experimental Research on Head Injury Mechanisms

3.1.1 The Linear Acceleration Mechanism

After spending about a decade and a half studying the biomechanics of skull fracture,

Gurdjian and Lissner turned their attention to brain injury. Their first paper on

experimental head injury appeared in 1953 (Gurdjian et al. 1953), followed by a

string of papers that led to the WSTC. In that first paper, 24 anesthetized dogs were

impacted with a ball-peen hammer with or without padding, and the head was free to

move after impact. Some dogs received multiple blows (up to 5) and most were

concussed to varying degrees. The dog skulls were instrumented with a strain gagetype

accelerometer with a natural frequency of 1600 Hz and weighing over 120 g and

a strain gage-type diaphragm pressure sensor located on the skull opposite to the site

of impact. The measured accelerations ranged from 190 to about 780 g with

durations ranging from 0.5 to 1.5 ms. Measured intracranial pressures ranged from

60 to 95 psi (414 to 655 kPa) with durations ranging from 0.5 to 5 ms. The skull

was fractured in 21 of the 24 animals tested. It was concluded that acceleration and

pressure duration appeared to be the significant factors related to the clinical effects

of head impact. However, if the acceleration or pressure was high enough, a long

duration was not necessary to produce concussion. This paper was the first biomechanical

paper on brain concussion. The authors noted that impacts to the skull using

a hammer was unable to produce durations longer than 1.5 ms. They invented the

fluid percussion method described in Sect. 2.4 of Chap. 2 to obtain a wider range of

impact durations (Gurdjian et al. 1954). From the 72 tests that were performed, it was

concluded that the shorter the duration of the impact, the higher the pressure

necessary to result in a concussive effect and the longer the duration, the lower

can the pressure be to cause a concussion. Impulse, defined as the product of peak

pressure and duration, may also be a parameter useful in predicting concussion. The

comment was made that there was no correlation between the measured acceleration

and concussion, and yet the measured increase in intracranial pressure appeared to

be correlated to concussion. The accelerometers were large and had a low natural

frequency of 1600 Hz. This meant that the measured acceleration would be accurate

to only a few hundred cycles per second, and it was not surprising that no correlation

with concussion was found. Another attempt was made by Haddad et al. (1956) to try

to resolve the observed contradiction and to relate acceleration and concussion by

the use of a different type of accelerometer. The output of the strain gage-type

accelerometer was compared with that of a crystal-type (piezoelectric) accelerometer

which should have a much higher natural frequency. However, the results of

their response were similar, possibly due to problems with conditioning of the

piezoelectric signal. The strain gage-type accelerometers only had a natural frequency

of 1600 Hz, and the output of the piezoelectric-type accelerometer did not

appear to have a higher natural frequency. Thus, the results of tests on 34 dogs again

showed a poor correlation of acceleration with concussion. A better accelerometer

was needed to unravel the mystery.

3.1 Experimental Research on Head Injury Mechanisms 79

By the late 1950s, a better accelerometer became available, a 1000 g Statham

accelerometer. Also, the test subject was changed to postmortem human subjects or

cadavers not because it was possible to concuss a cadaveric brain but because it was

known clinically that a simple linear skull fracture was frequently associated with a

minimal to moderate concussion (Lissner and Gurdjian 1960). In this study, four

cadaveric heads were instrumented with the aforementioned accelerometers and

with pressure sensors, and 23 whole-body drop tests were conducted, targeting the

heads to hit a 3 in. (76 mm) thick steel block, a steel plate, two different automobile

instrument panels, and padded surfaces. Additionally, there were four drop tests

involving three decapitated cadaveric heads hitting a steel block. Out of these tests,

there were six impacts against the 3 in. thick steel block, four whole-body impacts,

and two head drop tests, most of which resulted in fracture. Since fracture could be

identified with concussion, these six data points represented a tolerance level for

human concussion. They are plotted in Fig. 2.32 and would later become a part of

the WSTC. Note that the units for the ordinate were labeled erroneously. Instead of

ft/s 2 , they should be g’s. The contradiction was resolved and acceleration could be

correlated with concussion.

Returning to the pressure response of the brain to impact, we note from Lissner and

Gurdjian (1960) that the pressure/concussion data from about 125 dogs over a 6-year

period were summarized in Fig. 3.1 as a tolerance curve for both mild and severe

concussions. The data were obtained from about 125 dogs subjected to fluid percussion,

a method invented by Gurdjian et al. (1954). The head of these animals did not

undergo any acceleration and were concussed by pressure alone. An attempt was made

by Haddad et al. (1956) to determine the type of cellular injury sustained by the

neurons when they were subjected to a transient pressure pulse. The most significant

change they found was chromatolysis which is the disintegration of Nissl bodies in a

nerve cell. In the microscope, chromatolysis is associated with swelling of the neuron

cell body (the perikaryon) and shifting of the nucleus from its central position to the

periphery. Nissl bodies produce protein for the neuron. At that time, techniques were

not available to track changes in the brain of injured animals with time, such as looking

for changes indicative of neuronal death, glial cell proliferation, or the use of β-APP to

find axonal damage. However, there is ample evidence that the brain can be injured by

time-varying pressure alone and the linear acceleration mechanism was confirmed.

Finally, Lissner and Gurdjian (1960) made a physical model in the form of a

transparent plastic container representing a 25 mm thick midsagittal section of the

human brain including the brain stem and the foramen magnum and filled it with a

solution of milling yellow that would produce contours in the presence of a shear

stress. When a pressure pulse was applied to the contents of the model, by striking

the side of the container with a hammer, a pattern of closely spaced shear contours

appeared. They represent the existence of a high shear stress and were seen in the

brain stem area. Figure 3.2 is a frame taken from film recording the event at

500 frames per second. This shear is due to the high-pressure gradients in the

brain stem, as described in Chap. 1. It was theorized that brain stem shear was

responsible for concussion because the respiratory and vasomotor centers are

located in the brain stem and when concussed the victim’s blood pressure rises

and respiration ceases momentarily (Denny-Brown and Russell 1941).

INTRA CRANIAL PRESSURE - PSI


50

PRESSURE - TIME RELATION

PRODUCING CONCUSSION IN DOGS

40

30

SEVERE

CONCUSSION

20

MINIMAL

CONCUSSION

10

0 .02 .04 .06 .08 .10 .12

TIME DURATION - SECONDS

.14 .16

Fig. 3.1 Summary of concussion data collected using the fluid percussion device. The brain was

concussed in the absence of head acceleration (taken from Lissner and Gurdjian (1960))

3.1.2 The Angular Acceleration Mechanism

As mentioned in Chap. 2, Holbourn (1943) proposed that angular acceleration was

capable of producing brain injury, based on his experiments rotating a sphere filled

with a gel. This theory was picked up by Ommaya et al. (1966) who initiated

whiplash-type experiments using rhesus monkeys. They were seated facing forward

on a sled that was accelerated to produce head rotational accelerations on the order

of 100,000 rad/s 2 , based on high-speed film data taken at over 3000 frames/second.

With the head free to flex and extend (not constrained by a neck collar), concussion

occurred at about 100,000 rad/s 2 . However, if the animal wore a collar that

prevented flexion and extension, the observed head angular acceleration was

much lower than 100,000 rad/s 2 for the same sled acceleration, and it was not

concussed. Thus, it was postulated that angular acceleration or velocity could be a

cause of concussion. There were no angular accelerometers at that time, and it

required the authors to double differentiate the displacement film data to calculate

angular acceleration. This is a notably inaccurate method because the results are

3.1 Experimental Research on Head Injury Mechanisms 81

Fig. 3.2 Photoelastic pattern in milling yellow in a plastic model of a midsagittal section of the

brain. The closeness of the contours indicates a high shear stress in the brain stem region (taken

from Lissner and Gurdjian (1960))

noisy and the calculation of slopes is prone to error. Nevertheless, in their next

paper, Ommaya et al. (1967) picked a one percentile tolerance value for angular

acceleration for the rhesus monkey, as shown in Fig. 3.3, That is, the selected level

was 40,000 rad/s 2 which is below the concussion levels of 99 % of the 50 plus

animals tested. Using dimensional analysis, they projected what the tolerance

would be for the squirrel monkey, the chimpanzee, and man, based solely on the

mass of the brain. The projected tolerance for man was 7500 rad/s 2 . There was no

discussion regarding tolerance due to species differences. It was surprising that the

authors did not reference the work of Gurdjian and Lissner at all in both papers even

though they were well aware of the work at Wayne State. See, for example,

references in Ommaya (1966). On the contrary, they stated that pressure or compression

of the brain had little to do with concussion (Ommaya et al. 1966). This

ignited a long period of dissent and arguments that on one occasion almost came to

blows (13th Stapp conference in Boston, MA, 1968). Ommaya and Hirsch (1971)

came up with a revised human tolerance of 1800 rad/s 2 based on additional data

from testing chimpanzees and squirrel monkeys. This lower value has since been

shown to be far too conservative, based on data from an NFL study (King et al.

2003). The issue is not completely resolved, but supporters of both theories have

learned to disagree in a more “civilized” manner. In fact, both mechanisms are

valid, and both play a role in injuring the brain since neither mechanism can occur

without the other.

One of the last papers disputing the mechanisms of injury was by Gennarelli

et al. (1972) in which two different sets of experiments were described. One group


1000,000

Concussive

Non-Concussive

100,000

RAD/SEC 2

10,000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

MSECS.

Fig. 3.3 Tolerance curve for rhesus monkeys subjected to non-contact head angular acceleration.

At 40,000 rad/s 2 , over 99 % of the animals were concussed (taken from Ommaya et al. (1967))

of squirrel monkeys was subjected to a purely linear acceleration of the head, while

another underwent a purely angular acceleration. The tests were conducted after the

animals had awakened from the anesthetized state during which they were

instrumented and prepared for testing. For the 12 animals in the linear acceleration

group, the head was held within a helmet restraint system that did not allow any

head rotation while it was being accelerated by a Head Acceleration Device named

HAD II. The peak head accelerations ranged from 665 to 1230 g with the

corresponding deceleration peaks ranging from 427 to 900 g. The linear acceleration

duration ranged from 6 to 8 ms. The peak angular acceleration experienced by

the 13 animals using the HAD II machine ranged from 108,000 to 317,000 rad/s 2 ,

with a duration of 5.5–8 ms. None of the translated animals was concussed, while

all of the rotated animals were.

This paper appears to make the case for angular acceleration as the cause of

concussion and brain injury. It was surprising that the linear acceleration proponents

did not point out a fallacy in the experimental design of Gennarelli et al.

(1972). The scaling law used by Ommaya et al. (1967) can be used to estimate the

equivalent human exposure. For angular acceleration, we can use Eq. (2.1):

α h =α s ¼ ðm s =m h Þ 2=3 ð3:1Þ

where, now, the subscript s represents the squirrel monkey.

3.2 Experimental Research on Head Impact Response 83

According to Ommaya and Hirsch (1971), the brain mass of a squirrel monkey

averaged 23.5 gm. For a 50th percentile male human, the weight of the brain is

1400 gm. Applying these values to Eq. (3.1) and for an angular acceleration of

600,000 rad/s for the squirrel monkey, α h ¼ 19,667 rad/s 2 which is more than

enough to cause concussion in the human, recalling that the threshold for concussion

is approximately 6000 rad/s 2 , as described in Sect. 2.6.2 and Sect. 6.1.1.

In terms of linear acceleration, the scaling law is given by

where L is the length dimension

thus

a s =a h ¼ ðm h =m s

a s =a h ¼ ðm h =m s Þ= ðL h L s Þ 2

Þ= ðm h =m s

Þ 2=3 ¼ ðm h =m s Þ 1=3

For a mass ratio of 1400/29 ¼ 59.6 and for a linear head acceleration of 1000 g for

the squirrel monkey, the equivalent human head acceleration is 256 g. This acceleration

may cause a moderate concussion in the human in combination with angular

acceleration but may not do so in its absence. In any case, the experiment did not

compare acceleration inputs of equivalent severity. Furthermore, the acceleration of

the whole head may have a different effect on the brain than a direct impact which

causes deformation of the skull, as mentioned by Ommaya and Hirsch (1971). This

effect could not be reproduced in this experiment.

3.2 Experimental Research on Head Impact Response

Early researchers obtained impact response data in the process of trying to determine

the injury mechanisms. The researchers at Wayne State University measured

intracranial pressure and skull acceleration in dogs and cadavers and used these

response data to formulate the linear acceleration theory of brain injury. Similarly,

Ommaya and his team of researchers measured skull angular acceleration and

velocity in subhuman primates and swine to come up with their angular acceleration

theory of brain injury. So, in the absence of information regarding the response

of the brain, acceleration became a standard measure for head impact response.

Since 1939, there have been many studies on head impact response by

researchers from around the world. It would not be feasible to cover all of these

studies in this book, and the reader is referred to two excellent reviews by Goldsmith

(2001) and Goldsmith and Monson (2005) for a very comprehensive summary

of experimental head impact research, a lot of which dealt with impact

response. Some of the data are useful for the design of a surrogate heads, such as

the head for the Hybrid III dummy. The only intracranial data measurable were

intracranial pressure such as those produced by Nahum et al. (1977). Brain kinematic

response is less well known and will be discussed next.


3.2.1 Visualization of Brain Motion during Impact

One of the rare attempts to determine brain response to impact was made by

Dr. Warren Hardy who was a Ph.D. student at Wayne State at the time. With the

availability of miniature solid-state accelerometers, he was able to manufacture a

triaxial accelerometer which was no larger than a 3 mm cube and which was

wrapped in polyurethane so that its density was close to that of brain tissue.

It was called a neutral density accelerometer (NDA), and the purpose was to ensure

that when inserted into brain tissue, it would not lacerated the brain during an

impact (Hardy et al. 1997). Two of these devices are shown in Fig. 3.4 along with

hardware used to secure them to the skull and to provide an opening for the cables to

exit the head. The NDA was found to be linear upon calibration. It was inserted into

a cadaveric brain through a small hole in the skull, and the head was subjected to

impacts so that brain kinematics could be measured. Brain acceleration could be

compared with that of the skull. The attenuation in magnitude and time delay can

be seen in Fig. 3.5. The acceleration pulse was integrated twice to yield brain

displacement. What is shown in Fig. 3.6 is a comparison of the integrated displacement

with motion of the NDA tracked by a high-speed biplanar X-ray system

described earlier in Chap. 2. The two curves shown in Fig. 3.6 are displacement

data from two different head impacts, and there are actually four curves, two from

integration and two from X-ray measurement. The accuracy of the NDA is indeed

quite amazing. In the inset is a photograph of the NDA found in the cadaver brain

during necropsy. The NDA did not lacerate the brain. It was also possible to

calculate the strain or stretch by differentiating the displacement data, since strain

is given by

ε x ¼ du=dx

where ε is the strain and u is the displacement.

Fig. 3.4 Neutral density

accelerometers (NDA) are

triaxial accelerometers

which can measure brain

kinematics of a cadaveric

brain (courtesy of

Dr. Warren Hardy)


Acceleration (G)

Brain

Acceleration

50 75 100 125

Skull acceleration

0

25

-16 -8 8

16 24 32 40 48

-25

0

Time (ms)

Fig. 3.5 Comparison of resultant acceleration of the skull with that of the brain for two impacts,

one at 100 g and the other at 40 g. The NDA was used measure the brain acceleration which is

much lower than that of the skull and is shown as by a dotted and dashed curve. The solid curves

are the skull accelerations. The inset shows the NDA in the brain which was not lacerated by it

because of its neutral density feature (Both the figure and the inset were taken from Hardy et al.

(1997))


displacement data measured

using the NDA and the

high-speed biplanar X-ray

method. The NDA

acceleration was integrated

twice to yield displacement

which matched the X-ray

displacement data perfectly.

There are actually four

curves in this graph from

two tests. Both were

occipital impacts at 2.7 m/s

(Test C480-T1) and 4.2 m/s

(Test C480-T2) (taken from



Fig. 3.7 Calculated brain

stretch or strain obtained

by differentiating the

displacement data (taken

from Hardy et al. (1997))

The computed strain is shown in Fig. 3.7. It was estimated that the strain at the

location of the NDA was about 8 % for a 2.7 m/s impact. These data were the first of

its kind and provided kinematic data for specific locations in the brain. Since only a

limited number of NDA could be inserted into a given brain, this approach was not

practical for mapping relative motion of the brain with respect to the skull over a

larger volume of the brain. This methodology is described next.

Over the years, there have been attempts to measure brain response radiologically

(Nusholtz et al. 1984; Ommaya 1966; Shatsky et al. 1974), but there was

inadequate resolution to determine brain motion, or the duration of the observation

was limited. Accurate impact response was obtained by Hardy et al. (2001) in

conjunction with the use of a biplanar high-speed X-ray system developed by

Dr. Eric Radin and his team of researchers at the Bone and Joint Center of Henry

Ford Hospital in Detroit. See Chap. 2, Sect. 2.5.1 for a description of the system.

One of the first uses of the biplanar x-ray system was to determine brain motion

within the skull during a head impact. The procedure for testing was described in

Chap. 2 and will not be repeated here. Instead, the acquired data are analyzed in this

chapter. In the first series of tests, involving nine cadaver heads, neutral density

targets (NDT) were arranged in two columns to study brain motion in the sagittal

plane, as shown in Fig. 2.24. A right-handed Cartesian coordinate system was used

for all kinematic quantities. The positive x-axis ran posteroanteriorly, while the

positive z-axis was in the inferosuperior direction and the positive y-axis ran from

right to left. The origin was the presumed cg of the head.

The brain motion shown in Fig. 3.8 is for test C755-T3. It was a posterior impact

by a padded impactor that caused a peak head acceleration of 24 g (resultant) with

an associated peak resultant angular acceleration of 1995 rad/s 2 . The linear and

angular acceleration components are shown in Fig. 3.9. The dominant components

were the linear acceleration along the x-axis and the angular acceleration about the

y-axis. The x- and z-axis displacements of targets 1, 5, 7, and 12 are shown in

Fig. 3.10. These are the targets circled in Fig. 3.8. It is interesting to note that, at


Fig. 3.8 Brain motion data for a posterior impact causing a peak linear acceleration of 24 g and a

peak angular acceleration of 1995 rad/s 2 . The circled targets are selected for detailed study (taken


80

C755-T3 Linear

X

Y

Z

3000

C755-T3 Angular

X

Y

Z

Acceleration (g)

-80 -40 -20 0 20 40

15

30 45

60 75 90 105 120

0 0

Time (ms)

Acceleration (r/s/s)

-3000 -2000 -1000 0 1000 2000

15 30 45

Time (ms)

60 75 90 105 120

Fig. 3.9 Linear and angular acceleration components of the cadaver head in test C755-T3 (taken


10 ms after impact, the head had already experienced its peak linear acceleration,

but target motion was limited to about 1 mm. However, there were large target

displacements at 25 ms into the impact due to head rotation. The head angular

acceleration peaked at about the 17-ms mark. It can be concluded from these data

that linear acceleration does not cause much brain displacement and hence strain, if

at all, whereas angular acceleration is the principal cause of brain displacement and

Displacement (mm)

Displacement (mm)


10

5

C755-T3 Motion X

NDT-1

NDT-5

NDT-7

NDT-12

10

5

C755-T3 Motion Z

NDT-1

NDT-5

NDT-7

NDT-12

0

0

0 20 40 60 80 100 120 0 20 40 60 80 100 120

-5

-5

Fig. 3.10 The x- and z-displacements of the circled targets shown in Fig. 3.9. It is seen that linear

acceleration caused very little displacement, while angular acceleration is responsible for most of

the displacement (taken from Hardy et al. (2001))

Fig. 3.11 Brain motion is

due to the lag in brain

rotation relative to the skull

strain. That is, angular acceleration causes injury by straining the brain tissue, while

linear acceleration injures by a pressure mechanism, the reasons for which are still

unclear.

When we examine one of the circled targets for test C755-73, the impact caused

a clockwise rotation of the skull, as shown in Fig. 3.11, and we see that the targets

move in the counterclockwise direction at first. But when the skull rebounds, the

targets move in the opposite direction. Thus, the relative motion is due to the brain

lagging the skull as it rotates. The targets do not appear to return to their original

location because they went out of the field of view before that happened. However,

they do return to their origin locations because their pretest coordinates for each of

the repeated tests are always the same. The fact that the density of the targets was

close to that of brain enabled them to move with the brain and prevented them from

lacerating the brain.


3.2.2 Experiments on Diffuse Axonal Injury

Many experimental methods have been developed to study different kinds of brain

injury. These were summarized by Gennarelli (1994). Diffuse axonal injury (DAI)

is a common form of brain injury, and Gennarelli et al. (1982) demonstrated that

high angular acceleration could cause DAI in the brains of swine, even without a

direct impact to the skull. Since most head impacts involve both linear and angular

acceleration, it became necessary to find an animal model for DAI involving a

direct head impact to an intact skull. Marmarou et al. (1994) and Foda and

Marmarou (1994) developed a weight-drop method of impacting the crown of a

rodent to produce DAI in its brain. The setup is shown in Fig. 3.12. The animal was

placed at the bottom of a long (>2 m) Lucite guide tube through which a brass

weight (up to 450 g) was dropped to impact its head from a height of either 1 or 2 m.

The skull of the rat was prevented from being fractured by a small metal helmet that

was glued to the skull before impact. The rat was removed from the end of the tube

immediately after impact so as to avoid a second impact by the rebounding weight.

It was placed on a piece of soft foam, and its head underwent hyperflexion during

the impact. There was neuronal injury under the site of impact, and DAI was found

in the brain, mostly in the brain stem. The rat was concussed, but it is not clear if the

concussion was due to the stretching of the brain stem and cervical cord, brain

injury from the impact, or both. In any case, it is suspected that the DAI was due

mainly to the stretching of the brain stem and the upper cervical cord. This method

Fig. 3.12 The Marmarou

weight-drop device to

produce DAI in the brain of

a rodent (taken from

Marmarou et al. (1994)).

Reprinted from A.

Marmarou, M.A.A.-E.

Foda, W. Brink, J.

Campbell, H. Kita, K.

Demetriadou, A new model

of diffuse brain injury in

rats: Part I: pathophysiology

and biomechanics. J.

Neurosurg. 80, 291–300,

1994, with permission from

Rockwater, Inc. and Journal

of Neurosurgery Publishing

Group (JNSPG) and The

American Association of

Neurological Surgeons

(AANS)

Ring stand

with clamps

Plexiglas tubing

Inner diameter 19mm

Outer diameter 25mm

Brass weight made of

50 gram segments

diameter 18mm

Steel “helmet”

Foam

12 x 12 x 43cm

Plexiglas sides

Wood base

(2.5cm height)


of producing DAI in a rodent brain became immensely popular and was used by

many researchers to study a large variety of DAI-related brain injury issues.

3.2.3 Experiments on Focal Brain Injuries

Although focal brain injuries are not as common as diffuse injuries, they are

nevertheless an important component of brain injury that needs to be studied,

using experimental animals. Focal brain injuries are generally contusive injuries

to the brain caused by a local impact. It can be caused by skull in-bending or by an

object that has penetrated the skull. There are several ways to simulate a focal

injury. One of them is the dynamic cortical deformation (DCD) method shown in

Fig. 3.13. A craniotomy is performed, and the dura over the craniotomy is removed.

A short tube is fitted into the craniotomy for the purpose of generating a negative

pressure pulse that pulls a part of the brain through the craniotomy. Such an

experiment was conducted by Shreiber et al. (1997) to study the breakdown of

the blood-brain barrier (BBB). There was a finite element model of this experiment

in this paper, and it was validated against experimental data, as shown in Fig. 3.14

for the three sets of experiments conducted at 2, 3, and 4 psi negative pressure and

for durations of 25, 50, and 100 ms. Shreiber et al. (1997) found that BBB damage

was best correlated with logarithmic strain which is defined at the natural logarithm

of the ratio of the deformed length over the original length [ln(L/L 0 )].

A very common experiment to produce a focal injury is the controlled cortical

impact (CCI) method which was invented by Lighthall (1988) of General Motors

Research Labs. Lighthall, used a ferret model and, later on, Dixon et al. (1991) used

a rat model. It requires a craniotomy to be made in the skull and uses a probe with a

flat circular face of a given size (smaller than the craniotomy) that is made to impact

the dura at a specified speed and for a specified amount of penetration. The idea is to

create a localized injury and to measure the contusion volume as a function of the

characteristics of the probe. The most popular animal model is the rat which is

Fig. 3.13 The dynamic

cortical deformation

method of causing a focal

injury to the brain. A

negative pressure pulse is

applied through the tube,

and the brain is injured by

being sucked up the tube

(based on Shreiber et al.

(1997))

Cortical Displacement (mm)


O Mean experimental displacement

X Average computational displacement

3

Experimental Range

Experimental Standard Deviation

2.5

2

1.5

1

0.5

0

2 psi 3 psi 4 psi 2 psi 3 psi 4 psi 2 psi 3 psi 4 psi

25 msec 50 msec 100 msec

Fig. 3.14 Validation of a FE model of CCI developed by Schreiber et al. (1997) using data

produced by the same authors (taken from Shreiber et al. (1997))

Fig. 3.15 Test setup for a

controlled cortical impact

on a rat brain. A coronal

section of the brain is shown

with the impactor vertical

and normal to the brain

(courtesy of Dr. Haojie

Mao)

inexpensive, easy to handle, and repeatable. Figure 3.15 shows a test setup for a

vertical controlled cortical impact to a rat brain, and Fig. 3.16 is an example of an

oblique CCI conducted by Chen et al. (2003) who looked for contusion volume as

well as several pathological responses to the injury. They found both neuronal as

well as axonal injury in the area around the craniotomy. An experiment involving

bilateral craniotomies was first used by Meaney et al. (1994). The setup with an

additional contralateral craniotomy is shown in Fig. 3.17. The major difference in


Fig. 3.16 Controlled

cortical impact on a rat

brain with the 2.5 mm

impactor tip normal to the

brain but inclined at 22.5 to

the vertical. The velocity of

the impactor was 4 m/s and

the penetration was 2 mm.

Drawing based on Chen

et al. (2003)

Fig. 3.17 Setup for a

bilateral controlled cortical

impact in which the

contralateral craniotomy

allowed the brain the bulge

through it during impact.

Drawing based on Meaney

et al. (1994)

response was the creation of axonal injury in the underlying white matter beneath

the contralateral craniotomy. Biomechanically, there was less pressure on the brain

stem as the brain material was pushed out of the contralateral craniotomy. The

shape of the probe was modified by Igarashi et al. (2007). Instead of being a flat

surface, it was rounded in shape. The diameter of the impactor was 6 mm

(Fig. 3.18A), and the enlarged shape of the impactor is shown in Fig. 3.18B along

with the areas of injury below the craniotomy. They found injury to the cerebellum

of the rat in the form of loss of Purkinje cells in the cerebellar vermis.

3.3 Experimental Research on Human Head Tolerance

to Impact

Human tolerance to head impact is an important topic in injury biomechanics because

designers of equipment and vehicles interested in the safety of the user need to know

such limits, not only for the head but also for the rest of the body. So this is a wide

field of interest, and it will be addressed for each body region in this book.

The automotive industry was a major contributor to study of human tolerance

because of the frequency of crashes and the high fatality rates in the latter half of the

twentieth century. Recalling that tolerance among humans is highly variable and

3.3 Experimental Research on Human Head Tolerance to Impact 93

Fig. 3.18 A modified controlled cortical impact test using an impactor with a rounded tip (A). The

tip in (B) is enlarged to show its exact shape (Courtesy of one of the co-authors, LJN, of Igarashi

et al. (2007))

that such limits can only be reliably deduced from testing cadavers, the automotive

community assembled a set of data for the 50th percentile (middle-aged, mid-sized)

male for their design target. This may not be the best target, but younger cadaver

data were generally male due to a lower life expectancy and thus there were more

suitable male than female data. The tolerance values are known as Injury Assessment

Reference Values (IARV) and were first written up by Mertz (1984) ina

General Motors petition to NHTSA. These reference values were updated by Mertz

et al. (2003). The source for some of the IARVs is discussed under each body

region.

For the head, we have already discussed the origin of the Wayne State Tolerance

Curve (WSTC) and the derived injury criteria, such as the HIC or the GSI. These

are the accepted criteria used in the automotive industry (HIC) and in the sports

industry (GSI). They are acceleration-based criteria which are easily measured in

the head of a Hybrid III dummy and were developed based on cadaver and animal

data. The equations for HIC and GSI can be found in Chap. 2 (Eqs. 2.2 and 2.3). As

will be discussed in Chap. 6, the use of criteria related to brain strain is biomechanically

more desirable, but technology was not available to measure strain at the

time these criteria were developed. With the advent finite element modeling and the

development of sophisticated FE models in the beginning of this century, it became

possible to express tolerance as a function of strain. However, to comply with

current Federal Motor Vehicle Standard (FMVSS) 208 that is based on the Hybrid

III dummy, we are restricted to the use of acceleration-based injury criteria. It

should be mentioned that the HIC has been the standard for head injury since the

1970s and appears to be working quite well for automotive as well as

nonautomotive head impacts, such as in American football, as described in

Chap. 6. In a way, this is quite a surprise because the WSTC was drawn by a


student assistant working for Professor Lawrence Patrick of Wayne State University

in 1960. He was instructed to fit a hyperbola through a bunch of points on a

graph of average head acceleration on the ordinate (y-axis) and duration of impact

on the abscissa (x-axis). He was told to “eyeball” the best fitting curve he could

manage without the use of any statistical or other mathematical methods. The

original curve is shown in Fig. 2.33.

Many other head injury criteria were proposed by various researchers over the

years, and there were persistent calls to replace the HIC with a criterion that took

into account head angular acceleration. For some reason, this never happened, and

as of now, we do not have a standard for head angular acceleration although the

NHTSA is working on proposals for such a standard. If and when the FMVSS is no

longer based on the dummy but on FE models, then it will be possible to replace the

HIC with criteria related to brain strain. However, this change may take many years

to implement and is, as of now, a distant dream for those in favor of a more

biomechanically realistic criterion.

3.4 A Hypothesis for the Cause of Acute Subdural

Hematoma

The accepted injury mechanism for acute subdural hematoma (ASDH) is bridging

vein rupture. However, from an engineering point of view, the acute formation of a

hematoma from a ruptured vein violates the principles of fluid mechanics. The

mechanism proposed in this chapter is taken from King (2015) and is a hypothesis

with no data to support its veracity. The reader is asked to consider the logic of the

hypothesis and decide if it has more merit than the accepted mechanism.

The physiopathogenesis of ASDH formation has been a subject of debate since

the early thinking of an organized space between the arachnoid and dura. It was

detailed by Retzius and Key (1875), who described the structures of the meninges

and experimentally determined that substances injected into the presumed subdural

space did not mix with other substances within the tissue. Early researchers

believed that fluids within the alleged space could move between compartments

of the brain (Weed 1917). Thus, authors of this time period believed and offered

evidence that a fluid-filled space existed between the dura and arachnoid (Cushing

1914; Penfield 1923; Weed 1917, 1920, 1938). As Weed continued his studies, he

determined that the structures were fused together in embryos but could be separated

in mature animals (Weed 1938). These early investigators injected fluids into

the subdural area and visualized the distinctive compartmentalization of these

fluids. Microscopically, layers of unique cells between the dura and arachnoid

tissue were recognized, and these cells were thought to produce a fluid which

appeared to be present within the “space.” Leary (1939) concluded that the inner

dura was lined with fibroblasts and that the cells lining the outer arachnoid were

dissimilar. Thus, investigators began examining the dura and arachnoid as two

exclusively separate identities.

3.4 A Hypothesis for the Cause of Acute Subdural Hematoma 95

3.4.1 The Dura Mater

The dura mater appears to be a thick layer of fibroblasts and extracellular collagen

(Allen and Didio 1977). The cells look large and flattened and the collagen is

abundant and somewhat organized. Haines (1993) summarized the dura-arachnoid

organization. The dura is characterized as having an inner and outer portion. The

periosteal dura is adherent to the inner skull, and the meningeal layer of the dura

contains a specialized layer that Nabeshima et al. (1975) named the dural-border

cell layer. This layer appears to be continuous with the dural aspect of the arachnoid,

and the histological aspects of this dural-border cell layer have brought much

interest to researchers (Alcolado et al. 1988; Nabeshima et al. 1975; Rascol and

Izard 1976; Yamashima and Yamamoto 1984). This amorphous layer appears to

have flattened cell processes, varying sizes of extracellular spaces, and little

collagenous material. The amorphous structure possibly makes this an area of

weakness within the tissue. A cross section of the meninges and cell layers is

shown in Fig. 2.4. If an ASDH is to form, the bleed needs to occur in the border

cell layers.

3.4.2 The Arachnoids

The arachnoid portion of the meninges also consists of two distinct areas, the

arachnoid barrier cell layer, which is attached to the dural-border cell layer, and

the arachnoid trabeculae, which are closely attached to the pia mater. Both the cells

and the extracellular material are dissimilar as compared to the dura mater. The

cells are larger, more densely packed, having numerous mitochondria and filaments

within their cytoplasm making the layer distinctive (Alcolado et al. 1988;

Nabeshima et al. 1975; Schachenmayr and Friede 1979). This closely packed

structure of the arachnoid border cell layer excludes the presence of extracellular

space, making it distinctive from the attached dural-border cell layer. Existing

literature supports this idea. The description of the layers above has been verified

(Frederickson 1991; Friede and Schachenmayr 1978; Haines et al. 1993), and

testing has shown that the “space” is not preexisting. However, the junction

between the dural and arachnoid border cells would be an area of weakness in

cases of brain impact injury because the loosely organized dural-border cell layer is

attached to the more rigid arachnoid border cell layer. In fact, there is evidence that

the space is easily created by a mechanical separation (Orlin et al. 1991; Reina et al.

2002; Yamashima 2000). Since the biomechanical properties of the border cell

layers have not been investigated, the adhesive properties of the layers in radial

traction or in shear need to be quantified. These properties are crucial to the

understanding of the formation of ASDH because of the close association of the

bridging vein and cortical arteries with these layers. Only when this mechanism is


established will preventative and clinical strategies be able to be discovered and

tested. This will ultimately decrease morbidity and mortality rates associated with

these types of brain injuries.

On the other hand, neurosurgeons are often of the opinion that the dura is

attached to the skull and the arachnoid goes with the brain. Thus, even if there is

no space in the subdural layer in the young, an actual space maybe created in the

elderly should their brain shrink because not all of that space can be accommodated

in the CSF layer. Since this is still controversial, we need to consider the mechanism

of ASDH with no subdural space as well as in the presence of a subdural space

occupied by CSF.

3.4.3 Anatomy of Cortical Vessels

The cortical vessels consist of bridging veins and cortical arteries and veins. The

bridging veins traverse the dural-arachnoid complex. Their rupture has been traditionally

considered responsible for ASDH, and they have been studied extensively

by researchers (Andrews et al. 1989; Ehrlich et al. 2003). The number of veins and

their range of diameters have all been documented. Yamashima and Friede (1984)

provided a detailed description of the vessel wall as it traverses the dura-arachnoid

complex in a straight course with no tortuosity to allow for the possible

displacement of the brain. The cranial end is firmly attached to the rigid dura,

while the cerebral end is attached to the movable hemisphere. Leary (1939) found

that the thickness of the bridging vein walls varied remarkably in the subdural

portion, the thinnest part measuring 10 μm with a range of 10–600 μm. In the

subarachnoid portion, the walls have a more consistent thickness of 50–200 μm.

The collagen fibers in the subdural portion were loosely woven with a pattern that

was more resistant to distension while less resistant to traction. That is, bridging

veins are vulnerable to leakage in the subdural region. In fact, Yamashima and

Friede (1984) speculated that the bridging vein can rupture in the dura-arachnoid

complex due to a physiological increase in venous pressure or due to cardiac

resuscitation as well as due to a head impact. Trotter (1914) regarded the rupture

of the bridging vein as the cause of chronic subdural hematoma. However, another

bleed source is the cortical artery traversing the dura-arachnoid complex. Information

on the size, distribution, and number of cortical vessels is sparse. Cortical

arteries are found in the CSF layer. They run along the surface of the brain for a

short distance and penetrate the pia to enter the cerebral cortex. However, some of

the arteries running under the arachnoid can extend branches into the subdural

layer. There is even evidence of a cortical artery forming a kink (knuckle) in the

subdural space, as shown in Fig. 3.19 (Bongioanni et al. 1991). When the dura

separates from the arachnoid, the vessel wall of the knuckle is torn off, and bleeding

from this tear results in an ASDH.


Fig. 3.19 (A) Bridging cortical artery connected to the dura. (B) Adherence of cortical arterial

knuckle to dura and arachnoid (Bongioanni et al. 1991). Reprinted from F. Bongioanni, A.

Ramadan, A. Kostli, J. Berney, Acute subdural hematoma of arteriolar origin. Traumatic or

spontaneous? Neurochirurgie 37, 26–31, 1991, with permission from Elsevier

3.4.4 Acute Subdural Hematomas

Subdural hematoma (SDH) is a clinical condition due to a quickly clotting blood

collection amid the dura and arachnoid membrane. ASDHs are most frequently the

result of an acute head injury; however they can sometimes occur spontaneously in

the elderly. The mechanism behind the separation of the arachnoid from the dura

has yet to be determined. ASDHs usually transpire when the brain is subjected to a

high-energy, short-duration force from trauma. It is thought that this shearing force

will tear the bridging veins, and as a consequence, an ASDH will form. However,

epidemiological studies have shown that injuries other than bridging vein rupture

accounted for a significant portion of ASDH cases. Thus, the need to determine the

mechanism behind the injury is vital before any effective preventive and therapeutic

strategies can be attempted and implemented. Finding the pathogenic mechanism

through a more open-minded approach will lead to new innovative treatments

for this disabling condition.

3.4.5 Epidemiology

Traumatic ASDHs are among the most lethal of all head injuries, carrying the

highest risk to the patient, with a mortality rate of greater than 50 % in most studies.

ASDH kills or severely disables more head-injured patients than any other complication

of cranial trauma. The main pathological factor involved is ischemic


neuronal damage that results from cerebral vascular damage, raising the intracranial

pressure. ASDH was found in patients who were involved in motor vehicle crashes,

falls, and assaults (Wilberger et al. 1991). It is also found in boxers (Guterman and

Smith 1987). According to Gennarelli and Thibault (1982), ASDH is the most

important cause of death in severely head-injured patients due to high incidence

(30 %), high mortality (60 %), and head injury severity (2/3 with Glasgow Coma

scores of 3–5). They also found that the cause of ASDH by falls or assaults was

72 %, while that due to motor vehicle crashes was only 24 %. Maxeiner (1997)

attributed the source to bleeding in ASDH cases to extensive brain surface damage

(contusion) and ruptured superficial cerebral vessels, including bridging veins and

small arteries of the cortex. However, he also indicated in another publication

(Maxeiner et al. 1999) that rupture of the bridging veins did not lead to the

formation of ASDHs. In fact, Maxeiner and Wolff (2002) showed that there was

an equal probability of ASDH caused by bridging vein rupture and by cortical

artery rupture. Moreover, Shenkin (1982) reviewed 39 consecutive cases of ASDH

and found that there was a high incidence of cortical artery rupture (61.5 %). Bleeds

of venous origin constituted 25.6 % of the cases, and cerebral contusions were the

cause in 7.7 % of the cases. The elderly were found to be more susceptible to ASDH

(Howard et al. 1989; Maxeiner 1991). Since there can be brain shrinkage with age

resulting in stretching of the bridging veins, the high incidence among the elderly

can be explained by bridging vein rupture. However, the simple rupture of the

bridging vein should not lead to ASDH formation unless additional mechanical

factors are present, as explained below. Thus, clear mechanisms of ASDH formation

need to be formulated before we can claim to understand why there is a high

incidence of ASDH among the elderly. Karnath (2004) found that ASDH usually

occurs in younger adults, while chronic SDH usually occurs in older individuals

between 60 and 70 years of age. Finally, although the literature is silent in terms of a

detailed injury mechanism, there is an implication that ASDH occurs when there is

head contact with a rigid surface. However, in their experiments on subhuman

primates, Gennarelli and Thibault (1982) applied a pure angular acceleration to the

head without direct impact to cause ASDH in these animals. More than one injury

mechanism is in play in the formation of ASDH.

In terms of the locations of ASDH, not all ASDHs occur along the superior

sagittal sinus into which the bridging vein empties the venous blood. Obviously,

non-bridging vein related ASDHs are caused by bleeds from other sources, such as

cortical vessels and brain contusion or laceration (Tandon 2001). We will now

consider the mechanism of ASDH formation from cortical bleeds for reasons stated

in the section below.

3.4.6 Biomechanical Mechanisms for the Formation

of ASDH

Based on current thinking, ASDH can arise from one of three sources, the first being

the cortical arteries and veins. Laceration or rupture of these vessels can occur with


penetrating injuries. Secondly, closed head injuries resulting in large contusions can

cause similar bleeding into the adjacent subdural area. Thirdly and the most

common type of ASDH is thought to occur from tearing of the veins that bridge

the subdural area as they travel from the surface of the brain to the various dural

sinuses. This last mechanism assumes rupture of the bridging vein in the subdural

space since if it ruptured below the arachnoid, the result would be a subarachnoid

hematoma. Ultimate strain to failure of the bridging veins and possibly other tissue

components is inversely related to the strain rate (L€owenhielm 1974). Thus, the

threshold for injury decreases as the strain rate or acceleration is increased.

Gennarelli and Thibault (1982) opined that ASDH is due to the rupture bridging

veins during angular acceleration of the head associated with rapid onset rates (high

strain rate). They contend that nothing needs strike the head in order for ASDH to

occur. That is, although impact to the head is certainly the most common cause of

ASDH, it is the angular acceleration induced by the impact and not the head contact

that causes ASDH. Examples include violent non-cranial impacts of football

players and motorcycle riders. A rapid head movement is sufficient to exceed the

bridging vein tolerance. This group also demonstrated sensitivity of the ultimate

strain of bridging veins to strain rate and provided acceleration tolerance data for

subdural hematoma in primates (Gennarelli and Thibault 1982). Lee and Haut

(1989) reported the insensitivity of tensile failure properties of human cerebral

bridging veins to strain rate. However, data scattering drew concerns regarding this

finding. To confirm their data, this group performed similar experiments on the

carotid arteries and jugular veins of ferrets (Lee and Haut 1989). These vessels were

stretched longitudinally in vitro at either a low (0.2–2.0 s 1 ) or high rate (200 s 1 ).

The ultimate stretch ratios and loads were found to be independent of strain rate in

all the vessels tested. Therefore, the results appeared to support their previous

finding on human bridging veins. Maxeiner (1997) tested the hypothesis that

subdural hematomas are less frequent in acceleration injuries in traffic accidents

compared to falls or assaults. They reported that this hypothesis did not hold true in

the same way for bridging vein ruptures. Ruptures of these vessels without subdural

bleeding were only seldom mentioned in the literature. However, if no subdural

hematomas were present, no one would look for these structures. They predicted

that the frequency of bridging vein lesions in severe head injuries was likely

underestimated in the clinical as well as in the postmortem literature, hypothesizing

that a rapid increase of intracranial pressure after the accident produced a collapse

of the cerebral circulation which is probably responsible for the absence of the

subdural hematomas in the presented cases. Most recently, Monson et al. (2003)

examined the mechanical behavior of human cerebral blood vessels. This group

determined that cerebral arteries were noticeably stiffer than the cerebral veins.

Pang et al. (2001) studied the morphological properties of pig cerebral bridging

vein. They demonstrated that there is a narrow cuff at the junction of the cerebral

bridging veins and the superior sagittal sinus. This finding could play an important

role in maintaining intracranial pressure (ICP) and ASDH formation. Collectively,

all these reports implicate that failure of the bridging vein structure is associated

with a large number of subdural hematomas.


Fig. 3.20 ASDH formation due to bridging vein rupture is not possible in the subdural layer,

based on principles of fluid mechanics (taken from King (2015)). Reprinted from Accidental

Injury: Biomechanics and Prevention, 3rd edn., Introduction to and applications of injury biomechanics,

2015, pp.1–32, A. King, With permission of Springer

However, how the failure of bridging veins causes the venous blood to form an

ASDH is difficult to explain based on the principles of fluid mechanics. Since the

path to the sagittal sinus is still open and the creation of a subdural space constitutes

resistance to fluid flow, it is not clear how this can happen in the absence of other

mechanical factors. This principle is demonstrated in Fig. 3.20. We see that for the

blood to form a space, and thus an ASDH, in the border cell layer, it must overcome

the adhesive resistance between the dural and arachnoid border cells and enlarge

the space until it becomes symptomatic and visible on scans. On the other hand, the

flow of venous blood into the superior sagittal sinus is the path of least resistance

because there is no need to push apart solid boundaries (cell layers) and the

formation of an ASDH in the subdural layer by venous blood would violate this

very basic principle of fluid mechanics, namely, flow will proceed in the direction

of least resistance.

If we consider the possible preexistence of a subdural space filled with CSF, then a

rupture of the bridging vein in the subdural space will allow the blood to enter this

space. However, it is not likely that this flow is strong enough to progress into an

ASDH because the ICP in the CSF is essentially the same as the pressure in the veins.

To summarize findings to date, ASDH is found in victims of falls, assaults, and

motor vehicle crashes who sustain a direct impact to the head against a rigid

surface. The head undergoes both linear and angular acceleration. However,

Gennarelli and Thibault (1982) have demonstrated the formation of ASDH with

extremely high pure angular acceleration in subhuman primates and found ruptured


bridging veins in these animals. Similarly, Depreitere et al. (2006) used a reverse

injection method to demonstrate the feasibility of ASDH formation after a direct

impact that resulted in high angular accelerations. They may have indeed created

the observed SDH by reverse injection which is unnatural and not representative of

a venous overpressure. Nevertheless, the circumstantial evidence of associating

bridging vein rupture with ASDH is extremely strong. However, as mentioned

above, why would the normal flow of blood into the superior sagittal sinus be

diverted into the subdural space to form an ASDH against a much higher resistance

or against the ICP in the CSF? It violates the basic principle of fluid flow in that the

flow will go in the direction of least resistance. We can hypothesize a series of

mechanisms that can explain the observed phenomenon and provide a logical

explanation for the formation of ASDH. However, before we list the various

hypotheses, it is necessary to reiterate the assumption that the bridging vein rupture

we are concerned with needs to occur in the dural-arachnoid complex because if it

occurred below the arachnoid, a subarachnoid hematoma (SAH) would be the

result. It is also necessary to reiterate the finding that the dural and arachnoid

border cells can be easily separated although the amount of force needed to achieve

this separation has never been measured. It is also interesting to note that a

subarachnoid hematoma will form in the CSF space, but a SDH will not form in

the subdural space from a ruptured bridging vein. The explanation is rather simple.

A torn bridging vein below the arachnoid should open the CSF to the sagittal

superior sinus, and there will be leakage of CSF into the sinus. As a result, venous

blood from the torn bridging vein will fill the CSF space to maintain the volume of

the CSF layer. Thus, a subarachnoid hematoma can easily form when the bridging

vein is ruptured below the arachnoid.

Hypothesis I Almost all ASDHs from non-penetrating impacts are due to the

rupture of cortical arteries in the dural-arachnoid complex, not including the

bridging veins.

We postulate that border cell layers need to either separate radially or deform in

shear to a sufficient extent to tear these cortical vessels and that the tearing of the

cortical arteries will generate enough pressure in the subdural layer to cause the

separation to progress, resulting in an ASDH. If this hypothesis can be validated, it

can provide a logical explanation for the formation of ASDH.

Hypothesis II Radial separation of the border cell layers can occur when there is

skull in-bending and skull rebound due to a direct impact.

Not all direct impacts produce high angular accelerations, but they are more

likely to cause skull deformation in the form of in-bending and subsequent rebound.

This in-bending can cause delamination of the border cell layer sandwiched

between two layers with dissimilar material properties, and the rebound applies

tension to the dura to cause separation of the border cells and rupture of the cortical

vessels within the dural-arachnoid complex. Large deformations can occur in the

temporal area of the adult skull as well as in the skulls of children. This mechanism

can also explain the formation of ASDH at sites remote from the site of impact

because the skull is a closed container which will increase in diameter in one


direction when the orthogonal diameter is decreased by impact. This hypothesis can

be tested using an animal model as well as a computer model.

Hypothesis III Shearing deformation of the border cell layer can rupture the

cortical vessels when the head is subjected to high levels of angular acceleration

Results of the brain motion mapping study reported by Hardy et al. (2001) reveal

that most of the relative motion of the brain with respect to the skull occurs near the

center of the brain, above the brain stem. Relative motion of the brain surface is

small, but it is not nonexistent under angular accelerations below 10,000 rad/s 2 .Itis

conceivable that under very high angular accelerations, the border cell layers will

undergo shear deformation that is large enough to rupture the cortical vessels. We

also postulate that the relative motion does not occur in the cerebral spinal fluid

(CSF) layer because the trabeculae in the CSF layer have a higher shear resistance

as compared to the border cells. A study to measure the shear resistance of the

pia-arachnoid junction was completed by Jin et al. (2011). This hypothesis can

again be tested using either an animal model or a computer model.

Hypothesis IV Even though the bridging vein in the border cell layer may be

ruptured, it does not result in the formation of ASDH.

The prevailing understanding of ASDH formation due to bridging vein rupture is

inconsistent with all known principles of fluid mechanics. Yet, bridging vein

rupture was found in patients with ASDH, in cadaveric subjects and animal subjects.

This hypothesis can be tested by rupturing the bridging vein of an animal in

the border cell layer with no head impact to demonstrate that the rupture will not

cause an ASDH to form and progress. The reverse injection method used by

Depreitere et al. (2006) forces the contrast medium out of the ruptured vessel into

the border cell layer which can then be easily separated. There is no reversal of flow

of this type in vivo unless there is a large increase in venous pressure. It is also

necessary to test the amount of pressure needed to reverse the flow and cause an

ASDH to form. However, for an ASDH to progress, a sustained venous over

pressure is needed for a period of several hours, which is physiologically unlikely

to occur. If the hypothesis is valid, the inevitable conclusion is that many of the

observed bridging vein ruptures were due to the autopsy or surgical procedure used

to identify the ASDH or that there is cortical bleeding associated with the observed

rupture that was not detected. In addition, SDH associated with a pure bridging vein

rupture will likely result in a chronic SDH, from occasional increases in venous

pressure, such as in a Valsalva maneuver.

The reader is encouraged to do research in this area to confirm these hypotheses

or to prove them wrong.


3.5 Concluding Remarks

It is certainly not possible to summarize all of the experimental research that has

been done on head injury. Worldwide interest in this virtually “incurable” injury

has resulted in an overwhelming number of publications on this subject. And, more

questions are being raised than researchers can find answers for them. For example,

the issue of mTBI due to blast overpressure calls for an explanation as to how a

pressure wave passing through the brain can injure the brain. These questions point

to the need for basic research at the cellular level where we may be able to find

answers.


3.1. Select the statement that is NOT valid, as it relates to brain injury:

[ ] (i) The dura and arachnoid are separated by two layers of border cells

[ ] (ii) Rupture of the bridging vein in the border cell region is not a prime

cause of subdural hematomas

[ ] (iii) It is valid to model the space between the dura and arachnoid as a

Newtonian fluid

[ ] (iv) The space between the pia and the arachnoid contains cerebral spinal

fluid

[ ] (v) The radial adhesion (normal traction resistance) between the dura and

arachnoid border is low

3.2. For a direct blunt impact to the head, the initial pressure relative to ambient

atmospheric pressure developed at the contrecoup site is:

[ ] (i) Always negative

[ ] (ii) Always positive

[ ] (iii) Always below the vapor pressure of water

[ ] (iv) Always above 50 kPa



atmospheric pressure developed at the coup site is:



[ ] (iii) Always below the pressure of one atmosphere




3.4. Brain injury resulting from blunt impact can take the form of:

[ ] (i) Diffuse axonal injury

[ ] (ii) Contusion of the brain surface

[ ] (iii) Laceration of the brain

[ ] (iv) Injury to the corpus callosum


3.5. Brain injury due to a blunt impact can take the form of:

[ ] (i) Intracerebral hemorrhage

[ ] (ii) Subdural hematoma

[ ] (iii) Subarachnoid hematoma

[ ] (iv) Injury to the brain stem



atmospheric pressure developed at the coup site is:



[ ] (iii) Always less than the pressure in the corpus callosum



3.7. For a direct blunt impact to the head with both linear and angular acceleration,

large brain motions occur

[ ] (i) On the surface of the hemispheres

[ ] (ii) In the cerebellum

[ ] (iii) Near the center of the brain above the brain stem

[ ] (iv) Near the sagittal sinus


3.8. The motion of the brain resulting from a blunt impact takes the form of:

[ ] (i) Horizontal (transverse plane) motion

[ ] (ii) Sagittal plane motion

[ ] (iii) A Figure 8 pattern

[ ] (iv) (i) and (ii)


3.9. The mechanism of brain injury due to linear acceleration is due to

[ ] (i) The high strain rate it causes in the brain

[ ] (ii) The high strain it causes in the brain

[ ] (iii) The high pressure developed in the cerebellum

[ ] (iv) An as yet unknown mechanism



3.10. The mechanism of brain injury due to a blast pressure wave is due to

[ ] (i) The high strain rate it causes in the brain

[ ] (ii) The high strain it causes in the brain

[ ] (iii) The shear stresses developed in the cerebellum

[ ] (iv) An as yet unknown mechanism


3.11. The mechanism of brain injury due to a blast pressure wave can be

prevented by

[ ] (i) The use of a standard army helmet

[ ] (ii) Turning away from the blast

[ ] (iii) By wearing body armor that protects the chest and abdomen

[ ] (iv) Facing the blast


3.12. The neutral density accelerometer used in some of the tests on cadaveric

heads

[ ] (i) Has a single axis of sensitivity

[ ] (ii) Is over 5 mm in size in its smallest dimension

[ ] (iii) Can measure angular and linear acceleration simultaneously

[ ] (iv) Is a tri-axial accelerometer

[ ] (v) Can be purchased commercially from an instrumentation company

3.13. Select the statement that is invalid, as it relates to brain injury:

[ ] (i) To generate high shear strains in the brain, it is necessary to subject

the head to angular accelerations

[ ] (ii) Mild traumatic brain injury cannot occur unless the victim was

unconscious for a short time

[ ] (iii) A head impact resulting in a linear acceleration of about 100 g and a

rotational acceleration of about 6000 rad/s 2 can cause a mild traumatic

brain injury

[ ] (iv) Subdural hematoma is due solely to bridging vein ruptures


3.14. Finite element models of the head, simulating blunt impact can assume a rigid

skull. One of the drawbacks is:

[ ] (i) It cannot be used to simulate head impacts involving direct head

contact with a rigid object

[ ] (ii) It cannot be used to simulate indirect head impacts involving large

rotational accelerations

[ ] (iii) It may not predict brain motion accurately for non-contact head

impacts

[ ] (iv) It cannot be used to simulate a helmeted head impact

[ ] (v) (i), (iii), and (iv)


3.15. Neutral density accelerometers described by Hardy et al. (1997)

[ ] (i) Are 5 mm in diameter

[ ] (ii) Are 3-mm cubes

[ ] (iii) Are uniaxial sensors

[ ] (iv) Are sold by more than one commercial accelerometer manufacturers

[ ] (v) Tend to lacerate the brain if the impact is too severe

3.16. Select the statement that is not valid, as it relates to brain injury:

[ ] (i) Diffuse axonal injury (DAI) occurs right after head impact

[ ] (ii) Brain motion within an intact human skull during an impact is more

sensitive to angular acceleration than to linear acceleration

[ ] (iii) DAI can only occur in the white matter of the central nervous system

(CNS)


[ ] (v) If HIC is under 1000, there can still be brain injury

3.17. The dynamic cortical deformation method of studying brain injury:

[ ] (i) Is aimed at studying diffuse injury of the neurons

[ ] (ii) Applies a positive pressure pulse to the brain through a hole in the

skull

[ ] (iii) Does not cause contusion to the brain

[ ] (iv) Causes massive brain hemorrhage


3.18. The controlled cortical impact method of studying brain injury:

[ ] (i) Was invented by researchers at Wayne State University

[ ] (ii) Cannot be used on rats

[ ] (iii) Uses a negative pressure pulse to injure the brain

[ ] (iv) Uses a positive pressure pulse to injure the brain


3.19. The following statements refer to blunt impact to the head. Which one is

correct?

[ ] (i) High-speed X-ray data on brain motion are not available from

cadavers

[ ] (ii) High-speed X-ray data on brain motion are available from living

animals

[ ] (iii) High-speed X-ray data on brain motion are available from living

human subjects

[ ] (iv) High-speed X-ray data on brain motion are now available in the

literature

[ ] (v) High speed X-ray data on brain motion can only be acquired at

50 frames/s or slower

References 107

3.20. It was shown by Lissner and Gurdjian in 1960 that pressure pulses without

head acceleration can cause cerebral concussion. This conclusion was arrived

at based on

[ ] (i) Head impacts on dogs using a hammer

[ ] (ii) Application of negative pressure pulses to the brain surface through a

hole in the skull

[ ] (iii) Application of positive pressure pulses to the brain surface through a

hole in the skull

[ ] (iv) Impact to the brain with a metal impactor through a hole in the skull



Prob

Ans

1 (iii)

2 (i)

3 (ii)

4 (v)

5 (v)

6 (ii)

7 (iii)

8 (iii)

9 (iv)

10 (iv)

11 (v)

12 (iv)

13 (iv)

14 (v)

15 (ii)

16 (iv)

17 (v)

18 (v)

19 (iv)

20 (iii)

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Chapter 4

Head Injury Research: Computer Models

of Head Impact

The purpose of modeling head impact is to try to understand the effect of a blow to

the brain. Thus, it is essential that the brain be modeled in as much detail as

possible. Then, of course, it will be necessary to assess injury to the brain by

computing its response. Based on what we know about brain injury, we hypothesize

that strain in the axons is a likely cause of diffuse axonal injury (DAI) and

intracranial pressure wave propagation can be a second parameter of interest.

Because of the complexity of the geometry of the head and brain, the many

different types of tissues involved, and the lack of data on their material properties

under high strain rate conditions, the modeling task is far from beingsimple.In

the pre-finite element era, simplifying assumptions were made to facilitate the

formulation of equations that describe the impact event. For example, the first

known model of head impact was proposed by Anzelius (1943) who assumed the

head to be a rigid sphere and the brain to be a liquid. He solved the governing

equations in closed form, and his model predicted coup and contrecoup pressures

at the site of impact and at a site diametrically opposite to the site of impact,

respectively.

4.1 Pre-finite Element Models of Head Impact

In the 1960s a major effort was launched by the National Institutes of Health (NIH)

to study head injury. Professor Werner Goldsmith of the University of California,

Berkeley, authored a book entitled Impact and was an expert in the mechanics of

impact. Although he did not have a biomechanical background, he was selected to

lead a biomechanical survey of head injury research in the USA. He was instrumental

in galvanizing the biomechanics community to intensify head injury

research. One of his proposals was the formulation of models of blunt head impact

as part of the effort to understand injury mechanisms. Research proposals to

develop these models were solicited and funding was made available by the NIH.



111

112 4 Head Injury Research: Computer Models of Head Impact

As a result of this stimulus, approximately 25 non-finite element models were

published in the archival literature. A summary of these models can be found in

King and Chou (1976).

Cylinders were used to model head impact in one dimension, and spheres and

ellipsoids were used for three-dimensional models, most of which were loaded

axisymmetrically. These geometries were selected to facilitate the formulation of

equations that describe the interaction of skull deformation with the dynamic response

of the brain. There were no models that had the actual geometry of the skull and brain.

The skull was simulated by an elastic shell, an elastic membrane, or a rigid shell.

There was at least one model with a three-layered skull (Khalil et al. 1974). The brain

was modeled as a viscoelastic solid, an elastic solid, or an incompressible fluid. Finer

features, such as the ventricles and the meninges, were not modeled.

Despite the simplifying assumptions that had to be made to formulate head

impact models, the equations involved were still quite complex. For a threedimensional

model, there were three independent space coordinates and one

independent time coordinate. To describe the change in shape of the skull and

the motion of the brain, partial differential equations were formulated. The shell

equations for the skull were linked by boundary conditions to the continuum

equations describing the brain, and the entire set of equations was generally

solved numerically to predict skull and brain responses, such as stresses and

strains in the skull and brain as a function of time or intracranial pressure if the

brain was a fluid.

The models could be divided into two broad categories. There were direct

impact models which received an impact to the skull, and there were indirect

impact models which sustained an acceleration without head contact with a surface,

in which case the skull could be assumed to be rigid. In each category, there were

models that underwent pure translation or pure rotation. There were no continuum

models that simulated both translation and rotation in the same impact. The only

models that simulated both translation and rotation were discrete parameter models

consisting of mass-spring-dashpot systems.

It is not known why an attempt was not made to validate the models against

available data, such as the pressure data produced Gurdjian et al. (1954). Perhaps, in

the late 1960s and early 1970s, such data were already considered to be archaic and

inaccurate. Alternately, the predictions of some of the models were quite unrealistic

and not comparable to experimental data. A case in point is the model by Engin

(1969) which predicted very high intracranial pressures. Kenner and Goldsmith

(1973) created a physical model to provide validation data. They made an aluminum

spherical shell which was filled with water and instrumented with quartz

crystal pressure sensors that were suspended in the water. It was impacted by a

metal ball and the pressure wave traveling through the sphere was measured. The

results were compared against a brain model consisting of a thin shell containing an

incompressible fluid by Kenner and Goldsmith (1972). Model and experimental

results were comparable.

The analytical approach has obvious limitations in being able to solve the

general head injury modeling problem. It called for the derivation of complex

4.2 Finite Element Models of the Brain 113

partial differential equations and the use of theoretical or numerical techniques to

solve those equations. The geometry of the head was necessarily restricted to a

shape that can be described by simple equations, such as a sphere or an ellipsoid.

While the last of these models were appearing in print, the finite element method

became available in terms of software programs that relieved the modeler of the

chores of solving complex differential equations. This form of modeling is

discussed in the next section.

4.2 Finite Element Models of the Brain

The first finite element (FE) model of the skull was developed by Hardy and Marcal

(1971). It was a 3-D static model simulating the actual skull geometry but it did not

contain a brain within. The model was exercised for frontal and lateral loading. The

first head and brain FE model was proposed by Shugar and Katona (1975). It

simulated the actual human anatomy and assumed an elastic skull and brain. The

skull was layered. Ward and Thompson (1975) formulated a detailed 3-D FE model

of the head and brain, but the skull was rigid. Khalil and Hubbard (1977) formulated

a multilayered spherical skull and brain model. It was a parametric study that

determined the effect of the spatial distribution and duration of loading on the

skull. It was found that spatial distribution of the load strongly influenced skull

strain. In an attempt to correlate primate injuries to human tolerance, Ward et al.

(1980) formulated models for the human and the nonhuman primate. Results show

that an intracranial pressure that can cause a moderate brain injury was about

172 kPa (25 psi) and a pressure of 234 kPa (34 psi) would result in a severe injury

in animal brains. Using these pressure levels, the Ward model predicted head

accelerations that would cause these injuries. When the accelerations were compared

with the WSTC, the Ward model predicted higher accelerations than the

WSTC for the same level of injury. The next advance in modeling was provided by

Hosey and Liu (1982) who developed a comprehensive brain injury model similar

in concept to the current versions. However, it was too complex for the computing

power available at that time and it was run only once up to 10 ms.

4.2.1 Brain Model by Ruan et al. (1994)

There was almost a decade of hiatus in head modeling research in the 1980s. The

next effort was initiated by Ruan et al. (1991) who developed a 2-D plane strain FE

model to study the effect of the meninges on intracranial pressure. It was found that

the meninges affected the frequency response of the brain and its spatial pressure

distribution. Ruan et al. (1994) went on to develop a 3-D model of a 50th percentile

male head with a mass of 5.06 kg. It had 7205 nodes and 9149 elements which

modeled the scalp, skull, dura, CSF, cerebral hemispheres, cerebellum, falx, and


tentorium. The brain was represented by a single viscoelastic material, while the

other tissues were considered as linearly elastic. The material properties used for

this model are shown in Table 4.1. A midsagittal section of the model is shown in

Fig. 4.1. To validate the model, the only brain response data available at the time

were intracranial pressure in cadaveric brains, published by Nahum et al. (1977).

The model was set up to simulate the pendulum impacts carried out by Nahum et al.

(1977), but the impact angle of the pendulum to the forehead was incorrectly

simulated. A horizontal impact was simulated while, in the actual experiment, the

impact was directed at 45 to the horizontal from above the head. Nevertheless, the

predicted results compared favorably with experimental data. Figure 4.2 is a

comparison of the contact force, and Figs. 4.3 and 4.4 are comparisons of coup

and contrecoup pressures, respectively. It was then used to perform a parametric

study in which the mass and velocity of the pendulum were changed for frontal

impact. The pendulum mass and velocity were decreased by 25 % and 50 %, as

shown on the left half of Fig. 4.5. The responses are more sensitive to pendulum

velocity than to mass. Additionally, the responses were computed for horizontal

impacts to the rear (the occiput), the left and right side, and the crown of the head,

Table 4.1 Material properties of head tissue used in the Ruan et al. (1994) model of head impact

Tissue Bulk modulus (kPa) Shear modulus (Pa) Density (kg/m 3 ) Poisson’s ratio

Outer table 7.3E + 09 5.0E + 09 3.00E + 03 0.22

Diploe 3.4E + 09 2.32E + 09 1.75E + 03 0.22

Inner table 7.3E + 09 5.0E + 09 3.00E + 03 0.22

CSF 2.19E + 07 5.0E + 05 1.04E + 03 0.489

Brain 2.19E + 07 1.68E + 06 1.04E + 03 0.4996

Scalp

Falx cerebri

Transverse sinus

Facial bone

Inner table

Dipole

Outer table

Z

Cerebral spinal fluid

X

Neck bone

Y

Fig. 4.1 Finite element model of the head by Ruan (1994)



pendulum impact force

(taken from Ruan et al.

(1993))

0.0

Contact Force (kN)

-2.0

-4.0

-6.0

Model

Test

-8.0

0.0 2.0 4.0 6.0 8.0

Time (ms)

10.0 12.0 14.0


coup pressure (taken from

Ruan et al. (1993))

160.0

Coup Pressure (kPa)

40.0 80.0 120.0

Model

Test

0.0

0.0 2.0 4.0 6.0 8.0

Time (ms)

10.0 12.0 14.0



contrecoup pressure (taken

from Ruan et al. (1993))

20.0

Contrecoup Pressure (kPa)

-60.0 -40.0 -20.0 0.0

Model

Test

0.0 2.0 4.0 6.0 8.0

Time (ms)

10.0 12.0 14.0

Fig. 4.5 A parametric study using the model by Ruan et al. (1994). The left half shows changes in

response when pendulum mass and velocity are decreased by 25 and 50 %. The effects of impact

direction are shown on the right (taken from Ruan (1994))


using the baseline pendulum mass and velocity. It is seen from the right half of

Fig. 4.5 that an occipital impact elicited the largest contrecoup pressure, while a

crown impact resulted in a low level of response.

4.2.2 Brain Model by Zhou et al. (1995)

The next improvement was made by Zhou et al. (1995) who decreased the element

size and quadrupled the number of elements. The model continued to represent a

50th percentile adult male head with a mass of 5.06 kg. The white and gray matter

of the brain were assigned different material properties because it was noted that

model could not accurately predict locations of DAI with a single material representation

of the brain. The brain was modeled as a viscoelastic material and the

shear modulus, G(t), is given by

Gt ðÞ¼G 1 þ ðG 0 G 1 Þe βt ð4:1Þ

where G 1 is the long-term modulus, G 0 is the instantaneous modulus, and β is the

decay constant.

The values for the long-term and instantaneous modulus were based in part on

Ruan et al. (1994). This is the first model with an inhomogeneous brain and is

shown in Fig. 4.6. The shear modulus of the white matter was assumed to be 60 %

SKULL

SCALP

FALX

CSP

BRIDGING

VEINS

PIA

GRAY

MATTER

WHITE

MATTER

VENTRICLES

FACIAL BONE

Fig. 4.6 Inhomogeneous brain model by Zhou (1995). The gray and white matter have different

shear moduli based on their microstructure (taken from Zhou et al. (1995))


Fig. 4.7 Comparison of predicted head-pendulum contact force with data provided by Nahum

et al. (1977) (taken from Zhou et al. (1995))

higher than that of the gray matter, based on its microstructure. Axons are more

fibrous than the homogeneous nature of neurons. This model was validated against

the intracranial pressure data in Nahum et al. (1977). These were the only human

(albeit cadaveric) data available at the time the work was done. The contact force

comparison is shown in Fig. 4.7 and that for the coup and contrecoup pressures is

shown in Fig. 4.8. The inhomogeneity assumption yielded higher shear stresses

than those in the homogeneous model, especially at the junction of the brain and the

ventricles where DAI was seen to occur in the porcine brain.

4.2.3 Brain Model by Al-Bsharat et al. (1999)

Improvements were made to the Zhou et al. (1995) model by Al-Bsharat et al.

(1999). They include an improved mesh, a three-layered skull, modified shear

modulus for the white matter, and a new sliding interface at the brain-dura junction.

The model is shown in Fig. 4.9 which shows a three-layered skull. The material

properties used for this model were similar to those used by Zhou et al. (1995)


Fig. 4.8 Comparison of predicted coup and contrecoup pressures with data provided by Nahum

et al. (1977) (taken from Zhou et al. (1995))

except that the shear modulus of the white matter was assumed to be only 20 %

higher than that of the gray matter, based on the work of Shuck and Advani (1972).

As for the modeling of the subdural space, Ruan et al. (1994) as well as Turquier

et al. (1996) simulated the CSF layer with a low shear modulus solid, and Mendis

(1992) ignored it completely. Miller et al. (1998) assumed that there was a frictional

interface between the skull and brain. To ignore the CSF appears to be

non-anatomical, and the use of a frictional interface does not allow a continuous

deformation of the brain with respect to the skull. Thus, an acceptable modification

made by Al-Bsharat et al. (1999) was to introduce a sliding interface between the

low shear modulus CSF layer and the dura, allowing the brain to move more freely

than just using a low shear modulus layer. The model was validated against

intracranial data from several runs performed by Nahum et al. (1977) as well as

against newly obtained brain motion data which were formally published by Hardy

et al. (2001) at a later date.

Nahum et al. (1977) conducted a total of seven frontal impacts during which

intracranial pressure was measured at the coup and contrecoup sites. The tests were

run at different pendulum impact speeds and used pendulums of different masses.

Pressures obtained in two of the seven tests appeared to be outliers in that they were


Fig. 4.9 The brain model by Al-Bsharat et al. (1999) is an improved version of that by Zhou et al.

(1995). It has a three-layered skull and a sliding interface between the CSF layer and the dura

(taken from Al-Bsharat et al. (1999))

inconsistent with the data from the other five. However, the data were provided in

tabular form, and data from only one test was provided as plots of contact force or

intracranial pressure as a function of time. There was good correlation between

model results and experimental data for contact force for the one test in which

graphical data were available. This is shown in Fig. 4.10. It was also possible to

compare peak contact forces between model and experiment. Kinetic energy of

impact was used to make the comparison to include the effects of both mass and

velocity of the pendulum. Figure 4.11 shows the comparison. Predicted and measured

coup and contrecoup pressures for all five runs are shown in Figs. 4.12 and

4.13, respectively.

Unpublished data on brain motion relative to the skull were used to further

validate the model. The data were from four occipital impacts to cadaveric heads

which were later published by Hardy et al. (2001). The mass of the impactor used

was 11.7 kg and the impactor velocities were 2.3, 2.7, and 3.6 m/s. Just as in the

Ruan model, the contact force was calculated and compared against the measured

force. Brain motion was also calculated and compared with the high-speed X-ray

data. Table 4.2 compares the calculated contact force with the measured data for

three occipital impacts. The error was within 12 %. As for the relative


Force (kN)

8

CONTACT FORCE

Experiment

Model

7

6

5

4

3

2

1

0 0 1 2 3 4 5

Time (ms)

6 7 8 9 10

Fig. 4.10 Validation of the Al-Bsharat model—comparison of contact force for a single run


Fig. 4.11 Validation of the Al-Bsharat model—comparison of contact force for all five runs



Fig. 4.12 Validation of the Al-Bsharat model—comparison of coup pressure for all five runs


Fig. 4.13 Validation of the Al-Bsharat model—comparison of contrecoup pressure for all five

runs (taken from Al-Bsharat et al. (1999))

displacements of the brain with respect to the skull, the video data acquired at that

time was at 250 frames per second (fps) instead of 1000 fps, a speed that was

achieved later. Thus, the experimental displacement curve is a series of straight


Table 4.2 Comparison of computed and measured contact loads for three occipital head impacts


Test

Test and model

speed (ms) Test load (N) Model load (N)

C731-T2 2.3 1080 950 12

C731-T3 2.7 1380 1240 10

C731-T4 3.6 1800 1990 +11

Load

differences (%)

Fig. 4.14 Validation of the Al-Bsharat model—comparison of skull-brain relative displacement

for Test No. C731-T3 (taken from Al-Bsharat et al. (1999))

lines joining points that are 4 ms apart. The validation of the model in terms of

relative displacement is shown in Figs. 4.14, 4.15, and 4.16. In Fig. 4.14, the video

data are in phase with model predictions, while in the other two figures (Figs. 4.15

and 4.16), the amplitude match is acceptable, but there is a 4 ms phase difference

due to the difficulty with synchronization of the coarse data to the model results and

it is easy to skip a frame in the analysis. We conclude that the modeling of a sliding

interface produced reasonable relative motions between the skull and the brain as

well as realistic intracranial pressures.







4.2.4 Brain Model by Zhang et al. (2001): The Wayne State

University Brain Injury Model (WSUBIM)

Zhang et al. (2001) totally revised the Al-Bsharat model by decreasing the mesh

size and improving mesh quality. The motivation was to improve the stability of the

model and enable it to run under severe impact conditions with large angular

acceleration. The skull-brain sliding interface was maintained, and a new facial

model was added, including teeth. In previous versions, the face was represented by

a surface with no detailed anatomical or structural features of facial bones. The

geometry of the 14 facial bones was taken from MRI and CT scans, and anatomical

features included the mandible, zygoma, maxilla, nasal bones, nasal cartilage, and

facial soft tissue. The final model was made up of 278,100 elements for the cranium

and 36,400 elements for the face, for a total of 314,500 elements. Its total mass was

4.5 kg. The model is shown in Fig. 4.17. The characteristic length of elements was

less than 2 mm, enabling the model to have a high-quality mesh and to simulate the

anatomical features more accurately and in greater detail. The CSF layer was

modeled as solid elements with the bulk modulus of water and with a very low

shear modulus to represent the trabeculae in the CSF. The inhomogeneous nature of

the brain was maintained with the white matter assumed to be 25 % stiffer than the

gray matter. Additionally, based on Arbogast and Margulies (1997), the moduli for

the brain stem were assumed to be 80 % higher than those of gray matter. The

values used in the model are shown in Table 4.3. The facial bones were modeled as

Fig. 4.17 The Wayne State

University Brain Injury

Model (WSUBIM)

developed by Zhang et al.

(2001) (taken from Zhang

et al. (2001))


Table 4.3 Material

properties of gray and white

matter used in the WSUBIM

(Zhang et al. 2001)

Brain tissue G o (kPa) G 1 (kPa) Decay (1/s)

Gray matter 10 2 80

White matter 12.5 2.5 80

Brainstem 22.5 4.5 80

Fig. 4.18 Definition of

elasto-plastic characteristics

of facial bone, including

fracture behavior. The

failure strain is denoted by

ε f (courtesy of Dr. Liying

Zhang)

an elastoplastic material capable of simulating fracture at a specified failure strain.

For cortical bone, the failure strain was assumed to be 1.6 % (Giesen and Van

Eijden 2000) and that for cancellous bone was assumed to be 4.5 % (Yamada and

Evans 1970). The stress-strain curve is shown in Fig. 4.18.

The WSUBIM was validated against five data sets:

• Intracranial pressure data

• Intracranial and ventricular pressure data

• Brain motion data

• Nasal impact data

• Midface impact data

Validation against intracranial pressure data of Nahum et al. (1977) isshownin

Table 4.4. It is seen that six tests are listed in the table. This is one more than the

number of tests used for validating the model by Al-Bsharat, and the extra run

included in this validation effort is Case No. 43. For this run, the discrepancy in

pressure for the parietal and posterior regions is very large, due to experimental error.

The intracranial and ventricular pressure data used for validation were obtained

by Trosseille et al. (1992) who performed frontal head impact tests on cadavers with

a 23.4 kg impactor at 7 m/s and measured pressure in the frontal and occipital areas

of the brain as well as in the lateral of the third ventricle. The comparison between

model results and test data is shown in Fig. 4.19. Model predictions were the

average of several elements taken from two locations in the region described in

the experiments because the precise location of the pressure sensors in the brain was


Table 4.4 Validation against intracranial pressure data of Nahum et al. (1977) in the WSUBIM by

Zhang et al. (2001)

Intracranial pressure (KPa)

Case no. Test/model Force (kN) Front Parietal Posterior fossae

36 Test 7.8 136 79 64

Model 7.6 145 70 57

% Difference 2% 7% 9% 12 %

37 Test 7.9 141 74 60

Model 8.0 154 72 62

% Difference 1 % 9 % 2.8 % 3 %

38 Test 10.8 139 66 65

Model 9.3 146 68 58

% Difference 14 % 5 % 3 % 10 %

43 Test 10.6 270 222 18

Model 10.0 276 132 77

% Difference 6% 2% 68 % 328 %

44 Test 6.5 101 20 3

Model 5.9 95 36 1

% Difference 10 % 6 % 44 % 20 %

54 Test 10.8 274 180 64

Model 9.8 268 130 76

% Difference 10 % 2% 38 % 18 %

TROSSEILLE ET AL. 1992

Pressure (kPa)

100

80

60

40

20

-40

Frontal Pressure

Location 1

Location 2

Test

0

0

-20

5 10 15 20 25

Pressure (kPa)

50

40

30

20

10

Lateral Ventricle

Test

Location 1

Location 2

0

0

-10

5 10 15 20 25

-60

Time (ms)

-20

Time (ms)

Pressure (kPa)

15

10

5

0

-10

-15

Occipital Pressure

Test

Location 1

Location 2

0 5 10 15 20 25

-5

Pressure (kPa)

40

30

20

10

Location 1

Location 2

Test

Third Ventricle

0

0 5 10 15 20

-10

-20

Time (ms)

-20

Time (ms)

Fig. 4.19 Validation of the WSUBIM against intracranial and ventricular pressure (taken from

Zhang et al. (2001))


HARDY ET AL. 2001

MODEL RESULTS

10

C577-T2: Experiment

10

C755-T2: Model Prediction

X (mm)

X (mm)

0

0

-20 -10 0 10 20 30 40 50 -20 -10 0 10 20 30 40 50

-10

-10

-20

-30

-40

-50

Z (mm)

-20

-30

-40

-50

Z (mm)

Fig. 4.20 Validation of the WSUBIM against brain motion data (based on Zhang et al. (2001))

unknown. The experimentally determined pressure did not return to zero as it

should, but the initial peaks appeared to match quite well with model results.

Brain motion data were taken from Hardy et al. (2001). Figure 4.20 shows the

experimental data on the left and the model predictions on the right. The model

predicted a curvilinear motion of the targets, but the excursions were not as large as

those obtained experimentally, and none of them was in the shape of a figure eight.

Also, the direction of motion of the fourth target from the top is opposite to that

observed experimentally on both sides of the midsagittal line.

Nasal impact data from Nyquist et al. (1986) were used to validate the facial

model. There were six experimental force deflections for nasal impact. Out of the

six, there were three curves that were reasonably similar. Using the known head

accelerations for these impacts and the shape of the impactor, model predictions of

force and deflection were computed. The validation results are shown in Fig. 4.21

where the solid curves are the simulated results and the dotted curves are the test

data. The match is quite good.

Maxillary impact results are compared in Fig. 4.22. The experimental data were

from several cadaver tests conducted at the same impact speed, using a cylindrical

impactor (Allsop et al. 1988). The bone was fractured in every case and fracture was

predicted by the model as well. The correlation between model and experiment is

good.

The stability of the model was also tested to ensure that it will perform properly

under severe impact conditions. It was run with progressively increasing levels of

angular and linear acceleration. It was found to be stable for an input consisting of a

peak linear acceleration of 200 g and a peak angular acceleration of 12,000 rad/s 2 .

The hourglass energy to internal energy ratio was less than 10 % for the sinusoidal

inputs shown in Fig. 4.23.


Fig. 4.21 Validation of the

WSUBIM against nasal

impact data (taken from

Nyquist et al. (1986)). T

stands for test data and S for

simulation or model

prediction (taken from

Zhang et al. (2001))

Fig. 4.22 Validation of the WSUBIM against maxillary impact data taken from Allsop et al.

(1988) (taken from Zhang et al. (2001))

4.2.5 Other Finite Element Models of Brain Injury

There are many other finite element brain injury models in the archival literature

developed by researchers around the world. It is not possible to mention them all,

and it would be difficult to assess them without having personally used them.

However, it is worth mentioning that the US automotive industry, with participation

by the federal government, is developing a total human body model, including a


Fig. 4.23 Hourglass energy to internal energy ratio computed for a linear acceleration input of

200 g and an angular acceleration input of 12,000 rad/s 2 , demonstrating stability of the model

under severe impact conditions (taken from Zhang et al. (2001))

brain injury model, for the use in automotive safety design. A group of universities

is developing models for various body regions, under sponsorship of the Global

Human Body Consortium (GHBC) and under the leadership of Dr. Joel Stitzel of

Wake Forest University. Wayne State University is the lead organization for the

development of the brain injury model. It is hoped that, after the global model

becomes functional, the entire US automotive industry will use the model for

vehicle design in much the same way the Hybrid III dummy is being used currently

for this purpose.

4.3 Computer Models of Animal Brains

Many animal experiments were done in an attempt to understand the mechanism of

brain injury due to impact, as described in Chap. 3. The value of developing animal

brain impact models is the ability to extend the experimental results by being able to

compute responses throughout the brain and to perform virtual experiments on

animals to examine brain responses in cases that were not tested experimentally

either due to cost or time limitations. Verification of a model assumption can be

another reason. First, we will look at a 2-D model of a swine brain to verify the

assumption that Zhou et al. (1995) made in developing the inhomogeneous brain

model, that of assigning different values for the shear modulus to the gray and white

matter of the brain. Since DAI was difficult to detect in a living brain before the turn

4.3 Computer Models of Animal Brains 131

of the century, it became necessary to model an animal brain for which DAI data

were available The swine brain was chosen because many experiments were

performed by the group at the University of Pennsylvania to study the effect of

high angular acceleration on swine brain. Dr. David Meaney of the University of

Pennsylvania agreed to supply the DAI data so that we could justify the inhomogeneity

assumption for the brain. In a preliminary study, Zhou et al. (1994)

developed a 3-D model of a swine brain and found that if the white matter had a

higher shear modulus than that of gray matter, regions of high shear strain would

match more closely with regions where experimentally observed DAI would occur.

If the brain was homogeneous, the match was poor. To verify that a model with an

inhomogeneous brain would be able to predict the locations of DAI better than one

with a homogeneous brain, 2-D coronal brain models of the swine were developed

for a detailed comparison of regions of high shear with regions of DAI seen in the

swine. This would be much less time-consuming than studying a full-blown 3-D

model.

4.3.1 Two-Dimensional Swine Model

with an Inhomogeneous Brain

As mentioned in Chap. 3, the experiments consisted of accelerating the swine head

in axial rotation (in the coronal plane) at a high rate and then decelerating it at an

even higher rate to produce DAI in swine brain. There was no translational

acceleration input. A painfully tedious histological process was needed to count

the number of broken axons, in the form of retractions balls or swollen axons per

unit area for large areas of the brain white matter. These DAI data can then be

compared to the predicted strains in a 2-D model of the swine brain subjected to the

same level of angular acceleration as in the experiment. If there was a qualitative

match of strain with DAI data, then the assumption of an inhomogeneous brain was

justified.

The three 2-D models formulated by Zhou et al. (1994) were for three coronal

sections of the porcine brain. These sections are shown in Fig. 4.24A–C and are

similar to the sections published by Ross et al. (1994) which showed areas of DAI.

Section or Model I is located at the septal nuclei and anterior commissure level,

while Model II is a section taken from the rostral-thalamic level, and Model III is a

section through the caudal hippocampus. The approximate locations in the brain are

shown in Fig. 4.25. Each model has a three-layered skull, dura, CSF, pia, and gray

and white matter. The number of nodes, solid elements, and membrane elements for

each model and for the gray and white matter is shown in Table 4.5. The material

properties shown in Table 4.6 were based on the human data used by Ruan et al.

(1991) as experimental data for porcine brain were not available. White matter was

assumed to have a shear modulus 60 % higher than that of gray matter based solely

based on the fact that a stiffer white matter yielded high shear regions qualitatively


Fig. 4.24 (A–C) The three

2-D models by Zhou et al.

(1994) which were the first

models to feature an

inhomogeneous brain.

When white matter was

assumed to be 60 % stiffer

than gray matter to achieve

better correspondence of

strain with observed DAI

(taken from Zhou et al.

(1994))


Fig. 4.25 Approximate

locations of the three 2-D

models by Zhou et al.

(1994) (taken from Zhou

et al. (1994))

Table 4.5 Statistics for the 2-D porcine models (based on Zhou (1995))

Solid Element Membrane Elements

Model Nodes Total Skull

White

matter

Gray

matter CSF Ventricles Total Dura Pia

I 1052 490 132 148 152 46 12 108 44 64

II 1468 644 156 190 202 54 42 130 52 78

III 1228 544 134 162 188 46 14 104 46 58

Table 4.6 Material properties of head tissue used in the 2-D porcine model by Zhou et al. (1994)

Poisson’s

Tissue Density (kg/m 3 ) Bulk modulus (Pa) Shear modulus (Pa) ratio

Cortical 3.0E + 03 7.3E + 09 5.0E + 09 0.22

bone

Spongy 1.75E + 03 3.4E + 09 2.32E + 09 0.22

bone

Meninges 1.13E + 03 1.087E + 07 0.45

CSF 1.0E + 03 (1.04E + 03) 2.19E + 09 (2.19E + 07) 5.0E + 02 (5.0E + 04) 0.49999

Gray 1.04E + 03 2.19E + 08 1.68E + 05 0.4996

matter

White 1.04E + 03 4.39E + 08 (2.19E + 08) 2.68E + 05 (1.68E 0.4996

matter

+ 05)

Note: Values in parentheses were used in the human model (Ruan et al. 1991)

closer to where DAI was found in the swine brain. The modulus for CSF was also

assumed to be different from that used in the human model. These selected material

properties provided a qualitative match with experimental data for Model I. They

were unchanged for Models II and III. A rotational impulse was applied to the

model through the outer table of the skull which was assumed to be rigid. The


50000

Angular Acceleration (rad/s^2)

30000

10000

–10000

–30000

–50000

–70000

–90000

280

240

0. 4. 8. 12. 16. 20.

Time (ms)

Angular Velocity (rad/s)

200

160

120

80

40

0

0. 4. 8. 12. 16. 20.

Time (ms)

Fig. 4.26 Kinematic input for the 2-D model by Zhou et al. (1994) (taken from Zhou et al. (1994))

rotation was about the cg of the head. The input was a prescribed angular velocity

pulse obtained by integrating the measured angular acceleration. Both the angular

acceleration and velocity time traces are shown in Fig. 4.26. The head was accelerated

to a peak angular acceleration of 58,610 rad/s 2 in about 8 ms, and the peak

deceleration of 104,070 rad/s 2 was reached at 14 ms. The maximum angular

displacement was about 105 . The impact duration was 23 ms and the pulse

shape was comparable to that used by Abel et al. (1978).

For these three models, plane strain conditions were used to constrain the

displacement in the coronal plane, and the PAMCRASH finite element code was


used to perform the simulation. This is a commercial, large displacement, explicit,

Lagrangian, dynamic finite element code commonly used in crashworthiness analysis.

The following results were reported:

Model I: The maximum strains attained in this model are shown in Fig. 4.27A.

Many regions with strains in excess of 4 % corresponded to regions in which

Ross et al. (1994) found DAI. The correspondence was not perfect as there were

two areas of high strain where no DAI was found.

Model II: Correspondence of strain with DAI is also seen in this model, but the level

of shear strain was higher, varying from 10 to 27.6 %. There was one region of

high strain (24 %) that was close to where DAI was found, as shown in

Fig. 4.27B. The gray matter was predicted to sustain strain levels of 21 and 30 %.

Model III: In this model, DAI was found in areas of high strain (8.7–24.9 %) in the

white matter, as shown in Fig. 4.27C. High strains were also predicted for the

gray matter but neuronal injury was not studied histologically.

Meaney et al. (1993) suggested that a shear strain of 10 % would correspond to a

mild DAI, while 15 % would be a moderate DAI. Thus, in Model I, the DAI was

mild, while in Models II and III, the DAI would be moderate. We conclude from

this study that gray and white matter of the brain should be characterized by

materials with different shear moduli.

4.3.2 Models of Focal Brain Injuries

In Chap. 3, two focal traumatic brain injury (TBI) experiments were discussed.

They are the dynamic cortical deformation (DCD) and the controlled cortical

impact (CCI) models. Most of the experiments were conducted using rodents that

sustained axonal and cellular injuries, vascular damage, and blood-brain barrier

breakdown. CCI testing was almost as popular as the Marmarou model in terms of

journal publications. To model the DCD and CCI experiments, a detailed finite

element model of the rat brain is needed. Such a model was developed by Mao et al.

(2006) and is shown in Fig. 4.28. The anatomy or geometry of the rat brain was

taken from Paxinos and Watson (2005) which can be accessed at http://www.

apuche.org/OIA/Anatomical-Page¼03.htm. The purpose of modeling was to

develop validated models of DCD and CCI so that we can model variations of

these experiments as well as look at the overall response (strain) of the brain.

4.3.2.1 FE Simulation of the DCD Test

As described in Chap. 3, a DCD test was described. The procedure was to make a

5 mm diameter hole in the crown of the skull of a rat. The dura was excised but the

pia-arachnoid complex was left intact. A vacuum (negative pressure) pulse was

applied directly to the brain. The extent of cortical (brain) displacement was


Fig. 4.27 (A–C) Results of the three 2-D simulations by Zhou et al. (1994). The shear strain

magnitudes are shown along with darkened areas of observed DAI in porcine experiments (taken

from Zhou et al. (1994))


Fig. 4.28 Finite element model of a rat brain (taken from Mao (2009))

2.5

Cortical Displacement (mm)

2

1.5

1

0.5

0

2psi 3psi 4psi

2psi 3psi 4psi

2psi 3psi 4psi

25ms

50ms

100ms

Fig. 4.29 Validation of the rat model by Mao et al. (2006) using data from a DCD experiment

performed by Shreiber et al. (1997). The solid circles are the model predictions, and the histograms

represent the experimentally measured means and standard deviations (taken from Mao et al.

(2006))

measured during the test for different levels of applied negative pressure (for

details, see (Shreiber et al. 1997)). Figure 4.29 shows the results of tests at three

pressure levels and at three instants of time after pressure application. The circular

data points represent model predictions for each pressure level. It can be seen that

model results all fall within the spread of the experimental data. Validation of the

DCD model gives us confidence to proceed with the modeling of the CCI experiment

which can only be validated by comparing the measured contusion volume

with that predicted by the model. In a CCI test, a craniotomy is performed so that it

is larger in diameter than the impactor(s) to be used. The dura is left intact, and the

impactor tip can be driven into brain dynamically to a predetermined depth at a


Fig. 4.30 The six different CCI experiments simulated by Mao et al. (2006) (taken from Mao

et al. (2006))

predetermined velocity. It can be held in contact with the brain for a variable

duration before being retracted. The contact duration generally varies from 25 to

250 ms. The location of the craniotomy can be varied and so can the angle of the

impactor. It is also possible to do multiple craniotomies to study the effect of brain

extrusion in the open craniotomy and to produce DAI in the white matter near the

open craniotomy.

Mao et al. (2006) simulated six different CCI experiments. They are shown in

Figure. 4.30. Series 1–4 are unilateral craniotomies and Series 5 and 6 are bilateral

craniotomies. Since brain material was assumed to be almost incompressible but

with low shear resistance, it could be easily distorted, causing numerical instability.

For the six series of CCI simulations, the amount of hourglass energy required to

stabilize the model was monitored at the time maximal tissue deformation or tissue

strain. The ratio of hourglass energy to total energy was found to be between 23 and

35 % which is higher than the normally accepted ratio of 10 %. A more detailed

study of brain tissue deformation was carried out to visualize the deformation of the

tissue at the time high hourglass to total energy ratio. For elements that experienced

the most severe principal strains, the elements maintained a reasonable aspect ratio,

warpage angle, and Jacobian, and the simulations remained stable with no excessive

mesh distortion. Thus, the simulation results were considered valid. One of the

reasons for model stability is the use of a fine and high-quality mesh when the

model was constructed.

The rat model was qualitatively validated in the CCI experiments by comparing

the volume of brain tissue contused by the impact. In the model, it was necessary to

define a strain threshold for contusion. It was found that a strain threshold of 30 %

best predicted contusive brain injury in the four series of unilateral CCI tests,

because it resulted in the smallest residual variance and a significant correlation

with experimentally determined contusion volumes, as shown in Fig. 4.31. A more

rigorous validation is described below.

The CCI experiment using a modified impactor tip and performed by Igarashi

et al. (2007) was modeled by Mao et al. (2010), using the same rodent model by


Experimental value (mm 3 )

80

Threshold: 0.30

70 r: 0.818, p: 0.047

60

50

40

30

20

10

0

0 10 20 30 40 50 60 70 80

FE predicted contusion(mm 3 )

Series 1_Test A

Series 1_Test B

Series 2

Series 3_Test A

Series 3_Test B

Series 4

Fig. 4.31 Correlation of model predicted brain contusion volume with that measured experimentally,

using a first principal strain of 30 % as the contusion threshold. The residual variance was

10 mm 3 . The 45-deg line represents a perfect correlation, while the error bars represent 1

standard deviation from the experimentally determined mean contusion volume for each test

series (taken from Mao et al. (2006))

Impactor tip

7-mm Diameter

Craniotomy

Rat head

6-mm Diameter

Impactor tip

Fig. 4.32 Modeling the Igarashi et al. (2007) experiments using the model by Mao et al. (2006)

(taken from Mao (2009))

Mao et al. (2006). The brain model and the impactor used are shown in Fig. 4.32 to

simulate experiments with impact depths of 1.5, 2.0, and 2.7 mm, representing

mild, moderate, and severe injury, respectively. The impactor was meshed with

care to duplicate exactly the shape of the tip used in the experiments. Additionally,

four sets of parametric studies were carried out to determine the effect of changing

the impactor size, decay constants for brain tissue, material properties of white

matter, and impactor velocities. The study focused for the most part on the

moderate injuries produced in the rodent—a 7 mm diameter craniotomy, a 2 mm

impact depth, and a 4 m/s impactor velocity. Maximum principal strains were

computed for five regions of the rat brain, namely, the superficial and deep cortex,

the hippocampus (CA2/CA3), the lateral thalamus, and the cerebellar vermis. More

severe injuries were simulated using impactor velocities of 6 and 8 m/s.


Maximum principal strain

0.6

0.4

0.2

Moderate injury

0.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time (msec)

SC

DC

Hipp

Thala

CBV

Fig. 4.33 Computed maximum principal strains in the superficial cortex (SC), deep cortex (DC),

hippocampus (Hipp), lateral thalamus (Thala), and cerebellar vermin (CBV) for a moderate injury

(taken from Mao (2009))

100%

80%

60%

y = 1.992x – 0.028

R 2 = 0.602

Thala

SC

DC

Mild

Moderate

Severe

40%

Hipp

20%

CB

0%

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 4.34 Correlation of computed maximum principal strain with observed neuronal loss, for

mild, moderate, and severe injury, in the five regions of the brain monitored by the model. The

error bars are for 1 standard deviation of the observed neuronal loss (see the caption for Fig. 4.33

above for an explanation of the symbols) (taken from Mao (2009))

In terms of results of the simulation of the Igarashi et al. (2007) experiments, the

maximum principal strains in the 5 regions monitored by the models are shown in

Fig. 4.33 for the moderate injury case. The strain in the deep cortex is just over 40 %

and is higher than that in the superficial cortex. The reason for this is unclear. When

the maximum principal strain is compared to neuronal loss, it can be seen from

Fig. 4.34 that they are linearly related, with a correlation coefficient of 0.602 and a

slope that is significantly different from zero. Results of the parametric study

revealed that brain size was not a significant factor affecting the maximum principal

strain because the difference in strain was less than 0.025. The decay constant was

varied from a baseline value of 20 ms to 8 s, but the difference in computed

maximum principal strain did not exceed 2 % for all five regions of the brain.

Changing the shear modulus of white matter from 70 % to 125 % of the baseline


value revealed that the computed strains were higher in the cortex and hippocampus

for a stiffer white matter. The authors concluded that FE rat brain model predicted

strains that correlated with in vivo findings of neuronal loss.

Modeling of Blood Vessels in the Brain

As shown in Fig. 2.7, the cerebral vasculature is very dense and what is shown are

just the arteries. The veins double the density, and it is quite obvious that adding the

vasculature to a brain model would increase its complexity severalfold. In fact, the

inclusion of blood vessels in a brain model calls for the insertion of a tubular

structure with a modulus several times stiffer than that of brain into a soft brain

material. And this is not a simple task requiring large amounts of computing power.

However, the development of a 2-D model was found to be feasible. Zhang et al.

(2002) formulated such a model with arteries and compared its response to a 2-D

model with no arteries. These two models are shown in Fig. 4.35A, B. The intent in

Model II was to simulate the major arteries in the brain, for a parasagittal section

near the midsagittal plane. Figure 4.36 shows the branches of the anterior, middle,

and posterior cerebral arteries that are large enough to be modeled. The reason why

it is possible to simulate an arterial tree in a 2-D model is the fact that certain

elements can be assigned material properties of arteries without having to introduce

another structure. That is, by assigning some of the brain elements in Model I

properties of arteries, the major branches of the cerebral arteries can be simulated.

Of course, the simulated arteries do not contain blood but are solid elements with a

characteristic width of 1.5 mm. This size does not represent all arteries some of

which are as large as 3.74 mm (Monson et al. 2000).

Model I has a total of 4501 elements with a mass of 41.07 g. Model II also has

4501 elements but 287 of these were used to represent arteries, as shown in

Fig. 4.35B. The plane strain condition was imposed on the models to ensure that

motion of the brain was restricted in the sagittal plane. In terms of material

A

B

Skull

(Tables & Dipole)

Cerebrum

Corpus

Callosum

Cerebral

spinal fluid

Cerebellum

Bridging

Veins

Ventricle

Brainstem

Major

Cerebral

Vessels

Model I without blood vessels

Model II with blood vessels

Fig. 4.35 Two-dimensional parasagittal models of the brain, (A) without blood vessels and (B)

with blood vessels (taken from Zhang et al. (2002))


Fig. 4.36 Large arteries

in a parasagittal section

of the human brain

near the midsagittal

plane (Zhang et al. (2002))

5

Stress (MPa)

4

3

2

1

E = 15 MPa

0

1.0 1.1 1.2

Stretch

1.3

Fig. 4.37 A typical stress-stretch curve for cerebral arteries. The modulus used in the model is

15 MPa. It is for stretch beyond the physiological range but less than that at failure (based on

Fig. 6 of Monson et al. (2000))

properties for the head and brain tissues in the model, the skull was assumed to be

elastic, and the brain was viscoelastic with properties identical to those used by

Zhang et al. (2001) in both Models I and II. The shear moduli values used were

higher than the data reported by Arbogast and Margulies (1997) who tested brain

slices in shear between two plates. Those values were too low for use in finite

element models because they would cause numerical instability and the justification

for increasing the shear moduli was that the tethering effect of the blood vessels was

lost when they were tested in vitro. Thus, one of the purposes of the model was to

determine if the presence of blood vessels would allow for the use of a lower value

of the instantaneous value of the shear modulus (G o ). The material properties of the

cerebral arteries were taken from Monson et al. (2000) who tested human cortical

arteries dynamically and obtained the typical stress-stretch curve of soft tissue, as

shown in Fig. 4.37. However, because the model only permitted the use of linearly

elastic elements for the vessels, a single value for its modulus had to be selected.



experimental intracranial

pressure data from Nahum

et al. (1977) with pressures

predicted by Models I and II

(taken from Zhang et al.

(2002))

Pressure (kPa)

150

100

50

Intracranial Pressure Validation

Frontal-Experimental

Frontal-w/o Vessel

Frontal-w. Vessel

Occipital-Experimental

Occipital-w/o Vessel

Occipital-w. Vessel

0

0 2 4 6 8 10

–50

–100 Time (ms)

In an impact, the vessel is expected to encounter strains above those experienced

under normal physiological conditions (<10 MPa), but less than those close to

failure (21 MPa), the selected modulus was 15 MPa. A stiffness of 0.219 N/mm was

selected for bridging veins.

Model validation was performed by comparing the predicted intracranial pressures

and brain motion relative to the skull for both models. The intracranial

pressure data used were taken from Nahum et al. (1977), while the brain motion

data were taken from Hardy et al. (2001). To compare intracranial pressures, the

input energy for the model was scaled down based on its mass (0.041 kg vs. 4.5 kg),

assuming the same impactor velocity. The results are shown in Fig. 4.38 which

compares the coup and contrecoup responses of both models to the experimental

data. Pressure magnitudes matched reasonably well. The contrecoup peak pressures

were delayed 2–3 ms compared to the measured data. Ten locations in the model

were identified as those of the targets used in the experiments by Hardy et al.

(2001), for Test C755-T2. They were not in the same locations because the actual

targets were about 30 mm lateral of the midsagittal plane, while the model section

was about 4 mm lateral to the midsagittal plane. Both models predicted figure eight

patterns of motion for the targets with a range of 3 mm for Model I and a range of

2 mm for Model II. The range of motion measured experimentally did not exceed

5 mm. These results are shown in Fig. 4.39. While the comparisons made were

not for the motion of targets in the actual sagittal planes, there is qualitative

validation of the two models.

Model II was used to study the relationship between the presence of blood

vessels and the effect of lowering the shear modulus. In this parametric study, the

shear modulus was reduced to 5 kPa (Case 5K w.V) and then to 1 kPa (Case 1K w.

V). The experimentally reported value was about 0.5 kPa. The baseline case was

Model I with a shear modulus of 10 kPa (Case 10K w/o.V). A rotational input with a

peak velocity of 25 rad/s was used. However, for Case 1K w.V, a negative volume

problem was encountered, and this case was run with a peak velocity of 10 rad/s.

The maximum principal strains computed for the three simulations are shown in

Fig. 4.40. It is seen that in Case 5K w.V, the strains are lower compared to the


Fig. 4.39 Comparison of relative brain motion between data from Hardy et al. (2001) and that

predicted by Models I and II (taken from Zhang et al. (2002))

4.4 Concluding Remarks 145

Max. Principal Strain

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

Parametric Study - Rotational Impact

10K w/o. V 5K w. V 1K w. V

Region A Region B Region C Region D Region E Region F

Fig. 4.40 Parametric study of Model II in which G o was varied. For G o ¼ 5 kPa, the strains are

lower, implying that blood vessels enhance brain stiffness. For G o ¼ 1 kPa and for a 40 % lower

rotational input, the strains were comparable to those with G o ¼ 5 kPa, implying that the use of low

values of G o may require a brain model with a very fine vascular structure. The brain regions are

shown in the figure below the bar charts (taken from Zhang et al. (2002))

baseline case (Case 10K w/o.V) even though the modulus had been halved. These

results imply that blood vessels increase the structural properties of the brain. The

strains in Case 1K w.V were close to or even higher than those predicted by Case

5K w.V, even though the input was only 40 % of that used in the other two cases.

We conclude from this modeling effort that blood vessels enhance the stiffness of

the brain and that without the simulation of the fine vascular structures in the brain,

direct use of the very low in vitro properties of the brain will yield unrealistically

high strains.


There is no question that the use of the FE methods is the obvious way to model

head impact. The complex geometry of the skull and brain can be simulated, and

different material properties can be assigned to the many tissues that constitute the

head. The input can be a direct impact force or an acceleration with or without

direct contact of the head with an impactor. The results of the simulation could be

improved by decreasing the mesh size and increasing the quality of the mesh. The

WSUBIM is a well validated model that has a fine enough mesh to accurately

predict brain responses in comparison with experimental data. In addition, the

model can provide the response of the entire brain and predict intracranial pressure,

displacement, and strain in the brain at any site of interest. Model stability is also an

important factor. It must be able to yield accurate results under severe input

conditions, especially if the angular acceleration is very high (over 10,000 rad/s 2 ).


It is virtually impossible to cover all of the FE models of the brain that have

appeared in the archival literature, and the ones discussed in this chapter are

familiar to the author. More importantly, they have all been subjected to some

form of validation against experimental data. For a model to be useful as a predictor

of injury, it must have been subjected to a validation process, and it is the author’s

considered opinion that no journal should publish models that have not been

validated.

Since 1943 when Anzelius published the first brain injury model, we have come

a long way in being able to simulate brain response to impact. With ever-increasing

computational speeds becoming available, the use of finite element models in

vehicular safety design is not only feasible but also desirable because modeling is

a much less costly alternative to either laboratory or proving grounds testing.

Presently, the worldwide automotive industry is using the Hybrid III dummy as

its surrogate for safety testing, yielding test results that are comparable from vehicle

to vehicle. To switch over to computer modeling to achieve the same aims raises a

host of different problems. The first is the multiplicity of FE models that already

exist or can be developed by anyone with knowledge of FE methods and a

computer. Hopefully, the GHBC and similar consortia around the world can unify

the community to use the same models just like the Hybrid III is being used now.

Secondly, the use of different FE codes can produce disparate results and some way

of controlling their use needs to be agreed to and implemented.


4.1. Before the finite element method was available, modeling of blunt head

impact was

[ ] (i) Done by assuming the whole head to be an elastic solid

[ ] (ii) Achieved by assuming that the brain was an incompressible fluid only

[ ] (iii) Accomplished without the aid of numerical methods

[ ] (iv) Described by partial differential equations representing an axisymmetric

elastic shell containing various materials representing the head

[ ] (v) Not possible due to the complexity of the anatomy of the head

4.2. Finite element models of the head, simulating blunt impact can assume a rigid

skull. One of the drawbacks is:

[ ] (i) It cannot be used to simulate indirect head impacts involving large

rotational accelerations

[ ] (ii) It cannot be used to simulate direct head impacts involving large

translational accelerations

[ ] (iii) It may not predict intracranial pressures accurately for direct head

impacts

[ ] (iv) (i) and (ii)



4.3. The principal difference between the model developed by Ruan et al. (1993)

and Zhou et al. (1994) is

[ ] (i) The lack of ventricles in the Ruan model

[ ] (ii) That the Ruan model has a rigid skull

[ ] (iii) That the Ruan model does not distinguish the material properties of

gray and white matter

[ ] (iv) That the Ruan model has more elements than the Zhou model


4.4. The latest version of the WSUBIM is Version 2001. Its features include:

[ ] (i) Detailed modeling of the brain, meninges, CSF, scalp, skull, and facial

features

[ ] (ii) The brain is allowed to slide relative to the CSF

[ ] (iii) The shear modulus of the white matter is higher than that of the gray

matter

[ ] (iv) There are over 314,000 elements


4.5. The WSUBIM Version 2001 is

[ ] (i) A totally revamped version of the WSUBIM Version II

[ ] (ii) Has many more nodes and elements than all previous versions

[ ] (iii) Has a model of the facial bones

[ ] (iv) (i) and (iii)

[ ] (v) (i), (ii), and (iii)

4.6. The WSUBIM Version 2001 has been validated against both intracranial

pressure data and brain motion data

[ ] (i) The motion data were obtained from living human subject

[ ] (ii) The pressure data were obtained at Ford Hospital

[ ] (iii) The motion data were obtained at Ford Hospital

[ ] (iv) The pressure data were obtained from living human subjects

[ ] (v) The pressure data were obtained from pigs tested at the University of

Pennsylvania

4.7. There are many blood vessels in the brain. Select the statement that is

incorrect

[ ] (i) These blood vessels can provide the brain with mechanical strength

[ ] (ii) The bridging veins can rupture due to high angular acceleration,

causing a subdural hematoma

[ ] (iii) The blood vessels consist of veins and arteries but no capillaries

[ ] (iv) The blood vessels can have a significant influence on the stress

distribution in the brain during an impact

[ ] (v) The bridging veins drain into the sagittal sinus which is formed by the

two layers of the dura


4.8. The use of different material properties for gray and white matter of the brain

in the finite element models developed at Wayne State University was based

on:

[ ] (i) Test data from human cadaver impacts

[ ] (ii) Test data from living human subjects who volunteered to be impacted

[ ] (iii) Test data from living porcine (pig) subjects undergoing high linear

accelerations

[ ] (iv) Test data from living porcine (pig) subjects undergoing high angular

accelerations

[ ] (v) Test data from living subhuman primates subjected to both linear and

angular accelerations

4.9. The best predictor for brain injury is

[ ] (i) Angular acceleration

[ ] (ii) Strain rate of brain tissue

[ ] (iii) Maximum principal strain of brain tissue

[ ] (iv) Product of strain and strain rate of brain tissue

[ ] (v) HIC

4.10. The use of different material properties for gray and white matter of the brain

in the finite element models developed at Wayne State University was based

on:

[ ] (i) Test data from impacts to dogs and monkeys

[ ] (ii) Test data from living human subjects who volunteered to be impacted

[ ] (iii) Test data from living porcine (pig) subjects undergoing high linear

accelerations

[ ] (iv) Test data from cadaveric porcine (pig) subjects undergoing high

angular accelerations



Prob

Ans

1 (iv)

2 (v)

3 (iii)

4 (v)

5 (v)

6 (iii)

7 (iii)

8 (iv)

9 (iv)

10 (v)

References 149

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C. Ward, M. Chan, A. Nahum, Intracranial pressure–a brain injury criterion, in 24th Stapp Car

Crash Conference, SAE Paper No. 801304, Troy, MI, 1980

H. Yamada, F.G. Evans, Strength of biological materials (Williams and Wilkins, Baltimore, 1970)




References 151

L. Zhang, J. Bae, W.N. Hardy, K.L. Monson, G.T. Manley, W. Goldsmith, K.H. Yang, A.I. King,

Computational study of the contribution of the vasculature on the dynamic response of the

brain. Stapp Car Crash J. 46, 145–164 (2002)

C. Zhou, T.B. Khalil, A.I. King, Shear stress distribution in the porcine brain due to rotational

impact, in 38th Stapp Car Crash Conference, SAE Paper No. 942314, Ft. Lauderdale, FL, 1994

C. Zhou, Finite element modeling of impact response of an inhomogeneous brain. Ph.D. Dissertation,

Wayne State University, Detroit, MI, 1995

C. Zhou, A.I. King, T.B. Khalil, A new model comparing impact responses of the homogeneous

and inhomogeneous human brain, in 39th Stapp Car Crash Conference, SAE Paper

No. 952714, San Diego, CA, 1995

Chapter 5

Measurement of Angular Acceleration

Angular acceleration was implicated as a cause of brain injury, beginning with the

theory by Holbourn (1943) and the extensive research conducted by Ommaya and

Hirsch (1971), Ommaya et al. (1967), and Gennarelli et al. (1982). The concept of

angular acceleration was proposed by Sir Isaac Newton in the 1680s (Newton’s

Principia) where he laid down the laws of motion. However, Newton did not say

how this quantity could be measured. In 2-D, the measurement is accomplished by

using a pair of linear accelerometers placed a known distance apart and facing the

same direction (Mertz 1967). For 3-D motion, many schemes have been proposed

(see, e.g., Kane 1968). It turns out that all of the schemes can potentially yield

unreliable results even though the equations used are sophisticated. In this chapter,

the traditional method is first described and is shown to be numerically unstable.

Then a different scheme is introduced to show that it is numerically stable but

requires more sensors.

5.1 The Unstable Six-Accelerometer Scheme

A more recent study by Morris (1973) details a scheme for measuring angular

acceleration in 3-D. He showed that to measure the three linear and the three

angular components of a rigid body, a total of six linear accelerometers is needed.

We will first develop the equations for angular acceleration for 3-D motion of a

rigid body in space, as shown in Fig. 5.1. The inertial reference frame (IRF) is

designated by the rectangular coordinate system, X, Y, and Z. Theoretically, it is a

reference frame fixed in (outer) space, but, for practical purposes, it can be a

laboratory-fixed frame. The body-fixed frame (BFF) is attached to moving rigid

body and is designated by the coordinate system, x, y, and z. The origin of the bodyfixed

system is located at a distance R from the origin of the inertial reference frame

where the vector quantity, R, is in bold font and underlined. An arbitrary point, P, is

defined on the surface of the rigid body, located at a distance ρ from the origin of the



153

154 5 Measurement of Angular Acceleration

Fig. 5.1 Definition

of coordinate systems

for the moving rigid

body. The X-Y-Z

system is the inertial

reference frame while

the x-y-z system is the

body-fixed frame

R

~

Z

ρ

z ~

P

Y

X

0

y

x

body-fixed frame. The aim of this exercise is to determine the angular acceleration

of the point P, based on measurements made with six linear accelerometers attached

to P.

If the body is deformable, the acceleration of the point P is given by

A P

¼ €R þ a þ 2 ω V þ ω ω ρ þ _ω ρ ð5:1Þ

P

P

where A P

is the absolute acceleration of the point P, €R is the acceleration of the BFF

with respect to the IRF ¼ d 2 R/dt 2 , a is the acceleration of the point P relative to the

BFF, ω is the angular velocity, _ω is the angular acceleration ¼ dω/dt, V is the

velocity of the point P relative to the BFF, ρ is the position vector of the point P

P

relative to the origin of the BFF, and denotes a vector cross product.

For a rigid body, the point P does not move relative to the origin of the BFF.

Thus, a is 0, V is 0, and Eq. (5.1) becomes

A P

¼ €R þ ω ω ρ P

þ _ω ρ P

ð5:2Þ

The vectors A P

, R, ω,and ρ can be expressed in terms of their components in the

P

BFF, such as

R ¼ R x i þ R y j þ R z k

where i, j, and k are the unit vectors along the x-, y-, and z-axes of the BFF.

5.1 The Unstable Six-Accelerometer Scheme 155

Fig. 5.2 The five

accelerometers needed

to compute angular

acceleration, using

Eq. 5.3a, 5.3b, and 5.3c

Z

Y

X

R

z

z

0

y

ρ 1

1

2

z

ρ 2

y

Hence, we can write component equations for A P

along the BFF, after expanding

the two vector cross products in Eq. (5.2):

A xP ¼ €R x þ ω y ω x ρ yP ω y ρ xP ωz ðω z ρ xP ω x ρ zP Þþ _ω y ρ zP _ω z ρ yP ð5:3aÞ

A yP ¼ €R y þ ω z ω y ρ zP ω z ρ yP ωx ω x ρ yP ω y ρ xP þ _ω z ρ xP _ω x ρ zP ð5:3bÞ

A zP ¼ €R z þ ω x ðω z ρ xP ω x ρ zP Þω y ω y ρ zP ω z ρ yP þ _ω x ρ yP _ω y ρ xP ð5:3cÞ

The arrangement of accelerometers is shown in Fig. 5.2. They are placed at the

point P and form a rectangular Cartesian coordinate system with its origin at 0.

There are two accelerometers at the origin in the y- and z-directions. There is a

similar pair at point 2 and a single accelerometer in the z-direction at point 1. The

sixth accelerometer is placed along the x-direction at the origin to provide the third

component of linear acceleration. These accelerometers provide enough data for us

to use Eqs. (5.3a), (5.3b), and (5.3c) to compute the three components of angular

acceleration.

If we denote all measured accelerations with the letter A, it can be seen from

Fig. 5.2 that

€R x ¼ A x0 ,

€R y ¼ A y0 , and

€R z ¼ A z0 .

Also,

ρ 1

¼ ρ y1 j

ρ 2

¼ ρ x2 i

ρ 0

¼ 0


Then, using Eq. (5.3c), for P ¼ 1 and 2,

A z1 A x0 ¼ ω y ω z ρ y1 þ _ω x ρ y1

A z2 A z0 ¼ ω x ω z ρ x2 þ _ω y ρ x2

ð5:4Þ

ð5:5Þ

And from Eq. (5.3b), for P ¼ 2,

A y2 A y0 ¼ ω x ω y ρ x2 þ _ω x ρ x2

ð5:6Þ

Upon rearranging Eqs. (5.4), (5.5), and (5.6),

_ω x ¼ ðA z1 A z0 Þ=ρ y1 ω y ω z ð5:7Þ

_ω y ¼A ð z2 A z0 Þ=ρ x2 ω x ω z ð5:8Þ

_ω x ¼ A y2 A y0 =ρx2 ω x ω y ð5:9Þ

Equations (5.7) through (5.9) can be solved for the angular acceleration components

if the quantities A z0 , A z1 , A z2 , A y0 , and A y1 are measured. However, these

equations are nonlinear ordinary differential equations, and the nonlinear terms are

the products of angular velocities. Generally, nonlinear differential equations

cannot be solved in closed form, and a numerical method, such as the Runge–

Kutta method, is used to solve them. In practice, it may not be possible to carry out

the numerical solution to the end of the impact event due to error build up. Take, for

example, Eq. (5.7). The first term on the right is the difference of two accelerations.

A small measurement error in either A z1 or A z0 or both causes an error in the

computed value of ω x , and this error is propagated into Eq. (5.8), resulting in an

error in ω y . The erroneous results of ω x and ω y are used in the integration of

Eq. (5.9), resulting in an even larger error in ω z . With each integration time step,

the errors accumulate, and in a short time the angular acceleration components

become infinitely large. This problem is especially serious when high-range (less

sensitive) sensors are used to measure relatively small linear accelerations because

the magnitudes of these linear accelerations could not be accurately predicted

before the test. There are also other sources of measurement errors, such as crossaxis

sensitivity of the transducers and calibration nonlinearities. These error sources

are discussed later on in this chapter.

5.2 The Stable Measurement of Angular Acceleration

Using the Wayne State Method

To circumvent these computational problems, an alternate scheme using nine accelerometers

was proposed by Padgaonkar et al. (1975). It is also known as the 3-2-2-2

method of measuring angular acceleration. For simplicity, it will be call the Wayne

5.2 The Stable Measurement of Angular Acceleration Using the Wayne State Method 157

Fig. 5.3 Arrangement of the nine accelerometers used in the Wayne State method of measuring

angular acceleration (taken from Mital (1978))

State method. Figure 5.3 shows the arrangement of the accelerometers on a mount

that takes the form of a 3-D rectangular Cartesian coordinate system and is shown in

Fig. 5.3. Comparing Figs. 5.2 and 5.3, we see that two accelerometers were added at

point 3 (A x3 and A y3 )andoneatpoint1(A x1 ). With these three additional accelerometers,

it is possible to use a second set of five accelerometers to formulate another

set of equations for calculating angular acceleration, using Eq. (5.3). These are A x0 ,

A y0 , A x1 . A x3 ,andA y3 . This set of equations is shown below:

_ω x ¼ A y3 A y0 =ρz3 þ ω y ω z ð5:10Þ

_ω y ¼ ðA x3 A x0 Þ=ρ z3 þ ω x ω z ð5:11Þ

_ω z ¼A ð x1 A x0 Þ=ρ y1 þ ω x ω y ð5:12Þ

Now, if we add Eqs. (5.7) and (5.10), Eqs. (5.8) and (5.11), and Eqs. (5.9) and

(5.12), we eliminate the nonlinear terms, and the resulting equations become

algebraic:

_ω x ¼ ðA z1 A z0 Þ=2ρ y1 A y3 A y0 =2ρz3 ð5:13Þ

_ω y ¼ ðA x3 A x0 Þ=2ρ z3 ðA z2 A z0 Þ=2ρ x2 ð5:14Þ

_ω z ¼ A y2 A y0 =2ρx2 ðA x1 A x0 Þ=2ρ y1 ð5:15Þ


Since Eqs. (5.13) through (5.15) are algebraic and solve for the angular acceleration

components directly, any measurement error would cause an error at each instant of

time. The errors do not propagate and the calculated results are stable.

The actual mount for the nine accelerometers is shown in Fig. 5.4. If we look at

Eqs. (5.13) through (5.15), we see that the distance of the accelerometers from the

origin appears in the denominator and accuracy is improved if the arms are made

longer. However, the downside to using a large mount is the need to make it very

hefty so that it will not bend and vibrate under high-impact conditions. For the

Hybrid III dummy head, it already contains a triaxial accelerometer at its cg. If a

pair of accelerometers is mounted near the surface in the frontal, lateral, and top of

the head form, the nine-accelerometer configuration can be achieved without the

use an actual or external mount. This is shown in Fig. 5.5.

Fig. 5.4 A nineaccelerometer

mount used

for measuring angular

acceleration in cadavers and

animals

Fig. 5.5 The nine accelerometers for measuring the angular acceleration of a Hybrid III dummy

head are built into the head form, centered around the triaxial accelerometer at its cg (taken from

Franklyn et al. (2005))

5.3 Other Methods of Measuring Angular Acceleration 159

It is also possible to compute the angular velocity using the same Eqs. (5.7)

through (5.12). Instead of adding, the equation pairs are subtracted from each other

to eliminate the angular acceleration term, and the result is a second-order algebraic

equation in terms of the angular velocity components, as shown in Eqs. (5.16)

through (5.18). The downside of using this approach is the ambiguity of the sign of

the angular velocity because when an algebraic equation is solved, the result can be

either positive or negative. The more reliable approach would be to integrate the

angular acceleration directly:

ω y ω z ¼ ðA z1 A z0 Þ=2ρ y1 þ A y3 A y0 =2ρz3 ð5:16Þ

ω z ω x ¼ ðA x3 A x0 Þ=2ρ z3 þ ðA z2 A z0 Þ=2ρ x2 ð5:17Þ

ω x ω y ¼ A y2 A y0 =2ρx2 þ ðA x1 A x0 Þ=2ρ y1 ð5:18Þ

5.3 Other Methods of Measuring Angular Acceleration

The statement made in the introduction that many existing schemes are numerically

potentially unreliable is now obvious. The equations used to compute angular

acceleration from measured linear accelerations are generally nonlinear differential

equations which are solved numerically. If the measurements are error-free, they

work fine, but because of the existence of errors in most measurements and the

rapid accumulation of errors when a numerical integration scheme is used, the

methods are potentially unreliable.

5.3.1 Other Measurement Schemes Using Linear

Accelerometers

Nusholtz et al. (1986) proposed a nine-accelerometer scheme consisting of three

triaxial clusters of linear accelerometers. They used six of those to solve the

nonlinear differential Eqs. (5.3a), (5.3b), and (5.3c). To correct for any measurement

errors, the linear acceleration at the locations of the three accelerometers that

were not used in the calculation was computed from the angular results and

compared with what was measured. This was done at every time step of the

integration process and the angular acceleration components were corrected until

they matched the measured values. In this way, the error propagation was reduced

considerably, and it was possible to compute the angular acceleration of the head

for the entire impact event without the computer aborting the run due to large

numerical values. Although the method works, it still carries with it the potential of

error accumulation because there can be errors in all nine measured accelerations


and the iterative process attempts to adjust the calculated angular accelerations

against a set of measurements that can also be erroneous. In fact, the Wayne State

method is a special configuration that does not require the integration of differential

equations and thus there is no error accumulation.

A more recent development is the use of a new configuration of only six

accelerometers that results in a set of algebraic equations for the angular acceleration

components. Tan et al. (2001) proposed the attachment of six linear accelerometers

to the sides of a cube of length 2l. The sensitive axis of each sensor is

aligned with the diagonal of the cube surface, and the sensor is placed at the center

of each diagonal, normal to the diagonal. It turns out that with this configuration of

accelerometers, the resulting equations for angular acceleration are algebraic and

similar to those derived for the Wayne State method. The equations for the angular

acceleration components are listed below:

2 3 2

3

_ω 1

þA 1 A 2 þA 5 A 6

6 7

4 _ω 2 5 ¼ p

1

2 ffiffiffiffi 6

7

4 A 1 þA 3 A 4 A 6 5 ð5:19Þ

2l

_ω 3

þA 2 A 3 A 4 þA 5

where _ω i is the angular acceleration of the ith axis (i ¼ 1–3), A j is the measured

p

accelerations ( j ¼ 1–6), and 2

ffiffiffiffi

2l is the length of the diagonal.

Although the angular acceleration can be measured with only six transducers,

the method requires the computation of the linear acceleration components from the

measured values as there is no triaxial cluster to provide this information.

5.3.2 Measurement Schemes Using Specially Designed

Angular Accelerometers

Since angular acceleration induces an inertial response, it is possible to design a

transducer using a small mass to bend a cantilever beam when a centripetal

acceleration acts on it. But there are many other methods to sense angular acceleration,

as evidenced by the many patents that have been filed, claiming that the

invention can reliably measure this quantity. Ideas range from using mercury,

measuring change in capacitance and combinations of the use of an inertial mass

and the change in capacitance. The devices are being miniaturized but their

frequency response is generally not as high as that of linear accelerometers.

There are also rate sensors that measure angular velocity from which angular

acceleration can be computed by differentiating the signal with respect to time.

Differentiation is not a desirable operation when dealing with impact type data

because it introduces a lot of noise and is prone to large errors. Also, rate sensors

also have a low frequency response.

If it is necessary to use these angular devices instead of linear accelerometers,

they should be calibrated against the gold standard for measuring angular

5.4 Validation of the Wayne State Method 161

acceleration—the Wayne State method. One way to perform such a calibration is to

carry out an impact test similar to the tests in which it will be used. For measuring

head angular acceleration, the device can be mounted on the head of a crash dummy

along with the nine accelerometers used in the Wayne State method.

5.4 Validation of the Wayne State Method

The preliminary results from the work of Padgaonkar et al. (1975) and Nusholtz

et al. (1986) were presented to the impact biomechanics community at about the

same time in 1974. Initially, they appeared to be two competing methods with equal

capabilities of yielding reliable angular acceleration data. Thus, it was necessary to

demonstrate that the data acquired using the Wayne State method was indeed

accurate and reliable. Validation was carried out in two separate steps. The first

step was to test the Bortz method using some hypothetical 3-D data. The second

step was to carry out actual impact tests to compare the output of the Wayne Sate

method with data that can be verified independently.

5.4.1 Criteria for Validation

It was quite obvious in the 1970s that there were no angular accelerometers

available to calibrate the Wayne State system. In fact, even now, there are no

angular accelerometers up to this task. Thus, the validation had to be made using an

independent or unrelated parameter. For rotation, angular displacement is an

obvious choice since it can be measured independently by optical means. That

meant that the measured angular accelerations needed to be integrated to yield

angular displacements before we can compare the results. However, there is slight

hitch in carrying out the integration. Recall that rotation is noncommutative and is

dependent on the order of rotation. So, for motion in 3-D, it is not possible to just

perform a straight integration of angular velocity to angular displacement in the

way it is done for linear velocity and displacement. In dynamics, we learn that only

infinitesimal rotations are commutative and for most rotations, special methods are

necessary to determine angular displacement from angular velocity, if we do not

wish to carry out the integration with infinitesimal time steps. Incidentally, it is not

known what the magnitude of an infinitesimal rotation might be. We found that

even small fractions of a second of arc were not small enough for an infinitesimal

rotation and thus it was not practical to perform the integration using very small

time steps. The solution came from NASA which was involved in making lunar

landings at the time, and a backup system on the lunar lander used a newly

developed method to compute the orientation of the lander based on angular

velocity data supplied by the rate gyros. Bortz (1970) had developed a method of

integrating angular velocity to yield angular displacement by integrating the


noncommutative part of the rotation separately. It is beyond the scope of this course

to go into the details of the Bortz method, suffice it to say that the problem of

noncommutativity was overcome and it was possible to carry out the integration.

Some of the details of the method can be found in Mital (1978).

The Bortz method was put to the test using some hypothetical data. A set of three

angular velocities with a half-sine wave shape and an area under them equal to a 90

rotation were integrated separately. The order of rotation was about the X-axis,

the new Y-axis, and the next new Z-axis, as shown in Fig. 5.6. The three angular

velocity profiles are shown in Fig. 5.7 and the integrated result is shown in Fig. 5.8.

Fig. 5.6 Hypothetical data

used to test the Bortz (1971)

method (taken from Mital

(1978))


60.00

HYP: XYZ–90 SINE

WX [B]

WY [B]

WZ [B]

RAD/SEC

0.00 30.00

0.00 50.00 100.00 150.00 200.00

TIME [MS]

Fig. 5.7 Angular velocity components for the X-, Y- and Z-sequence of rotations (taken from

Mital (1978))

X10

18.

HYP: XYZ–90 SINE

YAW

PITCH

ROLL

DEGREES

–18. 0.

0. 50. 100. 150.

200.

TIME [MS]

Fig. 5.8 Computed yaw, pitch, and roll for the hypothetical data used (taken from Mital (1978))

5.4.2 Validation of the Wayne State Method Using Sled

Impact Data

The independent method used to validate the Wayne State method was an optical

one, and it was conducted in conjunction with a sled test (Mital and King 1979).

The optical target was a 76 mm cube attached to the head of a test dummy. The cube


Fig. 5.9 Schematic drawing of the experimental setup for a frontal sled impact. It shows the cube

for measuring the angular data and the position of the three orthogonally placed cameras (taken

from Mital (1978))

weighed 58 g and was made of urethane foam. It was covered with yellow and black

target tape to facilitate optical tracking. The 9-accelerometer mount was mounted

on the head of the dummy below the cube. The test setup is shown in Fig. 5.9. The

optical target was tracked by three orthogonally placed onboard high-speed cameras

which provided the direction cosines that were used to compute the angular

displacement data. For details of how the film data were analyzed, the reader is

referred to Mital (1978).

However, before the tests could be run, all nine accelerometers had to be

recalibrated against a standard accelerometer that has been calibrated in a lab

with equipment traceable to the National Institute of Standards and Technology

(NIST). The calibration data are shown in Fig. 5.10.

The raw data needed to be filtered to remove high-frequency components that

are due to noise or other artifacts, such spikes from old trailing cables that

conducted the signals from the sled to stationary data recorders. Figure 5.11 is an

example of an unfiltered data trace, and Fig. 5.12 is the same trace after it had been

de-spiked and passed through a 100 Hz fast Fourier transform (FFT) filter.


Fig. 5.10 Calibration data of three of the accelerometers used and of the standard accelerometer.

A uni-axial shaker at 20 Hz was used. The standard was calibrated against a known NIST standard

to calibrate all accelerometers used in the experiment (taken from Mital (1978))

ACCELERATION (G)

-10.00 10.00 30.00

RUN NO.: CD3271-3

.00 80.00

160.00

TIME (MS)

FIS: UNF

RIS: UNF

240.00 320.00

Fig. 5.11 Raw (unfiltered) accelerometer data containing spikes due to cable problems (taken

from Mital (1978))

Fig. 5.12 Two channels of filtered accelerometer data using an FFT filter (taken from Mital

(1978))


Fig. 5.13 Angular velocity components of the dummy head computed from the measured angular

accelerations using the Wayne State method. The dummy was restrained by a lap or shoulder belt

and was subjected to a 15 g frontal impact (taken from Mital (1978))

Acceleration traces were integrated to yield angular velocity, an example of which

is shown in Fig. 5.13.

Two different sled tests were carried out using a belted crash dummy. In the first

test, the dummy was subjected to a 15 g frontal impact and was restrained by a

single three-point belt. As a result, the head rotated about all three axes. In the

second test, the dummy was subjected to an 18 g frontal impact with its torso

restrained by only a lap belt. Consequently, head motion was largely limited to

rotation about the transverse or y-axis, but the amount of head rotation was greater

than the three-point belted case.

For the first run with a three-point belt, the computed and measured Euler angles

(yaw, pitch, and roll) are found to match quite well, as shown in Fig. 5.14. What is

more important is that at the end of the run, at about 200 ms, the results were still

well matched and show trends of returning to their pre-impact values. That is, there

was no tendency for them to become inordinately large as the computed angular

accelerations did when only six accelerometers were used. Other angular measures

were also compared by Mital and King (1979). One of them was the rotation vector

which is defined as the magnitude of rotation (angle) about an axis with the

direction of rotation defined by the right-hand rule. The computed and measured

rotation vectors are shown in Fig. 5.15 and the match is excellent.

The angular velocity components for the second run are shown in Fig. 5.16.

Since the dummy was lap belted, the principal component of rotation was about the

y-axis or the transverse axis. The computed and measured rotation vectors are

shown in Fig. 5.17. The match is quite good and the values at the end of the run

trend toward the pre-impact value. The computed yaw, pitch, and roll values are

shown in Fig. 5.18 where a numerical problem was encountered and the 180 shift

of the data needed to be performed manually. This was the reason why Euler chose

to use his Euler angles instead of the more convenient rotational sequence of yaw,

pitch, and roll.

Fig. 5.14 Angular displacements computed from the angular velocity data shown in Fig. 5.13 are

compared with measured 3-D film data. The computed data at the end of the test also matched the

measured data and show a trend to return to their pre-impact values (taken from Mital (1978))

Fig. 5.15 Rotation vector computed using the Wayne State method is compared with the optically

measured rotation vector for the 15 g sled run (taken from Mital (1978))

Fig. 5.16 Angular velocity components of the dummy head computed from the measured angular

accelerations using the Wayne State method. The dummy was restrained by a lap belt and was

subjected to an 18 g frontal impact (taken from Mital (1978))


Fig. 5.17 Rotation

vector computed

using the Wayne

State method

is compared with

the optically

measured rotation

vector for the 18 g sled

run (taken from Mital

(1978))

Fig. 5.18 Yaw, pitch, and roll computed from the measured head accelerations. The 90 shift in

yaw and roll is indicative of the numerical problems that can be encountered when the Euler angles

are not used to define 3-D rotation (taken from Mital (1978))

Fortran code is available to compute 3-D rotations from the angular velocity

data. The code is available in Appendix B of Mital (1978).

5.4.3 Concluding Remarks

The Wayne State method of measuring angular acceleration has been validated

experimentally. The process is quite rigorous and we can use this method with

confidence. No other method has been subjected to such scrutiny, such as the

six-accelerometer method proposed by Tan et al. (2001). Because of the validation,

the Wayne State method is considered to be the gold standard for measuring angular

5.5 Miscellaneous Problems in the Measurement of Angular Acceleration 169

acceleration. Since currently available angular accelerometers have a low natural

frequency and may yield unreliable results, they should always be calibrated against

the Wayne State method before use in a new impact situation.

5.5 Miscellaneous Problems in the Measurement

of Angular Acceleration

In addition to the intrinsic problem of integrating angular velocity to obtain angular

displacement, measurement problems include frequency response of the linear

accelerometer, cross talk in commercially available linear accelerometers, multiple

methods of calibrating linear accelerometers, the change in calibration factors of

these accelerometers at very low frequencies and the effect of error in one of the

nine accelerometers.

5.5.1 Frequency Response of Linear Accelerometers

Accelerometer manufacturers provide the user with a natural or resonant frequency

of the device and the percent deviation from their stated sensitivity (calibration

factor) at a certain frequency which is well below the resonant frequency. Upon

request, they may provide frequency response curve for the accelerometer, such as

the one shown in Fig. 5.19 where it can be seen that the response is flat out to about

2 kHz. There are also frequency response problems at low frequencies which will

be discussed later.

5.5.2 Cross Talk in Linear Accelerometers

The accelerometer is a single axis device that measures acceleration in only one

direction by nature of its construction. A small mass at the end of a cantilever beam

in the device bends the beam when the device is accelerated, and the beam can be a

piezoresistive strain gauge which yields a signal proportional to the acceleration. In

practice, the accelerometer may yield signals when it is accelerated in the other two

orthogonal directions. Such signals are called cross talk or transverse sensitivity and

are an undesirable feature of the accelerometer because they contaminate the true

signal. Cross talk is not totally avoidable, but it can be minimized to a small

percentage of the maximum output, such as one percent. If the cross talk error is

known, it is possible to use software to correct for cross-axis sensitivity, as

discussed in (Mital 1978, Appendix B5)


Fig. 5.19 Typical calibration curve provided by Meggitt (Endevco) for their Model 7264C

accelerometer. Its response is flat to about 2 kHz and its resonant frequency is about 25 kHz

(courtesy of Meggitt (Orange County) Inc.)

5.5.3 Methods of Calibrating Accelerometers

There are three basic methods of calibrating accelerometers. They are:

1. Shaker table tests

2. Drop tests

3. Rate table tests

In all three methods, a standard accelerometer with output traceable to the

NTIS standard is mounted on the test device along with one or more of the

accelerometers to be calibrated. Manufacturers of accelerometers usually use

the first method with the shaker table set to vibrate sinusoidally at 100 Hz at a

fixed peak magnitude consistent with the range of the accelerometer. The sensitivity

they provide to the user in mV of output per g is based on this frequency.

The output of the accelerometer being calibrated is compared with that of a

standard accelerometer.

In a well-equipped laboratory, drop test and rate table calibration devices are

available. The drop test device consists of a rigid table mounted on a piston that

slides on roller bearings inside a vertical cylinder. The table is raised and dropped


onto the bottom of the cylinder which is lined with an energy-absorbing material.

The g-level is controlled by the height of the drop and the stiffness of the energyabsorbing

material. Drop tests are more realistic in terms of shock testing of the

accelerometer, but the impact pulse contains many frequency components, and it is

difficult to associate errors with input frequency and magnitude. However, the test

checks the sensitivity provided by the manufacturer and the adequacy of its

frequency response compared to the standard.

The rate table spins at a constant speed and accelerometers mounted on the table

at a known and fixed radius, with their sensitive axis along a radial line, are

subjected to a constant centripetal acceleration if the rotation is kept constant.

A synchronous motor provides a constant speed of rotation, 600 rpm in this case,

and is the equivalent of a steady-state calibration (at 0 Hz). It provides another

check on the validity of the shaker table calibration. The zero-frequency calibration

is frequently different from the shaker table calibration. The rate table is also a

convenient device for measuring cross talk.

5.5.4 Low-Frequency Response of Accelerometer

Several accelerometers were tested by the Metrology Lab of Ford Motor Co. on

their shaker table to check for their frequency response at low frequencies under

100 Hz. The errors approach 8 % as the frequency approaches zero. A sample test

result is shown in Fig. 5.20. It is not known if this problem has been solved in

present-day accelerometers as these data were collected some 25 years ago.

Deviation from the standard vs Frequency

6

Deviation from the standard (%)

4

2

0

0 100 200 300 400 500

-2

-4

ENTRAN

KISTLER

ENDEVCO

-6

Frequency (Hz)

Fig. 5.20 Errors magnify at low frequencies for three different brands of accelerometers

manufactured in the 1980s


5.5.5 Effect of Errors in the Data

It is possible to study the effect of errors in accelerometer data by considering some

hypothetical cases. For simplicity, we will consider a case in which there is only

rotation about the y-axis, simulating pure head flexion or extension and assume that

there are errors in the measured angular velocity about the roll axis (x-axis). We will

assume that ω y is a steady-state oscillation of 10 Hz with a peak of 40 rad/s and

that ω z ¼ 0. Sensitivity of angular displacement to the following hypothetical errors

in will be evaluated:

Case 1: ω x ¼4 rad/s with a frequency of 30 Hz and with no offset or baseline shift

(10 % error)

Case 2: ω x ¼2 rad/s with a frequency of 30 Hz and an offset of 2 rad/s (5 % error

and 5 % offset)

Case 3: ω x ¼4 rad/s with a frequency of 30 Hz and an offset of 4 rad/s (10 % error

and 10 % offset)

Case 1 The angular velocity components for this case are shown in Fig. 5.21, and

the resulting angular displacements are shown in Fig. 5.22. A 10 % sinusoidal error

with no offset did not result in significant errors in the computed angular displacements.

That is, noise in the data is not a major factor in the accuracy of the

computed angular displacements.

Case 2 Figure 5.23 shows the velocity components. It is seen that the 5 % offset in

the velocity about an axis that should be zero (the roll axis) resulted in a 30 error in

roll and about a 20 error in pitch, as shown in Fig. 5.24. The importance of

ensuring that the zero baseline is maintained for all accelerometers is brought out

by this example.

Fig. 5.21 Error Analysis—Case 1: Velocity components for a hypothetical case with a 10 %

error in the roll velocity component but with no offset error (baseline shift) (taken from Mital

(1978))


Fig. 5.22 Computed

angular displacements

as a result of a 10 %

error in ω x (roll axis)

without offset (baseline

shift) (taken from

Mital (1978))

Fig. 5.23 Error Analysis—

Case 2: Velocity

components for a

hypothetical case with

a 5 % error in the roll

velocity component and

with a 5 % offset error

(baseline shift) (taken from

Mital (1978))

Fig. 5.24 Computed


as a result of a 5 % error

in ω x (roll axis) with a 5 %

offset (baseline shift) (taken

from Mital

(1978))


Fig. 5.25 Error Analysis—

Case 3: Velocity

components for a

hypothetical case with a

10 % error in the roll

velocity component and

with a 10 % offset error

(baseline shift) (taken from

Mital (1978))

Fig. 5.26 Computed


as a result of a 10 % error

in ω x (roll axis) with a 10 %

offset (baseline shift) (taken

from Mital

(1978))

Case 3 In this case, the offset and error magnitudes are twice that of Case 2, as

shown in Fig. 5.25. The resulting displacements about the x- and z-axes (pitch and

yaw axes) are as large as that about the main (roll) axis (Fig. 5.26). This is an

unacceptable result.

5.6 Conclusions

A reliable method of measuring angular acceleration is available using the Wayne

State method. Its accuracy depends on the size of the mount, the accuracy of the

accelerometers used and a high signal to noise ratio. The Wayne State method uses

a unique configuration of linear accelerometers that does not require the numerical

solution of nonlinear differential equations and hence has no accumulation of errors

due to measurement errors. At the same time, it yields the linear acceleration


components at a point on the rigid body. The newly developed method of using only

six accelerometers, by Tan et al. (2001), is elegant, but the linear acceleration

components at a given location on the rigid body needs to be computed. The general

disadvantage of using linear accelerometers to measure angular acceleration is the

basic assumption that the body is rigid. In biomechanics, no body part is really

rigid, not even the skull. It is not known what errors arise because of skull

deformation in a severe head impact. However, zero offset errors in the measured

accelerations need to be minimized to avoid large errors in the computed

displacements.

There are alternate methods of measuring angular acceleration. Angular accelerometers

are available, but generally, their frequency response is inadequate for

shock testing. Similarly, angular rate sensors can be used to yield angular velocity,

but they also suffer from inadequate frequency response. Furthermore, the angular

acceleration computed from velocity data by numerical differentiation yields noisy

results with a high probability of errors.


5.1. A reliable method for the measurement of angular acceleration, using linear

accelerometers, was invented by:

[ ] (i) Sir Isaac Newton

[ ] (ii) Prof Kane at Stanford University

[ ] (iii) Guy Nusholtz at the University of Michigan

[ ] (iv) Researchers in biomechanics at Wayne State University

[ ] (v) Researchers at the Naval Biodynamics Lab in New Orleans

5.2. When using linear accelerometers to measure angular acceleration

[ ] (i) It is better to use the 3-2-2-2 configuration than the three triaxial

configuration

[ ] (ii) The accelerometers must have low cross-talk sensitivity

[ ] (iii) The accelerometer calibration should not change with frequency

content of the impact pulse

[ ] (iv) A new six-accelerometer method is now available without having to

integrate the equations


5.3. The major difference between using 9 accelerometers in the 3-2-2-2 configuration

instead of the 6 accelerometers to measure angular acceleration is:

[ ] (i) Minimization of error because the extra measurements can be used

to check the computation

[ ] (ii) The angular acceleration can be computed from algebraic instead of

differential equations


[ ] (iii) There is no accumulation of error during the computational process



5.4. To verify an angular acceleration measurement, it is necessary to integrate

the data twice to obtain angular displacement to compare this displacement

with that measured by a different method, such as an optical method. The

integration of

[ ] (i) Angular acceleration to angular velocity cannot be done directly

because angular velocity is non-commutative and special methods

are needed to perform this integration

[ ] (ii) Angular velocity to angular displacement cannot be done directly

because angular displacement is non-commutative and special

methods are needed to perform this integration

[ ] (iii) Angular acceleration to angular velocity and that of angular velocity

to angular displacement can be done directly because they are both

commutative and no special methods are needed

[ ] (iv) Angular velocity to angular displacement can be done directly

because angular displacement is commutative and no special

methods are needed to perform this integration


5.5. When angular acceleration is measured with only 6 accelerometers, the

resulting equations in terms of the angular velocity components are nonlinear

ordinary differential equations. Numerical solution of these nonlinear equations

can result in instability of the computed angular acceleration because

[ ] (i) The differential equations have unstable solutions

[ ] (ii) The errors in measurement accumulate over time as the integration

progresses

[ ] (iii) The errors propagate because the numerical subroutine used to

integrate the equations is unstable



5.6. The use of three triaxial accelerometers to measure angular acceleration is

less reliable than the use of the 3-2-2-2 configuration of linear accelerometers

because

[ ] (i) The triaxial method still requires integration of nonlinear differential

equations

[ ] (ii) The use of the three additional accelerometers in the triaxial configuration

to check the computed angular acceleration from the other

6 accelerometers can still result in error accumulation

[ ] (iii) It is not possible to align the triaxial accelerometers accurately

[ ] (iv) (i) and (ii)

[ ] (v) (i) and (iii)


5.7. When linear accelerometers are used to measure angular acceleration, it is

important that these transducers:

[ ] (i) Have a steady zero baseline which does not drift with time

[ ] (ii) Have low cross-talk sensitivity

[ ] (iii) Respond linearly to increase in linear acceleration

[ ] (iv) Have adequate frequency response to handle short duration impacts


5.8. An accurate and reliable alternate method of measuring angular acceleration

is the:

[ ] (i) Use of an angular accelerometer which yields this value directly

[ ] (ii) Use of an angular velocity transducer and differentiating the data to

yield angular acceleration

[ ] (iii) Use of a high-speed video camera at 1000 frames per second and

differentiating the angular displacement twice

[ ] (iv) Use of intersecting laser techniques to obtain angular acceleration

directly


5.9. Linear accelerometer manufacturers calibrate their accelerometers against a

standard accelerometer using:

[ ] (i) A shaker table

[ ] (ii) Optical methods

[ ] (iii) Rate table tests

[ ] (iv) Drop tests


5.10. The major difference between using 9 accelerometers in the 3-2-2-2 configuration

instead of the 6 accelerometers to measure angular acceleration is:

[ ] (i) Minimization of error because the extra measurements can be used

to check the computation

[ ] (ii) The angular acceleration can be computed from algebraic instead of

differential equations

[ ] (iii) There is no accumulation of error during the computational process

[ ] (iv) (ii) and (iii)

[ ] (v) (i) and (ii)



Prob

Ans

1 (iv)

2 (v)

3 (v)

4 (ii)

5 (ii)

6 (iv)

7 (v)

8 (i)

9 (i)

10 (iv)

References

P.C. Begeman, J. Kopacz, W.N. Hardy, R.S. Levine, A.I. King, Strains and forces in the human medial

collateral ligament during lateral impacts, in 1987 ASME Applied Mechanics Bioengineering,

and Fluids Engineering Conference, vol 84, ASME, AMD, New York, 1987, pp. 233–236

J.E. Bortz, A new concept in strapdown inertial navigation, in Technical Report No. NASA-TR-R-

329, National Aeronautics and Space Administration, Washington, DC, 1970

M. Franklyn, B. Fildes, L. Zhang, K. Yang, L. Sparke, Analysis of finite element models for head

injury investigation: reconstruction of four real world impacts. Stapp Car Crash J. 49, 1–32 (2005)

T. Gennarelli, L. Thibault, J. Adams, D. Graham, C. Thompson, R. Marcincin, Diffuse axonal

injury and traumatic coma in the primate. Ann. Neurol. 12, 564–574 (1982)


T.R. Kane, Dynamics (Holt, Rinehart and Winston Inc, New York, 1968)

H.J. Mertz, Kinematics and Kinetics of Whiplash, PhD Dissertation, Wayne State University,

Detroit, MI, 1967

N. Mital, A. King, Computation of rigid-body rotation in three-dimensional space from body-fixed

linear acceleration measurements. J. Appl. Mech. 46(4), 925–930 (1979)

N. Mital, Computation of rigid-body rotation in three-dimensional space from body-fixed acceleration

measurements, PhD Dissertation, Wayne State University, Detroit, MI, 1978

J. Morris, Accelerometry—a technique for the measurement of human body movements.

J. Biomech. 6(6), 729–736 (1973)

G.S. Nusholtz, P.S. Kaiker, R.J. Lehman, Critical limitations on significant factors in head injury

research, in 30th Stapp Car Crash Conference, San Diego, CA, 1986



A.K. Ommaya, P. Yarnell, A.E. Hirsch, E.H. Harris, Scaling of experimental data on cerebral

concussion in sub-human primates to concussion threshold for man, in 11th the Stapp Car

Crash Conference, SAE Paper No. 670906, Anaheim, CA, 1967

A.J. Padgaonkar, K. Krieger, A. King, Measurement of angular acceleration of a rigid body using

linear accelerometers. J. Appl. Mech. 42(3), 552–556 (1975)

C.-W. Tan, S. Park, K. Mostov, P. Varaiya, Design of gyroscope-free navigation systems, in 2001

IEEE, Intelligent Transportation Systems (2001)

G. Teasdale, B. Jennett, Assessment of coma and impaired consciousness – a practical scale.

Lancet 304(7872), 81–84 (1974)

Chapter 6

Real-World Brain Injuries

In this chapter, three real-world problems will be discussed to show how head

injury modeling can be helpful in providing information on human tolerance to

head impact and the impact parameters that are good predictors of brain injury. The

first deals with the problem of estimating human tolerance to mild concussion as

experienced by athletes who play American football. It was of interest to professional

football in the USA, and the study reported below was supported in part by

the National Football League (NFL) which is a nonprofit trade association made up

of professional football teams around the country. The second problem is to

simulate a well-documented automotive crash at an intersection, including the

injuries sustained by one of the drivers. The third problem is the simulation of the

crash of a racecar and the response of the brain to the crash.

6.1 Tolerance of US Football Players to Mild Concussion

Mild concussion which may be reversible with no sequelae or which may result in a

mild traumatic brain injury (mTBI) is a serious problem for football players of all

ages and can have devastating consequences for professional football players who

sustain frequent and repeated helmeted head impacts over their professional career.

A video of many such collisions was released by the NFL to show the many ways in

which two helmets can collide in a football game. This video can be accessed by

using the following link: https://youtu.be/NmSeDmO6hqI. Please note that since

2002, the NFL has made more than 40 rule changes dedicated to the health and

safety of the sport with a focus on reducing/eliminating helmet to helmet contact.

As a result, these game videos may not accurately reflect those changes. For

research purposes, films of 53 cases of on-field helmet to helmet impacts in

which at least one of the players was concussed were provided with detailed

information on the helmets used. It was a multicenter program involving Duke

University, Biokinetics, Inc., of Canada and Wayne State University to determine



179

180 6 Real-World Brain Injuries

the velocity of impact from game films; to reproduce these impacts in the laboratory,

using Hybrid III dummies, so that head linear and angular accelerations can be

measured; and to determine brain response to establish levels of human tolerance to

mild concussion. The injury information about the players was not released,

including the names of the players and the level of concussion they sustained. At

the end of the project, the model predictions were compared with the concussion

data by an NFL neurological consultant to verify the validity of the model

predictions.

6.1.1 Study Methodology

Undergraduate biomedical engineering students at Duke University, under the

guidance of Professor Jim McElhaney, used stereophotogrammetric methods to

develop software that computed the closing velocity of helmeted heads during a

concussive impact. To accomplish this task, they needed video coverage of the

impact by at least two non-collinear cameras which also had in their fields of view

at least one vertical and one horizontal target of known dimensions. The horizontal

targets were the yard markers on the field, and the vertical targets were whatever

structure or item of known height the analyst could pick out from the game films.

They also estimated the location of impact on the helmet for both the striking

player and the struck player. These results were sent to Biokinetics, Inc. of Ottawa,

Canada. Two dummies, wearing the same brand of helmets involved in the impact,

were made to collide simulating the events recorded on game films. A drop test

device was used to accomplish the impact. In the event that the velocity of impact

Fig. 6.1 Drop test device

used by Biokinetics, Inc. to

reproduce the on-field

impacts recorded on game

videos (taken from Zhang

(2001))

6.1 Tolerance of US Football Players to Mild Concussion 181

Table 6.1 NFL Data – 53 cases of head impact data reconstructed from game films and drop

testing (based on data supplied by the NFL)

Concussion

Noninjury

No. cases

53 22 31

Resultant translational acc (G) Mean (1 SD) 94 (27) 55 (21)

Range 48–138 19–102

Resultant rotational acc (rad/s 2 ) Mean (1 SD) 6398 (1978) 3938 (1406)

Range 2615–9678 1170–6613

could not be achieved by gravity alone, the speed of the moving head/helmet

combination was enhanced by the use of elastic bands that helped to accelerate it

to the desired speed. Figure 6.1 shows the drop test device and the helmets at the

instant of impact. The struck head/helmet combination was mounted on a Hybrid III

neck to allow it to flex, while the striking head/helmet combination was attached to

a rigid frame. For each simulation, the six components of head acceleration of each

head were measured. There was a triaxial linear accelerometer at the cg of each

head to measure its linear (translational) acceleration, and there were six other

linear accelerometers placed strategically in the dummy head form so that its

angular (rotational) acceleration could be computed using the Wayne State method

described by Padgaonkar et al. (1975). A summary of the measured accelerations is

shown in Table 6.1. On average, concussion occurred at a linear acceleration of

94 27 g and a concomitant angular acceleration of 6398 1978 rad/s 2 .

Time histories of the measured dummy head acceleration were then given to

Wayne State University as input to the WSUBIM of Zhang et al. (2001) to calculate

brain response, case by case. The Pam Crash FE solver was used to compute brain

response. At that time, the solver was not programmed to provide strain rate results

which were computed manually after the simulation was done. The following brain

responses were computed by the model:

Intracranial pressure (ICP)

Von Mises stress (σ)

Maximum principal strain (ε)

From these calculated quantities, the strain rate (dε/dt) and the instantaneous

product of strain and strain rate (ε.dε/dt) were computed. The idea of using the

product of strain and strain rate as a possible predictor of concussion came from the

use of the Viscous Criterion by Viano and Lovsund (1999) as a predictor of chest

injury. They found that the instantaneous product of chest wall velocity and

compression of the chest as a fraction of its depth was a good predictor of chest

injury for frontal impacts to the chest.


Fig. 6.2 Example of computed ICP in a concussed individual 9 ms after impact. The peak positive

pressure in the left frontal area was 110 kPa, and the peak pressure in the right occipital region was

a negative 78 kPa (Courtesy of Dr. L Zhang)

Fig. 6.3 Comparing strain contours in an injury case with a non-injury case


Fig. 6.4 Elements of the brain experiencing principal strain in excess of 10 % for the injury case

on the left and noninjury case on the right (based on King et al. (2003))

6.1.1.1 Results of the Simulation

Figure 6.2 shows the ICP contours for one of the impacts to the left front of the head

where high pressure was predicted. The corresponding negative pressure in the

right occipital region was also predicted. Principal strain contours are shown in

Fig. 6.3 for both an injury (concussed) case and a noninjury case. Another way of

showing strain in the brain is to highlight regions of the brain that experienced strain

over 10 %. This is shown in Fig. 6.4 where it can be seen that the injured brain had a

much larger volume brain that experienced strains of over 10 % than the uninjured

brain.

We can exploit the results of 53 simulations further by seeking parameters that

are good predictors of concussion. Before brain responses could be calculated using

an FE model, the predictors of injury of readily measurable variables, such as linear

acceleration of the head and parameters derived from it, including HIC, need to be

identified. We can hypothesize that brain injuries could be more directly explained

by parameters that govern its mechanical response, such as strain, rather than the

head input variables, such as head acceleration. It has long been debated as to which

type of acceleration was more injurious to the brain – linear or angular. If the linear

and angular acceleration data from the 53 NFL reconstructions are cross plotted, as

shown in Fig. 6.5, we see that these two quantities increase monotonically and it

would be difficult to identify which one is a better predictor of concussion.

However, strain-related parameters could be the key to the understanding of injury

causation. So, if we do a logistic regression analysis using both head impact

parameters (model input) and brain response parameters (model output), we can

compare the results from these two groups to ascertain the more reliable predictors

of injury. Parameters representative of input acceleration take on several forms.


Fig. 6.5 Cross plot of acceleration data from NFL data, obtained from reconstructions of head

impacts using dummies by Biokinetics, Inc

Table 6.2 List of predictor variables for logistic regression

Brain response variables

Head impact input variables

Cumulative strain at 15 %

Head injury criterion (HIC)

Intracranial pressure

Gadd Severity Index (GSI)

Max. stress

Head impact power (HIP)

Max. strain in midbrain

Head impact jerk (HIJ)

Strain rate

Max. resultant linear acceleration

Product of strain and strain rate

Max. resultant angular acceleration

Besides HIC, there are head impact power (HIP) which is the rate of change of

kinetic energy and head impact jerk (HIJ) which is the rate of change of acceleration.

HIP is given by Eq. (6.1):

P ¼ Σma v þ ΣIα ω

ð6:1Þ

where P is the head impact power, m is the mass, a is the acceleration, v is the

velocity, I is the mass moment of inertia, α is the angular acceleration, and ω is the

angular velocity.

HIJ is given by Eq. (6.2):

HIJ ¼ da=dt

ð6:2Þ

A logistic regression was carried out with concussion outcome as the independent

variable and two sets of dependent (predictor) variables, one for brain response and

the other for head impact input. These predictor variables are listed in Table 6.2.


Table 6.3 Rank order of mTBI predictors based on logistic regression (based on King et al.

(2003))

Rank order Predictor variable 2.log χ 2 Likelihood p

1 ε.dε/dt| max (s 1 ) 41.0 0.0000

2 dε/dt| max (s 1 ) 33.1 0.0000

3 HIC 15 31.5 0.0000

4 GSI 31.2 0.0000

5 Linear accel. (m/s 2 ) 28.3 0.0000

6 ε max 28.0 0.0000

7 Max stress 27.3 0.0000

8 Cum. strain at 15 % 26.0 0.0000

9 Angular accel. (rad/s 2 ) 24.0 0.0000

Fig. 6.6 Logistic plot of

the probability of an mTBI

as a function of the product

of strain and strain rate

(taken from King et al.

(2003))



as a function of strain rate


(2003))




as a function of HIC (taken




as a function of linear

acceleration (taken from

King et al. (2003))



as a function of angular

acceleration (taken from

King et al. (2003))

The results of the logistic regression are shown in Table 6.3 for the first nine

variables, ranked according to the χ 2 statistic computed for each variable. The

product of strain and strain rate was found to be the best predictor followed by strain

rate. Surprisingly, HIC 15 came in third. It was also a surprise that angular


Fig. 6.11 Estimation of

tolerance levels from a

logistic curve (taken


Table 6.4 Comparison of model-predicted values with field data

Parameter Model Field data

50 % probability of injury Average value

Linear acceleration (g) 81 94

Angular acceleration (rad/s 2 ) 5488 6398

Fig. 6.12 The optimal

tolerance is at 29 % for a

product value of 23 s 1 .

The first and second

tolerances are also shown.

See Fig. 1.14 for an

explanation of these

tolerance values (based

on King et al. (2003))

acceleration was in the ninth place, while linear acceleration was in the fifth place.

The logistic plots for the product of strain and strain rate, strain rate, HIC, linear

acceleration, and angular acceleration are shown in Figs. 6.6, 6.7, 6.8, 6.9, and 6.10.

It is seen that the steepness of the rise of the S-curve is a good indicator of how well

a parameter can predict mTBI. Additionally, a good predictor will have less overlap

of injury and noninjury data. Also, tolerance to mTBI can be estimated from any of

the five curves. For example, the probability of concussion as a function of the

product of strain and strain rate is shown in Fig. 6.11, and the tolerance levels for a

25, 50, and 75 % probability of mTBI for several of the predictor variables are


shown in Table 6.4. An optimal tolerance can be found for which the sum of the

sensitivity and specificity ratio is a maximum. This is shown in Fig. 6.12 along with

the first and second tolerances. (See Sect. 1.6.3 for details.)

6.1.2 Discussion of the Results of the NFL Study

There are several important lessons we can learn from this study.

1. The data used in this study constitute actual human concussion data that cannot

be obtained in a laboratory because research policy and ethics do not allow

investigators to injure volunteer subjects. It can be argued that the data were

obtained from professional football players whose tolerance may be higher than

the average human being. It is true that to become a professional football player,

the athlete came up the ranks of high school and college football and had

experienced several if not a large number of concussions. There is information

to support the theory that repeated concussions can make the brain more

susceptible to concussion and thus the tolerance could be lower than average.

On the other hand, the professional athlete may have a tolerance that is higher

than average in order for him to become a professional football player. Thus, the

tolerance data arrived at in this study may be close to the average human

tolerance. In any case, they are the only reliable human data available so far.

Attempts have been made to collect on-field head impact data to ascertain if a

player has received a concussive blow. However, so far, the reliability and

accuracy of the data are poor. The most popular system in use is the Head

Impact Telemetry (HIT) System invented by Virginia Tech. Jadischke et al.

(2013) have shown that the method is fraught with errors and cannot be used to

ascertain if a given player sustaining a specific head impact is concussed or not.

Hopefully, more reliable systems will be available to reduce the long-term

effects of concussion by identifying players who have been actually concussed

and are not allowed back onto the field until they undergo neurological testing.

2. The tolerance data that resulted from this study are for mild concussions (mTBI)

which generally have no long-term sequelae. These data are useful in other areas

of safety research. In particular, the angular acceleration data can be used by

NHTSA for formulating a safety standard on limits of rotational motion for

vehicular occupants. It should be noted that the published literature estimated

human tolerance to angular acceleration to range from 1800 (Ommaya et al.

1970) to 16,000 rad/s 2 Margulies et al. (1990) and Pincemaille et al. (1989). NFL

data suggest that the tolerance for mTBI in terms of angular acceleration should

be about 6000 rad/s 2 .

3. It is difficult to change the culture of the impact biomechanics community that is

used to using head input parameters as criteria for tolerance. However, the

results of this study showed that tolerance to injury can be better predicted by

brain response parameters, such as brain strain and strain rate. Of course,

6.2 Simulation of Real-World Vehicular Crashes 189

response parameters can only be computed using a finite element model. This is

a deterrent for many engineers in industry who do not have the luxury of time

and resources to run the results of every dummy test they do through a model to

check for brain responses.

4. It is surprising to find that HIC ranked very high as a predictor of mTBI. As

described in Chap. 2 (Sect. 2.6.2), HIC was based on the Wayne State Tolerance

Curve (WSTC) which is a hyperbolic curve drawn in by hand through some

scattered data points with no mathematical or scientific basis. For mTBI, the

value of HIC for a 50 % probability of a mild concussion is around 250, much

lower than the 700 limit set by the NHTSA for automotive occupants.

5. It is equally surprising to find that angular acceleration ranked very low as a

predictor of mTBI considering the volume of literature that supports this parameter

as the principal (or even the only) cause of brain injury. Hardy et al. (2001)

also found that relative motion of the brain relative to the skull was due almost

entirely to head rotation and relative motion is what causes high strains in the

brain. It is contradictory to say that the product of strain and strain rate is the best

predictor while the cause of strain and strain rate (angular acceleration) is not a

good predictor. This dilemma needs to be resolved if we are to fully understand

brain injury mechanisms.

6. Viano et al. (2005) compared the predictions of the WSUHIM with the injuries

sustained by the concussed football players. They compared the predicted “hot

spots” in the brain with the signs and symptoms exhibited by the injured players.

The “hot spots” are regions of high strain or strain rate. It was found that the hot

spots migrate through the brain with time. The early strain hot spots occur in the

temporal lobe adjacent to the impact. They migrate to the far temporal region

after head acceleration. The largest strains occur later in the midbrain area which

significantly correlated with removal from play, cognitive and memory problems,

and loss of consciousness. It is concluded that strains occurring late in the

impact correlated with memory and cognitive problems.

6.2 Simulation of Real-World Vehicular Crashes

Our next example is to predict occupant injury from real-world crashes which has

been thoroughly investigated. This is a study performed by Wayne State in conjunction

with Monash University in Melbourne, Australia, by Franklyn et al. (2005)

and the crashes occurred in Australia. The first crash was at an intersection

involving a red Toyota Paseo which broadsided a large gray sedan on the right

side when it failed to stop at a red light. Recall that vehicles drive on the left side of

road in Australia and it would be a near-side impact for the driver of the sedan.

There were two occupants in the front seats of the sedan, and there was only the

driver in the Toyota. The damage to both vehicles is shown in Fig. 6.13. The driver

of the sedan had a brief period of loss of consciousness, but at the hospital, he was

assigned an AIS of zero. In this two-pronged study, the crash and its effect on the


Fig. 6.13 Damage to the two vehicles involved in an intersection crash that occurred in Australia

(taken from Franklyn et al. (2005))

Fig. 6.14 Computed

damage to the struck vehicle

(sedan) compared to the

actual damage shown on the

left side of Fig. 6.13 (taken

from Franklyn et al. (2005))

occupants were simulated by computer after which a crash test was carried out to

replicate the accident. Computer simulation involved the use of FE models of the

two impacting vehicles to replicate the damage to both so as to estimate the speeds

of the vehicles at the time of collision. A video of the computer simulation can be

found under the link https://youtu.be/wCi4bwnwAiw, and the computed damage

to the struck vehicle is shown in Fig. 6.14. The speeds that best matched the

actual damage to both vehicles would be accepted as the collision speeds from

which the vehicular accelerations and the degree of penetration of the target

vehicle were estimated. Since the FE models of the impacting vehicles included

occupants, it was possible to compute the accelerations and forces sustained by

the occupants during the crash. In our case, the region of interest was the head of

the driver of the sedan but he also sustained chest injuries. The computed head

accelerations were used as input to the WSUHIM by Zhang et al. (2001) to

compute the strain field and intracranial pressures developed in the driver’s

brain. The maximum principal strain predicted by the model was 20 %, and

approximately 2.5 % of the brain experienced a strain of 15 % or higher. The

6.2 Simulation of Real-World Vehicular Crashes 191

Midsagittal view

Coronal view

AIS 0 Case T=40 ms

Fringe Levels

A B 1.500e-01

1.350e-01

1.200e-01

1.050e-01

9.000e-02

7.500e-02

6.000e-02

4.500e-02

3.000e-02

1.500e-02

0.000e+00

Fig. 6.15 Strain contours in the brain of the sedan driver as predicted by the WSUHIM by Zhang

et al. (2001). (A) Midsagittal section and (B) coronal section (taken from Franklyn et al. (2005))

Fig. 6.16 Damage to exemplar vehicles used in a crash test to replicate the intersection accident

described by Franklyn et al. (2005). The target vehicle is on the left and bullet vehicle is on the

right (taken from Franklyn et al. (2005))

strain contours are shown in Fig. 6.15. Both the coup and contrecoup peak pressures

were less than 100 kPa. That is, the driver did not have a brain injury since the

injury threshold for strain in the midbrain and brain stem was estimated by King

et al. (2003) to be 35 % and the ICP threshold for concussion was 172 kPa for a

moderate brain contusion or small vessel hemorrhage, according to a study by Ward

et al. (1980). The crash was replicated with two exemplar vehicles at the speeds

predicted by the FE model. The damage to the test vehicles is shown in Fig. 6.16,

and the measured HIC to the head of the BIOSID dummy (a type of side impact

dummy) in the driver’s seat of the sedan was less than 75. According to Fig. 6.8, a

HIC of 75 corresponds to a probability of about 10 % for an mTBI, and according to

NHTSA estimates for AIS 1 brain injuries, the probability is less than 2.5 %


Fig. 6.17 Impact of a large

sedan with a telephone pole,

resulting in massive

intrusion of driver (right)

side compartment and an

AIS 5 brain injury to the

driver (taken from Franklyn

et al. (2005))

Fig. 6.18 A left-hand drive vehicle was used as an exemplar vehicle to recreate the pole impact in

a crash test (taken from Franklyn et al. (2005))

(NHTSA 2000). Thus, the head injury prediction of the computer simulation of the

accident is consistent with the actual injuries sustained.

Another example of a real-world crash is also taken from Franklyn et al. (2005)

who described a total of four cases. This case involved a single-vehicle crash of the

right side of a sedan into a telephone pole. The damaged vehicle is shown in

Fig. 6.17. It was driven by a 39-year-old male who sustained a maximum AIS

5 head injury due to extradural hemorrhage, temporal bone fractures, and contusions.

He also had severe chest and pelvic injuries. FE modeling was performed to

6.3 Head Injuries Sustained in Indy Racecars 193

Fig. 6.19 Posttest photographs of the pole tests show that it was a less severe impact than the

actual crash. The pole is seen in the photograph on the right (taken from Franklyn et al. (2005))

estimate the speed of impact by matching the deformation pattern. Note that an

exemplar vehicle with a right-hand drive for the planned crash test was not

available and the test vehicle had a left-hand drive. Consequently, the model also

used a left-hand drive vehicle, as shown in Fig. 6.18. The model-predicted speed of

impact was between 43 and 45 km/h, and in the crash reconstruction, the damage to

the exemplar vehicle was less severe. As shown in Fig. 6.19, the maximum crush

depth was only 2/3 of the actual depth. The measured HIC for head impact with the

B-pillar was 1789, and the corresponding probabilities for an AIS 4 and 5 injury are

43 % and 37 %, respectively (NHTSA 2000). These estimates are lower than

expected for a maximum AIS 5 injury to the driver because the crash test was not

as severe as the actual crash. This is an example of the need to validate computer

models whenever possible as their predictions can be off the mark.

6.3 Head Injuries Sustained in Indy Racecars

The raceway is also another area where injury-causing crashes frequently occur

because of the high speeds involved. Research to mitigate these injuries has not

only benefited the race drivers but also the ordinary driver on our highways.

General Motors was involved in this effort, and Dr. John Melvin was a pioneer in

promoting racecar safety. A paper coauthored by Melvin is reviewed in this chapter

to demonstrate the accelerations involved in high-speed crashes of vehicles

designed to protect the occupant.


Fig. 6.20 Top and side cutaway views of a typical Indy-type racecar (taken from Melvin et al.

(1998))

6.3.1 Some Background Information About Racecar Safety

and Crash Severities

Safety features in Indy racecars evolved over many years based on crash injury data

and the use of biomechanical knowledge to protect and restrain the driver.

Figure 6.20 is a drawing of a typical Indy racecar. The vehicle has a carbon fiber/

aluminum honeycomb composite chassis with substantial crush zones in the front

and sides, providing excellent protection for the centrally seated driver. The engine

and gearbox are located in the rear of the racecar, behind the fuel tank which is

directly behind the driver’s seat. Rear impacts can produce higher decelerations

because of the lack of energy-absorbing structures. The driving population is almost

exclusively male between the ages of 25 and 50, and their anthropometry can be

described as being similar to the 50th percentile male. Melvin et al. (1998) initiated

the installation of crash recorders in Indy cars in 1992, and by 1996, all Indy cars

were equipped with this recorder. It is rectangular box 107 112 56 mm in size

and weighs 1.14 kg. It records and stores three channels of acceleration data along

the three principal axes, sampling the data at 2000 Hz. The recording is continuous

but the storage of the data is triggered by an acceleration above 5 g for at least 5 ms.

The system can record up to ten separate impacts with each recording lasting 2 s. An

example of a deceleration trace for a severe rear impact is shown in Fig. 6.21. Note

that the duration of the pulse is almost 90 ms and is much longer than passenger

car impacts. The recorded data are routinely filtered by a SAE Channel Class

60 filter to yield vehicle chassis decelerations that characterize the rigid body

motion of the chassis. The driver is restrained by two 75-mm-wide shoulder belts

6.3 Head Injuries Sustained in Indy Racecars 195

Fig. 6.21 Example of a vehicular deceleration pulse for a severe rear impact causing a Delta V of

70 km/h (44 mph) (taken from Melvin et al. (1998))

Table 6.5 Indy car crash data summary and head response (Courtesy of Dr. L. Zhang)

Crash

number

Impact

direction

Delta

V (mph)

Peak vehicle

decel. (g)

Res linear

head accel.

Res angular

head accel.

HIC

PPK97 Rear 30 66 245 21,439 2671

IND14 LRear/ 65 120 200 11,734 3440

side

99TX LRear/ 60 130 185 12,982 2977

side

IND97 RFront 60 87 206 10,796 2836

LV99 Rear 40 102 168 10,910 2900

LAS12 LRear/ 54 127 241 17,140 2684

side

PHX99 Rear 30 90 166 11,637 2569

IND98 Rear 48 72 157 15,678 1750

IND11 Front 36 36 122 16,770 1525

and a 75-mm-wide lap belt with two rearward facing 50-mm-wide antisubmarining

straps. The head is protected by padded structures in the rear and on both sides.

Even though the driver is securely restrained in the vehicle, the decelerations

experienced by his head and arms can be quite different and higher than those

recorded by the crash recorder. Begeman and Melvin (2002) have computed head

accelerations of Indy drivers involved in crashes, using the MADYMO rigid body

model, described in Chap. 1. Zhang et al. (2004a, b) selected nine of these cases for

detailed analysis of brain response.


Table 6.6 Summary of brain responses as predicted by the WSUHIM

Injury

cases

Noninjury

cases

Intracranial

pressure

(kPa)

Coup range

Intracranial

pressure

(kPa)

Contrecoup

range

96–262 28 to

197

40–149 43 to

139

Max

principal

strain

Max

principal

strain

Max

strain

rate

(s 1 )

Max

strain

rate

(s 1 )

Product

of strain

and

strain

rate

(s 1 )

Range Average Range Average Range

0.58–0.77 0.68 172–338 259 124

0.25–0.70 0.38 65–198 107 82

6.3.2 Use of the WSUHIM to Predict Brain Response in Indy

Car Crashes

The computed head accelerations from the MADYMO model were used as input to

determine brain responses. The crash data along with the MADYMO predicted

head response are listed in Table 6.5. The first four cases listed in this table resulted

in some form of brain injury, while the last five had no brain injury but may have

injuries to other body regions. The WSUBIM calculated ICP, principal strains,

strain rates, and the products of strain and strain rate for all nine cases. The results

were not tabulated and can only be summarized under two categories, with brain

injury and without brain injury, as shown in Table 6.6. Based on known Injury

Assessment Reference Values (IARV) for passenger car occupants, these data and

results defy a logical explanation. Part of the reason is the fact that impact durations

are considerably longer than the usual automotive head impacts, as shown in

Fig. 6.21, and the traditional injury criteria may not apply. Additionally, with the

helmet hitting a padded surface, the head impact duration could even be longer.

There are no other head impact data that are in the range of duration and magnitude

experienced by racecar drivers, and more research is needed to try to understand the

increased tolerance of the human brain to these impacts. Looking at Table 6.6, we

see that there is a substantial difference in the strain-related parameters between the

brain-injured drivers and those that were not. In particular, the maximum principal

strain for the uninjured drivers was close to the limit of 0.35, a limit suggested by

King et al. (2003). Also, the noninjury ICP values were not exceptionally high,

considering the magnitudes of the input acceleration.



The use of computer models to simulate real-world events has many advantages.

Since the exact conditions of the event are unknown, the computer can be used to do

a parametric study and yield a set of results from which intelligent decisions can be

made as to the probable cause of the injuries sustained in the crash. The model can

also be used to assess human tolerance to impact injury by finding the parameters

that are good predictors of injury. The NFL study is a case in point. So far, the NFL

data stands as the only reliable source for human tolerance to head impact at the

mTBI level. For the first time, it was possible to cite a value for human tolerance to

angular acceleration without reliance on animal concussion data or the scaling of

noninjurious human volunteer data to the injury level. The model is also useful for

forensic purposes. It can and has been used in the US court system to aid the expert

witness in providing the court with reliable opinions on injury causation and

possibly the speeds involved and the directions of impact.


6.1. Mild traumatic brain injury sustained by American football players:

[ ] (i) Is due solely to angular acceleration

[ ] (ii) Can be prevented by using a well-designed helmet

[ ] (iii) Occurs with a probability of 50% if the angular acceleration is

6400 rad/s 2 and the linear acceleration is about 100 g


[ ] (v) Can best be predicted by angular acceleration

6.2. Mild traumatic brain injury sustained by American football players:

[ ] (i) Is due solely to linear acceleration

[ ] (ii) Cannot be prevented by using a current well-designed helmet

[ ] (iii) Occurs with a probability of 50% if the angular acceleration is

15,000 rad/s 2 and the linear acceleration is zero

[ ] (iv) The tolerance of the brain to linear acceleration is less than 100 g

[ ] (v) Can best be predicted by the head injury criterion (HIC)

6.3. The best predictor for mild traumatic brain injury is

[ ] (i) Angular acceleration

[ ] (ii) Strain rate in the brain

[ ] (iii) The product of strain and strain rate in the brain

[ ] (iv) HIC

[ ] (v) Linear acceleration


6.4. NFL concussion data used in conjunction with the WSUHIM show that

[ ] (i) Angular acceleration is the best predictor for concussion

[ ] (ii) HIC is not a bad predictor for concussion

[ ] (iii) The product of strain and strain rate is a poor predictor of concussion

[ ] (iv) The value of HIC for a 50% probability of concussion is well over

500

[ ] (v) Current football helmets can reduce angular acceleration

substantially

6.5. Human brain tolerance to angular acceleration is

[ ] (i) 5000 rad/s 2

[ ] (ii) 16,000 rad/s 2

[ ] (iii) 2000 rad/s 2

[ ] (iv) 100,000 rad/s 2


6.6. NFL concussion data show that

[ ] (i) The striking player is usually the one who is concussed

[ ] (ii) The average HIC for concussion is 750

[ ] (iii) The average angular acceleration required for concussion is approximately

4400 rad/s 2

[ ] (iv) Higher linear accelerations of the head result in lower angular

accelerations


6.7. The best estimate for the human limit in terms of HIC for a 50% probability

of a reversible mild traumatic brain injury is

[ ] (i) 250

[ ] (ii) 300

[ ] (iii) 350

[ ] (iv) 400

[ ] (v) 450

6.8. For minor traumatic brain injury, the angular acceleration needed to cause

concussion is approximately

[ ] (i) 6400 rad/s 2

[ ] (ii) 16,000 rad/s 2

[ ] (iii) 1800 rad/s 2

[ ] (iv) 100,000 rad/s 2

[ ] (v) 235 rad/s 2

6.9. Indy racecars are equipped with a crash recorder which

[ ] (i) Monitors the head acceleration of the driver

[ ] (ii) The impact speed of the racecar

References 199

[ ] (iii) The acceleration of the racecar

[ ] (iv) All of the above


6.10. The response of Indy racecar drivers involved in a crash has been modeled

and it was found that

[ ] (i) The resultant head linear acceleration was well below 100 g

[ ] (ii) The resultant head angular acceleration ranged from 6000 to

9000 rad/s 2

[ ] (iii) The coup intracranial pressures were almost the same for injured and

non-injured drivers

[ ] (iv) The maximum strain in the brain was less than 35%

[ ] (v) The computed HIC values were well in excess of 1000


Prob

Ans

1 (iii)

2 (ii)

3 (iii)

4 (ii)

5 (v)

6 (iii)

7 (i)

8 (i)

9 (iii)

10 (v)

References

P. Begeman, J. Melvin, Mathematical modeling of crash-induced dynamic loads on race car

drivers, in Motorsports Conference, SAE Paper No. 2002-01-3305, 2002

M. Franklyn, B. Fildes, L. Zhang, Y. King, L. Sparke, Analysis of finite element models for head

injury investigation: reconstruction of four real-world impacts. Stapp Car Crash J. 49, 1–32

(2005)



Crash J. 45, 337–368 (2001)

R. Jadischke, D.C. Viano, N. Dau, A.I. King, J. McCarthy, On the accuracy of the Head Impact

Telemetry (HIT) system used in football helmets. J. Biomech. 46(13), 2310–2315 (2013)





S.S. Margulies, L.E. Thibault, T.A. Gennarelli, Physical model simulations of brain injury in the

primate. J. Biomech. 23, 823–836 (1990)

J.W. Melvin, J. Pierce, T.W. Gideon, W.C. Little, K.J. Baron, Biomechanical analysis of Indy race

car crashes, in 42nd Stapp Car Crash Conference, SAE Paper No. 983161, Tempe, AZ, USA,

1998

NHTSA, Regulatory analysis & evaluation plans and policy final economic assessment FMVSS

No. 208 advanced air bags, Chapter III, National Highway Traffic Safety Adiminstration,

Washington, DC, 2000

A. Ommaya, R. Grubb, R. Naumann, Coup and contrecoup cerebral contusions: an experimental

analysis. Neurology 2, 388–389 (1970)


linear accelerometers. J. Appl. Mech. 42, 552–556 (1975)

Y. Pincemaille, X. Trosseille, P. Mack, C. Tarriere, F. Breton, B. Renault, Some new data related

to human tolerance obtained from volunteer boxers, in 33rd Stapp Car Crash Conference, SAE

Paper No. 892435, Washington, DC, USA, 1989

D.C. Viano, P. Lovsund, Biomechanics of brain and spinal-cord injury: analysis of neuropathologic

and neurophysiology experiments. Traffic Inj. Prev. 1, 35–43 (1999)

D.C. Viano, I.R. Casson, E.J. Pellman, L. Zhang, A.I. King, K.H. Yang, Concussion in

professional football: brain responses by finite element analysis: part 9. Neurosurgery 57,

891–916 (2005)

C. Ward, M. Chan, A. Nahum, Intracranial pressure–a brain injury criterion, in 24th Stapp Car

Crash Conference, SAE Paper No. 801304, Troy, MI, USA, 1980

L. Zhang, Computational biomechanics of traumatic brain injury: an investigation of head impact

response and American football injury. PhD Dissertation, Wayne State University, Detroit,

Michigan, 2001




L. Zhang, P. Begeman, J.W. Melvin, Brain injury prediction for indy race car drivers using

finite element model of the human head, in 2004 SAE Annual Congress, SAE Paper

No. 2004-01-3539, Detroit, MI, USA, (2004a)

L. Zhang, K.H. Yang, A.I. King, A proposed injury threshold for mild traumatic brain injury.

J. Biomech. Eng. 126, 225–236 (2004b)

Chapter 7

Impact Biomechanics of Neck Injury

The three major functions of the neck are to support the head, to allow it move

three-dimensionally, and to conduct nerve signals to and from the brain via the

spinal cord. Many muscles in the neck provide the flexibility for head motion,

while a bony vertebral column protects the delicate tissues of the spinal cord.

This protection, however, is not adequate for high-speed crashes, and a variety

of neck injuries occur when the head is impacted directly or inertially. In order

to attain a better understanding of the injury mechanisms involved, a brief

review of spinal anatomy is needed. This review covers the cervical spine as

well as the thoracolumbar spine to avoid repetition in subsequent chapters. It

also stresses certain anatomical features that are normally glossed over in

anatomical texts.

7.1 A Brief Anatomical Review of the Spinal Column

Anatomically, the spinal or vertebral column is divided into three segments. The

neck portion is called the cervical spine, and the segment in the chest is known as

the thoracic spine. The lower end of the column is called the lumbar spine and is

located behind the abdomen. Figure 7.1 illustrates the entire column as viewed

frontally, laterally, and posteriorly. It can be seen that the cervical and lumbar

spines have a similar curvature, with an anterior convexity or lordosis. The thoracic

spine is convex posteriorly and its curvature is kyphotic. The spinal column is made

up of 24 individual bones, called vertebrae, which are generally separated by

intervertebral discs, a cartilaginous tissue. There are seven cervical (C) vertebrae,

12 thoracic (T) vertebrae, and five lumbar (L) vertebrae. Typically, each vertebra

has a cylindrical vertebral body anteriorly which is composed of a thin layer of

compact bone around the sides and spongy bone inside. The ends are covered by

cartilaginous endplates. Behind the body, there is an almost circular space formed

by the pedicles or neural arch and laminae, as shown in Fig. 7.2, for a lumbar



201

202 7 Impact Biomechanics of Neck Injury

Atlas

Axis

Cervical

curvature

7 th cervical

1 st thoracic

Thoracic

curvature

12 th thoracic

1 st lumbar

5 th

lumbar

Lumbar

curvature

Pelvic

curvature

A B C

Fig. 7.1 (A–C) The spinal column viewed frontally, laterally, and posteriorly (taken from Gray

(1995)). Reprinted from Gray’s Anatomy: The Anatomical Basis of Medicine and Surgery, 38th

edn. by Gray, (Churchill Livingstone), 1995, with permission from Elsevier

vertebra. This space is called the vertebral or spinal canal through which the spinal

cord and its associated membranes pass. There are superior and inferior facets

which project from the laminae to form the facet joints which are true synovial

joints covered by a capsule, the facet capsule. The typical vertebra also has a

spinous process which extends posteriorly, and the distal ends of these processes

can be felt by running the fingers down the middle the back. There are also two

transverse processes which project laterally from the pedicles.

Intervertebral discs are located above and below each vertebral body except

between the skull and C1 and between C1 and C2. There is a disc between L5 and

the sacrum, which is part of the pelvis. A typical disc has a central core containing a

7.1 A Brief Anatomical Review of the Spinal Column 203

Fig. 7.2 Top, side, and rear views of a typical vertebra. In this case, it is a lumbar vertebra

gel-like material called the nucleus pulposus and an outer ring of 16–20 layers of

cartilage, called the annulus (anulus) fibrosus. The nucleus is mainly made up of

proteoglycans with some type II (hyaline) collagen fibers, while the annulus is

mainly composed of type I (skin) collagen with some proteoglycans. The annular

layers of the disc are shown in Fig. 7.3 in which the thickness of the annular layers

has been exaggerated to demonstrate their anatomy. The collagen fibers run

obliquely and in orthogonal directions in alternate layers. Within each layer, there

is a vertical joint located principally in the posterolateral quadrant of the disc. These

joints represent weak spots for the disc and disc herniations tend to occur in this part

of the disc. The disc is avascular and receives its nutrients via the endplates.

Mechanically, the discs act as shock absorbers and cushion the spine when it is

subjected to a vertical (caudocephalad) impact. They increase in size from the

cervical spine to the lumbar spine in proportion to the body weight they bear. Note

that proteoglycans is hygroscopic. That is, it absorbs water and tends to expand.

Since the nucleus pulposus contains a large amount of proteoglycans, it builds up an

osmotic pressure when it cannot absorb the water around it. This osmotic pressure

partially supports the load borne by intervertebral discs.

In addition to the intervertebral discs, the vertebral column is also held together

by ligaments which run along the spine. There are continuous ligaments which run

along the entire length of the spine, and there are short ligaments that hold adjacent

vertebrae together. Ligaments at the lumbar level are shown in Fig. 7.4.


Fig. 7.3 Annular layers of an intervertebral disc in which the collagen fibers run at an oblique

angle to the axis of the spine with the angles in alternating layers almost orthogonal to each other

Anterior longitudinal ligament

Superior articular process

Ligamenta flava

Interspinous

ligament

Supraspinous

ligament

Intervertebral disc

Posterior longitudinal ligament

Inferior articular process

Fig. 7.4 Ligaments of the spine—there are three continuous ligaments and several shorter ones

that run between vertebrae (taken from Drake et al. (2008)). Reprinted from R.L. Drake, A.W.

Vogl, A.W.M. Mitchell, R.M. Tibbitts, P.E. Richardson, Gray’s Atlas of Anatomy, 2008, with

permission from Elsevier

7.1 A Brief Anatomical Review of the Spinal Column 205

The continuous ligaments are the anterior longitudinal ligament which runs along

the anterior surfaces of the vertebral bodies and discs, the posterior longitudinal

ligament which runs along the posterior surfaces and discs, and the supraspinous

ligament which connects the posterior tips of the spinous processes of the vertebrae

in the back of the spine. The short ligaments include the ligamentum flavum (also

known as the yellow ligament) which are found between the laminae of adjacent

vertebrae, the interspinous ligament which connect the adjacent spinous processes,

and the facet capsules that surround the facet joints at each vertebral level. This

complex of ligaments provides the spine with mechanical stability which is also

maintained by the many muscles that originate and insert into spinal processes and

posterior aspects of the vertebrae.

The spinal cord begins at the foramen magnum of the skull and is a continuation

of the brain stem. It gives off a pair of nerve roots at each vertebral level through the

space between adjacent neural arches, behind the intervertebral discs. The dura

mater and the other meninges which cover the brain also surround the cord up to the

L1 level. There the cord splits into pairs of lumbar nerve roots that emerge from

each of the lumbar vertebrae. The nerve roots have an anterior and dorsal component,

as shown in Fig. 7.5. The anterior root is composed mainly of motor nerve

fibers that activate muscles, while the dorsal root consists mainly of sensory fibers

that carry signals to the brain. The cord has both gray and white matter, but, in

contrast to the brain, the gray matter is found in the center of the cord and is

surrounded by white matter which constitute the long fibers conducting signals to

and from the brain.

Synapses

Gray

matter

White

matter

DORSAL ROOT

Interneuron

Spinal ganglion

(dorsal root ganglion)

Cell body of sensory neuron

Ventral

rootlets

Ventrolateral sulcus

VENTRAL

ROOT

Ventral

ramus

SPINAL NERVE

Dorsal ramus

To effector muscle

From receptor

Fig. 7.5 Sketch of the cross section of the spinal cord and a pair of nerve roots. Unlike the brain,

the white matter is in the periphery of the cord enclosing the gray matter. Each nerve root has a

ventral (anterior) root that is mainly motor and a dorsal (posterior) root that is mostly sensory

(taken from Carola et al. (1992)). Republished with permission of McGraw-Hill Education, from

R. Carola, J.P. Harley, C.R. Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992;



Fig. 7.6 The C1 and C2

vertebrae are linked

through the odontoid

process which is held

by a transverse ligament

to C1 (taken from

morphopedics.wikidot.com/

broken-neck)

Atlas (C1)

Articular facet

for dens

Lateral mass

Superior articular

facet for occipital condyle

Axis (C2)

Superior articular

facet for the atlas

Dens

Transverse foramen

Lateral mass

In terms of the cervical spine, the first two cervical vertebrae are atypical. The

first cervical vertebra, C1, articulates with the skull and is also known as the atlas

because it holds up the head, analogous to the Greek god that holds up the globe. It

allows axial rotation of the head and is also known as the “no” vertebra. C1 does not

have a vertebral body but has a space that is occupied by a projection of the body C2

into it. This projection is known as the odontoid process or dens because it is shaped

like a tooth, as shown in Fig. 7.6. The dens is held in place by a transverse ligament.

C2 is called the axis and the relative motion between C1 and C2 results in a nodding

motion of the head. Thus, C2 is also known as the “yes” vertebra. The other cervical

vertebrae (C3–C7) are more like the typical vertebrae described above. However,

there is a unique feature of the cervical vertebrae. The vertebral artery on both sides

of the cervical spine passes through the neural arch of each vertebra, and the two

holes in the arch are unique to these vertebrae.

The facets of the cervical spine are best visualized laterally, as shown in Fig. 7.7.

They form an oblique angle which is steeper in the upper cervical spine and

becomes shallower further down the spine. This anatomical feature may have

implications as to why neck pain due to whiplash occurs mainly in the lower

cervical spine. See Chap. 8 for details.

The spine is a complex structure made up of many different types of tissue. It not

only has a mechanical function to keep the body upright but also has a neurological

function to control motor activities and to sense changes in the surroundings of the

body. Next to the brain, it is a marvelous structure that is compact and efficient.

Some of these features will become evident when we study its biomechanics.

7.2 Impact Injuries of the Cervical Spine 207

Anterior tubercle

of CI (atlas)

Posterior tubercle of CI (atlas)

CI (atlas)

Lateral

atlanto-axial

joint

CII (axis)

Intervertebral

disc

Zygapophysial joint

CIII

CIV

Intervertebral

foramen

CV

Anterior tubercle

of CVI

(carotid tubercle)

CVI

Foramen

transversarium

CVII

Column of articular

processes

Spinous

processes

Vertebra prominens

(spinous process of CVII)

Fig. 7.7 Lateral view of the cervical spine which shows that the slope of the facet (zygapophysial)

joint tends to decrease at the lower cervical levels (taken from Drake et al. (2008)). Reprinted from

R.L. Drake, A.W. Vogl, A.W.M. Mitchell, R.M. Tibbitts, P.E. Richardson, Gray’s Atlas of

Anatomy, 2008, with permission from Elsevier

The fact that head motion is dependent on the response of the neck means that an

understanding of neck response will enable the vehicle designer to determine the

extent of head excursion in crash situations and thus avoid head contact with the

interior of the vehicle.

7.2 Impact Injuries of the Cervical Spine

The cervical spine has the capability of supporting and controlling the motion of the

head and of transmitting nerve signals to and from the brain via the spinal cord. It is,

however, vulnerable to injury when large loads are applied to the head. It is more

frequently injured in automotive crashes compared to frequency of injuries to the

thoracolumbar spine. For biomechanical engineers, catastrophic neck injuries that

cause paralysis in the form of quadriplegia are a major concern, and such injuries

are known to have occurred in vehicular rollovers, severe rearend collisions, and

out-of-position airbag deployments. On the other end of the spectrum of neck

injuries is the issue of “whiplash” due to minor rearend collisions. We will discuss

this subject in the next chapter as it is biomechanically an “unusual” injury to say

the least and does not fit in with how injury is normally studied.


7.2.1 Activities that Can Cause Neck Injuries

Neck injuries occur during motor vehicle crashes as well as in many forms of

sporting activities, including extreme sports, football, rugby, gymnastics, bicycling,

horseback and all-terrain vehicle (ATV) riding, jumping on trampolines and inflatable

“bouncers,” and diving into shallow pools. In motor vehicle crashes, the

principal mechanism is compression and flexion. That is, the occupant’s body is

moving relative to the vehicle, and the head is stopped by a vehicular structure, such

as a roof rail or the B-pillar. The neck is thus compressed and caused to flex by the

inertia of the body following the head. So with the exception of whiplash injuries,

most occupant neck injuries are due to this compression-flexion mechanism. It turns

out that in sporting activities, the compression-flexion mechanism is a frequent

cause of neck injuries. This is certainly true for football and rugby when a defender

uses his head to tackle an opposing player, resulting in a compression-flexion injury.

But in gymnastics, head contact with the mat (or ground) coupled with the inertia of

the rest of the body following the head will produce the same compression-flexion

injury seen in football. In rugby, the neck can be injured in hyperextension, while the

players are scrumming for the ball. In bicycling and horseback and ATV riding, the

rider will fly over the horse’s head or the handlebars if the horse or vehicle stops

suddenly, and the rider’s momentum carries him/her forward, causing the head to

strike the ground, and the neck is compressed by both the impact and by the inertia of

the body following the head. The same thing happens to bouncers on trampolines or

inflatable structures if they lose control and fall on their head. Diving into a shallow

pool produces the same result, but divers are often under the false impression that

resistance of the water will decelerate the body to a safe speed. In the first meter or

so, the speed is not substantially reduced, and a catastrophic injury will occur. The

biomechanics of the compression-flexion injury is described in the next section.

7.2.2 Mechanisms of Cervical Spine Injuries due to Impact

Various loading types on the head can cause cervical spine injuries. The leading

modes of impact are vertical compression, compression and flexion, compression and

extension, and torsional loading. Axial vertical compression of the head can cause a

Jefferson fracture which is a fracture of the anterior and/or posterior neural arch of

C1. Figure 7.8 shows a multipart Jefferson fracture. Axial loading can also cause

burst fractures of the vertebral body which causes the body to disintegrate and the

bony fragments to impact and possibly injure the spinal cord. An axial CT scan of a

C5 burst fracture is shown in Fig. 7.9 in which there is considerable retropulsion of

bony fragments into the spinal canal.

Catastrophic neck injuries can occur when there is compression and flexion of the

neck due to an eccentric compressive load. Injuries can vary from a wedge fracture

of the vertebral body to burst fracture or an anterior dislocation in which the inferior


Fig. 7.8 Jefferson fracture

of C1 – Multipart fracture of

the anterior and posterior

arch

Fig. 7.9 A vertebral

“burst” fracture in which the

fractured segments impact

the spinal cord during the

fracturing process

facets of the upper vertebra overrides the superior facets of the vertebra below and

the upper vertebra is displaced anteriorly, causing injury to the spinal cord. Quadriplegia

usually results from this injury. The three forms of flexion-compression

injury are shown in Fig. 7.10. In Fig. 7.11, there is a severe subluxation of C3 over C4

from a motorcycle crash in which the rider is thrown over the handlebars and the

head impacts the road surface and stops, while the rest of the body continues to move

in the direction of the head, causing compression and flexion of the neck. This type

of compression force is the result of the inertia of the body following the head and

neck and is a common mechanism for this catastrophic injury.


Fig. 7.10 Three forms of

compression-flexion

injuries: (A) Wedge

fracture. (B) Burst fracture.

(C) Anterior dislocation

with locked facets (taken

from McElhaney et al.

(2002)). Reprinted from

Accidental Injury, 2nd edn.

ed. by A. Nahum, J. Melvin,

Chapter 15, Biomechanical

aspects of cervical trauma,

J.H. McElhaney, R.W.

Nightingale, B.A.

Winkelstein, V.C. Chancey,

B.S. Myers, 2002, With

permission of Springer

Fig. 7.11 Compression-flexion neck injury sustained by a motorcyclist. The neck compression is

generated by the inertia of the body following the head and neck (taken from McElhaney et al.

(1993)). Reprinted from Accidental Injury, 1st edn. ed. By A.M. Nahum, J.W. Melvin, Chapter 14,

Biomechanical aspects of cervical trauma, J.H. McElhaney, B.S. Myers, 1993, With permission of

Springer


A combined compression extension load can cause injury to the spinous

processes. In the automotive environment, such loading is no longer common

because most occupants are now restrained by a lap-shoulder belt. For an unrestrained

occupant, especially the right front passenger, a frontal impact would cause

the body to slide forward on the seat and the face to impact the rearward slanting

windshield, while the occupant tends to rise from the seat creating a compressive

force in the neck. Another form of injury is due to torsion when the head is violently

rotated axially about the neck, perhaps causing dislocation of the atlanto-occipital

joint. This form of fatal injury is not known to occur in car crashes and is seen more

often in James Bond movies.

For a restrained occupant involved in a frontal crash, horizontal (transverse)

shear forces are developed in the neck while is also flexed forward. Severe shear

forces can cause the head to move forward and separate from the neck at the skull/

C1 (atlanto-occipital) joint. Similarly, in a severe rearend collision, the separation

can occur in reverse. In both cases, the odontoid can be fractured or the transverse

ligament holding it in place can be torn. If there is severe lateral bending of the neck

in a side impact, nerve roots exiting from the cervical spine can be avulsed, and the

transverse process can be fractured.

A pure tensile load on the neck can cause atlanto-occipital separation. If there is

tension coupled with flexion, there can be bilateral facet dislocations. Tension

coupled with extension is seen in whiplash. The associated injuries in severe

rearend collisions are anterior longitudinal ligament tears and splitting of an

intervertebral disc transversely. This latter injury occurs to degenerated discs and

is a severe injury. In some papers and books, disc separation is mistakenly

described as disc rupture, confusing this injury with the herniation of disc material

from the side of the annulus fibrosus. Based on available information, it is the

author’s opinion that it is not possible to rupture a disc with a single impact unless

there is massive fracture of the adjacent vertebral bodies. Further discussion of this

issue can be found in Chap. 9. The vertebral body can also fracture across a

transverse plane. The tension extension mechanism is shown in Fig. 7.12 which

shows impact with the dash in an automobile in Fig. 7.12A, whiplash hyperextension

with neck tension in Fig. 7.12B, and an out-of-position occupant being

injured by an airbag in Fig. 7.12C. Figure 7.13 is an example of a C1/C2

separation seen in a cadaver experiment involving impact with a pre-deployed

airbag (Cheng et al. 1982).

When a prisoner is hanged, the neck load is not purely tensile, with the neck

placed in extension. If the procedure is carried out correctly, the C2 vertebra is

fractured, causing the spinal cord to rupture at that level. Any injury to the cord

above C3 is inevitably fatal as all vital functions (heart beat and respiration) cease

with high cervical injuries. Figure 7.14 shows a hangman’s fracture in which the C2

vertebra is fractured and separated at the pedicles.

In summary, severe or catastrophic injuries involve the spinal cord. To injure the

cord, the alignment or integrity of the cervical spine needs to be disrupted. However,

it is not necessary to sever the cord to cause paralysis. Bony contact of the

vertebrae with the cord because of a decrease in the diameter of the spinal canal is


Fig. 7.12 Examples of

tension extension injuries:

(A) Chin impact with

an automotive dash.

(B) Whiplash

hyperextension

with neck tension.

(C) Out-of-position

occupant injured by an

airbag causing C1/C2

separation (taken from

McElhaney et al. (2002)).

Reprinted from Accidental

Injury, 2nd edn. ed. by A.

Nahum, J. Melvin, Chapter

15, Biomechanical aspects

of cervical trauma, J.H.

McElhaney, R.W.

Nightingale, B.A.




Fig. 7.13 Airbag induced

C1/C2 separation in a

cadaver (based on Cheng

et al. (1982))

7.3 Experimental Studies on Cervical Spine Injuries 213

Fig. 7.14 Hangman’s fracture at C2 which is separated at the pedicles causing failure of the spinal

cord and death (taken from Rockwood and Green (1984))

often sufficient to damage the cord. Mild injuries involve the ligaments and tendons

of the spine without neurologic damage. Whiplash pain is one such mild injury. The

mechanisms and causes of whiplash pain are discussed in Chap. 8.

7.3 Experimental Studies on Cervical Spine Injuries

Severe neck injuries were rarely reported in frontal automotive collisions, especially

among the restrained occupants. Patrick et al. (1974) found only three

cervical fractures among 128 cases of frontal collisions involving belted occupants

of Volvo cars. This injury picture was confirmed by other studies of accidents

involving occupants in frontal impacts (Hartemann et al. 1977; Rattenbury et al.

1979). Huelke et al. (1979) found severe neck injuries to be rare among three-point

belted occupants, but when they did occur, they sustained fatal upper cervical

fractures, such as hangman’s fractures and atlanto-occipital (C1/C2) separation.

Experimental studies involving neck response and injury mechanisms were

generally performed using human cadaveric subjects because the only animal that

has the erect cervical spine is the subhuman primate, and it has been difficult to

obtain permission from institutional review boards to carry out impact injury

studies on these primates over the last several decades. There was only one

experiment using rhesus monkeys by a group of federal government researchers

(Thomas and Jessop 1983) who attempted to determine the level of -G x acceleration

necessary to cause a fatal injury at the head/neck junction. Frontal impact studies

involving three-point belted cadavers were conducted by many researchers, and at


g-levels below 25 g, only a few injuries were observed (Schmidt et al. 1975;

Cromack and Ziperman 1975; Patrick and Levine 1975; Levine et al. 1978). At

higher g-levels, vertebral body and odontoid fractures as well as disc separation and

ligamentous ruptures were seen (Lange 1971).

With the advent of the airbag and an increase in highway speed limits, severe

neck injuries became more of a concern. Early airbags were found to cause a variety

of injuries among out-of-position occupants, including neck injuries. If the bag

interacted with an occupant’s head while it was deploying, it could cause severe and

fatal neck injuries. One example would be for the bag to deploy while the chest of

the driver was right up against the steering wheel. In this case, severe upper cervical

spinal injuries are the inevitable result. These data were never published, but the

automotive manufacturers were keenly aware of this problem. Also, with increasing

highway speeds, rollovers became a more common place, and occupants sustained

severe neck injuries as a result.

One of the only published experiments on airbag-related neck injury was

conducted by Cheng et al. (1982) who performed frontal impact tests of six

cadavers against a stiff pre-deployed airbag to study the risk of neck injury due to

airbag deployment. The original intent of the study was to evolve a standard testing

procedure for airbags and to eliminate deployment variability. A pre-deployed and

unvented driver-side airbag, with a vertically aligned steering wheel supporting it,

fixed to a rigid wall while a front-facing seated cadaveric subject was placed on a

sled and accelerated to 48 km/h (30 mph) to impact the airbag. The sled deceleration

peak was about 38 g, and the duration of the triangular deceleration pulse was

about 100 ms. The experimental setup is shown in Fig. 7.15. When three of the six

cadavers sustained fatal or life-threatening injuries, the project became a study on

airbag-induced injuries. One such injury is shown in Fig. 7.13. The estimated

resultant (tensile) neck loads in the three “fatal” cases exceeded 6 kN. However,

exactly how the airbag stretched the neck was unclear until a computer model of the

neck was used to simulate the experiment. This is described in Sect. 7.5 below.

Severe neck injuries due to vehicular rollovers can be sustained by restrained as

well as unrestrained occupants. They occur when the head and torso move toward

the roof rail or the roof. The head is stopped, but the torso continues to move in the

same direction, producing the classic compression-flexion load on the neck. As

mentioned above, this type of loading can lead to fracture dislocation and overriding

of facets with catastrophic results. One of the first cadaveric studies to simulate

crown-head impact with the interior of a vehicle in a rollover was conducted by

Nusholtz et al. (1983) who carried out free drop tests of whole cadavers to create a

crown impact. Since this was one of the first experiments of its kind, there was

inadequate control of the initial curvature of the cervical spine, and the data were

rather scattered. The force of impact was highly dependent on the alignment of the

cervical spine, and if it was able to flex, it could not carry a large load. Thus, the

impact loads generated at the head were inconsistent and so were the injuries. A

second attempt by the same research group (Alem et al. 1984) consisted of two

series of vertex impacts on 19 cadavers with a 10-kg padded impactor traveling at

speeds of 7–11 m/s. With better control of the initial curvature, compression


Fig. 7.15 Test setup for the pre-deployed airbag test. The airbag and steering column are

stationary, and the seated test subject is on sled that is accelerated into the airbag (taken from

Cheng et al. (1982))

fractures and tearing of the anterior longitudinal ligament were obtained.

Yoganandan et al. (1986) dropped 16 whole cadavers vertically with the head

down from a height of 1.5 m. The neck was aligned (flexed) to achieve maximal

axial load. Eight of the cadavers had additional neck restraint in the form of

simulated muscles. Vertebral body damage occurred most often when the head

remained in contact with the ground without substantial rotation or rebound,

indicating that the ability of the neck to withstand axial load depends in large part

on how straight the spine is. Because of the lordosis of the cervical spine, it

becomes straight when it is flexed.

Nightingale et al. (1997) of Duke University extended the crown impact study by

looking at the effect of a 15-deg change in the orientation of the surface that was

impacted. The change in the shape of the spine was recorded on high-speed video.

The test setup is shown in Fig. 7.16. The head and neck complex was attached to a

metal block weighing 16 kg at the level of T1 and was dropped upside down onto a

rigid or padded surface which was either horizontal or inclined at 15 deg with

respect to the horizontal. There were also some tests at +30 deg. The polarity of the

slopes is defined in Fig. 7.17. Anterior loading was positive and posterior loading

was negative. Vertical loading had a zero-degree slope. At 15 deg, the neck flexed

anteriorly, and the contact force or axial impulse was the lowest in this configuration

as the head was able to move out of the way. The neck did not have to manage

the mass of the following torso and was not injured. At 0 and +15 deg, there were


Fig. 7.16 Neck drop test experiment conducted by Nightingale et al. (1997)

Fig. 7.17 Surface orientations used for neck drop test experiments (courtesy of Dr. Roger

Nightingale)

many unstable injuries in the form of fractures and dislocations that could have

resulted in damage to the cord and a high risk for quadriplegia. When the surface

was padded, stable injuries occurred at 15 deg because the padding caused the

head to pocket and prevented it from moving out of the way. As a result, the

compressive neck loads increased even though padding decreased the head contact

force. Overall, padded impacts resulted in more severe injuries. For this reason, the


Fig. 7.18 Buckling

of the cervical spine

was observed during

the impact (Nightingale

et al. 1997)

underside of car roofs is not padded. It was observed that the neck underwent

buckling, as shown in Fig. 7.18. It is not clear how the S-shape is directly related to

the observed injuries, but injury was observed to occur long before the direction of

neck bending was determined. For rigid impacts, injury occurred between 2 and

9 ms after impact, while 90 deg of head rotation occurred at 90 ms. Thus, head

motion is not a predictor of the type of injury sustained. Flexion injuries can occur

when the head is found in the extended position at the end of the impact.

Another important contribution from Duke was by McElhaney et al. (1983) who

observed that small changes in the initial position of the head influenced the type of

neck injury sustained. That is, head position determines the initial curvature of the

cervical spine and that, in turn, affects how it will bend under a crown impact. This

was the reason why Nusholtz et al. (1983) had difficulty analyzing the data in their

paper. Similarly, Torg (1982), who was a college football coach, observed that the

neck is more easily injured when flexed, that is, when the vertebrae are aligned to

take axial load. Pintar et al. (1990) also noted that burst fractures could only be

produced with the neck pre-flexed so that almost all of the compressive load was

borne by the vertebral bodies. Hodgson and Thomas (1980) suggested that restriction

of the atlanto-occipital joint greatly increased the risk of injury, and

Yoganandan et al. (1986) noted that head constraint increased the measured axial

load and number of injuries. Myers and Nightingale (1999) stated pretty much the

same thing and added that neck fracture dislocations require a combined load of

compression and bending. The definitive experiment was done by Nightingale et al.

(1991), a colleague of Prof. McElhaney. They tested whole cervical spines with

different end conditions. The neck was able to withstand higher peak loads with

increasing amounts of constraint and so did the severity of the injuries. The three

end conditions are shown in Fig. 7.19. When unconstrained, the neck flexed easily

and was unable to withstand much of an axial load. Injuries were rare under these

conditions. With partial (rotational) constraint, the deformation was much less and

it could take more axial load. With a full constraint, there was minimal flexion

deformation, and the neck was able to withstand large axial loads. If these loads

exceeded the tolerance of the spine, catastrophic injuries occurred. Failure loads,

deflections, and injuries are shown in Table 7.1.


Fig. 7.19 Effect of end conditions on the deformation of the cervical spine. When unconstrained,

the spine bends easily and is not able to withstand axial loads. With rotational constraints, it does

not deform as much and can withstand more axial load. When fully constrained, it is capable of

withstanding large axial loads with little bending deformation. Injury severity increases with the

degree of constraint (taken from Nightingale et al. (1991))

Table 7.1 Neck response as a function of end condition restraints—peak loads, peak deflections,

and resulting injuries if the tolerance of the neck is exceeded (taken from Nightingale et al. (1991))

End condition Peak load (kN) Peak deflection (mm) Injury

Unconstrained 0.3 86 None

Rotational constraint 1.7 29 Bilateral facet dislocation

Full constraint 4.8 14 Wedge/compression fracture

7.4 Tolerance of the Cervical Spine 219

7.4 Tolerance of the Cervical Spine

7.4.1 Tolerance of the Cervical Spine to Extension

and Flexion

Early research by Mertz and Patrick (1967, 1971) formed the basis for tolerance

(or response) curves for neck extension and flexion. They were largely based on

tests performed on a single volunteer (Patrick) who was the dissertation advisor to

Mertz. Thus, the results are for voluntary tolerance at the “ouch” level at which

testing was stopped to avoid injury. They were finalized by Mertz et al. (1973) and

are shown in Figs. 7.20 and 7.21 for neck extension and flexion, respectively. The

envelopes were synthesized from static volunteer, dynamic volunteer, and cadaver

data and were representative of the response of a tensed individual. Patrick

volunteered to be the test subject because he had the body dimensions close to

those of a 50th percentile adult male and was the only known PhD advisor who rode

the sled to collect data for his student’s dissertation. The reasons used to develop the

envelopes can be found in Mertz and Patrick (1971).

A similar curve for lateral bending of the neck was obtained by Patrick and Chou

(1976) based on data from four volunteers, as shown in Fig. 7.22. The width of the

corridor is somewhat surprising. Again, this is an envelope for noninjurious lateral

bending.

There is another set of volunteer data obtained by Dr. Channing Ewing and his

team at the Naval Biodynamics Lab in New Orleans. Neck flexion and lateral

bending sled tests were conducted using Navy volunteers, and kinematic data of

80

MOMENT ABOUT HEAD-NECK JUNCTION (N-m)

60

40

20

0

0

(85,68)

(95,68)

(70,48)

(90,48)

(22.5,31)

(60,31) (80,31)

20 40 60 80 100

HEAD ROTATION RELATIVE TO TORSO (deg.)

Fig. 7.20 Neck loading corridor for extension (rearward bending), based on Mertz et al. (1973)



200

160

120

80

40

0

0

(70,190) (80,190)

(60,88)

(80,88)

(15,61) (45,61)

(70,61)

20 40 60 80 100


Fig. 7.21 Neck loading corridor for flexion (forward bending), based on Mertz et al. (1973)

60


50

40

30

20

10

(0,14)

(10,41)

(40,54) (50,54)

(35,41)

0

0

10 20 30 40 50


Fig. 7.22 Neck loading corridor for lateral bending, based on Patrick and Chou (1976)

head motion were collected with great precision. The lab no longer exists, and the

massive data set is now stored at the US Army Aeromedical Research Lab

(USAARL) in Dothan, AL. Several papers were published to report the data, but

only a limited amount of biomechanical analysis was done to analyze response and

7.4 Tolerance of the Cervical Spine 221

tolerance. This study was motivated by the observation that pilots of Navy planes

attempting to land on aircraft carriers and miss the deck do not survive. Although

these aircraft have ejection seats that work at zero velocity and zero altitude, the

ditched pilots do not eject and go down with the plane. Dr. Ewing wanted to find out

the reason for their failure to save themselves. A possible explanation is provided

below under cervical spine modeling.

7.4.2 Tolerance of the Cervical Spine to Compression

While it is of interest to know the tolerance of individual vertebrae to compression

(Sonoda 1962), the knowledge of the tolerance of the entire cervical spine is more

practical and relevant. In an attempt to study spearing injuries in American football,

Mertz et al. (1978) used the Hybrid III dummy to reconstruct high school football

spearing maneuvers in association with a mechanical tackling machine. Compressive

forces registered by the load cell at the occipital condyles of the dummy were

correlated with the injuries sustained. After considerable analysis of the data, the

results shown in Fig. 7.23 were offered for judging the severity of such loads to the

50th percentile adult male population (as opposed to high school football players).

For impact durations in excess of 30 ms, the tolerance of the neck is 1100 N. It is

higher for shorter durations. One criticism of this work that has been voiced is that

the Hybrid III neck is less compliant in axial compression than the human neck and

the forces sustained by the human may not be the same as those measured in the

dummy. Nevertheless, Mertz et al. (2003) extended this tolerance to large males,

females, and children of different ages. This 2003 paper is a treasure trove of

5000

AXIAL COMPRESSIVE NECK FORCE (IN)

4000

3000

2000

1000

0

0

POTENTIAL FOR SIGNIFICANT NECK INJURY

DUE TO AXIAL COMPRESSION LOADING

SIGNIFICANT NECK INJURY

DUE TO AXIAL NECK COMPRESSION

FORCE UNLIKELY

1100

10 20

30 40

DURATION OF LOADING OVER GIVEN FORCE LEVEL (ms)

Fig. 7.23 Tolerance of the cervical spine as a function of duration of impact for the mid-size male

(based on Mertz et al. (2003))


Fig. 7.24 Cervical spine

tolerance values from Duke

and the Medical College of

Wisconsin differ

considerably (courtesy of

Dr. Roger Nightingale)

tolerance (Injury Reference Assessment Values or IARV’s for short) information

for all types of impact to almost all body regions.

In separate studies by researchers at Duke University (Nightingale et al. 1997)

and the Medical College of Wisconsin (Pintar et al. 1990), the tolerance levels for

both male and female cervical spines differed considerably, as shown in Fig. 7.24.

One reason for this discrepancy is the initial curvature of the cervical spine. If the

tolerances for males are averaged and corrected for age, the tolerance for the young

human male is 3.58–3.73 kN (Nightingale et al. 1997). This tolerance is not

dependent on duration of impact and is much higher than the value proposed by

Mertz et al. (1978) for impact durations in excess of 30 ms.

7.4.3 Tolerance of the Cervical Spine to Tension

Mertz et al. (2003) also provided IARV’s for the neck in tension. Figure 7.25 shows

the tolerance to tensile loading as a function of impact duration for the midsize

(50th percentile) male. Again, the tolerance for impact durations in excess of 45 ms

is 1.1 kN. Data for other sizes and females are available in Mertz et al. (2003).

The dynamic load to cause failure of the occipito-atlantal ligaments was

1.5 0.5 kN (Sances et al. 1982), and the quasi-static failure load in tension was

0.5 kN with an extension moment of about 4 N.m (Panjabi and Myers 1995). These

loads are low compared to the proposed tensile tolerance load of 1.16 kN by Mertz

and Patrick (1971) for posteroanterior acceleration. Clemens and Burow (1972)

suggested loads between 1.6 and 2.2 kN. Chancey et al. (2003) suggested that by the

inclusion of the neck musculature, the maximum tensile load can be as high as

3.1 kN for the unaware subject and 3.7 kN for the tensed subject.

7.5 Computer Models of the Cervical Spine 223

SPINE

POTENTIAL FOR SIGNIFICANT NECK INJURY

DUE TO AXIAL NECK TENSION LOADING

AXIAL TENSILE NECK FORCE (IN)

4000

3000

2000

4170

3670

SIGNIFICANT NECK INJURY DUE

TO NECK TENSION FORCE UNLIKELY

1100

1000

0

0 10 20 30 40

DURATION OF LOADING OVER GIVEN FORCE LEVEL (ms)

Fig. 7.25 Tolerance of the cervical spine to tensile loading, based on Mertz et al. (2003)

7.4.4 Tolerance of the Cervical Spine in Shear

Tolerance data for shear are limited to loads required to produce transverse ligament

failure and odontoid fracture at the atlanto-occipital joint. According to a

study by Fielding et al. (1974), the transverse ligament failure load for anterior

motion of C1 is 824 N (185 lb). There is also a fracture load for the odontoid. In

extension, it is 1.74 0.44 kN (391 99 lb), based on a study by Doherty

et al. (1993).

7.5 Computer Models of the Cervical Spine

One of the first models developed was by Belytschko et al. (1973). It was a 3-D

discrete parameter model of the thoracolumbar spine, consisting of rigid vertebrae

connected by springs and dashpots. Prasad and King (1974) formulated a 2-D

discrete parameter model of the entire spine, including the cervical spine. Similar

models were developed by Deng and Goldsmith (1987) and de Jager et al. (1996).

In both of these models, there was simulation of the passive resistance of the neck

musculature. The last model of this ilk was by Camacho et al. (1997). It simulated

the cervical spine with rigid bodies, but it had a finite element head model to

simulate the near vertex impact tests conducted by Nightingale et al. (1997). The

model was validated against several experimental parameters.


Fig. 7.26 The 3-D neck

model by Kleinberger

(1993)

Saito et al. (1991) developed a 2-D finite element model of the cervical spine to

study clinical problems related to spinal surgery, while Clausen et al. (1996)

formulated a model of C5–C6 to study the effect of surgical intervention. FE

models simulating neck response to impact were developed by Kleinberger

(1993), Nitsche (1996), Yoganandan et al. (1996), and Yang et al. (1998). The

Kleinberger model had accurate geometric representation of the vertebrae, but the

facet joint was modeled incorrectly because the joint cartilage had the same

properties as those of the intervertebral disc (Fig. 7.26). Validation was based on

an 8-g neck flexion test conducted at the Biodynamics Research Lab. The model

predicted the same trend, but the predicted magnitude of neck flexion was less than

that measured experimentally. The 3-D FE model by Nitsche (1996) also simulated

the volunteer runs performed at the Biodynamics Research Lab and was validated

against these data. A simplified neck geometry was used. The FE model by

Yoganandan et al. (1996) only simulated the motion segments from C4–C6, as

shown in Fig. 7.27. The anatomical representation was accurate, but, because it did

not simulate the entire cervical spine, it could only be validated against data from

static tests. The FE model by Yang et al. (1998) is discussed in the next section.

7.5.1 The Three-Dimensional Neck Model by Yang et al.

(1998)

This is one of the latest and most comprehensive neck models available in the

literature. While new models continue to appear in the literature, this model has

withstood the test of time and should be studied in detail. The purpose of developing

this model was to create a realistic FE model of the neck that could be validated

against more than one data set and to demonstrate its use in the simulation of an

injury producing experimental study.

The 3-D geometric data needed to formulate the model was taken from an MRI

scan of the neck of healthy 29-year-old male subject with a body weight of 75 kg.


Fig. 7.27 The 3-D partial

cervical spine model by

Yoganandan et al. (1996)

Fig. 7.28 Human neck

geometry obtained from an

MRI of a 50th percentile

male (taken from Yang et al.

(1998))


Fig. 7.29 Side view of the

neck model by Yang et al.

(1998)

The subject’s body dimensions were close those of a 50th percentile male. The MRI

is shown in Fig. 7.28. The subject had his neck flexed while it was imaged, and,

during mesh generation, neutral lordosis was introduced (Harrison et al. 1996).

Ligaments and discs were added, based on neck anatomy. Fifteen pairs of muscles

were modeled, using data from Deng and Goldsmith (1987), and a FE head model

developed by Ruan et al. (1994) was integrated with the neck model so that it can be

used to simulate crash situations. A side view of the complete model is shown in

Fig. 7.29, and a detailed view of the C1–C2 vertebrae is shown in Fig. 7.30. The C3

vertebra and the C2/C3 intervertebral disc are shown in Fig. 7.31. In summary, the

model is composed of seven cervical vertebrae (C1–C7) and the first thoracic

vertebra (T1), intervertebral discs, major biomechanically relevant ligaments,

15 pairs of head-neck muscles, and the articular facet joints. It has 11,489 solid

elements, 3071 shell/membrane elements, and 108 spring/bar elements.

In terms of model features, each vertebra is divided into two parts; the body or

anterior part has a lower modulus than the posterior structures to account for the

difference in modulus of cortical and trabecular bones. The proportion of the latter

is higher in the vertebral bodies. The elements representing bone were modeled as

elastoplastic solids, while those simulating the ligaments were modeled as

nonlinear tension-only membrane elements. For the intervertebral discs, the annulus

and nucleus were modeled separately as linearly viscoelastic elements. For the

facets, sliding interfaces were defined to model facet joint articulations. Capsular

ligaments were modeled as nonlinear tension-only bar elements because of the


Fig. 7.30 Detailed view of

the C1–C2 vertebrae in the

model by Yang et al. (1998)

(courtesy of Dr. King

H. Yang)

Fig. 7.31 Detailed view of

the C3 vertebra and the

C2/C3 disc in the model by

Yang et al. (1998) (courtesy

of Dr. King H. Yang)


Fig. 7.32 Validation of the model by Yang et al. (1998) against crown impact data from

Nightingale et al. (1997) (taken from Yang et al. (1998))

difficulty simulating the entire capsule. For the neck muscles, only their passive

response was modeled. Muscle material properties were taken from published test

data and verified by comparing them against those used by previous researchers.

The model was first validated against the data generated by Nightingale et al.

(1997). It was a crown impact against a horizontal rigid surface with a vertical

downward speed of 3.2 m/s. The experimental setup is shown in Fig. 7.16. Model

predictions of head acceleration, head contact force, and neck force are compared

with experimentally generated corridors in Fig. 7.32. The correlation is quite good,

considering the fact that the model did not have the exact geometry or material

properties of the specimens tested. A second validation was attempted using data

from a rearend impact sled test. Figures 7.33, 7.34, 7.35, and 7.36 show a

comparison of the overall head kinematics predicted by the model with highspeed

film data of the test. A comparison of model predictions and test data for

head acceleration in the horizontal (x-axis) and vertical (z-axis) directions is

showninFig.7.37. The predicted percent facet capsule stretch at C6/C7 is

showninFig.7.38. It is always good practice to take data from more than one

element of the soft tissue to assess the response. In this case, the estimated stretch

Fig. 7.33 Head kinematics as predicted by the model by Yang et al. (1998) compared with sled

data at time 60 ms (adapted from Yang et al. (1998))







data at time 140 ms (taken from Yang et al. (1998))

of the capsule due to whiplash was from 19 to 27 %. The significance of this result

will be discussed in Chap. 8.

The model was used to simulate a cadaveric head-neck impact with a

pre-deployed airbag (Cheng et al. 1982). Three non-survivable neck injuries

occurred in the six sled tests conducted. The injuries were complete severance of

the spinal cord, complete avulsion of the dens, and atlanto-occipital separation with

ring fracture. The airbag pressure was 10.3 kPa. In order to simulate the sled impact,

an upper torso or chest model was attached to the lower end of the neck model. The

thoracic viscera were not simulated, but it was necessary to add membrane elements

to the anterior portion of the neck and torso to avoid bony contact with the airbag.

The sequence of head/neck contact with the airbag is shown in Fig. 7.39. These

global views do not appear to explain the lethal injuries caused by the airbag.

However, the model can provide more detailed information in the form of a

midsagittal view of the interaction, as shown in Fig. 7.40. It is seen that at 40 ms,

there is major upward thrust on the chin causing the injuries described above. The

upward thrust appears to be sustained even at 80 ms.

The model has limitations. More validations are needed, and the material

properties used for the various tissues are generally based on static tests, whereas

for impact loading, material properties at high strain rates should be used. Unfortunately,

such data were and still are unavailable. The model was also CPU

intensive at the time it was developed.


Head Acceleration - x (g)

Head X-acceleration

Rear-End Inpact Validation

18

15

12

9

6

Model Result

Test Run #1

Test Run #2

Test Run #3

3

0

-3

-6

-9

0 20 40 60 80 100

Time

120 140 160 180 200

MS

Rear-End Inpact Validation

Head Acceleration - z (g)

3

6

3

0

-3

-6

-9

-12

-15

-18

-21

-24

Head Z-acceleration

Test Run #1

Test Run #2

Test Run #3

Model Result

0 20 40 60 80 100

Time

MS

120 140 160 180 200

Fig. 7.37 Horizontal and vertical head acceleration predicted by the model by Yang et al. (1998)

compared with experimental data


33

30

27

24

21

18

15

12

9

6

3

0

0

C6-C7 Capsule Element # 28002

C6-C7 Capsule Element # 28008

15 30 45 60 75

Time (ms)

90 105 120 135

Fig. 7.38 Predicted facet capsule stretch by the model by Yang et al. (1998)


Most of what we know about neck injury comes from crash reconstruction and

cadaveric studies. Neck injury mechanisms have been defined but not fully understood.

Injury mechanisms and responses are dependent on neck orientation and

impact direction. New findings include buckling modes and the effects of constraints.

The important lesson to remember is that catastrophic injuries occur due to

a combined compression and flexion load. Compression-flexion injuries due to a

“following” torso need not occur at high speeds (~3 m/s).

In the automotive crash environment, tolerance needs to be specified for a

variety of impact directions. Tolerance to flexion-compression varies widely with

end conditions, orientation of the head and neck, and the linear and angular motions

of the head. Although failure load increases with more restraint, the consequences

of failure are also more catastrophic. There is insufficient information of the effects

of age, size, shape, and gender on tolerance, and more experimental research is

needed to determine neck injury criteria for arbitrary impacts to the head.

Computer models of the neck are still in an early stage of development. Validated

FE models are available for impacts in the sagittal plane, but a validated

omnidirectional neck model has yet to be developed. However, with the advances

made in automotive safety, the need to study and model neck injury is no longer

urgent because severe neck injuries are rare in automotive impacts. On the contrary,

neck pain resulting from minor rearend impacts (whiplash) looms as a larger

problem than severe neck injuries. Whiplash is discussed in the next chapter.


Fig. 7.39 Interaction of the head with a pre-deployed airbag, predicted by the model by Yang

et al. (1998)


Fig. 7.40 Demonstration of the mechanism of injury when the head interacts with the

pre-deployed airbag, as predicted by the model by Yang et al. (1998)


7.1. The principal cause of a bilateral fracture/dislocation of the cervical spine is:

[ ] (i) Hyperextension of the head and neck

[ ] (ii) Axial compression of the neck

[ ] (iii) Combined flexion and compression of the neck

[ ] (iv) Lateral bending of the neck


7.2. The principal cause of quadriplegia due to diving into a shallow pool is

[ ] (i) Hyperextension of the head and neck

[ ] (ii) Axial compression of the neck

[ ] (iii) Combined flexion and compression of the neck

[ ] (iv) Lateral bending of the neck


7.3. Neck injury is a multi-faceted problem. Only one of the following is valid:

[ ] (i) The injury mechanism can be determined based on the direction of

head rotation

[ ] (ii) Paralysis results only when the spinal cord is severed

[ ] (iii) Injury to the spinal cord above the level of C3 is rarely fatal

[ ] (iv) Vertebral body fracture and dislocation occur before head rotation

takes place

[ ] (v) Severity of neck injury is independent of the end conditions of the

neck



[ ] (i) Tolerance to injury is dependent on bending moment only

[ ] (ii) Injury tolerance is dependent on axial force only

[ ] (iii) Injury to the spinal cord above the level of C3 is rarely fatal

[ ] (iv) In crown impacts, vertebral body fracture can be easily reproduced

in the cadaver

[ ] (v) Severity of neck injury is dependent upon the end conditions of the

neck

7.5. Identify the incorrect statement:

[ ] (i) Diving into shallow pools can produce a flexion-compression injury

of the neck

[ ] (ii) Out of position occupants can sustain a severe flexion-compression

injury of the neck when the airbag is deployed

[ ] (iii) Severe injury to the cervical cord above C3 is invariably fatal

[ ] (iv) Injury of the cord above T1 can produce partial or total quadriplegia

[ ] (v) Impact of the head with the windshield can produce an extensioncompression

injury

7.6. Identify the incorrect statement:

[ ] (i) Unstable neck injuries occur when the neck has to manage the inertia

of the body following the head

[ ] (ii) Unstable neck injuries tend to occur when the head is trapped in a

soft or padded surface

[ ] (iii) Under flexion and compression the neck undergoes a buckling mode

in which part of it is in extension and the other part is in flexion

[ ] (iv) The final position of the head is a good indicator of the type of

bending the neck underwent

[ ] (v) If both ends of the neck are constrained, it is more likely for the neck

to sustain an unstable injury

7.7. Cervical disc ruptures

[ ] (i) Can occur following a single crash or impact

[ ] (ii) Are the same as cleavage of the disc in which the disc is split into

two across a transverse plane

[ ] (iii) Are usually associated with long term degeneration of the disc

[ ] (iv) Can be prevented by the use of headrests

[ ] (v) Are the only source of neck pain following a neck injury

7.8. Select the incorrect statement:

[ ] (i) There have been several studies attempting to create compressionflexion

type neck injuries using cadavers

[ ] (ii) There have been many studies attempting to create catastrophic

tension-extension type neck injuries using cadavers


[ ] (iii) It is quite difficult to produce fracture dislocation and burst fractures

in cadaveric necks

[ ] (iv) It is virtually impossible to load the entire neck in pure compression

[ ] (v) It is very difficult to cause severe injuries to an unconstrained neck

7.9. Select the incorrect statement

[ ] (i) Tolerance corridor for the neck in flexion is available

[ ] (ii) Tolerance corridor for the neck in extension is available

[ ] (iii) Tolerance corridor for the neck in lateral bending is available

[ ] (iv) Tolerance for the neck in compression is available

[ ] (v) Tolerance corridor for the neck in tension for children is available

7.10. Select the incorrect statement

[ ] (i) Tolerance of the neck in torsion has been studied

[ ] (ii) Tolerance of the neck to transverse shear has been studied, but not

extensively

[ ] (iii) Tolerance of the neck to pure tensile loading has been studied

[ ] (iv) Loads required to fracture the odontoid process have not been

measured or estimated

[ ] (v) Transverse cleavage of cervical discs is usually seen in elderly

cadavers

7.11. Computer models of the neck simulating impact response

[ ] (i) Were available as early as 1966

[ ] (ii) Were not available until the early 1980s

[ ] (iii) Were available in the early 1970s

[ ] (iv) Were originally developed as finite element models in the 1970s


7.12. Finite element models of the neck for impact response:

[ ] (i) Were developed by researchers at the University of California,

Berkeley

[ ] (ii) Were developed by researchers at the University of California, San

Diego

[ ] (iii) Were developed by researchers at Ohio State University

[ ] (iv) Were developed by researchers at the University of Michigan


7.13. The Wayne State University neck model has many features. Select the

incorrect statement:

[ ] (i) This model simulates neck ligaments

[ ] (ii) This model simulates individual vertebrae and discs

[ ] (iii) This model simulates active muscle response

[ ] (iv) This model simulates passive muscle response

[ ] (v) This model simulates the geometry of the upper cervical vertebrae


7.14. The Wayne State University neck model was validated against several

different test situations. Select the incorrect statement:

[ ] (i) It has been validated against flexion-compression tests done at Duke

University

[ ] (ii) It has been validated against whiplash type tests done at Wayne State

University

[ ] (iii) It has been validated against airbag tests done at the University of

Virginia

[ ] (iv) It has been tested against airbag tests done at Wayne State University

[ ] (v) It has not been validated against torsional tests

7.15. The following spinal ligaments are continuous from C1 to the sacrum

[ ] (i) The supraspinous ligament

[ ] (ii) The ligamentum flavum

[ ] (iii) The posterior longitudinal ligament


[ ] (v) (i) and (ii)

7.16. The following spinal ligaments are not continuous down the spine but span

only adjacent vertebrae:

[ ] (i) The anterior longitudinal ligament

[ ] (ii) The interspinous ligament

[ ] (iii) The ligamentum flavum



7.17. The intervertebral disc is made up of an annulus and a nucleus. Select the

incorrect answer:

[ ] (i) The nucleus contains more collagen fibers than the annulus

[ ] (ii) The water content in the nucleus is higher than that of the annulus

[ ] (iii) There are approximately 18 annular layers in a normal lumbar disc

[ ] (iv) The chemical in the disc that absorbs water is proteoglycans

[ ] (v) The collagen in the annulus is different from that of the nucleus

7.18. There are many differences between the facets of the cervical spine and those

of the lumbar spine. Some of these differences are listed below. Select the

incorrect answer

[ ] (i) The articulating surface of the lumbar facets is flatter (closer to the

transverse plane) than that of the lower cervical facets

[ ] (ii) The lumbar facets bottom out on the lamina below but the cervical

facets do not

[ ] (iii) The lower cervical facets can resist antero-posterior shear better than

the lumbar facets


[ ] (iv) There are biomechanical data to show that lumbar facets transmit

vertical (supero-inferior) loads down the spine

[ ] (v) Lumbar vertebrae have inferior and superior facets and so do the

cervical vertebrae

7.19. The Wayne State University neck model was validated against several

different test situations. Select the correct statement:

[ ] (i) It has been validated against flexion-compression drop tests done at

the Medical College of Wisconsin

[ ] (ii) It has been validated against crown impact tests done at Wayne State

University

[ ] (iii) It has been validated against airbag tests done at the University of

Virginia

[ ] (iv) It has been used to simulate airbag tests done at Wayne State

University

[ ] (v) It has been validated against torsional tests

7.20. In the airbag tests conducted by Cheng et al. (1982), fatal neck injury

occurred in three of the six cadavers tested. Identify the correct statement:

[ ] (i) The airbag was deployed at the time of impact

[ ] (ii) The fatal neck injuries were due to the development of a large

compressive force in the neck

[ ] (iii) The fatal neck injuries were due to the development of a large tensile

force in the neck

[ ] (iv) The fatal neck injuries were due to severe impact of the chest with

the airbag



Prob

Ans

1 (iii)

2 (iii)

3 (iv)

4 (v)

5 (ii)

6 (iv)

7 (iii)

8 (ii)

9 (v)

10 (iv)

11 (iii)

(continued)

References 239

Prob

Ans

12 (v)

13 (iii)

14 (iii)

15 (v)

16 (v)

17 (i)

18 (ii)

19 (iv)

20 (iii)

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A. Sances Jr., J. Myklebust, C. Hourterman, R. Webber, J. Lepkowski, J. Cusick, S. Larson,

C. Ewing, D. Thomas, M. Weiss, M. Berger, M.E. Jessop, B. Saltzberg, Head and spine

injuries, in AGARD Conference on Injury Mechanism, Prevention and Cost, Paper

No. 13, Koln, Germany, 1982

G. Schmidt, D. Kallieris, J. Barz, R. Mattern, Results of 49 cadaver tests simulating frontal

collision of front seat passengers, in 18th Stapp Car Crash Conference, SAE Paper

No. 741182, Ann Arbor, MI, 1975

T. Sonoda, Studies on the strength for compression, tension and torsion of the human vertebral

column. J. Kyoto Pref. Med. Univ. 71, 659–702 (1962)

C.E. Strother, G.C. Smith, M.B. James, C.Y. Warner, Injury and intrusion in side impacts and

rollovers. SAE Paper No. 840403, 1984

D.J. Thomas, M.E. Jessop, Experimental head and neck injury, in Impact injury to the head and

spine, ed. by C.L. Ewing et al. (Charles C Thomas, Springfield, 1983), pp. 177–217

J.S. Torg, Athletic injures to the head, neck and face (Lea and Febiger, Philadelphia, 1982)

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human neck, in 42nd Stapp Car Crash Conference, SAE Paper No. 983157, Tempe, Arizona,

1998

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spine modeling. Spine 21, 1824–1834 (1996)

Chapter 8

The Biomechanics of Whiplash

Up until the advent of active safety systems, rearend collisions are a common

occurrence, especially on busy urban roads where drivers are distracted, going

too fast, and in a hurry. The most common scenario is the impact of a car stopped

at a red light or on the roadway by the car behind it. The impacted vehicle is

accelerated forward and the seatbacks push the torso of the occupants forward as

well. Without a headrest in contact with the head, the head is left behind until shear

forces are developed at each cervical vertebral level to bring the head forward along

with the torso. This delay results in hyperextension of the head and neck or in

whiplash. Many whiplash victims complain of neck pain, some for a few days or

weeks, while others develop chronic pain syndromes that are difficult to treat. The

problem is aggravated by our legal system which allows plaintiffs to sue for

damages without having to pay their attorney in advance. Safety engineers are

thus faced with a challenge to prevent this injury. Prior to the availability of an

active pre-collision braking and warning system, the only recourse was to install

headrests to prevent hyperextension. The federal government required these headrests

to be installed in passenger cars in 1969, but complaints of neck pain did not

abate. This called for research into the causes of neck pain due to whiplash because

it became obvious that it is difficult to prevent an injury if the cause is not well

understood. Additionally, without knowing the cause, it is also difficult to treat

whiplash-related neck pain. Usually, there is little that can be seen from CT or MRI

scans to indicate the source of the pain.

8.1 Anatomy of the Spinal Cord and Neurophysiology

of Pain

In this section, the anatomy of the spinal cord is reviewed, and a simplified

explanation of how pain is interpreted in the brain is presented.



243

244 8 The Biomechanics of Whiplash

Fig. 8.1 Anatomy of the spinal cord (taken from Gray (1973))

8.1.1 Spinal Cord Anatomy

The spinal cord begins at the atlanto-occipital junction where the brain stem ends. It

consists of a bundle of nerve fibers that extend to the level of about L1 where it

splits into nerve roots that supply the lower extremities. At each vertebral level, a

pair of nerve roots splits off of the spinal cord to supply a specific region of the

body. Figure 8.1 is a cross-sectional view of the spinal cord which, like the brain, is

surrounded by the three meninges, the dura, arachnoid, and pia. It is bathed in CSF.

The anterior aspect of the spine is on the bottom of the figure. The nerve roots have

two branches – a ventral root which consists primarily of efferent (motor) fibers and

a dorsal root which consists primarily of afferent (sensory) fibers. These roots are

shown in Fig. 8.1. The dorsal root has an enlargement known as the dorsal root

ganglion (DRG), a cluster of cell bodies, the axons of which have a sensory

function, including nociception, the ability to sense pain.

8.1.2 Neurophysiology of Pain

The perception of pain by the brain originates at the site of pain where an injury

might have occurred. There, the nociceptors or pain-sensing fibers are stimulated to

fire when the tissue in which they are embedded is stretched or deformed

8.2 Hypotheses for Whiplash Pain 245

Fig. 8.2 The process for

the perception of pain by

the brain

sufficiently. This is known as transduction. Nociceptors are high-threshold nerve

endings that only fire when the stimulus is large. For example, the facet capsules of

the facet joints of a vertebra need to be stretched substantially before they will fire.

When a nociceptor fires, it sends a signal along an afferent nerve fiber to the spinal

cord via the dorsal root. This is known as transmission. At the cord, the signal is sent

up tracts of the spinal cord to the brain where it is interpreted as pain. This is known

as perception. The process is shown in Fig. 8.2. In addition to having a high

threshold, nociceptors are conducted along smaller nerve fibers and hence travel

at a lower conduction velocity. When you touch a hot object, you usually get burned

before you can withdraw your hand because of the low conduction velocity of the

nerve fiber. The threshold of nociceptors can be lowered by a variety of factors.

Tissue degeneration leads to occasional inflammation of the tissue when a repair is

in progress. This can lower their threshold and the body region may sense pain with

less than normal stimuli. For the spine, degenerated intervertebral discs are known

to develop nociceptors that cause discogenic pain. Similarly, facet joint degeneration

can lower the threshold of nociceptors in the facet joint capsule, facilitating

facet pain when the capsule is stretched by spinal extension.

8.2 Hypotheses for Whiplash Pain

Over the years, many hypotheses for whiplash pain have been proposed. They

include the hyperextension hypothesis based on the early observations of tests on

rhesus monkeys and hares, two muscle injury hypotheses, a pinching hypothesis, a

pressure hypothesis leading to injury of the dorsal root ganglion (DRG) of spinal

nerve roots, and a shear hypothesis that involved the stretching of the capsules of

the articular facet joints. Each of these hypotheses is discussed below.


Fig. 8.3 High acceleration whiplash testing of rhesus monkeys in forward-facing mode (+G x

acceleration) (taken from Ommaya et al. (1966))

8.2.1 The Hyperextension Hypothesis for Whiplash Pain

The early work of Ommaya et al. (1966) involved the use of rhesus monkeys that

were subjected to high forward-facing (+G x ) accelerations. As shown in Fig. 8.3,

the animal was placed in a seat with a low seatback. The acceleration caused

hyperextension of the head followed by hyperflexion. The aim of the study was

not to study whiplash but to generate high-head angular accelerations without

directly impacting the head, but neck hyperextension was associated with whiplash.

There were also studies by Martinez et al. (1965) and McKenzie and Williams

(1971) which demonstrated the hyperextension phenomenon. These observations

formed the basis for the hyperextension hypothesis proposed by McNab (1965a, b).

Injuries were observed in test animals for severe whiplash, but the hypothesis is

apparently considered valid for mild impact with no visible neck injury. The

validity of the hyperextension hypothesis is questionable because it does not

identify the source of pain.

8.2.2 The Muscle Hypothesis for Whiplash Pain

Extension of the head stretches the anterior muscles of the neck, including the

sternocleidomastoid muscles, shown in Fig. 8.4. These muscles are at risk for injury

because eccentric contraction is necessary for injury (Warren et al. 1994). That is,

injury occurs in muscles which are being lengthened as they contract.


Fig. 8.4 Muscles of the

neck, highlighting the

sternocleidomastoid

muscle which is stretched

during head hyperextension

(taken from Gray (1973))

The contraction is due to the stimulation of muscle spindles in the muscle that is

stretched. These anterior muscles may hurt for a day or two after the rearend impact

but they do not persist. The large neck extensor muscles are in compression during

neck extension and are unlikely to contract or be injured during whiplash. If most

people had long-lasting pain in the back of the neck after whiplash, the pain is not of

muscular origin. This hypothesis is, therefore, not viable.

8.2.3 The Muscle Flexion Hypothesis for Whiplash Pain

This hypothesis (Tencer et al. 1999) states that the extensor muscles are injured

during rebound (and flexion) of the head and neck after the initial impact. The logic

behind this hypothesis is faulty because head and neck flexion occurs in frontal

crashes which can be much more severe than that due to a rebound from head

hyperextension and there are few long-term complaints of neck pain following a

frontal impact. This is another nonviable hypothesis.


8.2.4 A Pinching Hypothesis

Ono et al. (1997) and Yoganandan et al. (1998) have both proposed the hypothesis

that the pain is due to pinching of the facet joint capsule between the articular

cartilage of the facet joint. No biomechanical evidence was provided that pinching

can indeed occur within the facet joint and that the capsule is loose enough to allow

pinching to occur. Moreover, the pinched portion of the capsule needs to contain

nociceptors to cause pain, and there is no evidence that the pinched capsule is so

innervated. It should be mentioned that articular cartilage of synovial joints is

devoid of nerve endings and compression of the facet surfaces cannot produce

pain. There is also no evidence that nociceptors in the subchondral bone can be

made to fire by joint compression.

8.2.5 The Pressure Hypothesis

Aldman (1986) was credited with this hypothesis because he proposed in his 1986

paper that there is a change in volume of the CSF surrounding the spinal cord

during neck bending and that, under dynamic conditions, the pressure cannot be

dissipated by CSF flow, resulting in possibledamagetothenerverootsasthey

exit the cord. But at the time of publication of the paper, it was still a hypothesis

because the pressure studies were still in progress. Temporal changes in CSF

pressure due to whiplash were published by Svensson et al. (1993). Pigs were used

in the experiments, and pressure in the spinal canal was measured in two animals,

six times in the first animal and 14 times in the second. A pressure increase for

about 100 ms was observed in all of the tests, with the measured maximum

pressure varying from 50 to 150 mmHg. Negative pressure was measured in the

spinal canal when the head was rapidly placed in flexion in a single test. The peak

negative pressure was about 80 mmHg. Injuries to the DRG were found in the

form of membrane dysfunction in the ganglia. There were no macroscopic injuries

to the 12 pigs used for histological studies. As mentioned above, the major

symptom in whiplash-related victims is neck pain, and DRG injuries do not

explain the neck pain because it would be interpreted as radicular pain by the

brain. Furthermore, a generalized increase in spinal canal pressure cannot selectively

affect the nerve roots and DRG in the lower cervical spine where most of

the problems appear to reside. In other studies on radiculopathy and pressure on

nerve roots, it was found that long periods of pressure on nerve roots (months and

years) can result in nerve root degeneration and radiculopathy. Transient pressures

of 100 ms in duration are not likely to be injurious. The originators of this

hypothesis also failed to provide objective evidence regarding DRG dysfunction

due to transient pressures. Because of these inconsistencies, this hypothesis is not

likely to be valid.


8.2.6 The Shear Hypothesis for Whiplash Pain

As described in the introduction to this chapter, shear forces are developed in the

neck to bring the head forward along with the torso. This shear force is a likely

candidate to cause soft tissue injury to the intervertebral joints of the cervical spine

and became the source of a hypothesis first proposed by Yang et al. (1997).

However, before this hypothesis is discussed in detail, we need to digress

because it is important to consider the effect of the seatback on the cervical spine

when a car is hit from behind. The thoracic spine is straightened when the seatback

pushes on it to accelerate the occupant forward. The spine-straightening phenomenon

had been studied previously by Prasad (1973) who developed a 2-D discrete

parameter model of the entire spine. The model was meant to simulate spinal

response to caudocephalad (tail-to-head or +G x ) acceleration, as described in

Chap. 10, but it could also simulate a horizontal deceleration, such as in a frontal

car crash. The model predicted that if the thorax was restrained by a shoulder

harness, a compressive load was developed in the lumbar spine during the frontal

impact. The model-predicted load on the lumbar spine was demonstrated experimentally

by Begeman et al. (1973), as shown in Fig. 8.5. These data were obtained

from a seat pan load cell under a seated cadaver that was fully restrained by a lap

belt and a double shoulder harness. The seatback was vertical. The cadaver was

subjected to an approximately 17 g frontal impact (Fig. 8.5B), and the measured

seat pan load is shown in Fig. 8.5A. The vertical component of the lap belt load

from both belts amounted to about half the seat pan load, and the difference

between the seat pan load and the lap belt load can only be due to a vertical load

transmitted to the seat pan by the spine. Thoracolumbar wedge fractures confirmed

the presence of this spinal load. Incredulous as this may sound, an axial compression

load is developed in the lumbar spine when the torso is subjected to a horizontal

deceleration. And the phenomenon was first predicted by a computer model and

confirmed subsequently by experimentation. To explain how this unexpected form of

loading in the lumbar spine, we need to look at the kyphotic thoracic spine. When the

torso is decelerated against the shoulder harness, it tends to straighten thoracic spine,

and the result is the development of compressive spinal load.

Now, how does this phenomenon relate to whiplash and the cervical spine? First,

a push on the kyphotic thoracic spine from behind also tends to straighten it and to

cause a compressive load to be developed in the lumbar spine. However, this

straightening will also compress the cervical spine as it tries to push the head

up. That is, just prior to the head whipping forward, the cervical spine undergoes

compression and all the ligaments are slackened, while tension in the spinal

musculature is relaxed. The result of this compression is the loosening of the

ligamentous and muscular constraints on the cervical vertebra just as the neck is

about to undergo shearing. Relative translation and rotation of cervical vertebrae

are increased, especially along the lower cervical spine which has shallower facet

angles. As a result, there can be stretching or deformation of intervertebral soft

tissues. Facet joint capsules are stretched and possibly torn, resulting in


Fig. 8.5 (A–B) Spinal compression due to shoulder belt loading on the chest (taken from

Begeman et al. 1973)

inflammation and pain because there are nociceptors in the capsule that are induced

to fire (Bogduk and Marsland 1988). The stretching occurs early in the impact event

and explains why headrests placed several inches behind the head do not protect the

neck. This hypothesis is based on sound biomechanical and neurophysiological

principles and is likely to be valid.

8.3 Experimental Studies on Whiplash 251

8.3 Experimental Studies on Whiplash

There have been many experimental studies to determine the injury mechanisms

involved in whiplash or a rearend impact. They can be divided into two groups of

experiments, those using volunteer subjects and those using cadaveric subjects.

8.3.1 Whiplash Experiments Using Volunteers

In the literature, there are a large number of studies using volunteers who were

subjected to low-speed car-to-car impacts. They include the work of McConnell

et al. (1993, 1995), Szabo and Welcher (1996), and Siegmund et al. (1997).

Volunteer sled impacts were performed by Patrick and Mertz (1967), Van den

Kroonenberg et al. (1998), Matsushita et al. (1994), and Ono et al. (1997).

McConnell et al. (1993) published one of the first papers dealing with volunteer

testing of rearend impacts to try to find the cause of neck pain. Low-velocity car-tocar

collision tests were carried out using four healthy middle-aged volunteers. Four

different types of vehicles were used in the ten tests that were carried out at Delta

V’s ranging from 4 to 8 km/h. They observed an upward neck movement that was

attributed to the straightening of the thoracic spine. Because of the use of headrests,

the neck extension was within the normal range of motion, and an explanation for

whiplash pain could not be found. In a follow-up study by McConnell et al. (1995),

the Delta V was increased to 10.9 km/h, and seven test subjects participated in

14 car-to-car rearend impacts. The head-to-headrest distance varied from 5.1 to

11.7 cm (2 to 4.6 in.). Many of the test subjects complained of transient headaches,

while some others had transient neck discomfort. There were no long-lasting pain

syndromes. Although ramping of the torso up the seatback was observed, neck

compression was not seen at impact speeds above 8 km/h. Again the normal range

of motion of the neck was not exceeded because of the presence of the headrest.

It was concluded that hyperextension was not the cause of neck pain due to

whiplash. The authors speculated that the pain was of muscular origin without

clinical evidence.

Szabo and Welcher (1996) measured the electromyographic (EMG) signals,

using surface electrodes, from neck muscles of volunteers who were subjected to

rearend impacts at Delta V’s as high as 10 km/h. A standard seat with an integrated

head restraint was used, but in some tests, the distance between the head and

headrest was reduced by 5 cm (2 in.). Five volunteers (four males and one female)

participated in ten tests, each undergoing two rearend impacts, one with the

standard headrest and a second with the head-to-headrest distance reduced by

5 cm. The vehicles used were two late 1970s 240 series Volvo sedans. One was

the target vehicle and the other was the bullet vehicle. One of the reasons for

measuring neck muscle EMG was to ensure that volunteers were relaxed prior to

impact because many whiplash victims report that they were unaware of an


impending impact. The EMG was indeed quiescent for all volunteers prior to

impact. A more valuable result is the quantification of the delay time in muscle

response. Bilateral electrodes were placed over the paraspinal lumbar muscles, the

sternocleidomastoid (SCM) muscles, the suboccipital cervical extensor muscles,

and the superior trapezius muscles. In terms of the delay times, the shortest was for

the paralumbar muscles, averaging 100–113 ms. The delay times for the SCMs, the

cervical extensors, and the trapezius were in the range of 114–125 ms. Note that this

is the delay between the onset of vehicle acceleration and the first measurable EMG

signal. There is an additional delay before maximal force is developed in the

muscle. It was also interesting to note that the reduction in the space between the

head and headrest resulted in decreases in head acceleration, cervical extension, and

a reduction in the subjects’ perception of impact severity.

Siegmund et al. (1997) did a large series of tests involving 42 volunteers

(21 males and 21 females), most of whom underwent rearend impacts at Delta

V’s of 4 and 8 km/h. The target vehicle was a 1990 Honda Accord, while the bullet

vehicle was a Volvo 240DL station wagon. The purpose for using a large cohort of

subjects was the ability to perform statistical analyses on the data. Sagittal plane

motion was monitored and linear and angular kinematics of the head and neck were

compared. There were statistically significant differences in some of the variables

due to both gender and speed change. However, the extension range of motion was

within normal limits, and it was apparent that biomechanical data alone were not

able to provide clues regarding the mechanism for neck pain. Initial flexion of the

head was observed in all tests, confirming again the effect of the straightening of the

thoracic spine by the seatback.

The first sled test simulating whiplash and using a volunteer was conducted by

Patrick and Mertz (1967) with Patrick as the volunteer. In addition to being the first

study to report on live human response to a rearend impact, the authors developed

an analytical procedure to calculate the reaction forces at the occipital condyles for

a freely whipping head and a method to measure angular acceleration of a rigid

body in 2-D, a precursor to the 3-D method developed by Padgaonkar et al. (1975).

The volunteer underwent tests with and without a headrest while seated in a rigid

seat with a rigid seatback. Except for two tests, the volunteer’s head was in contact

with the headrest. The volunteer underwent a series of runs with the head supported

by the headrest, beginning with a 9 mph Delta V impact and ending with a 14-mph

impact. Without a headrest, he underwent two tests at 8.4 mph with a stopping

distance of 22 in. and at 8.9 mph with a stopping distance of 10 in. The volunteer

declined to undergo a more severe impact. The initial position of the volunteer’s

head for the last unsupported runs was about 18 of flexion. There was an initial

flexion of several degrees before it reached a peak extension of 27 relative to the

normal upright posture for a total excursion of over 45 . The volunteer’s muscles

were tensed prior to the run.

The next reported volunteer sled test was by Van den Kroonenberg et al. (1998)

who tested 19 volunteers, three of whom were females. They underwent 43 impacts,

27 of which were instrumented with transducers to measure head and neck kinematics.

The added feature to these tests was the measurement of the acceleration of


T1 and that of the head restraint contact force. The finding of an initial head flexion

was confirmed but it was with respect to T1. The head acceleration for women was

higher than that for men, and the increase was correlated with neck circumference

or neck muscle mass. Female T1 accelerations were also higher, but there were only

three female test subjects, and a statistically significant difference could not be

established. Again, the real cause of neck pain eluded the investigators.

X-ray cinematography at 90 frames/second was used by Matsushita et al. (1994)

when they tested 19 subjects on a sled which was accelerated by a pendulum and

stopped by a urethane-covered impact surface. The rearward facing volunteers

experienced a rearend impact at Delta V’s ranging from 2.5 to 5 km/h. Three

different automotive seats with headrests and different seatback stiffnesses were

used. It was possible to visualize the outline of the cervical spine every 11 ms or so,

but the system was not accurate enough to yield relative motion data between

adjacent vertebrae. However, they did notice an initial compression of the neck and

upward ramping of the torso. The description of cervical spine motion during

whiplash was not totally consistent with that from a more detailed study by Deng

et al. (2000), as discussed in Sect. 8.3.3.1 below. Some of the visual data were lost

because of the low framing rate of the X-ray video. Again, hyperextension was not

experienced by the volunteers, and a clear explanation for neck pain due to

whiplash was not provided.

The study by Ono et al. (1997) also used a similar or the same X-ray cinematography

system with a framing rate of 90 frames per second. As with the Matsushita

et al. study, the framing speed was too low (approximately 25 frames per test), and

relative vertebral motion of the entire cervical spine, including both rotation and

translation, could not be accurately assessed. However, the authors produced a set of

curves depicting the rotation of cervical vertebrae from C2 to C6 from a single test

subject, using a “template” method to obtain the data. These data are shown later in

the chapter where a comparison can be made with cadaveric data obtained by means

of high-speed X-ray cinematography (Sect. 8.3.3.1). The authors also noted the

formation of an S-shape in the cervical spine during the impact. They attributed the

initial compression of the cervical spine to the upward ramping of the torso and

hypothesized that the pain mechanism originated in the facet capsules, especially at

the C5/6 level where they noted “nonphysiological” motions without providing any

quantitative data. The hypothesis that a kyphotic cervical spine results in more facet

joint contact and hence a higher incidence of neck injuries is biomechanically

incorrect. The vertebral bodies tend to carry more compressive load when the

cervical spine loses lordosis, and the facets would tend to carry less load.

8.3.2 Whiplash Experiments Using Cadavers

In their volunteer study on whiplash, Patrick and Mertz (1967) also tested two

cadavers and two different dummies at higher impact severities. Cadaveric head

extension was larger than that experienced by the volunteer. Also, the headrest


contact force increased with an increase in the backset or the space between the

headrest and the back of the head. When the head was in contact with the headrest,

the headrest force was 180 lb for a 23 mph simulation. For a backset of 3 1/2 in., the

force ranged from 310 to 440 lb.

In the cadaver study by Bertholon et al. (2000), three elderly cadavers were

tested on a sled with a Delta V of 10.8 and 16.2 km/h, while seated in a rigid seat.

There were 8 tests without a headrest and 11 tests with a headrest. Two cervical

vertebrae (C2 and C5) and T1 were instrumented with accelerometers so that their

kinematics could be measured. The authors reported an initial neck compression

with head flexion, the development of an S-shaped cervical spine, and global

extension of all cervical vertebrae relative to a stationary observer. Relative rotations

of the head with respect to C2, of C2 with respect to C5, and of C5 with respect

to T2 were reported for the 10.8 km/h runs. Other than these relative rotations, the

data they reported on were similar to those of previous studies.

8.3.3 Whiplash Experiments Using Cadavers and High-

Speed X-ray Cinematography

There have been two such cadaveric experimental studies that used a high-speed

X-ray system to determine cervical vertebral motion at 4 ms intervals. They were

reported by Deng et al. (2000) using a rigid seat and by Sundararajan et al. (2004)

using a standard automotive bucket seat.

8.3.3.1 The Whiplash Study by Deng et al. (2000)

A comprehensive study of cervical spine kinematics was carried out by Deng et al.

(2000) using whole-body cadavers and the high-speed biplanar X-ray system at

Henry Ford Hospital. This system was described in Chap. 2 (Sect. 2.5.1). For this

application, the framing rate was reduced from 1000 to 250/s because the impact

was a low-speed event. A mini Hyge sled was designed and fabricated to be used in

conjunction with the high-speed X-ray unit at the hospital. A rigid seat rode on rails

which were attached to a frame. The seat was propelled by compressed air and

could accelerate a 91-kg (200 lb) payload up to 15 g to a terminal velocity of 6.1 m/s

(22 km/h). The sled with a Hybrid III payload is shown in Fig. 8.6. The seatback

angle was either zero or 20 .

Since the experimental protocol called for a low-speed rear impact, the cadaver

was forward facing and was subjected to a horizontal acceleration of 5–10 g.

However, before the test could be run, much preparation was necessary. All

seven cervical vertebrae needed to be targeted with radiopaque markers. At least

two 2 mm diameter tungsten spheres were pressed into each cervical vertebra, so

that its 2-D motion could be tracked. The tools used to install the markers are shown


Fig. 8.6 Mini Hyge sled

designed for us with

the Henry Ford Hospital

high-speed X-ray unit

(courtesy of Dr. Bing Deng)

Fig. 8.7 Tools used to

install radiopaque

(tungsten) targets on

individual cervical

vertebrae. (1) Tungsten

markers. (2) Pin. (3) Drill

bit. (4) Pusher. (5) Guide

tube. (6) Guide tube

(courtesy of Dr. Bing Deng)

in Fig. 8.7. Under X-ray guidance, a 1.8 mm Steinmann pin was inserted into the

neck of the cadaver to locate the point where a marker was to be placed. Then a

guide tube was placed over the Steinmann pin. The pin was removed and replaced

by a 2 mm diameter drill bit which made a hole in either the vertebral body or

spinous process. The bit was then withdrawn and a tungsten ball was dropped into

the guide tube. It was tamped into place by a pusher. A third marker was installed in

some vertebrae on the transverse process. The targeting of all seven vertebrae was a

time-consuming process. Figure 8.8 shows a completed installation with a pair

tungsten targets attached to each cervical vertebra. The C7 vertebra could not be

visualized because it was shielded by the shoulder. Upon completion of the target

installation, a nine-accelerometer mount was screwed into the crown of the skull,


Fig. 8.8 Radiograph of a

cadaver neck with a pair of

tungsten targets installed in

each cervical vertebra. Note

that C7 is shielded by the

shoulder (Deng et al. 2000)

Fig. 8.9 Instrumented cadaver seated on a sled in front of a biplanar high-speed X-ray unit. The

strap holding the head upright was released just prior to the initiation of sled acceleration (Deng

1999)

and a redundant angular rate sensor was attached to the mount with its sensitive axis

about a lateral axis. A triaxial accelerometer was attached to T1, by means of bone

screws. To collect the neck motion data, both sets of X-ray sources and image

intensifiers were used, initially, similar to the arrangement used in the brain motion


Fig. 8.10 A twodimensional

setup of a

0-deg seatback angle test

with head restraint. One

X-ray unit and one image

intensifier was used (Deng

et al. 2000)

study described in Chap. 2 (Fig. 8.9). However, this was largely a 2-D event and it

was not necessary to perform a 3-D analysis of the data. In fact, if only one X-ray

tube and one image intensifier were used, more motion data could be captured. The

2-D setup is shown in Fig. 8.10. Because whiplash neck motion occurs over a longer

period of time, the framing speed for the video cameras was reduced from 1000 to

250 per second. This speed is over 2 1/2 times faster than previous rates used by

Matsushita et al. (1994) and Ono et al. (1997), but with the superior resolution of the

biplanar X-ray system, it was adequate to ascertain relative vertebral motion.

Data processing consisted of tracking the tungsten targets, analyzing the measured

accelerations of the head T1 and the sled, and performing a kinematic

analysis of the relative motions of the cervical vertebrae.

A large volume of data was generated in this study, and only a summary of the

more significant results is reported here. The reader is referred to the original paper

(Deng et al. 2000) or to the dissertation (Deng 1999) for details. Six cadavers were

subjected to a total of 26 runs at 5–10 g with the sled reaching a velocity of

1.4–4.3 m/s. Relevant information regarding the cadavers used is summarized in

Table 8.1. Before delving into the details of the results, a few general statements can

be made. The head and all cervical vertebrae went into extension relative to the

global reference frame. However, the upper cervical spine was in relative flexion,

while the lower cervical spine was in relative extension during the impact, with the

neck assuming an S-shape. It was also possible to determine the strain in the facet

capsule by identifying anatomical landmarks in the neighborhood of the facet joint.

The distance between the upper and lower facet landmarks could be computed for

each image, and the change in that distance was used to calculate facet capsular

strain. The shear and compressive forces generated in the neck were computed


Table 8.1 List of cadavers used in the whiplash tests by Deng et al. (2000)

CAD# Gender Age Weight (kg) Height (cm)

Neck

Circumference (cm) Height (cm)

558 Female 81 41.3 158 32 10

582 Female 50 72.6 163 39 9

625 Male 81 69.4 169 39 9

730B a Female 88 63.1 169 32 9

IIAM b Male 43 55.0 N/A 41 6

804 c Male 91 54.9 166 38 9

a The C5/C6 disc of CAD 7308 was degenerated

b In this cadaver, the right leg was amputated pre-mortem at the mid-femur level, left leg was

amputated post-mortem at the mid-femur level, and the arms were amputated post-mortem at the

end of the humerus

c The C6/C7 disc of CAD 804 was calcified

using the method described by Patrick and Mertz (1967). These forces could be

compared with data from other studies.

To get an overall picture of cervical response, we compare the data from two

runs using the same cadaver but at two different seatback angles. The peak sled

acceleration peaks were 5.2 g for the zero-degree seatback run (HFH19) and 6.1 g

for the 20-degree seatback run (HFH20). The impact speeds for the two runs were

6.6 and 7.3 km/h (4.5 and 5.0 mph), and the impact durations were 152 and 166 ms,

respectively.

Data from HFH19 are presented first before a comparison is made with data from

HFH20. Figure 8.11 shows transducer data for HFH19. Sled acceleration and

velocity are shown in Fig. 8.11A, and the seat pan load is depicted in Fig. 8.11B,

confirming the development of a compressive force down the lumbar spine when

the thoracic spine is pushed from behind and is made to straighten out. The reaction

forces at the occipital condyles were computed from head acceleration data and are

shown in Fig. 8.11C. The instant of head contact is at the 225 ms mark. The upper

neck moment (M y ) is shown in Fig. 8.11D. The absolute rotation of each vertebra

relative to the inertial reference frame is shown in Fig. 8.12A, and the relative

rotations of adjacent vertebrae are shown in Fig. 8.12B. These data are the first of

their kind and are the basis for the design of a surrogate or dummy neck. Unfortunately,

the motion of C7 could not be visualized because it was below the shoulder

level. Figure 8.12A can be compared with the volunteer data of Ono et al. (1997)

who provided cervical vertebrae rotational data from a single test subject, as shown

in Fig. 8.13. The major difference between these two data sets is the extent of

rotation of the lower cervical spine. The Ono data show the lowest rotation for the

lower cervical vertebrae, whereas the Deng data show the most rotation for this

portion of the cervical spine. Of course, the test conditions are different for these

two studies, one of which used a headrest and the other did not. However, the

differences are apparent in the data before head contact is made with the headrest.

In addition to rotation, there is also relative translation of adjacent vertebrae.


Fig. 8.11 Transducer data for HFH19 (0 seatback run). (A) Sled acceleration and velocity.

(B) Seat pan load. (C) Shear and compressive force at occipital condyles. (D) Upper neck moment.

(taken from Deng et al. (2000))

A 60 Extension HFH19

B 6

Extension HFH19

50 Head

4

C1

40

C2

C3

2

0

30

C4

-20 20 60 100 140 180 220 260 300

C5

-2

C1-C2

20

C6

-4

C2-C3

C3-C4

10

-6

C4-C5

C5-C6

Head and Cervical Vertebrae

Rotations (deg)

0

-40 0 40 80 120 160 200 240 280 320 360

-10 Flexion Time (ms)

Relative Cervical Vertebrae Rotations

(deg)

-8

-10

-12

Flexion

Time (ms)

Fig. 8.12 Cervical vertebrae rotations in HFH19. (A) Absolute rotations with respect to an inertial

reference frame. (B) Relative rotation of adjacent cervical vertebrae. The upper cervical vertebrae

are in flexion, while the lower vertebrae are in extension (Deng et al. 2000)

We define the body-fixed x-axis for each vertebra as the line connecting the two

tungsten targets and z-axis as the line perpendicular to it. The relative displacements

of C1 with respect to C2 along the body-fixed x- and z-axes are shown in Fig. 8.14.

The two targets on each vertebra may move in the opposite direction due to rotation.

As shown in Fig. 8.14, the posterior target of C1 (C1P) moved rearward by 2.1 mm


80

Rotational Angle (degrees)

70

60

50

40

30

20

10

0

C2

C3

C4

C5

C6

-10

0 50 100 150

Time (ms)

200 250

300

Fig. 8.13 Crash extension motion – Pattern of rotational angle of each vertebra (From the

horizontal plane) (taken from Ono et al. (1997))

Head Contact

Head Contact

1.00

-2.1 mm at 212 ms

6.00

5.5 mm at 228 ms

0.50

5.00

C1 Relative to C2 X Disp. (mm)

0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-0.50

-1.00

-1.50

C1 Relative to C2 Z Disp. (mm)

4.00

3.00

2.00

1.00

0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-1.00

-2.00

C1P

-2.00

C1P

-2.50

C1A

-3.00

C1A

Time (ms)

Time (ms)

+x – P-A in BF Coordinates. +z – I-S in BF Coordinates

Fig. 8.14 Relative displacement of C1 with respect to C2 along the body-fixed x- and z-axes.

C1P and C1A are, respectively, the posterior and anterior targets on the C1 vertebra (taken from

Deng (1999))

and upward by 5.5 mm, while the anterior target (C1A) moved forward by 0.7 mm

and downward by 2 mm. For the sake of completeness, the relative motions of

C2/C3, C3/C4, C4/C5, and C5/C6 are shown in Figs. 8.15, 8.16, 8.17, and 8.18.

These data are also the first of their kind and are needed for the design of


2.00

1.5 mm at 236 ms

3.00

2.8 mm at 212 ms

1.50

2.50


1.00

0.50

0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-0.50

-1.00

+x - P-A

in BF Coords.

C2P


2.00

1.50

1.00

0.50

0.00

-0.50

+z - I-S

in BF Coords.

C2P

C2A

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-1.50

C2A

-1.00

Time (ms)

Time (ms)

Head Contact

Head Contact

Fig. 8.15 Relative displacement of C2 with respect to C3 along the body-fixed x- and z-axes. C2P

and C2A are, respectively, the posterior and anterior targets on the C2 vertebra (Deng et al. 2000)

3.50

3.2 mm at 200 ms

7.00

6.0 mm at 200 ms

3.00

6.00


2.50

2.00

1.50

1.00

0.50

0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-0.50

+x - P-A

in BF Coords.

C3P

C3A


5.00

4.00

3.00

2.00

1.00

0.00

-1.00

+z - I-S

in BF Coords.

C3P

C3A

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-1.00

-2.00

Time (ms)

Time (ms)

Head Contact

Head Contact



surrogate necks. Such data could not be derived from X-ray images taken at

90 frames/second. Facet capsule stretch could be estimated from bony landmarks

across the joint. They are illustrated in Fig. 8.19. If the distance between the

landmarks is l 0 and the change in this distance is Δl, capsular strain, ε, is estimated


1.20

1.1 mm at 224 ms

1.00

-1.4 mm at 248 ms

1.00

0.50


0.80

0.60

0.40

0.20

0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-0.20

+x - P-A

in BF Coords.

C4P

C4A


0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-0.50

-1.00

-1.50

+z - I-S

in BF Coords.

C4P

-0.40

-2.00

C4A

Time (ms)

Time (ms)

Head Contact

Head Contact




0.50

0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-0.50

-1.00

-1.50

-2.00

-2.50

-3.00

-3.50

-4.00

-4.50

-5.00

-4.3 mm at 220 ms

+x - P-A

in BF Coords.

C5P

C5A

Time (ms)

Head Contact


1.50

1.00

0.50

0.00

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300

-0.50

-1.00

-1.50

-2.00

-2.50

-3.00

-2.4 mm at 228 ms

+z - I-S

in BF Coords.

C5P

C5A

Time (ms)

Head Contact




z

z

z

Upper facet landmark

x

x

x

Lower facet landmark

Fig. 8.19 Coordinate systems for individual vertebrae based on neck targets are used to estimate

facet capsular strain as a function of time. Bony landmarks on either side of the facet joint are

identified, and the change in distance between the landmarks was used to estimate the strain (Deng

et al. 2000)

Fig. 8.20 (A) Trajectories of facet bony landmarks used to estimate facet capsular strain shown in

(B) for the C4/C5 capsule (Deng et al. 2000)

from the ratio Δl/l 0 . As an example, the relative displacement of the C4 and C5

targets in the x- and z-directions was determined from the X-ray video (Fig. 8.20A),

and Δl is the resultant of the displacements. The estimated capsular strain is shown

in Fig. 8.20B for the C4/C5 motion segment.


Fig. 8.21 Transducer data for HFH20 (20 seatback run). (A) Sled acceleration and velocity. (B)

Seat pan load. (C) Shear and compressive force at occipital condyles. (D) Upper neck moment

(taken from Deng et al. (2000))

Table 8.2 Peak relative rotations of cervical vertebrae for the 20-deg seatback tests

Run#

SB angle

(deg)

C1/C2

(deg)

C2/C3

(deg)

C3/C4

(deg)

C4/C5

(deg)

HFH5 20 7 10

HFH9 20 17 6 13

HFH16 20 6 8 13 4 3

HFH17 20 9 3 6 5 2

HFH20 20 9 3 8 5 3

HFH21 20 11 6 6 14 14

HFH23 20 13 8 5 9 13

HFH24 20 12 5 4 10 14

HFH25 20 12 6 5 13 16

Average 11 6 8* 9* 9

S.D. 3 2 3 4 6

C5/C6

(deg)

For HFH 20, the companion runs with a 20-deg seatback angle, and the same

transducer data channels as those in Fig. 8.12 are shown in Fig. 8.21A–D. Instead of

repeating what was done for HFH19, the relative rotations for all nine tests at the

20-deg seatback angle are summarized in Table 8.2 where flexion is designated as


Table 8.3 Peak relative rotations of cervical vertebrae for the 0-deg seatback tests

Run#

SB angle

(deg)

C1/C2

(deg)

C2/C3

(deg)

C3/C4

(deg)

C4/C5

(deg)

HFH15 0 6 4

HFH18 0 4 4 11 2 8

HFH19 0 10 4 11 3 4

HFH22 0 11 6 2 5 12

HFH26 0 12 7 2 4 13

Average 9 5 7 4 9

S.D. 3 1 5 1 4

C5/C6

(deg)

Fig. 8.22 Comparison of relative rotations of cervical vertebrae for the two seatback angles. The

rotations for the 0-deg seatback angle in Run HFH19 (A) are generally larger than those for the

20-deg seatback angle in Run HFH20 (B) (taken from Deng et al. (2000))

negative. The equivalent table for the 0-deg seatback tests is shown in Table 8.3.

The peak relative rotations for the two seatback angles are compared in Fig. 8.22.

There is more relative rotation for the 0-deg seatback angle.

It has already been mentioned that data on relative motion between cervical

vertebrae are necessary for the design of a dummy neck for whiplash. Relative

rotation data are available from all tests done in this study, as shown in Figs. 8.23,

8.24, 8.25, 8.26, and 8.27, for both the 0-deg and 20-deg seatback angles. Corridors

can be drawn for these curves, and the relative rotation of individual vertebrae of a

dummy neck needs to fall within these corridors. The currently available dummy

neck in the BioRID (Rear Impact Dummy) dummy has never been tested to

determine if the relative rotations of the dummy vertebrae fall within these corridors.

Furthermore, there is relative translation between vertebrae during whiplash.

The BioRID neck vertebrae are hinged to each other and do not allow relative

translation. In that sense, its biofidelity is low.


Fig. 8.23 Relative motion of C1 with respect to C2 from all available tests (Deng et al. 2000)

Extension

2

0

-80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180

C2-to-C3 Relative Rotations (deg)

20-deg SB

0-deg SB

-2

-4

-6

-8

Flexion

-10

Time (ms)



Extension

8

6

4


2

0

-80 -60 -40 -20

-2

0 20 40 60 80 100 120 140 160 180

-4

20-deg SB

-6

0-deg SB -8

-10

Flexion

-12

-14

Time (ms)


Extension

16


14

12

20-deg SB

10

8

0-deg SB

6

4

2

0

-80 -60 -40 -20

-2

0 20 40 60 80 100 120 140 160 180

Flexion

-4

Time (ms)



Extension

16

14


20-deg SB

0-deg SB

12

10

8

6

4

2

0

-80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180

Flexion -2 Time (ms)


This study also estimated facet capsular strain due to whiplash. Relative displacements

and axial deformation of facet capsule landmarks for tests using a 20

seatback are shown in Table 8.4. Some large strains in excess of 60 % are seen in the

lower cervical vertebrae with the maximum strain at 97 %. For the 0-deg seatback,

the same data are shown in Table 8.5. The strains appear to be less for this seatback

angle. These strain data need to be interpreted with caution. The estimated values

are not the same as the physical stretching of the capsular surface. They do not take

into account the straightening of the collagen fibers in the capsule that may have

been loose in the static state. Also, the actual stretch needed to set off nociceptors

depends on the location of these nerve endings relative to where large stretch is

occurring. According to a study by Lu et al. (2005), capsular strains in a caprine

(goat) model of 47.2 % were most likely to be noxious or painful, but the capsule

was not stretched during a whiplash test.


Table 8.4 Peak relative displacements and axial deformations of facet capsule landmarks of 20-degree seatback tests

Run#

SB angle

(deg)

C1/C2 C2/C3 C3/C4 C4/C5 C5/C6

X (mm) Z (mm) % X (mm) Z (mm) % X (mm) Z (mm) % X (mm) Z (mm) % X (mm) Z (mm) %

HFH16 20 1.5 1.7 16 1.5 2.1 43 1.6 3.2 97 2.4 1.5 62 3.4 0.8 51

HFH20 20 6.4 4.3 8 2.1 3.0 17 3.6 2.0 46 3.5 2.5 26 4.2 1.4 62

HFH24 20 1.7 7.8 10 3.1 N/A 36 4.4 N/A 41 6.0 2.4 29 4.8 1.4 35

HFH25 20 3.0 4.9 7 2.3 N/A 32 4.1 2.7 50 4.5 4.1 26 4.1 2.8 22


Table 8.5 Peak relative displacements and axial deformations of facet capsule landmarks of 0-degree seatback tests

Run# SB angle

(deg) C1/C2 C2/C3 C3/C4 C4/C5 C5/C6

X (mm) Z (mm) % X (mm) Z (mm) % X (mm) Z % X (mm) Z (mm) % X (mm) Z (mm) %

HFH15 0 3.5 2.5 14 1.3 N/A 41 2.0 1.1 21 1.5 1.0 N/A 1.5 Small N/A

HFH19 0 3.9 6.4 10 1.9 1.1 22 3.2 1.9 30 3.8 3.3 25 4.3 2.6 51

HFH26 0 0.5 2.2 9 3.4 N/A 21 1.4 Small 39 2.3 2.2 19 6.0 Small 69

8.4 Tolerance of the Neck to Whiplash 271

8.4 Tolerance of the Neck to Whiplash

The NHTSA has proposed a neck injury criterion involving the axial force and

bending moment sustained by the neck in an impact situation. It is called the N ij

criterion and it takes the following form:

N ij ¼ F z =F c þ M=M c ¼ 1

where N ij is the neck injury criterion, F z is the axial force in the neck, F c is the

critical axial force, M is the bending moment in the neck at the occipital condyles,

and M c is the critical bending moment.

The proposed critical values are shown in Fig. 8.28. For whiplash, the neck

would be in tension and extension and F c is 4500 N, while M is 125 N,m. These

values are much too high for whiplash because they were obtained for a totally

different purpose. Out-of-position occupants in an airbag deployment are at risk of

sustaining a severe neck injury, as described in Chap. 7, and the criterion was

designed to address this problem. Thus, the N ij criterion is not applicable to minor

rearend collisions. So we ask the question: What is the tolerance of the neck to

whiplash? The answer to the question is: It depends on how healthy the neck

is. That is, the tolerance is lowered by degenerative processes in the neck and it

is therefore different for different individuals. As will be explained in Chap. 9, the

threshold for spinal pain is variable, depending on the degenerative state of

the spine and if there is an active inflammatory process in progress at the time

of the impact. That is, the crash victim may experience pain, but the cause may not

be tissue damage but rather the lowered threshold to pain due to inflammation that

accompanies degeneration. In other words, pain is not necessarily equal to injury,

except perhaps in a court of law.

Fig. 8.28 Neck injury criteria for a 50th percentile male (taken from Eppinger et al. (1999))



After almost four decades of research, we now understand the mechanism of neck

pain due to whiplash. All available evidence points to the facet joint capsule as the

principal source of pain. When the capsule is stretched, it can produce pain, and if it

is torn or overstretched, persistent pain may result. The shear hypothesis of Yang

et al. (1997) appears to be the only valid hypothesis, and it is gratifying to see that

newer car models now have a headrest that can be adjusted to be in contact with or

very close to the head in the normal driving posture. This change in headrest

configuration is significant because Deng et al. (1997) found that peak facet strains

occurred before there was head contact with the headrest which was placed 10 cm

behind the head. The ideal passive safety solution would be to design the headrest

and seatback so that their stiffness will enable the head and torso to be pushed

forward at the same rate during a rearend collision. This will eliminate all shear

forces in the neck and thus prevent neck pain. Although active collision warning

and braking systems will prevent most rearend impacts, such crashes are not totally

avoidable, and a good passive system is still needed. The lesson learned is the same

in all studies related to injury prevention. You cannot prevent an injury if you do not

know the mechanism or cause. The solution may be harmful if you are not sure of

the etiology. A case in point is the Volvo WHIPS seat or the Saab catcher’s mitt

headrest. The front seats in these vehicles were designed to prevent hyperextension

of the neck. In the Volvo, a mechanical switch in the seatback is activated when it

pushes the occupant forward due to the rearend impact. The activation of the switch

initiates a controlled and energy-absorbing rearward motion of the seatback with

respect to the seat pan, thus reducing the effect of the whipping motion (Jakobsson

et al. 2008). It is not clear if the preventive action can be activated in time to avoid

injury because the study by Deng et al. (2000) showed that the harmful effects

occurred in the first 100 ms after impact and the question is whether the mechanical

system in the WHIPS seat can react fast enough to move the seatback rearward in

that time period. Similarly, for the catcher’s mitt headrest in the Saab, the headrest

moves forward to prevent neck extension using the same type of seatback switch as

in the Volvo. The ability of the system to respond in less than 100 ms is questioned.

Even though these systems may not be totally effective, they are not likely to

aggravate the situation. However, they were designed and installed in cars without a

full understanding of the cause of whiplash pain. The pressure hypothesis led the

Insurance Institute for Highway Safety (IIHS) to recommend that headrests should

be placed 10 cm behind the head until the federal government recommended a

reduced offset distance for the headrest. Since the IIHS issues safety ratings for new

cars, it has a large influence on car design, and this 10 cm gap was maintained in

most cars for a long time. In this case, the design caused harm to occupants, albeit

unwittingly. In fact, in a company report by Volvo, Jakobsson et al. (1994) stated

that whiplash victims who had their heads up against the headrest during the impact

did not sustain any whiplash injury. It behooves the biomedical engineer to know

the cause of the injury before trying to prevent it and to heed the age-old medical

maxim from Hippocrates: “Above all, do no harm.”



8.1. Whiplash is a difficult biomechanical problem. One of the following hypotheses

is likely to be valid:

[ ] (i) Pain is due to impingement of the facet capsule by the facet joint

surfaces

[ ] (ii) Pain is due to a transient increase in pressure in the spinal canal

[ ] (iii) Pain is due to neck shear and relative vertebral body rotation,

causing facet capsule stretch

[ ] (iv) Pain is due to injury to the extensor muscles of the neck

[ ] (v) Pain is due to extensor muscle stretch during head rebound after

whiplash

8.2. In a mild rearend collision (less than 15 km/h), the neck undergoes a variety

of motions. Select the incorrect answer:

[ ] (i) Initially the upper cervical spine is in flexion and the lower cervical

spine is in extension

[ ] (ii) There is no axial compression of the neck

[ ] (iii) The facet capsules are stretched to over 50% in some cases

[ ] (iv) Towards the end of the impact, the entire cervical spine is in

extension

[ ] (v) Without a headrest, a shear force is transmitted across each vertebral

level to move the head forward

8.3. Intractable neck pain following a rearend impact could be due to one of the

following reasons. Select the correct answer:

[ ] (i) Injury to the neck muscles

[ ] (ii) Disc rupture caused by the rearend impact

[ ] (iii) Pain coming from the facet capsules

[ ] (iv) Damage to the nerve roots and the dorsal root ganglion

[ ] (v) Severe hyperextension of the neck


[ ] (i) The injury mechanism is the same for all directions of impact—Disc

rupture

[ ] (ii) Tolerance to whiplash is not the same as that due to a compressionflexion

load

[ ] (iii) The headrest has been effective in preventing whiplash injuries

[ ] (iv) Airbag deployment in front of an out-of-position occupant imposes a

severe compression load on the neck

[ ] (v) In side impact, neck injury is more common than head injury


8.5. For neck injury, only one of the following is valid:

[ ] (i) The injury mechanism is the same for all directions of impact—Disc

rupture

[ ] (ii) Tolerance to whiplash is the same as that due to a compressionflexion

load

[ ] (iii) The headrest has been effective in preventing whiplash injuries

[ ] (iv) Airbag deployment in front of an out-of-position occupant imposes a

severe compression load on the neck

[ ] (v) Whiplash pain is not necessarily an injury

8.6. For neck injury due to whiplash, only one of the following is NOT valid:

[ ] (i) Disc rupture does not occur

[ ] (ii) Tolerance to whiplash is the same as that due to a compressionflexion

load

[ ] (iii) The headrest has not been effective in preventing whiplash injuries

[ ] (iv) Airbag deployment in front of an out-of-position occupant can

impose a severe tensile load on the neck

[ ] (v) Whiplash pain is not necessarily an injury

8.7. Several hypotheses have been proposed as the cause of neck pain due to

whiplash. Select the correct answer:

[ ] (i) Injury to the nerve roots and dorsal root ganglia because of pressure

in the spinal canal

[ ] (ii) Injury to the synovium of the facet joints due to facet impingement

[ ] (iii) Injury to the posterior neck muscles due to head extension

[ ] (iv) Injury to the facet capsules of the cervical vertebrae due to shear

[ ] (v) Injury to the intervertebral discs due to compression of the neck

8.8. High-speed X-ray data of neck motion during whiplash provided some

important results. Select the incorrect answer:

[ ] (i) There is relative rotation between adjacent vertebrae

[ ] (ii) There is relative translation between adjacent vertebrae

[ ] (iii) There is no compression of the neck

[ ] (iv) There is significant facet capsule stretch

[ ] (v) Initially the upper cervical spine is in flexion and lower cervical

spine is in extension

8.9. Work on whiplash has included the following studies. Select the incorrect

answer:

[ ] (i) Development of headrests that can prevent neck shear

[ ] (ii) A more detailed study of the facet capsule to determine if it is

actually torn

[ ] (iii) A more detailed study of muscle response to whiplash

[ ] (iv) A neurophysiological study of the pain response of soft tissues of the

neck

[ ] (v) Testing of volunteers in cars simulating severe rearend impacts


8.10. The reasons why the pressure hypothesis for whiplash injury is suspect are:

[ ] (i) Pressure down the spinal canal should affect all levels of the cervical

spine and yet only the lower cervical spine is frequently painful after

whiplash

[ ] (ii) Pressure on the nerve roots can cause numbness in the upper extremities

but not pain

[ ] (iii) Pressure on the dorsal root ganglion cannot cause neck pain but can

cause upper extremity pain

[ ] (iv) Pressure on the nerve roots that lasts for less than a second should

have no effect on these roots


8.11. The reasons why the muscle hypothesis for whiplash injury is suspect are:

[ ] (i) Extensor muscles cannot be injured during head flexion

[ ] (ii) Flexor muscles cannot be injured during head extension

[ ] (iii) Muscle pain is usually in the back of the neck and extensor muscles

are in concentric contraction during whiplash

[ ] (iv) Muscle pain in the front of the neck is usually long lasting and severe


8.12. The reasons why the facet impingement hypothesis for whiplash injury is

suspect are:

[ ] (i) The synovium has not been shown to contain nociceptors

[ ] (ii) The cartilaginous articular surfaces of the facets are devoid of

nociceptors

[ ] (iii) The facet capsule is too thick for it to be pinched by the facets

[ ] (iv) There is no histological evidence that there are nociceptors in the

synovium at the facet joint line


8.13. The reasons why the shear hypothesis for whiplash injury is valid can be one

or more of the following:

[ ] (i) To move the head forward along with the rest of the body, a shear

force needs to be transmitted up the cervical spine from C7 to the

occiput

[ ] (ii) The shear will not result in relative translation of adjacent vertebrae

[ ] (iii) The shear will not result in relative rotation of adjacent vertebrae

[ ] (iv) The shear will be resisted effectively by the facets because the facet

joint line is almost vertical


8.14. Several hypotheses have been proposed as the cause of neck pain due to

whiplash. Select the correct answer:

[ ] (i) Injury to the nerve roots and dorsal root ganglia because of pressure

in the spinal canal


[ ] (ii) Injury to the synovium of the facet joints due to facet impingement

[ ] (iii) Injury to the posterior neck muscles due to head extension

[ ] (iv) Injury to the facet capsules of the cervical vertebrae due to shear

[ ] (v) Injury to the intervertebral discs due to compression of the neck

8.15. In the whiplash study by Deng et al. (2000), the following statement is true:

[ ] (i) Volunteer test subjects were used

[ ] (ii) High-speed X-rays at 90 frames/second were taken

[ ] (iii) All cervical vertebrae were visible in the X-ray videos

[ ] (iv) The data obtained from this study can be the basis for a whiplash

dummy neck


8.16. In the whiplash study by Deng et al. (2000), the following parameter was not

measured:

[ ] (i) Relative translation of adjacent cervical vertebrae

[ ] (ii) Relative rotation of adjacent cervical vertebrae

[ ] (iii) Surface deformation of the cervical facet capsules

[ ] (iv) Instant of contact of the head with the headrest

[ ] (v) Shape of the cervical spine during whiplash

8.17. In the study by Deng et al. (2000), identify the incorrect statement below:

[ ] (i) The seatback angles used were 10 and 30 degrees

[ ] (ii) Bony landmarks were used to measure the stretch of the facet

capsule

[ ] (iii) The X-ray images were acquired at 250 frames/second

[ ] (iv) The measured facet strain exceeded 60% in some cases

[ ] (v) Tungsten spheres were used to identify and measure vertebral

motion

8.18. Identify the incorrect statement

[ ] (i) There have been many volunteer tests to study the whiplash

phenomenon

[ ] (ii) Cadavers were used in the whiplash study by Deng et al. (2000)

[ ] (iii) Ono et al. (1997) used a high-speed X-ray system that ran at

1000 frames/second

[ ] (iv) Two separate whiplash studies using a high-speed X-ray unit were

conducted at Wayne State University

[ ] (v) Ono et al. (1997) were not able to provide relative motion data

between vertebrae

8.19. Tolerance of the neck to whiplash

[ ] (i) can be estimated from the N ij criterion proposed by NHTSA

[ ] (ii) does not exist because the symptoms depend on the state of spinal

degeneration

[ ] (iii) is the same for males and females


[ ] (iv) has been studied extensively by researchers


8.20. Headrests are installed above the seatback of car seats. Identify the incorrect

statement:

[ ] (i) They were initially mandated by the NHTSA to prevent hyperextension

of the head and neck

[ ] (ii) They were initially recommended to be placed 10 cm behind the

occupant’s head by the Insurance Institute for Highway Safety

[ ] (iii) They are now adjustable and can be placed very close to the back of

the head

[ ] (iv) They are to be installed in the lowest position possible above the

seatback

[ ] (v) In the Volvo, a mechanical system translates the seatback rearward

and reclines it, minimizing occupant acceleration


Prob

Ans

1 (iii)

2 (ii)

3 (iii)

4 (ii)

5 (v)

6 (ii)

7 (iv)

8 (iii)

9 (v)

10 (v)

11 (iii)

12 (v)

13 (i)

14 (iv)

15 (iv)

16 (iii)

17 (i)

18 (iii)

19 (ii)

20 (iv)


References

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N. Bogduk, A. Marsland, The cervical zygapophysial joints as a source of neck pain. Spine 13,

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B. Deng, Kinematics of human cadaver cervical spine during low speed rear-end impacts, PhD

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B. Deng, P.C. Begeman, K.H. Yang, S. Tashman, A.I. King, Kinematics of human cadaver

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Takhounts, R. Tannous, A. Zhang, R. Saul, Development of improved injury criteria for the

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L. Jakobsson, H. Norin, C. Jernstrom, S.-E. Svensson, P. Johnsen, I. Isaksson-Hellman,

M.Y. Svensson, Analysis of different head and neck responses in rear-end car collisions using

a new humanlike mathematical model. Volvo Co. Internal Report, G€oteborg, Sweden, 1994

L. Jakobsson, I. Isaksson-Hellman, M. Lindman, WHIPS (Volvo Cars’ Whiplash Protection

System): the development and real-world performance. Traffic Inj. Prev. 9, 600–625 (2008)

Y. Lu, C. Chen, S. Kallakuri, A. Patwardhan, J.M. Cavanaugh, Neural response of cervical facet

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Automotive Medicine, Chicago, IL, 1965, pp. 11–15

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animals, in ASME Winter Annual Meeting, Paper No. 65-WA/HUF-6, Philadephia, PA, 1965

T. Matsushita, T.B. Sato, K. Hirabayashi, S. Fujimura, T. Asazuma, T. Takatori, X-ray study of the

human neck motion due to head inertia loading, in 38th Stapp Car Crash Conference, SAE

Paper No. 942208, Ft. Lauderdale, FL, 1994

W.E. McConnell, R.P. Howard, H.M. Guzman, J.B. Bomar, J.H. Raddin, J.V. Benedict,

H.L. Smith, C.P. Hatsell, Analysis of human test subject kinematic responses to low velocity

rear end impacts, in 37th Stapp Car Crash Conference, SAE Paper No. 930889, San Antonio,

TX, 1993

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rear-end impacts: Understanding “Whiplash”, in 39th Stapp Car Crash Conference, SAE Paper

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FL, 1997


linear accelerometers. J. Appl. Mech. 42(3), 552–556 (1975)

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Conference, SAE Paper No. 670913, Anaheim, CA, 1967

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State University, Detroit, MI, 1973

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kinematic response of human subjects in low-speed rear-end collisions, in 41st Stapp Car

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Netherlands, 1993, pp. I-1 to I-15

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Whiplash ’98 Symposium, Phoenix, AZ, 1998, p. 23

Chapter 9

Impact Injuries of the Thoracolumbar Spine

Impact injuries to the thoracolumbar spine are rare in automotive crashes. They take

the form of vertebral body wedge fractures and, at times, burst fractures, particularly

among the elderly. The cause is not vertical acceleration of the vehicle but is

instead the straightening effect of the thoracic spine when the shoulder belt restraint

is used. However, impact injuries due to vertical acceleration do occur in other

environments, especially in the military environment. One of the first military

problems is that of seat ejection – the emergency exit of a pilot from a disabled

military jet aircraft. Some pilots sustain anterior wedge fractures of the

thoracolumbar spine due to the 20 g acceleration of the seat. The injury was first

recognized by the Luftwaffe or the German air force during World War II and was

studied intensely in Britain and the USA for several decades after the war. The

current problem is injury to the spine, pelvis, and lower extremities sustained by

mounted soldiers whose vehicle they are riding in encounters an improvised

explosive device. In this book, the seat ejection problem will be addressed, but

blast-related injuries will not. Civilian injuries to the thoracolumbar spine due to

falls also produce similar injuries. Falling from a height and landing on one’s

buttocks generate wedge-type vertebral injuries. Fracture-dislocations can occur

in more severe impacts. Such injuries are catastrophic because they can result in

damage to the spinal cord and paralysis from the waist down. Ejection from a

moving automobile or rollover of a vehicle can also cause these injuries.

9.1 Brief Anatomical Review of the Thoracolumbar Spine

The anatomy of the spine was reviewed in Chap. 7. The missing item is the anatomy

of the articular facets of the thoracic and lumbar spine which is described in this

section. Figure 9.1 shows a typical thoracic vertebra viewed from above. The

articular facet surfaces are almost vertical and in the coronal plane. It is unknown

if the articular facets can transmit a vertical load as a second load path, or if all of



281

282 9 Impact Injuries of the Thoracolumbar Spine

Costal fovea

Body

Pedicle or root of

vertebral arch

Lamina

Superior articular process

Fig. 9.1 A typical thoracic vertebra. The articular facet surfaces are almost vertical, and the

ability of the facet to transmit vertical load is unlikely (taken from Gray (1973))

the thoracic vertical compressive load is taken by the vertebral bodies. Figure 9.2

shows a typical lumbar vertebra. The articular facets stand vertically atop the

laminae and are oriented diagonally so that the vertebrae can resist posteroanterior

shear. This is necessary because large shear forces are developed in the lordotic

lumbar spine and the intervertebral discs do not have the shear strength to resist

them. The inferior facets that mate with the medial aspects of the superior facets can

bottom out on the laminar below to transmit a vertical load to the vertebra below.

The facets form a synovial joint with joint cartilage covering both facets. There is

also a facet capsule covering the joint. This capsule is implicated as a source of

low back pain because there are nociceptors (pain-sensing nerve endings) in the

capsule which tend to be stretched when the facets are transmitting load (Yang and

King 1984).

As shown in Fig. 7.1, the thoracic spine is kyphotic (convex rearward) and the

lumbar spine is lordotic (convex forward). The lordosis of the lumbar spine can be

changed by muscle action and by flexion. It is fully lordotic when it is in extension.

In flexion, the lumbar spine appears to be straight. There are biomechanical and

neurophysiological implications regarding the loss of lordosis in some patients with

low back pain.

9.2 Impact Injuries of the Thoracolumbar Spine 283

Pedicle

Transverse

process

Inferior

articular

process

Vertebral

canal

Superior

articular

process and

facet

Spinous process

Lamina

Fig. 9.2 A typical lumbar vertebra. The articular facet is vertical (normal to the laminae),

diagonally oriented to resist posteroanterior shear, and slightly curved when viewed from above.

The facets are located above the laminae and act as a load path to transmit vertical loads down the

spine (taken from Gray (1995)). Reprinted from Gray’s Anatomy: The Anatomical Basis of

Medicine and Surgery, 38th edn. by Gray, (Churchill Livingstone), 1995, with permission from

Elsevier

9.2 Impact Injuries of the Thoracolumbar Spine

Injuries to the thoracolumbar spine can be classified as follows:

• Anterior wedge fractures

• Burst fractures

• Dislocations and fracture-dislocations

• Chance fractures

• Hyperextension injuries

• Rotational injuries

Anterior wedge fractures are caused by the combination of a compressive load

and a flexion moment. This combination of loads puts a high compressive force on

the anterior aspect of the vertebral body and crushes it. As a result, the normal

rectangular shape of a vertebral body, seen in a lateral x-ray, becomes a trapezoid.

A wedge fracture of L1 is shown in Fig. 9.3.

Burst fractures are fractures of the vertebral body which appears to explode and

break up into multiple pieces. They occur when most of the compressive load is

transmitted to the body and when the spine is loaded axially. Examples of burst

fractures are shown in Fig. 9.4. These diagrams were taken from CT transverse

sectional views of the fractured vertebra and do not show the bursting of fractured

segments. However, during the fracturing process, the fragments move radially

outward far enough for the posterior segments to impact and injure the spinal cord,

Fig. 9.3 Wedge fracture of

L1 (taken from Raby et al.

(2015)). Reprinted from

Accident and Emergency

Radiology: A Survival

Guide, Chapter 12,

Thoracic & lumbar spine by

N. Raby, L. Berman, S.

Morley, G. de Lacey, 2015,

with permission from

Elsevier

Fig. 9.4 Examples of lumbar burst fractures (taken from Atlas et al. (1986))

9.2 Impact Injuries of the Thoracolumbar Spine 285

Fig. 9.5 Diagrammatic

depiction of a burst fracture,

showing the fragments

moving radially outward,

impacting (and injuring) the

spinal cord

causing paralysis. This is demonstrated in Fig. 9.5. When the impact is over, the

fragments retract and are apparently not the cause of the spinal cord injury. Burst

fractures are considered unstable because they can result in neurologic deficits.

Holdsworth (1970) classified burst fractures into five types, and Denis (1983)

opined that axial loading of the vertebral body was apparently the major reason

for the injury.

Dislocations and fracture-dislocations occur in the thoracolumbar spine when it

is put under a combined compressive load and flexion moment. Because of the high

degree of flexion, the inferior facets can override the superior facets and allow the

upper vertebra to slide forward. The result is a dislocation, often accompanied by

fracture of the anterior lip of the vertebral body, with the facets locked in the wrong

position, as shown in Fig. 9.6. The spinal canal space is compromised by the

overriding facets and there is cord injury. This mechanism is the same as that

described for the cervical spine subjected to a combined compressive and forward

bending load.

There is a seatbelt (lap belt)-related injury first described by Dr. George Chance,

a British radiologist, in 1948 (Chance 1948). It occurs in motor vehicle occupants

restrained solely by a lap belt. During a frontal crash, the occupant flexes over the

lap belt which was worn improperly above the pelvis. Alternately, the occupant

could have submarined. In either case, the belt rides over the pelvis and compresses

the abdomen. Thus, the lap belt becomes a fulcrum for the flexing torso, and a large

shear load is applied to one of the lumbar vertebrae. It starts to fracture posteriorly,

rupturing the supraspinous and interspinous ligaments, splitting the pedicles and the

posterior aspect of the vertebral body or disc. The main types of Chance fractures


Fig. 9.6 Fracture

dislocation with locked

facets (taken from

McElhaney et al. (2002)).

Reprinted from Accidental

Injury, 2nd edn. ed. by

A. Nahum, J. Melvin,

Chapter 15, Biomechanical

aspects of cervical trauma,

J.H. McElhaney, R.W.

Nightingale, B.A.




are shown in Fig. 9.7 (Denis 1983). In the USA, when three-point belts were first

installed in the front seats in 1969, there were only lap belts in the rear, and rear

seat-belted occupants were at risk of sustaining a Chance fracture. In 1990, all rear

seats in US cars were equipped with three-point belts, and Chance fractures were

thus eliminated. However, Chance fractures are seen again among mounted soldiers

riding in vehicles that are exposed to underbody blasts. A detailed discussion of

these fractures is beyond the scope of this book.

Hyperextension injuries of the thoracolumbar spine are rare and are not known

to occur during automotive crashes. They have occurred to jet pilots who eject from

disabled aircraft. One of the events that occur prior to ejection is the automatic

tightening of the shoulder harness to prevent excessive spinal flexion. Explosive

bolts are fired to retract the shoulder belts. This process is known to cause hyperextension

injuries to the thoracolumbar spine. One such example is shown in

Fig. 9.8 (Burke 1971). It shows rupture of the anterior longitudinal ligament and

the tearing apart of the T8–T9 disc due to hyperextension.

Another uncommon injury is rotational injury of the thoracolumbar spine. An

example of such an injury is shown in Fig. 9.9. The vertebra and disc are torn apart

by a combined twisting and compressive load and are described by Magerl et al.

(1994). This paper describes many other forms of thoracolumbar injury and systematically

classified a wide variety of spinal injuries, including automotive-related

injuries discussed in this chapter.

Fig. 9.7 Types of Chance fracture according to Denis (1983). It can involve one vertebra or two

vertebrae with fractures through the posterior aspect of the vertebra and rupture of the

interspinous ligament. The injury can result in splitting of the intervertebral disc, the vertebral

body, or both

Fig. 9.8 Thoracic

hyperextension injury

to T8–T9 (taken from Burke

(1971)). Reproduced with

permission of British

Editorial Society of Bone

and Joint Surgery via

PLSclear


Fig. 9.9 One form of

thoracic rotational injury

due to compression and

twisting (taken from Magerl

et al. (1994))

9.3 Experimental Studies on Lumbar Spine Injuries

due to +G z Acceleration

To escape from a disabled jet fighter, the pilot just cannot open the canopy, climb

out of the cockpit, and go over the side of the aircraft. He is prevented from doing so

mainly by the speed of the aircraft. The jet stream prevents him from standing up

and climbing over the side, and even if he was able to do that, the rest of the aircraft

would hit and possibly kill him when he tries to separate himself from the plane.

That is why ejection seats were developed to propel the pilot upward at a fast

enough speed so that he and the seat would clear the tail of the aircraft. As soon as

the pilot and the seat are in the jet stream, they are slowed down considerably by

aerodynamic drag, and if the vertical acceleration of ejection is not high enough,

they would be hit by the tall tail of the jet. Usually, a 20 g peak acceleration, lasting

for about 200 ms, is necessary to clear the tail. As mentioned earlier, some pilots

sustain anterior wedge fractures of the thoracolumbar spine, generally at the T8 to

L1 level (Vulcan et al. 1970). This injury was the motivation for the unique

experiments performed at Wayne State University to try to understand the injury

mechanism and thus solve the problem.

From 1956 to 1974, cadaveric studies were conducted in an elevator shaft which

housed a vertical accelerator that simulated pilot ejection. The simulated ejection

9.3 Experimental Studies on Lumbar Spine Injuries due to +G z Acceleration 289

Fig. 9.10 Schematic of the


vertical accelerator (taken

from Evans et al. (1962)).

Reproduced with

permission of American

Physiological Society in

the format Republish

in a book via Copyright

Clearance Center

seat or sled was propelled by compressed air stored in a 25 cu ft cylinder, rated at

1000 psi. As shown in Fig. 9.10, the sled was attached to an 8 foot long piston which

fitted into a 5 inch diameter cylinder. This cylinder was attached to the air supply

tank via a quick acting valve that allowed sufficient air to propel the sled upward at

the desired acceleration. The sled rode on two guide rails that stretched from the

first floor to the roof of the building and was equipped with air brakes that were

activated after the acceleration pulse had ended. The brakes were also designed to

mechanically lock up when the sled started to slide downward after the test. The

sled was capable of achieving a +G z acceleration of 26 g and created a loud bang

when it was launched. Thus, all testing was done at night when the building was

largely unoccupied. Figure 9.11 (King and Vulcan 1971) is a photograph of a

cadaver seated in the vertical accelerator sled with its feet and hand bound to

prevent limb flailing. Both the seatback and seat pan were rigid. The seatback

was at 90 to the seat pan, and the seat was equipped with a seat pan and a seatback

load cell as well as an accelerometer to measure the +G z or vertical acceleration.


Fig. 9.11 Vertical

accelerator sled (simulated

ejection seat) with an

embalmed cadaver ready

for an ejection test. The

cadaver was restrained by a

military lap-shoulder

harness (taken from King

and Vulcan (1971)).

Reprinted from A.I. King,

A.P. Vulcan, Elastic

deformation characteristics

of the spine. Journal of

Biomechanics 4, 413–429,


Elsevier

9.3.1 Early Results

Evans et al. (1962) reported on the results of the first series tests using this

accelerator. No wedge fracture injury was reproduced at 20 g. Strain gages were

attached to the anterior aspect of the bodies of thoracolumbar vertebrae to measure

the strain of the cortical bone during impact. It is important to note that in order to

install strain gages along the length of the thoracolumbar spine, it was necessary to

remove all of the abdominal contents below the diaphragm. After the gages were

waterproofed, the cavity was filled with liquid-soaked newspaper to replace some

of the lost weight. The amount of load transmitted to the spine from the abdominal

organs is not known, but it was assumed that most of the inertial load due to the

abdominal organs was transmitted to the pelvis. The use of a cushion resulted in

higher strain readings. That is, when an energy absorber bottoms out the impact can

be more severe than not using the absorber. However, the injury mechanism was not

found in these early studies.


9.3.2 Subsequent Test Results

Several PhD dissertations resulted from subsequent vertical acceleration studies by

Vulcan (1969), Prasad (1973), Hakim (1976), and Tennyson (1976). These investigations

looked into cadaveric, animal, and human response to vertical acceleration.

Each of these studies is described below.

9.3.2.1 Vulcan’s Research

In this study, Vulcan et al. (1970) measured the strain on the vertebral bodies of

cadavers subjected to +G z acceleration at Wayne State University. They found that

the anterior strain gages demonstrated a double peak during the impact. With the

head free to rotate, the second peak was higher than the first, occurring at the time of

maximum tension in the shoulder belts. This second peak could be eliminated if the

head was tied back or decapitated. Also, if the shoulder strap tension was increased,

the magnitude of the second peak could be reduced. It was concluded that forward

rotation of the head and flexion of the torso contributed to the increased strain and

that the wedge fracture seen in some of these tests was due to forward bending of

the spine. This was a landmark paper because it clearly showed that because the cgs

of the head and torso are located in front of the thoracolumbar spine, they exerted a

flexion moment on the spine and caused the anterior wedge fractures. At that time,

all mathematical models that simulated the pilot ejection problem considered only

axial loading of the spine and are therefore unrealistic.

9.3.2.2 Prasad’s Research

In his dissertation, Prasad (1973) accomplished several objectives. First, he was able

to confirm Vulcan’s bending hypothesis. He tested 12 cadavers under three different

restraint conditions. They were the erect, flexed, and hyperextended configurations.

In the erect mode, the initial shoulder harness tension was 20 lb (90 N), while in the

flexed mode, the harness was loosely placed over the shoulder. In the hyperextended

mode, the spine was forced into moderate hyperextension by means of a piece of

wood (2 by 4), nominally 2 in. (5 cm) thick, placed against the seatback at the level of

L1, while the tension in the shoulder harness was maintained at 20 lb (90 N). When a

specimen became available for testing, it was randomly assigned a restraint configuration

to avoid being influenced by the age of the cadaver. Each cadaver was tested

repeatedly until fracture occurred, starting at a low g-level and at 3–4 g increment.

X-rays of the thoracolumbar spine were taken after every run. The g-levels at which

fracture occurred are summarized in Table 9.1 for the three restraint configurations.

Statistical testing showed that there was a 71 % increase in fracture g-level due to

hyperextension of the spine and that difference was indeed significant at the 95 %

level of confidence. The complete statistical analysis is shown in Table 9.2.Detailsof

this study can be found in Ewing et al. (1972).


Table 9.1 Effect of spinal configuration on g-level for vertebral fracture (taken from Ewing et al.

(1972)). Journal of aircraft by American Institute of Aeronautics and Astronautics; Weeks,

Thomas M. Reproduced with permission of American Institute of Aeronautics and Astronautics

Spinal configuration Fracture g-level (G) No. of cadavers Average age

Hyperext 17.8 4 61.5

Erect 10.4 5 61.0

Flexed 9.0 3 54.3

Table 9.2 Student’s t-test of fracture data (taken from Ewing et al. (1972)). Journal of aircraft

by American Institute of Aeronautics and Astronautics; Weeks, Thomas M. Reproduced with

permission of American Institute of Aeronautics and Astronautics

Modes compared Sample size t p

Hyperextended/erect 9 2.36 0.05

Hyperextended/flex 7 2.56 0.05

Erect/flexed 8 0.58 >0.50

Fig. 9.12 The

intervertebral disc load cell

was used to measure the

load borne by the

intervertebral disc and the

line of action of the load

(taken from Prasad (1973))

Prasad’s second contribution was to find a biomechanical explanation for the

data described above (Prasad et al. 1974). That is, why was there such a dramatic

increase in fracture g-level due to spinal hyperextension? It was initially thought

that the seatback bore some of the vertical load. Thus, seatback and seat pan loads

were measured under the three spinal configurations. They were unchanged. The

only other viable explanation was that the articular facets were load-bearing

elements of the lumbar spine. To test this hypothesis, an intervertebral disc load

cell (IVLC) was designed and fabricated to measure the load borne by the

intervertebral disc which can be compared to the total load borne by the spine.

The IVLC is shown in Fig. 9.12. It is a two-channel sensor, measuring compressive

load and the moment exerted by this load relative to its geometric center. It was

about 1 cm thick and 5 cm in diameter. It was inserted into the lumbar spine by

means of a double-bladed saw which cut off the inferior portion of a lumbar

vertebra, just above the disc. In this way, there was minimal change to the stiffness

of the spine. The installation is shown in Fig. 9.13. A strap was placed around the


Fig. 9.13 IVLC installed in

the lumbar spine of a

cadaver by means of a

double-bladed saw. The

inferior portion of a lumbar

vertebra was removed to

insert the load cell above the

disc (taken from Prasad

(1973))

entire spine to keep the IVLC in place and the lip interacted with the strap as a loadbearing

surface. The total load borne by the spine could not be measured, but it can

be estimated from the sled acceleration and the body mass above the IVLC. Any

difference between the load measured by the IVLC and estimated total load would

have to be borne by the facets. The issue of using an estimated total load will be

addressed below (Sect. 9.3.2.3). The computed facet load is shown in Fig. 9.14. It

was compressive at the start of the impact but became tensile toward the end the

impact as the eccentric torso flexed the spine. The facet load was computed for both

the erect and hyperextended modes, as shown in Fig. 9.15. It crossed over from

compression to tension in the erect mode but remained in compression in the

hyperextended mode. In Fig. 9.14, the IVLC load was larger than the total load.

The reason for this can be seen in Fig. 9.16 which shows a lumbar segment

subjected to a compressive inertial load (total load), F I , and a flexion moment,

M. This moment can be replaced by a couple, d X F M , where d is the distance

between the facet tip and the center of the disc and F M is the facet load. Toward the

latter part of the pulse, the facets are in tension and the vertebral body is subjected to

a load larger than the total load. Prasad et al. (1974) went to extraordinary lengths to

show that there were two load paths down the lumbar spine because, at the time the

research was being done, anatomical texts all stated that spinal load was borne by

Fig. 9.14 (A) Measured intervertebral disc load and estimated total load. (B) The difference

between the two loads shown in (A) is the facet load. It is negative or compressive at the beginning

of the impact and becomes tensile toward the end of the impact due to spinal flexion. (C)

Confirmation of facet load from strain gages mounted on the posterior surface of the lamina.

The strain was compressive at the start of the impact pulse but became tensile later on, in

conformity with the direction of the facet load (taken from Prasad (1973))

Fig. 9.15 (A) Vertical sled acceleration. (B) Estimated total spine load. (C) Measured

intervertebral disc load for the erect and hyperextended modes. (D) Facet load for the erect and

hyperextended mode. In the erect mode, the facet load goes from compression to tension, but in the

hyperextended mode, the facet load remains in compression. (E) Confirmation of facet load based

on laminar strain at L3 and L4 (taken from Prasad et al. (1974))


Fig. 9.16 Reason why the

intervertebral disc load can

be larger than the total load

M

F M

d

F M

F I

F I

F I

F I

M

F M

d

F M

the vertebral bodies and that the facets were merely motion limiters that prevented

hyperextension. As to whether the facet capsule was capable of taking the tensile

load generated in the erect mode, Yang and King (1984) found that it was very weak

in tension and was not capable of withstanding much tension. It is presumed the

tensile force was resisted by other spinal ligaments, such as the ligamentum flavum.

Prasad (1973) also made a third contribution in the form of a 2-D computer model

of the entire spine, including the head and pelvis. This model is discussed in Chap. 10.

9.3.2.3 Hakim’s Research

To determine the total load, Hakim (1976) came up with an ingenious method of

duplicating the sled test in a materials testing machine, using a servo-controlled

loading system. In this way, the computed facet load would be based on a measured

total load. The procedure called for the performance of whole-body sled tests in the

vertical accelerator and recording the IVLC data on magnetic tape. Upon completion

of the sled tests, the lumbar spine segment was excised from the cadaver,

including the IVLC, and placed in a materials testing machine with a servocontrolled

loading system. The testing machine was instructed to load the lumbar

specimen by following the output signals from the prerecorded IVLC data that were

played back to activate the testing machine. Care had to be taken that the input to

the testing machine from the tape recorder was properly adjusted to reflect the

actual load measured during the whole-body tests. The servo controller compared

the tape-recorded signal with that generated by the IVLC in the lumbar spine while

being compressed by the testing machine. Figure 9.17 shows a schematic of the

elements of the servo control loop to duplicate the sled test in a material testing

machine, and Fig. 9.18 (Hakim 1976) shows the experimental setup. The replication

of a hyperextended run is shown in Fig. 9.19 (Hakim and King 1976). There was a


Error

detector

Command, program inputs

(prerecorded signal

from in situ run)

Servo

controller

Control

signal

Pressure

Hydraulic

power

supply

Return

Hydraulic

manifold

Pressure Return

Servo

valve

Hydraulic

actuator

Control

loop

Instrumented

spine segment

Feed back signal

To system failsafe

interlock circuits

Transducer

conditioner

IVL

(axial)

To recorder and

read out equipment

Intervertebral

load

measurement

Total load

measurement

Fig. 9.17 Schematic of the elements of the servo loop used to duplicate a vertical accelerator

experiment in a material testing machine (taken from Hakim (1976))

Fig. 9.18 Lumbar segment

in a material testing

machine which duplicated

the vertical accelerator test

this segment underwent

while it was in the body of

the cadaver (taken from

Hakim (1976))


-500

FL

Load (N), comp

0

500

1000

1500

50 100 150 200

Time, msec

TL

250 300 350

2000

IVL

Fig. 9.19 Duplication of a hyperextended run using a materials testing machine to measure the

total load. The facet load was in compression throughout the run (taken from Hakim and King

(1976)). Reprinted from N.S. Hakim, A.I. King, Programmed replication of in situ (whole body)

loading conditions during in vitro (substructure) testing of a vertebral column segment. Journal of

Biomechanics 9, 629–632, 1976, with permission from Elsevier

Load (N), comp

-500

0

500

1000

1500

2000

Time, msec

50 100 150 200

IVL

TL

250 300 350 400

FL

Fig. 9.20 Duplication of an erect run using a materials testing machine to measure the total load.

The facet load did go into tension at the end of the run (taken from Hakim and King (1976)).

Reprinted from N.S. Hakim, A.I. King, Programmed replication of in situ (whole body) loading

conditions during in vitro (substructure) testing of a vertebral column segment. Journal of

Biomechanics 9, 629–632, 1976, with permission from Elsevier

difference between the measured total load (TL) and the intervertebral disc load (IVL),

and the computed facet load was in compression throughout the run. Another example

is provided in Fig. 9.20 (Hakim and King 1976) which shows data for the replication

of a test in the erect mode. The facet load went into tension at the end of the run.

9.3.2.4 Tennyson’s Research on the Effect of Abdominal Pressure

Tennyson and King (Unpublished data) performed tests on the vertical accelerator

to assess the contribution of abdominal pressure as another load path, in addition to


the vertebral body and facet load paths. This research represented an effort to

transition from cadaveric studies to studies of living systems subjected to vertical

acceleration. The issue of abdominal pressure was raised because during the 1972

Olympic Games, the Soviet weightlifting athletes took most of the gold medals. It

was noted that they all wore a thick band around their waist when they performed

the lifting of incredible weights and it was hypothesized that abdominal pressure

generated in the lift had to be a load path because the computed stress on the

vertebral body exceeded the failure strength of the body. The role of the facets was

not well known to the sports biomechanics community at that time. The simple load

path idea was contradicted by the fact that, to generate this abdominal pressure, the

abdominal muscles had to contract and, in turn, the back extensor muscles needed

to contract to keep the torso from flexing forward. Thus, the load going through the

abdomen does not decrease the spine load which is increased by the contraction of

the back extensors. While the controversy raged, we undertook to simulate abdominal

pressure in the cadaver to determine how much load the abdomen could

transmit. A large rubber balloon was used to simulate a pressurized abdomen. It

bridged the space between the diaphragm and the floor of the pelvis. It was decided

that the maximum pressure that can be generated in the abdomen had to be less than

the systolic pressure of 120 mmHg because the descending aorta must remain

patent in order for the lower extremity muscles to be supplied with oxygen. The

initial pressure in the balloon was set at 13.8 kPa or approximately 100 mmHg.

IVLC data were collected during the abdominal tests and intra-abdominal pressure

was monitored. Figure 9.21 shows results of the testing in the erect mode with and

without abdominal pressure. Abdominal force was calculated from the measured

Fig. 9.21 Vertical accelerator data from erect mode runs with and without simulated abdominal

pressure in a cadaver (Unpublished data)


abdominal pressure and cross-sectional area of the abdomen at the level of the

IVLC. There was a slight increase in abdominal force during the impact, but the

amount of load transmitted by the abdomen was approximately 700 N for a 9 g run.

This is small compared the large loads transmitted to the discs and vertebral bodies.

Furthermore, abdominal pressure is not likely to increase with increased vertical

acceleration, and the peak acceleration for seat ejection is 20 g. Thus, the contribution

of abdominal pressure to load sharing is minimal or perhaps even zero if the

spinal extensors are used to generate the initial abdominal pressure. However,

abdominal pressure did have a hyperextensive effect on the lumbar spine and

caused the facets to remain in compression throughout the run (Fig. 9.21)

9.3.2.5 Tennyson’s Research on In Vivo Muscular Response to +G z

Acceleration

The last study to use the vertical accelerator was performed by Tennyson (1976)

who wanted to investigate the effect of muscular response during caudocephalad

acceleration (See also Tennyson et al. (1977). Unanesthetized dogs were used to

determine the delay in response of paraspinal extensor muscles because the sled

was not man rated to test volunteers. A protocol to subject unanesthetized dogs to

vertical acceleration was submitted and approved by the Wayne State University

Institutional Review Board. Low g-levels of 3–5 g were used to ensure that the dogs

would not suffer any pain or sustain any injury. The tool used to determine

muscular delay was electromyography (EMG) but at the time there were no

commercially impact-resistant EMG amplifiers available. Figure 9.22 shows a

bank of “homemade” EMG amplifiers designed and built with the latest available

semiconductor technology. They did not contain any of the now obsolete vacuum

Fig. 9.22 Bank of homemade solid-state (impact-resistant) EMG amplifiers used on board the

vertical accelerator (taken from Tennyson (1976))


Fig. 9.23 Null check of the EMG system. The sled was fired with the EMG system turned on but

no animal on board to ensure that the electrodes were not picking up spurious signals (taken from

Tennyson (1976))

tubes and were therefore impact resistant. These amplifiers were placed on board

the vertical accelerator to amplify the EMG signals. Before testing the dogs, the

EMG amplifiers and a pair of leads suspended in air were subjected to a vertical

acceleration to ensure that the leads would not pick up any spurious signals.

Figure 9.23 shows the sled acceleration and zero output from the EMG amplifiers,

ensuring that any output from the animals would be genuine EMG signals. Two

dogs (beagles) destined for sacrifice after participating in a medical experiment

were acquired from the research team that used them, with the promise that they

would be found a home after the vertical accelerator experiments. They were

anesthetized on the morning of the test day for the insertion of needle electrodes

into several of their paraspinal muscles. A specially made jacket was used to protect

the needles from being pulled out. The leads from the EMG needles were firmly

connected to a terminal junction in the jacket, as shown in Fig. 9.24. EMG

amplifiers were connected to this junction so that the signals could be amplified

and sent onto an analog tape recorder. Figure 9.25 shows an anesthetized animal

ready for testing. By the time the sled was prepared for launch, the dog would have

awakened from the anesthetic and was fully aware of its surroundings. Figure 9.26

shows the beagle in the accelerator seat, waiting for the test to begin. Each animal

was tested multiple times but not once did either animal try to get off the sled.

Examples of EMG data collected are shown in Figs. 9.27 and 9.28 for the lumbar

multifidus muscle and the spinalis cervicis muscle. The superimposed vertical

acceleration pulse was used to determine the delay between onset of acceleration

and appearance of EMG. The EMG onset delay is summarized in Table 9.3 for the

six muscles that were monitored. The delay times varied from 22 to 36 ms. The


Fig. 9.24 Junction box for EMG leads built into the jacket used to protect the EMG needles from

being pulled out by the animal (taken from Tennyson (1976))

Fig. 9.25 Anesthetized

animal ready for testing

after it wakes up from the

anesthesia (taken from

Tennyson (1976))

delay in humans is expected to be longer because the nerves involved are longer

than those in a dog. A 45 ms delay in the human would be a good estimate. In

Fig. 9.28, the parabolic curve is called the integrated EMG curve. It was obtained by

rectifying the EMG data (inverting all the negative spikes in the EMG data) and

calculating the area under the rectified EMG. There is experimental evidence that

the rectified EMG is proportional to the force developed in the muscle, but the

proportionality factor can vary from person to person and from time to time for a


Fig. 9.26 Fully awake

beagle in the vertical

accelerator sled waiting for

the next test (taken from

Tennyson (1976))

Fig. 9.27 EMG data from the lumbar multifidus muscle. The sled acceleration is superimposed on

the EMG data so that the delay time can be determined (taken from Tennyson (1976))


Fig. 9.28 EMG data from the spinalis cervicis muscle of a dog subjected to a mild (5-g) vertical

acceleration. The parabolically shaped curve is called the rectified EMG and is said to be

proportional to the force generated in the muscle (taken from Tennyson (1976))

Table 9.3 Average EMG onset delay (taken from Tennyson (1976))

Muscle group Delay Time SD (ms)

3 g Runs (N) 5 g Runs (n) All Runs (N)

Long. Cerv. 26 4.2 (7) 36 10.6 (11) 32 9.7 (18)

Long. Thor. (0) 22 (1) 22 (1)

Long. Thor. 36 22.3 (18) 25 8.8 (17) 31 17.8 (35)

Semispin. Cap. 25 5.7 (7) 28 12.9 (9) 26 10.2 (26)

Spinalis Cerv. 21 6.8 (12) 27 11.3 (14) 24 9.9 (26)

Spinalis Thor. 32 8.8 (13) 28 9.2 (14) 30 9.1 (27)

given person. However, the rectified EMG curve was not used to estimate muscle

force in this study. It was used to estimate the time delay between the appearance of

EMG and the generation of maximal contraction in the muscle. Data provided by

Hannam et al. (1975) and Inman et al. (1952) indicate that this second delay period

was about 80 ms in the human, referenced to the time of the peak EMG-derived

force or the rectified EMG curve. Thus, the time to peak force from the onset of

acceleration would be about 125 ms. For details on this study, please consult

Tennyson (1976).

9.3.3 Commentary

The results reported in Sect. 9.3.3 constitute a decade of research that resulted in

four PhD dissertations. The mechanism of spinal injury due to vertical acceleration


was found, the mechanics of load transmission down the spine was documented,

and the effect of muscular response to acceleration was studied. In addition, two

versions of a validated model of the spine were developed for impact simulation.

These models are described in Chap. 10.

9.4 Tolerance of the Thoracolumbar Spine

Although the injury rate for the thoracolumbar spine is less than 1 % in auto-related

crashes, they occur more frequently among the elderly population. In fact, anterior

wedge fractures can occur in an osteoporotic spine due to a minor bump (vertical

acceleration) or, at times, without a precipitating event. Generally, anterior wedge

fractures are due to high vertical accelerations encountered in a fall, during ejection

from a disabled aircraft or due to the shoulder belt restraint in a horizontal crash.

Since these fractures are common, a tolerance criterion is needed. For +G z impact,

the tolerance for young healthy males is 20 g for durations in excess of 5 ms (Eiband

1959). Figure 9.29 shows that, for seat-to-head (vertical) accelerations, the tolerance

is 20 g for durations between 5 and 500 ms. It is higher for durations less than

5 ms and it drops for durations in excess of 0.5 s. Because of age, this value can drop

by as much as 50 % by age 60. In Table 9.1, the average fracture g-level in the erect

mode was 10.4 g for cadavers that were 60 years old. This is about half the

tolerable acceleration for young males. Failure loads of individual thoracic

vertebrae were obtained by Kazarian and Graves (1977). Vertebrae were

Fig. 9.29 Human tolerance to vertical acceleration as a function of impact duration (Eiband 1959)

9.4 Tolerance of the Thoracolumbar Spine 305

subjected to a uniform compressive load at three different loading rates (2100,

21, and 0.21 in/min), and the vertebrae were placed in four separate groups with

the top three vertebrae (T1–T3) in the first group and the bottom three (T10–

T12) in the fourth group. It was found that the ultimate load to failure increased

with loading rate and with vertebral level. The lower vertebrae failed at an

average load of 2000 lb at the highest loading rate. The upper vertebrae failed

just above 500 lb at the lowest loading rate. These are basic data on tolerance

but have little practical value because vertebrae are seldom loaded in pure

compression. Yoganandan et al. (1988) performed quasi-static testing on 18 spinal

segments, two of which extended from C2 to L5, with the others extending

from a thoracic vertebra to L5. The segments were tested in flexion and

compression that caused wedge-type failures mostly in the lower thoracic levels

(T7–T12). The failure loads and moments are shown in Table 9.4. Unfortunately,

these were quasi-static tests, and the tolerance values could be much

higher at high loading rates.

The other injury of interest is burst fracture which can have catastrophic consequences.

There have been several biomechanical studies to create burst fractures,

but none was able to fully explain the mechanism. That is, does the fracture occur

because the facet load was nonexistent or minimal? The early work of Willen et al.

(1984) reproduced L1 burst fractures in seven T12–L2 spinal segments, using a

10 kg drop weight to generate a dynamic compressive load and thus create a burst

Table 9.4 Tolerance of the thoracolumbar spine to quasi-static compression-flexion loading (taken

from Yoganandan et al. (1988)). Reprinted with permission Copyright © 2017 SAE International.

Further distribution of this material is not permitted without prior permission from SAE

Specimen #

Spinal

level

Length

(cm)

Failure

level

Failure

load (N)

Eccentricity

(cm)

IL–10 T3–L5 30.5 L1 1730 8.5 148

IL–11 T3–L5 31.0 T12 1113 8.5 95

IL–12 T2–L5 33.0 T9 967 8.0 78

IL–13 T3–L5 31.0 T7 2220 6.0 133

IL–16 T2–L5 30.5 T11 1668 8.0 133

IL–17 T2–L5 30.5 T9 801 6.5 52

IL–18 T4–L5 33.0 T12 4444 8.0 289

IL–27 C2–L5 38.0 T7 556 11.5 64

IL–28 C2–L5 40.0 T12 801 13.0 104

IL–29 T2–L5 33.0 T12 1330 10.5 134

IL–31 T3–L5 30.5 T10 2891 9.0 260

IL–32 T3–L5 34.0 T9 2000 9.0 180

IL–33 T3–L5 32.0 T11 1775 9.5 169

IL–38 T3–L5 34.3 T11 4220 7.0 295

IL–72 T3–L5 33.0 T9 2224 6.0 133

IL–74 T3–L5 34.0 T7 2927 6.0 176

IL–77 T6–L5 22.0 T12 5560 5.0 278

IL–78 T6–L5 24.0 T12 5275 5.5 290

Failure moment

(Nm)


Fig. 9.30 Typical burst fracture patterns created by Willen et al. (1984), using a drop weight

impact testing method. There was a sagittal plane fracture and a couple of frontal plane fractures,

typical of four of the seven specimens tested

fracture. The paper gave the impression that repeated drop tests were not conducted

but a single impact from a drop height of about 2 m created the fracture. The

average force to fracture was 8 kN with a range of 6–10 kN. The age range of the

specimens was 17–40. The facet joints were intact during and after testing. Four of

the seven fractures were of the type shown in Fig. 9.30. However, it should be

mentioned that there are no data regarding the ability of thoracic facets to transmit

compressive load and the L1 vertebra is particularly vulnerable because the entire

spine load is carried by the L1 vertebral body and the T12–L1 disc if the thoracic

facets are not load-bearing elements. The issue of facet loading was a major focus in

the work of Langrana et al. (2002) who created burst fractures in nine

thoracolumbar segments in a testing machine at a loading rate of 100 mm/s.

The nine segments were divided into three groups of three, as shown in Table 9.5.

The lower thoracic segments in Group 1 failed at an average load of 2809 N. The

T12–L2 segments in Group 2 were tested in extension and failed at a considerably

higher load averaging 5802 N. The posterior elements in the third group were

removed, and the failure load was comparable to that of Group 2. These data tend to

show that the T12 thoracic facets were load bearing because of the high failure load

in Group 2. However, there were no facets in Group 3, and the failure loads were not

that much lower. Thus, the jury is still out as to whether thoracic facets can transmit

vertical load.

9.4 Tolerance of the Thoracolumbar Spine 307

Table 9.5 Summary of motion segment test data (taken from Langrana et al. (2002))

No.

Levels

Test

orientation

Failure

load (N)

Strain at 75 % failure load

(μ strain)

Anterior (A) Lateral (L)

L/A

Stiffness

(N/mm)

1 T10–T12 Neutral 2950 1078 1848 1.7 306

2 T11–L1 Neutral 2004 1725 3468 2.0 442

3 T10–T12 Neutral 3472 – 4955 – 385

Average 2809 1402 3424 1.9 378

4 T12–L2 15 ext. 7377 233 3138 13.7 825

5 T12–L2 15 ext. 6126 53 1056 19.9 881

6 T12–L2 15 ext. 3904 157 1865 11.9 300

Average 5802 148 2020 15.2 669

7 T10–T12 Neutral a 5674 716 794 1.1 365

8 T8–T10 Neutral a 5006 111 1347 12.1 730

9 T8–T10 Neutral a 5084 6883 690 0.1 761

Average 5255 2570 944 4.4 619

a Posterior elements removed

Clinical hypotheses were proposed to explain the biomechanical mechanisms

involved. Holdsworth (1970) described in great detail the various forms of spinal

injuries he had treated and classified them as either stable or unstable, more in the

mechanical sense than the neurological sense. Burst fractures were classified as

stable. He made mention of the role articular facets played in rotational injuries but

did not elaborate on their role in burst fractures. However, he did provide a

biomechanical explanation of the injury. The lumbar or cervical spine had to be

in flexion so that it is straight when a large compressive load is applied. This causes

the nucleus above the superior endplate to rupture through the endplate into the

vertebral body, resulting in the outward movement of the fragments of the body.

Denis (1983) differentiated burst fracture from wedge fractures by the loss of

integrity of the vertebral ring in the former. He found that the most commonly

affected vertebra was L1, based on a study of 59 cases. He proposed five types of

burst fractures and expressed the opinion that the degree of retropulsion of fragments

into the spinal canal as seen in CT scans after the injury was not correlated

with neurological deficit. This leads to the study by Panjabi et al. (1994) who

managed to create 10 burst fractures, using 13 thoracolumbar specimens. In those

tests, they inserted a spinal canal transducer into the canal and were able to measure

fragment encroachment in three specimens. The dynamic encroachment ranged

from 2.4 to 16 mm, while the static postimpact encroachment ranged from 0.7 to

4.1 mm. These data provide the explanation Denis (1983) was looking for. The

reported force to fracture averaged 6.1 kN. It was quite a bit lower than that reported

by Willen et al. (1984) because Panjabi’s specimens were older (19–70 years) and

were subjected to repeated impacts until fracture occurred. Data from repeated

impacts should not be used to compile tolerance data. The formation of microcracks

weakens the specimen with no outward sign of damage.


9.5 The Issue of Acute Rupture of the Intervertebral Discs

This is a controversial topic because many physicians are of the opinion that acute

disc ruptures can happen after a very minor car crash (or even after picking up a

potato chip). However, the biomechanical literature does not support this opinion.

To understand why, it is necessary to investigate the mechanism of disc rupture.

The normal disc is made up of an outer wall of fibrous tissue called the annulus

fibrosus which is made up of 16–20 layers of fibrocartilage with the fibers running

obliquely and in different directions from layer to layer. In the center is the nucleus

pulposus which is a gel-like material made up of proteoglycans mixed in with some

cartilaginous fibers. The disc, like all other tissue, degenerates with age, and the

layers of fibrocartilage in the annulus can rupture due to constant pressure exerted

upon it by the nucleus. The symptoms of a ruptured disc are back or neck pain and

radiculopathy, pain in the extremities due to constant pressure on the nerve roots

exerted by a ruptured or bulging disc. A herniated disc is shown diagrammatically

Fig. 9.31, and it is usually diagnosed by an MRI scan. Degeneration is a slow

process and can take months or years to develop into a full herniation, if ever. In the

meantime, there is back or neck pain accompanied by radicular symptoms.

When someone with a degenerative spine is involved in a motor vehicle crash,

the symptoms can be exacerbated by the unusual motions the body underwent. It

could also be facet pain which is clinically recognized as another source of spinal

pain. So the accident victim complains of pain, is seen by a physician, diagnosed

with a disc herniation, and files a lawsuit. The physician supports the claim because

his/her opinion is based on the history provided by the patient who relates the car

crash to the doctor. However, researchers in the field have found that the disc is

stronger than the vertebral body which would fracture before the disc ruptures. The

collective opinion in papers by Brinckmann (1986), Brown et al. (1957), Henzel

et al. (1968), Hirsch (1955), Markolf and Morris (1974), Roaf (1960), and Virgin

Fig. 9.31 Herniated

nucleus pulposus exerting

pressure on the exiting

nerve root. Back pain comes

from the herniation itself

but pressure on the nerve

root causes leg pain as well

9.5 The Issue of Acute Rupture of the Intervertebral Discs 309

(1951) is that discs do not rupture acutely (following a single loading event) but

they do so over a period of time. The experiment by Brinckmann (1986) was most

revealing. He tested weakened cadaveric lumbar discs by cutting through some of

the fibrous annular layers from the inside. He made a hole in the disc and inserted a

blade that was used to cut through the annulus on the opposite side, leaving about

1 mm of the outer annulus intact. The blade was withdrawn, and the disc was loaded

in compression with the posterior structure removed (no facets). When a load

equivalent to the weight of the body above it was applied to the disc, there was

no measurable bulge around the disc. When the vertebral body above or below it

was loaded to failure, there was no acute disc rupture, the bulge was minimal, and

no nucleus was extruded from the hole that was made to cut the annulus. Thus, it

was concluded that a disc cannot be ruptured due to a single loading event. There

have been several experiments to determine the number of loading cycles necessary

to rupture a disc. Figure 9.32 shows a ruptured disc in a study conducted by Gordon

et al. (1991) after it was loaded over 7000 times. It is seen that the nucleus is a

viscous material that does not flow easily and that the rupture is not akin to a

balloon bursting. In fact, a cross section of the same ruptured disc showed that the

individual annular layers were not ruptured along a radial line, as shown in

Fig. 9.33. The zigzag path taken by the nucleus to exit the disc is a demonstration

that disc rupture is a slow and degenerative process that cannot occur acutely. We

can safely say that the intervertebral disc does not rupture following a single

loading event, unless there is massive failure of an adjacent vertebral body.

However, the controversy rages, fueled by the many lawsuits filed to claim that

the ruptured disc was the result of the motor vehicle accident. Actual cases

describing these lawsuits can be found in King (2002).

Finally, there is the issue of loss of lordosis in low back pain patients. Lateral

X-rays show that the lumbar spine is almost straight and has lost its lordotic curve.

Radiologists diagnose this as an abnormality and list it as a significant finding

Fig. 9.32 An artificially

created disc rupture which

occurred after the

intervertebral disc was

loaded cyclically for over

7000 times. The nucleus

pulposus is viscous and

does not flow like a liquid

(courtesy of Dr. King Yang)


Fig. 9.33 The path taken by the nucleus pulposus for it to herniate from an intervertebral disc. It is

not radial, and each layer is ruptured at a different location, indicating that process is slow and

quite unlike the bursting of a balloon (courtesy of Dr. King Yang)

without explaining how that happened. Yang and King (1984) found that for the

facets to transmit vertical load, the lumbar spine needed to be in extension. They

also noted that as the facets transmitted load, the tip of the inferior facet bottomed

out on the laminar below and the facet rotated rearward pivoting about the facet tip.

This motion stretched the capsule visibly akin to watching a rubber band stretch.

These high strains resulted in facet pain, and the logical explanation for the loss of

lordosis is the voluntary action of the patient to minimize this pain by reducing facet

load. Facet load was found to be present when the torso was erect without any

external load applied to the spine, as described in Chap. 10. For details regarding

facet pain, see Cavanaugh et al. (2002).


9.1. One of the following statements relating to the anatomy of the human spine is

untrue

[ ] (i) The spine has a total of 24 vertebrae

[ ] (ii) There is a disc between every adjacent pair of thoracic and lumbar

vertebrae

[ ] (iii) There is a disc between the first and second cervical vertebra

[ ] (iv) The cervical and lumbar spine are lordotic and the thoracic spine is

kyphotic

[ ] (v) The first cervical vertebra does not have a body


9.2. One of the following statements does not apply to flexion-compression type

injuries of the neck:

[ ] (i) The injuries are due to a compression load applied to the head

anterior to the head c.g.

[ ] (ii) Flexion and compression can combine to produce wedge fracture of

vertebral bodies

[ ] (iii) Endplates can separate from the disc surface under flexion and

compression loads

[ ] (iv) Burst fractures of the vertebral bodies can occur due to flexion and

compression

[ ] (v) Anterior dislocation of facets can occur as a result of a flexion

compression load

9.3. Burst fractures of vertebral bodies

[ ] (i) Cause spinal cord injury because of the severe loss of the height of

the vertebral body

[ ] (ii) Are due to an axially directed compressive load on the body of the

vertebra

[ ] (iii) Do not propel fragments of the body into the spinal canal to injure

the cord

[ ] (iv) Are usually associated with rupture of the adjacent intervertebral

discs

[ ] (v) Can frequently occur during airbag deployments

9.4. The most common injury sustained by pilots who eject from disabled jet

aircraft is:

[ ] (i) A herniated lumbar intervertebral disc

[ ] (ii) Fracture of the spinous process

[ ] (iii) Burst fracture of a lumbar vertebral body

[ ] (iv) Fracture dislocation of thoracic or lumbar vertebrae

[ ] (v) Wedge fracture of a vertebral body of the thoracolumbar spine

9.5. Wedge fractures in the lumbar spine can occur in automotive crashes

because of:

[ ] (i) Vertical (z-axis) loads due to vehicle bounce

[ ] (ii) Vertical (z-axis) loads due to springs in the seat cushion

[ ] (iii) Vertical (z-axis) loads due to a lap belt

[ ] (iv) Vertical (z-axis) loads due to a shoulder belt restraint

[ ] (v) Vertical (z-axis) loads due to vehicle pitch during the crash

9.6. Chance fractures occur in automotive crashes:

[ ] (i) When there is a chance encounter of a vehicle with another object

[ ] (ii) When there is no shoulder belt and the lap belt rides over the pelvis

and fractures the lumbar spine


[ ] (iii) When the lumbar spine pivots around a lap belt holding a passenger

who does not have a shoulder restraint

[ ] (iv) When the shoulder belt is worn too tightly and there is no lap belt


9.7. During pilot ejection from a disabled jet aircraft, the most frequently injured

area of the spine is:

[ ] (i) The cervical spine

[ ] (ii) The intervertebral discs

[ ] (iii) The lamina

[ ] (iv) T1-T6 vertebral bodies

[ ] (v) T10-L2 vertebral bodies

9.8. During pilot ejection from a disabled jet aircraft, the most frequently injured

area of the spine is:

[ ] (i) The transverse processes

[ ] (ii) The spinous processes

[ ] (iii) The neural arch

[ ] (iv) The sacrum


9.9. Anterior wedge fractures of the thoracolumbar spine are caused by:

[ ] (i) High shear loads in the antero-posterior direction

[ ] (ii) High facet loads due to antero-posterior shear

[ ] (iii) High compressive loads without forward flexion

[ ] (iv) High compressive loads with forward flexion

[ ] (v) High bending loads without significant compressive loading

9.10. In pilot ejection, the tolerance of the vertebral body to fracture can be

increased by:

[ ] (i) Hyperflexing the spine prior to ejection

[ ] (ii) Hyperextending the spine prior to ejection

[ ] (iii) Placing the spine in lateral bending prior to ejection

[ ] (iv) Placing a cushion on the seat pan prior to ejection

[ ] (v) (ii) and (iv)

9.11. During pilot ejection (20 g peak), vertical load down the spine can be

efficiently transmitted by:

[ ] (i) The lumbar facets

[ ] (ii) The intervertebral discs

[ ] (iii) Voluntary generation of abdominal pressure


[ ] (v) (i) and (ii)


9.12. The average burst fracture load for a lumbar vertebra was found to be about

6 kN. This is equivalent to a vertical (+G z ) acceleration of about 13 g. This

value is lower than the whole-body acceleration tolerance. Possible reasons

for this are:

[ ] (i) Duration of impact not compatible with the ejection seat pulse

[ ] (ii) Cadaveric specimens used were not taken from a population of

healthy young males

[ ] (iii) The applied force was from a dropping weight and this is different

from an inertial load


[ ] (v) (i) and (ii)

9.13. A middle-aged male driver was involved in a frontal crash. He was belted and

sustained no fractures or lacerations. However, he complained of low back

pain immediately after the crash. Subsequently, he was diagnosed with a

ruptured disc at the L5-S1 level. He also has a history of intermittent low back

pain. The ruptured disc was not caused by the crash because:

[ ] (i) His lumbar spine did not sustain a vertical (infero-superior) load

during the crash

[ ] (ii) Discs do not rupture as the result of a single loading event or impact

unless there is massive bony fracture of the adjacent vertebral bodies

[ ] (iii) The immediate pain is due to the degenerated condition of his spine

and is not necessarily an indication of a permanent injury



9.14. During pilot ejection (20 g peak), vertical load down the spine can be

efficiently transmitted by:

[ ] (i) The ligamentum flavum

[ ] (ii) The extensor muscles behind the spine

[ ] (iii) Voluntarily generated abdominal pressure

[ ] (iv) The neural arch


9.15. The Prasad model of the spine can be used to simulate pilot ejection from a

disabled aircraft

[ ] (i) It was a finite element model

[ ] (ii) It was a lumped parameter model

[ ] (iii) It was a discrete parameter model

[ ] (iv) It was a 3-D model

[ ] (v) It was a continuum model

9.16. In cadaveric studies using the vertical accelerator, Prasad et al. (1974)

discovered the cause for anterior wedge fractures in pilots who eject from

disabled aircraft. Identify the incorrect statement


[ ] (i) the facets were able to transmit a vertical load down the spine

[ ] (ii) the spinal fracture load was increased dramatically if the spine was

put in hyperextension

[ ] (iii) In the erect mode, the facet load became tensile towards the end of

the acceleration pulse

[ ] (iv) The facet load was measured directly during the vertical accelerator

tests


9.17. During vertical acceleration of the whole body, abdominal pressure is a

possible load path to transmit the inertial load of the head and torso to the

pelvis

[ ] (i) Abdominal pressure was a load path that can transmit inertial load to

the pelvis

[ ] (ii) With abdominal pressure, the facet load remained in compression

[ ] (iii) To generate abdominal pressure in a living person, abdominal muscles

need to contract causing the spinal extensors to contract

[ ] (iv) The spinal extensors add compression to the spine and the spine load

is not decreased by abdominal pressure


9.18. Live dogs were subjected to vertical acceleration by Tennyson (1976). Select

the correct answer

[ ] (i) The purpose was to determine the spinal tolerance of the dog spine

[ ] (ii) The dogs were anesthetized during testing

[ ] (iii) The applied vertical acceleration ranged from 3 to 5 g

[ ] (iv) The dogs sustained anterior wedge fractures of the thoracolumbar

spine


9.19. There is delay between the onset of acceleration and muscular response in the

form of electromyographic signals (EMG). This delay was measured in spinal

muscles of dogs undergoing vertical acceleration

[ ] (i) The delay is in the order of 100–200 ms

[ ] (ii) The delay is in the order of 20–50 ms

[ ] (iii) Muscle force reaches a maximum at the end of this delay

[ ] (iv) There is another delay before muscle force reaches a maximum

[ ] (v) (ii) and (iv)

9.20. Muscular response to an impact is delayed by several mechanisms. Select the

incorrect answer:

[ ] (i) There is delay due to the time needed to cause the Golgi tendons to

fire

[ ] (ii) There is delay due to transmission of the efferent signal from the

cord

References 315

[ ] (iii) There is delay due to the time needed to stretch the muscle spindles

[ ] (iv) There is delay due to the time needed to generate muscle force after

activation of the muscle

[ ] (v) There is delay due to transmission of the afferent signal to the spinal

cord


Prob

Ans

1 (iii)

2 (iii)

3 (ii)

4 (v)

5 (iv)

6 (v)

7 (v)

8 (v)

9 (iv)

10 (ii)

11 (v)

12 (v)

13 (v)

14 (v)

15 (iii)

16 (iv)

17 (v)

18 (iii)

19 (v)

20 (i)

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Chapter 10

Biomechanics of Facet Loading

in the Lumbar Spine

Although the biomechanics community has now accepted the concept of facet

loading, the idea took a long time to take hold. Even in the 1980s, it was necessary

to continue to prove conclusively that facet loads are real. To that end, El-Bohy

et al. (1989) obtained contact pressure data from the tip of an inferior lumbar facet

to show that it did indeed bottom out on the lamina below in order to transmit spinal

load. Other topics covered in this chapter are spinal models simulating seat ejection,

a model simulating the ditching of an aircraft at sea, and a brief overview of finite

element models of the spine simulating impact.

10.1 Direct Measurement of Lumbar Facet Loading

In the 1970s, facet load was deduced from calculating the difference between the

total load borne by the lumbar spine and that borne by the intervertebral disc. In a

study to find causes of low back pain, Yang and King (1984) deduced from the

measurement of total load and disc load that under quasi-static loading, there was a

3–25 % facet load and that a possible cause of low back pain was the large amount

of stretch underwent by the facet capsule while the facets were carrying load. In

some cases, this stretch was visible to the naked eye. However, there was still no

direct evidence that the tip of inferior facet bottomed out on the lamina below to

form a facet load path. El-Bohy (1988) undertook the task of quantifying this

phenomenon despite the fact that the small area of contact presented many challenges.

The work in this dissertation appeared in El-Bohy et al. (1989). The first

challenge was to measure the contact force between the facet tip and the lamina.

This challenge could not be met as there simply was insufficient space to allow the

insertion of a load cell. However, to show that there was contact, it was not

necessary to measure the magnitude of the contact force because proof of the

existence of a contact pressure would be sufficient. Thus, El-Bohy set about to

develop a method for measuring contact pressure at the tip of a lumbar facet. The



319

320 10 Biomechanics of Facet Loading in the Lumbar Spine

Lead wires

Active diaphragm

Fig. 10.1 Schematic diagram of a facet pressure sensor (taken from El-Bohy (1988))

feasibility of inserting a small pressure sensor from the top of the inferior facet

down to the tip was investigated. He found that, using X-ray guidance, he could

drill a hole the size of a 13-gauge spinal needle from the top of the facet to reach the

facet tip. As a result, a diaphragm-type pressure transducer was fabricated, using a

13-gauge spinal needle. The sensing element was a 0.3 mm thick stainless steel

diaphragm to which was mounted a single strain gauge. The pointed end of the

needle was sawed off, and the instrumented diaphragm was glued to the end of the

needle with the strain gauge facing the open end of the needle. The lead wires were

threaded through the needle as shown in Fig. 10.1. Its outer diameter was 2.4 mm

and it was about 10 cm long. The transducer was calibrated hydrostatically to

ensure that it gave an acceptable level of output. But when it was used to sense

facet tip contact with the lamina, the pressure or force applied to the diaphragm was

not hydrostatic. Thus, the output of the transducer merely demonstrated contact,

and the absolute value of the contact force could not be ascertained.

To insert the needle transducer, a small surgical hand drill was used with a drill

bit just slightly larger than the needle. A series of X-rays was taken during the

drilling process to guide the bit toward the tip of the inferior facet. The drill did go

through the outer wall of the facet tip. The final position of the tip was determined

by monitoring the pressure during the insertion procedure. With the spinal

segment unloaded, the needle was pushed toward the facet tip until a pressure

was registered. It was pulled back until the pressure just returned to zero. Dental

acrylic was used to hold the transducer in place. Figure 10.2 is a radiograph of the

instrumented facet.

A three-segment lumbar spine was used for this experiment. They were either

the T12–L2 segment or the L3–L5 segment. The two ends were potted in metal

cups, using Ostalloy, an alloy that melts below 100 C and could be used to hold the

specimen in place when it solidified at room temperature. A rigid (metal) plate was

attached to the upper cup so that anterior eccentric loads could be applied to the

spinal segment. A materials testing machine was used to apply a static body weight

to the segment with an anterior eccentricity of 12–16 mm relative to the center of

the superior disc, to simulate the line of action of the cg of the torso. The middle

vertebra was sandwiched between two discs and was able to adjust to the applied

load. The experimental setup is shown in Fig. 10.3. Static superficial extensor

muscle action was also simulated in this experiment. Two wires were attached to

the rigid plate atop the upper cup, at the rear of the specimen, and were threaded by

means of two sets of pulleys to be anchored to load cells attached to the floor. A

turnbuckle was used to adjust the length of the wire and hence the tension in the

10.1 Direct Measurement of Lumbar Facet Loading 321

Fig. 10.2 X-ray of a facet

pressure sensor installed in

the tip of an inferior facet

just above the lamina (taken

from El-Bohy (1988))

wire (Fig. 10.4). The last piece of instrumentation was a disc nucleus pressure

sensor. The transducer is shown in Fig. 10.5. Basically, it was fabricated from a

13-gauge spinal needle with the tip preserved. However, at the tip, half of the needle

was ground off, and a strain-gauge diaphragm was glued over part of the semicircular

opening. The rest of the needle was filled with epoxy. It was inserted into the

nucleus pulposus of one of the discs. A side view of the entire test setup is shown in

Fig. 10.6. The segment was tested in an environmental chamber in which the

temperature was 37 C and the relative humidity was 95 %.

The test protocol was to simulate a static equilibrium condition of an erect

lumbar spine in a person who is just standing or carrying a weight in front of

him. This condition is shown in Fig. 10.7. Facet contact pressure was to be

measured with body weight alone followed by the addition of a 45 N weight placed

in front of the spine. The body weight was assumed to be 356 N, and the eccentricity

of the weight was 340 mm (13.4 in. anterior to the center of the disc. The procedure

was to place the specimen in the materials testing machine unloaded followed by

the application of an eccentric body weight, using the materials testing machine. As

a result, the specimen flexed anteriorly and the rigid plate attached to the upper cup

had a downward inclination. The “muscle” cables were tightened to bring the plate

to a horizontal position, using a bubble level. Pressure and muscle load data were

recorded continuously while the plate was being brought back to level and when it

was level. Then, the 45 N eccentric weight was added, and the plate was again

brought back to level. A second 45 N weight was added in some tests. All data were

recorded during the entire experiment which took about three minutes.


Fig. 10.3 Schematic diagram of the test setup to measure facet contact pressure (side view) (taken


A total of 21 tests were conducted on 6 lumbar segments that were taken from

4 cadavers. Data regarding the cadavers used and the test parameters are shown in

Table 10.1. Figure 10.8 shows the changes in facet pressure as the body weight was

added and as 45 N weights were added. After the addition of each force, the spine

was brought back to its erect position by leveling the plate. The changes in muscle

force are shown in Fig. 10.9. The sequence of events is described in Table 10.2

which should be read in conjunction with Figs. 10.8 and 10.9. The average facet

pressure for tests on all six segments is shown in Fig. 10.10. Facet contact pressure

was measured in every specimen. There were an increase in pressure when the

eccentric weight was added in four cases, no increase in one case, and a decrease in

the first specimen tested. It is suspected that the sensor was not quite in the right

place in the first test, but overall the difference in pressure was statistically

significant for the two loading cases. A Student’s t-test was performed with n ¼ 6,

even though there were 21 tests. There was a consistent increase in muscle force


Fig. 10.4 Wires simulating

muscle action are activated

by turnbuckles and attached

to load cells anchored to the

floor (based on El-Bohy

et al. (1989))

Fig. 10.5 Photograph of a

disc nucleus pressure

transducer made from a

13-gauge spinal needle

(based on El-Bohy et al.

(1989))

when the 45 N eccentric weight was put on. This is shown in Fig. 10.11. The

measured disc pressures are shown in Fig. 10.12. They are very sensitive to

eccentric loading. A 45 N weight at an eccentricity of 340 mm more than doubled

the disc pressure in every specimen. For people suffering from disc degeneration, it

is advisable to carry heavy things close to the chest or behind the back. It can be

concluded from this study that facet load is transmitted from the tip of the inferior


Fig. 10.6 Photograph of the test setup for sensing facet contact pressure with the lamina (taken


Fig. 10.7 The test protocol

was to simulate loading on

the lumbar spine due to

body weight and to a weight

carried in front of the chest

by hand. Simulation of

extensor muscle action was

included (taken from

El-Bohy (1988))

W h

W t

W a

Q

E

C

W h

W a

W t

Q

E

C

Head Weight

Arm Weight

Torso Weight

Weight Held by

the Hand

Tension in spine

Muscle

Compression on

the Spine


Table 10.1 Cadaveric data and test parameters (taken from El-Bohy et al. (1989))

Segment # 1 2 3 4 5 6

Vertebrae T12-L2 T12/L2 L3-L5 T12-L2 L3/L5 T12-L2

Disc grade a 2 3 3 2 3 2

Age/sex 63/M 51/M 51/M 54/M 54/M 43/F

BW (kg) b 51.2 52.6 52.6 68.0 68.0 52.6

Eccentricity (mm) 16 13 12 14 14 15

No. of tests 3 4 1 4 4 4

a Disc grade classifies degree of degeneration according to Galante (1967)

b Body weight (BW) above the top vertebra used in the tests

Fig. 10.8 Facet pressure

and disc pressure changes

due to body weight and an

eccentric weight. See

Table 10.2 for the testing

sequence (taken from

El-Bohy (1988))

Fig. 10.9 Simulated

extensor muscle forces with

the sum shown as the curve

at the top of the figure. See

Table 10.2 for the testing

sequence (taken from

El-Bohy (1988))

facet to the laminal below and that the facets bear load even in the normal erect

posture. Experiments or computer models simulating in vivo loading on the spine

need to include muscle forces.


Table 10.2 Sequence of events in the facet pressure test a (based on El-Bohy et al. (1989))

Time

(s) (Zone) Condition Action Remarks

0–10 (I) No load, no pressure Start to apply BW No facet pressure

10–25 (II) Spine is flexing Applying BW Disc pressure is increasing

and facet pressure is

appearing

25–50 Spine is becoming erect Adjusting plate to horizontal

Facet pressure rises

muscle force

increases

50–70 (III) Spine is erect Muscle force and facet System is in equilibrium

pressure remain steady

70–85 (IV) Spine is flexing 45 N weight is being

added

Muscle force increasing

as facet pressure drops

85–113 Spine becoming erect Adjusting plate to horizontal

muscle force

Disc pressure and muscle

force reach a new peak

increases

113–130 Spine is erect Muscle force and facet

pressure remain steady

System is in a new equilibrium

position

130–160 (V) Spine is flexing Another 45 N weight is

being added

Facet pressure drops and

muscle force increases

160 (VI) End of experiment The 45 N weights are

released

a This table should be read in conjunction with Figs. 10.8 and 10.9

Disc pressure drops and

facet pressure rises

Fig. 10.10 Average facet pressure for two loading cases, body weight only and body weight plus a

45 N eccentric weight (taken from El-Bohy (1988))


600

500

AVERAGE MUSCLE ACTIVITY

Legend:

BW only

BW and 45 N

400

300

200

100

0

Spec. 1 Spec. 2 Spec. 3 Spec. 4 Spec. 5 Spec. 6

Fig. 10.11 Simulated muscle force for the two loading cases – body weight only and body weight

plus the 45 N eccentric weight. The average increase was 182 N (taken from El-Bohy (1988)).

(Re-do this plot using data from El-Bohy’s dissertation, Table 4.2, p. 48)

2

AVERAGE DISC PRESSURE

PRESSURE MPa

1.8

1.6

1.4

1.2

Legend

BODY WEIGHT ONLY

BODY WEIGHT AND 45 N

1

0.0

SPEC. 2 SPEC. 3 SPEC. 4 SPEC. 5 SPEC. 6

Fig. 10.12 Average nucleus disc pressure for the two loading cases – body weight only and body

weight plus the 45 N eccentric weight (taken from El-Bohy (1988))


Table 10.3 Facet capsular strain due to applied extension and flexion moments (taken from King

and Cavanaugh (1996)) (The applied moments were 18 N.m in extension and 24 N.m in flexion)

Maximum tensile facet capsule stretch data (%Nm) a

Extension tests

Flexion tests

Cadaver no. x axis y axis z axis Resultant x axis y axis z axis Resultant

400 7.1 8.7 5.3 12.4 0.6 0.2 0.1 0.6

464 4.8 5.5 8.2 11.0 0.1 0.4 0.3 0.5

807 3.3 2.5 6.4 7.6 0.4 0.6 0.3 0.8

329 7.4 6.3 0.2 9.7 0.8 2.6 1.9 3.3

455 1.3 3.9 1.3 4.3 0.3 1.3 0.3 1.4

490 0.8 2.5 4.7 5.4 2.2 4.5 1.2 5.2

2 0.8 7.4 7.0 10.2 1.3 3.5 6.4 7.4

117 0.8 6.6 6.6 9.4 0.9 7.1 1.3 7.3

34 12.4 21.0 21.1 32.2 2.0 0.3 3.0 3.6

SD 4.0 5.6 6.0 7.8 0.7 2.4 2.0 2.6

CV 93.8 78.4 88.7 77.5 104.5 122.8

Average 4.3 7.2 0.8 11.4 1.0 2.3 1.6 3.3

a x axis is directed anteriorly in the transverse plane; y axis is directed laterally to the left in the

transverse plane; z axis is directed superiorly, normal to the transverse plane. SD standard

deviation, CV coefficient of variation

As a footnote to this study, El-Bohy quantified facet capsule stretch during

spinal extension and flexion by gluing small metal targets to the capsule and

observing their motion as the capsule stretched. The percent stretch per Newton-meter

of applied moment is shown in Table 10.3. It can be seen that the

percent stretch/N.m of extension moment varied from 4.3 to 32.2 % and that the

stretch was visible to the naked eye because it was well over 100 % in many

specimens for an applied moment of 18 N.m. The fact that the coefficient of

variation is very high is not surprising. Not everyone who extends or flexes

the spine complains of pain. These data can be found in King and

Cavanaugh (1996).

10.2 The Sequence of Events Occurring During Seat

Ejection

Escape from a disabled jet aircraft by means of a seat ejection is now a routine

procedure, even though some spinal injuries continue to occur. This is one impact

event that is well controlled from the point of view of vertical acceleration

imposed on the body. Research to improve ejection seats basically ceased in

the late 1970s, but seat development continued with each new model of aircraft.

10.2 The Sequence of Events Occurring During Seat Ejection 329

The basic data collected from the three decades of research form the basis of our

knowledge on the effects of vertical acceleration on the human body and for

solving new problems associated with the threat of IEDs to mounted soldiers.

Thus, it would be appropriate to document the sequence of events that occur

during seat ejection.

As mentioned in Chap. 9 (Sect. 9.3), jet aircraft move too fast for the pilot to bail

out the “old fashioned way” – climbing out of the cockpit and jumping out. There is

also usually not enough time to do this in a failing jet which drops like a rock

without power. To be ejected vertically out of the cockpit, it is necessary to clear

the tail of the aircraft before it hits the seat as it emerges from the cockpit. As

soon as the seat hits the airstream, it slows considerably, and a high seat

acceleration is needed for it to clear the tail in about 200 ms. The rocket that

propels the seat out of the cockpit can be angled to give it a forward thrust as it

ascends, to ensure that it would not be hit by the tail. The speed and attitude

envelope for ejection has been getting larger. Supersonic ejection has been

attempted, and inverted ejection is possible if there is enough ground clearance

(30 m minimum altitude). Pilots used to have to blow the canopy prior to ejection

or go through it during ejection. Currently, the canopy is blown prior to ejection.

All seats have a zero-zero capability. That is, ejection is possible at zero altitude

and zero velocity. Some can even eject while the plane is under water. Ejection is

initiated by activating a lever on the front of the seat pan, between the legs. A

British ejection seat, made by Martin Baker, used to employ a face curtain which,

when pulled down over the face, activates ejection. This is a preferred method

because it keeps the head from flexing forward prior to ejection. Vulcan et al.

(1970) found that head flexion causes additional compression on the spine.

However, this feature is no longer available because the pilot may encounter

difficulty moving the arm up above the head to reach the curtain and activate the

ejection. During ejection, limb flailing injuries can occur if the pilot does not try

to keep his/her arms away from the airstream. Leg restraints are used in some

seats. After the seat clears the aircraft, a seat-mounted parachute is deployed to

separate the pilot from the seat. In that process, the pilot needs to avoid being hit

by the tumbling seat. If the altitude at ejection is low, the parachute carried by the

pilot opens immediately to slow his descent. If, on the other hand, the ejection

occurred at a high altitude, the pilot is allowed to free fall so he/she would not

suffer the ill effects of extremely low temperatures and a barometrically controlled

parachute will open at the appropriate altitude. The parachute also carries

a survival pack for the pilot which lands before the pilot. Figure 10.13 shows an

ejection on progress. A video of an ejection can be found on the link https://www.

youtube.com/watch?v=HK1AW6PPWtw


Fig. 10.13 A zero-zero

ejection in progress. The

payload was a crash dummy

(taken from Wikimedia

Commons. Source: http://

holloman.af.mil/sunburst/

2003/april/April%204.pdf)

10.3 Mechanism of Injury to the Thoracolumbar Spine

due to Ejection

Based on the research described in Chap. 9, especially the work of King and Vulcan

(1971), it became abundantly clear that the anterior wedge fractures sustained by

pilots who eject from disabled aircraft were due to a combined compressive and

bending load. Data from the intervertebral disc load cell (IVLC) also showed that

this load can exceed that of the total load imposed on the spine because of the

flexion moment. However, models of the spine intended to simulate seat ejection

did not take bending into account until as late as 1971. Perhaps, early modelers

could be excused from overlooking this important factor, but the trend continued

despite the finding that bending was the culprit in causing anterior wedge fractures.

Similarly, the US Air Force (USAF) also did not understand or deliberately ignored

the bending injury mechanism and continued to push for an injury criterion called

the Dynamic Response Index (DRI) which is based on spinal compression alone

(Stech and Payne 1969). The unfortunate consequence is that the DRI is being used

by the military, including NATO, to assess current spinal injuries due to spacecraft

landing and the effect of IEDs on mounted soldiers. Many of the mounted soldiers

in troop transports are unrestrained or do not wear shoulder belts, and bending is a

significant contributor to their spinal injuries.

10.4 Early Models of the Spine Simulating Vertical Acceleration 331

10.4 Early Models of the Spine Simulating Vertical

Acceleration

To substantiate the statements made in Sect. 10.3 above, a series of spinal models

simulating seat ejection is discussed in this section. They can be classified into

several model types – lumped parameter models, discrete parameter models,

continuum models, and finite element models. Models developed before 1974

generally failed to consider the effect of bending on the spine during ejection. A

brief description of some of these models is provided to show how the field of

modeling progressed.

10.4.1 Lumped Parameter Spinal Models

The first model was suggested by Latham (1957), a medical doctor who worked at

the RAF Institute of Aviation Medicine, in the UK. It was a base-excitation model

consisting of a mass on a spring, both of which are accelerated upward, as shown in

Fig. 10.14. Latham recognized the lack of anatomical similarity of the model to the

human torso and did not provide any equations to describe the response of the mass

to the acceleration of the base. He was interested more in the operational aspects of

the ejection seat, including such factors as the maximum tolerable seat acceleration

and the effect of “jerk” or rate of change of acceleration on the spine. A large part of

the paper was devoted to the design of a cushion which contained the survival pack

for the pilot. Soft cushions are detrimental to the spine because when they bottom

out, they induce high accelerations. He also mentioned the advantages of using the

face curtain to prevent head flexion. This phenomenon was noticed by Vulcan et al.

(1970) and gave rise to the bending mechanism of injury.

Fig. 10.14 The baseexcitation

model used to

derive the Dynamic

Response Index

Mass, M

x

Spring

Stiffness, k

y

Base

Acceleration

..

y

Base


The equation of motion for the mass in Fig. 10.14 is given by

m€x þ kx ð yÞ ¼ 0

where m is the mass of the block above the spring, k is the stiffness of the spring, x is

the displacement of the mass, y is the displacement of the base and, €x is the

acceleration of the mass.

Let z ¼ x y;

k=m ¼ ω n 2 ,

where ω n is the natural frequency of the system;

Then

€z þ ω n 2 z ¼ €y

The initial conditions are:

At t ¼ 0,

x ¼ y ¼ 0orz ¼ 0

If a sudden acceleration, Y¨, was applied to the system,

2

z ¼ €Y= ω n ½ 1 cos an t

or

kz ¼

m€Y ½1 cos ω n t

and

kz max ¼ 2m€Y for ω n t ¼ 2nπ

where n ¼ 1, 2, 3, ............

That is, the compression in the spring (or spine) for an infinite rate of onset is

almost twice that of a slowly applied acceleration. Since DRI is the force in the

spring based on this spring-mass model (Stech and Payne 1969), the compression

force in the spine can only be twice that of a statically applied compressive load,

and this force varies with the rate of onset. Additionally, this model is anatomically

incorrect and does not consider bending of the spine which is not a linear spring

(Brown et al. 1957; King and Vulcan 1971). It is indeed surprising that the Air

Force claims the model works for ejection seat evaluation. It would be a mistake to

try to apply this model to a spine subjected to an underbody blast where the

accelerations are much larger than 20 g and have a shorter duration. The DRI was

probably tuned to the 20 g acceleration level and cannot be predictive of injury at

g-levels many times above 20 g.

10.5 A Two-Dimensional Model of the Thoracolumbar Spine 333

10.4.2 Simple Continuum Models

Hess and Lombard (1958) proposed a continuum model in the form of a vertical

elastic column subjected to an impact acceleration on the bottom with its top end

free of any restraint. No equations were provided in the paper, and according to the

authors, the mechanical properties of the human body are unknown. This model

was a precursor to finite element models that would appear in the literature many

years later, but, at the time of its publication, it did little to shed light on the

mechanism of injury to the thoracolumbar spine. A curved continuum spine model

with a head attached was developed by Cramer et al. (1976). It is an elegant model

that took into account the effects of bending, but it was not able to predict fracture

because a continuum model does not differentiate bone from discs. Consequently, it

could not be validated.

10.4.3 Discrete Parameter Models

The first known discrete parameter model was formulated by Orne and Liu (1971).

It was a 2-D model that simulated individual vertebrae and assumed the natural

shape of the spine. As a result, it took into account the effects of bending, but it did

not simulate the facets as a second load path. There was no attempt to validate the

model.

Prasad and King (1974) developed the first known validated model of the spine.

It was a 2-D model which simulated facet loads and was able to predict variations in

facet loading when the spinal curvature was changed. A detailed description of the

model is provided in the next section (Sect. 10.5).

Belytschko et al. (1978) developed a 3-D discrete parameter model of the spine

to simulate seat ejection. The head, vertebrae, and pelvis were assumed to be rigid

bodies, and soft tissues were simulated by deformable elements. Spring elements

and hydrodynamic elements were used to simulate the facets of the thoracolumbar

spine and the cervical spine, respectively, but the facets were primarily motion

limiters, and no load path was defined for the facets. Most of the simulations of

ejection were bilaterally symmetric, and the 3-D feature of the model was only

exercised in one simulation of an offset mass hanging from one side of the helmet.

Again, no attempt was made to validate the model.

10.5 A Two-Dimensional Model of the

Thoracolumbar Spine

As mentioned in Chap. 9 (Sect. 9.3.2.2), Prasad’s third contribution was the

development and validation of a 2-D model of the spine subjected to vertical

acceleration (Prasad 1973). Based on the experimental data collected from the


Fig. 10.15 Generic elements of Prasad’s 2-D spinal model in which the facets were simulated by a

spring between A’ and B’ (taken from Prasad (1973))

vertical accelerator, the model was required to have the capability of transmitting

facet load and to simulate both the erect and hyperextended postures Prasad (1973)

came up with a 2-D discrete parameter model made up of the head, the 24 vertebrae,

and the pelvis. In addition to being able to compute facet load for the erect and

hyperextended modes, the model had involuntary (passive) muscle response and

was validated against cadaveric data. A later version of the model developed by

Tennyson and King (1976) simulated active muscle tension. Both models were

validated against available data.

Figure 10.15 shows the generic elements of the model, the I th link and the I1

th link, where I ¼ 1–26. The vertebral bodies were represented by rigid bodies and

the intervertebral disc by a spring and a dashpot. The facets in the back were

connected by springs. To simulate the curvature of the spine, the local coordinate


system for each vertebra was at an angle, θ, with respect to the sled coordinate

system which was aligned with the inertial reference frame. Each vertebra was

assumed to carry the mass of a slice of the torso, the cg of which was eccentric to the

vertebral body and was anterior to it. The three equations of motion for the I th

vertebra were formulated using Newton’s second law, addressing the normal and

shear forces acting on the vertebra and facets and the moments acting on the

vertebral body. Thus, the result was a set of 78 equations of motion, in the form

of nonlinear second-order ordinary differential equations. When all the material

properties were provided, they were solved simultaneously using Hamming’s

predictor-corrector method. A Fortran program was written to reduce the 78 2 nd

order equations to 156 first-order equations which were solved simultaneously with

a set of initial conditions. There were also many auxiliary equations used to

simulate the seatback, the lap and shoulder belts, as well as the chin-chest contact

force. A detailed derivation of the equations of motion and a listing of material

properties of the disc and facets can be found in Prasad (1973).

The model was validated against cadaveric data obtained from tests done on the

vertical accelerator. Specifically, the computed and measured spinal loads were

compared in the erect and hyperextended modes. Prasad validated the model at

three different g-levels for three different subjects in both the erect and

hyperextended modes. The entire set of validation results at 6, 8, and 10 g for

three different cadavers in both modes can be found in Prasad (1973). Examples of

validation runs are shown in Figs. 10.16, 10.17, 10.18, and 10.19. The predicted and

measured intervertebral disc load and facet load for a 6 g run in the erect mode are

compared in Fig. 10.16. Figures 10.17 and 10.18 compare the same loads for

the 8 and 10 g runs in the erect mode on the same cadaver. A 6 g run in the

hyperextended mode is validated in Fig. 10.19. In all of the validations, the match is

TIME (ms)

0

50

100 150 200 250

-250

IVL(MODEL)

IVL(EXPERIMENTAL)

FORCE (lb)

-500

250

125

0

-125

-250

IVL = Intervertebral Load

TOTAL SPINE LOAD AT L3

50 100 150 200 250

FACET LOAD (EXPERIMENTAL)

FACET LOAD (MODEL)

Fig. 10.16 Comparison of model and experimental results of a 6 g run in the erect mode (taken

from Prasad (1973))


TIME (ms)

0

-500

50

IVL(MODEL)

100 150 200 250

IVL(EXPERIMENTAL)

FORCE (lb)

-1000

500

250

0

-250

-500



50 100 150 200 250

FACET LOAD (MODEL)


Fig. 10.17 Comparison of model and experimental results of an 8 g run in the erect mode (taken

from Prasad (1973))

TIME (ms)

0

50

100 150 200 250

-500

IVL(MODEL)

IVL(EXPERIMENTAL)

FORCE (lb)

-1000

500

250

0

-250

-500



50 100 150 200 250

FACET LOAD (MODEL)


Fig. 10.18 Comparison of model and experimental results of a 10 g run in the erect mode (taken

from Prasad (1973))

not perfect because a generic spine could not be expected to yield results identical

to those from individual cadaveric spines. However, the predicted facet load stayed

mainly in compression for the hyperextended mode while it crossed over from

compression to tension in the erect mode.

To extend the usefulness of the model and to apply it to the automotive crash

environment, Prasad (1973) changed the direction of the input acceleration from

+G z to G x (horizontal deceleration) to simulate a car crash. He discovered an


TIME (ms)

0

50

IVL (MODEL)

100 150 200 250

IVL(EXPERIMENTAL)

-250

FORCE (lb)

-500

250

125

0

-125

-250



50 100 150 200 250

FACET LOAD (MODEL)


Fig. 10.19 Comparison of model and experimental results of an 6 g run in the hyperextended

mode (taken from Prasad (1973))

unusual result for the G x simulations. The model predicted that the lumbar spine

continued to sustain a substantial compressive (vertical) load, even though the input

acceleration was horizontal. The model equations and computer program were

checked for errors, but none was found. Later, (Begeman et al. 1973) confirmed

the model prediction by subjecting shoulder- and lap-belted cadavers to G x

acceleration and measuring the seat pan load. As shown in Fig. 8.5, the seat pan

load was larger than the sum of vertical components of the lap belt loads. The

difference is the spine load predicted by the Prasad model. As explained in Chap. 8

(Sect. 8.2.6), the straightening of the kyphotic thoracic spine against the shoulder

belt caused the generation of a compressive spine load which in fact acted downward

on the lumbar spine and upward on the cervical spine, as discussed in Chap. 8.

Begeman et al. (1973) also found that the cadavers had sustained thoracolumbar

wedge fractures.

This is one of the rare examples of a model predicting an outcome that was

verified experimentally. There are reports in the literature on thoracolumbar fractures

of belted front seat occupants. Huelke et al. (1995) cited many cases of lower

thoracic and upper lumbar fractures associated with three-point belted occupants in

frontal or near-frontal crashes. The hypothesized mechanism was flexure of the

lumbar spine prior to impact, while the actual mechanism is the spine load generated

by the straightening of the thoracic spine. In another study by States et al.

(1990), the injury rates due to motor vehicle crashes were compared between the

years 1984 and 1985. New York State was the first in the Union to pass a mandatory

safety belt use law which became effective on January 1, 1985. This paper found

that injury rates were decreased in every category with the exception of

thoracolumbar injuries. Yoganandan et al. (1989) also reported that the use of


restraints did not significantly change the rate of AIS 3+ thoracolumbar injuries. All

three papers failed to recognize the development of a spinal load in a horizontal

crash despite the 1973 paper by Begeman et al. (1973).

10.6 Simulation of Combined Vertical and Horizontal

Acceleration

Tennyson and King (1976) developed a human spine model that was capable of

simulating active muscular response to the impact acceleration. It was based on the

Prasad model to which he added spinal musculature that responded to stretch. There

were muscles that linked adjacent vertebrae as well as muscles that originated at the

pelvis and were attached to different vertebrae up the spine. The stretch response

was modeled using the neural delay data obtained from Tennyson et al. (1977). A

series of +G z runs representative of falls and seat ejection were run to compare

responses with and without muscular action. However, there were no data available

to validate the results. The only source of data that could be used to validate the

model was the work of Ewing and Thomas (1972) who subjected volunteers to G x

tests while measuring the kinematics of the head and neck. The seated subjects were

restrained by a full military harness consisting of a lap belt and two shoulder belts.

The deceleration pulse (G x ) was triangular with a rise time of 22 ms (213 g/s onset

rate), a peak of 8.1 g, and a total duration of 286 ms. Validation consisted of

comparing the head kinematics in terms of linear and angular displacement and

linear and angular acceleration. Figure 10.20 compares the horizontal head displacement

relative to T1. The match could be better because the model predicted a

smaller displacement. The angular motion is compared in Fig. 10.21. It showed

excessive extension during the latter part of the run. Figure 10.22 is a comparison of

head horizontal acceleration. The model apparently has a higher natural frequency


head horizontal

displacement between

model results and

experimental data (taken

from Tennyson and King

(1976))

20.00

HOR. DISP. [CM]

-20.00 0.00

RUN NO.: RUN17A

0.00 80.00 160.00 240.00 320.00

TIME [MS]

HEAD-T1

EXPERIMENT

MODEL

10.6 Simulation of Combined Vertical and Horizontal Acceleration 339

Fig. 10.21 Comparison of head angular displacement between model results and

experimental data (taken from Tennyson and King (1976))

Fig. 10.22 Comparison of head horizontal linear acceleration between model results and

experimental data (taken from Tennyson and King (1976))

than the human. This is also reflected in the angular acceleration of the head which

is compared in Fig. 10.23 with the experimental data. The model did not simulate

neck flexors which can improve the prediction of the head linear and angular

displacement.

10.6.1 Application of the 2-D Model to the Aircraft

Ditching Problem

As mentioned in Chap. 7 (Sect. 7.4.1), Ewing set up a lab to study the problem of

ditching of Navy aircraft at sea when the pilot misses the deck of the aircraft carrier.


Fig. 10.23 Comparison of head angular acceleration between model results and experimental data

(taken from Tennyson and King (1976))

He and the US Navy never really did find out why these pilots do not eject in the few

minutes the aircraft was afloat on the ocean surface to save themselves from

drowning. King et al. (1979) used the Tennyson model in an effort to determine

if a combined G x and +G z acceleration can somehow adversely affect the spinal

cord and cause a cord concussion. Jet pilots do not use a steering wheel, and when

there is a forward deceleration of the aircraft coupled with a vertical acceleration,

the resulting head flexion can cause damage to the upper spinal cord. However,

head contact with the interior of the aircraft is highly unlikely and so is cerebral

concussion. The fact that these pilots wear a flight helmet to which are attached

weapons systems aggravates the load on the neck. The use of volunteers in this risky

experiment would be unethical, and the use of cadavers will not elicit a neurological

response. Similarly, approval for the use of primates would be difficult, and the

results may not be directly transferable to the human. Thus, the modeling option

was the best means of studying this problem.

The first thing was to find out the g-levels a ditching aircraft would encounter.

The US Navy Safety Center could not provide this information, presumably

because when the aircraft sank with the pilot on board, recovery of the crashed

aircraft was not attempted and any flight recorder data would be lost. To define the

problem, it was necessary to establish a g-level and pulse shape for both the

horizontal deceleration and the vertical acceleration. For simplicity, it was assumed

that the peak acceleration would be 10 g for both G x and G z and that the pulse shape

would be triangular, with a duration of 200 ms and a rate of onset of 200 g/s.

Because the peak accelerations could occur simultaneously or be offset, it was

necessary to do a parametric study for three input conditions. The peaks could occur

simultaneously or the vertical acceleration peak could precede or lag the horizontal

acceleration peak. The details of the parametric study are listed in Table 10.4, and

the acceleration pulses used in Case 2 are shown in Fig. 10.24.

10.6 Simulation of Combined Vertical and Horizontal Acceleration 341

Table 10.4 Parametric study

of the aircraft ditching

scenario

Case no. Symbol Condition

1 Together Simultaneous +G z andG x peaks

2 Z then X G z Peak 50 ms before G x Peak

3 X then Z G x Peak 50 ms before G z Peak

ACC. PULSE (G)

0.

10.

+G z

-G x

–10.

0. 10.

20.

TIME (MS)

30. 40.

X10

Fig. 10.24 Assumed accelerations experienced by an aircraft ditching in the ocean. The peak

accelerations were either coincident in time or one peak preceded the other in the three cases that

were modeled using the Tennyson model (King et al. (1979))

The Tennyson spine model was used by King et al. (1979) to simulate this

impact event. The subject was assumed to be in a seated position restrained by a full

military harness consisting of a lap belt and an inverted Y shoulder belt. The

pelvis was subjected to the combined accelerations of the form shown in Fig. 10.24.

The simulations were run with and without a helmet. Additionally, it was assumed

that a 13.3 N (3 lb) helmet would cause an anterior or upward shift of the head cg by

12.7 mm, depending on the type of weapons system attached to it. Active muscle

tension of the spinal extensors was assumed to take place after a delay of 100 ms. In

addition to head linear and angular acceleration, the model computed biomechanical

parameters that can potentially injure the upper cervical cord or cause a

cerebral concussion. These were odontoid process motion toward the spinal cord,

stretch of the cervical cord, and the chin-chest contact force. The predicted

odontoid process rearward displacement is shown in Fig. 10.25, with and without

a helmet. For the helmeted case, the posterior odontoid displacement was 5.2 mm

for a 10 g pulse. For higher g-levels, a displacement in excess of 10 mm would be

sufficient to cause a cord concussion, according to Fielding (1974). Figure 10.26

shows the amount of stretch of the spinal cord with and without a helmet. Again, the

stretch is larger for the helmeted case, but no human data existed regarding the

amount of stretch necessary to cause a concussion. The chin-chest contact force is

shown in Fig. 10.27. The magnitudes were not likely to cause a cerebral concussion.

The model also computed head linear and angular accelerations. These quantities

were found to be below concussive levels, even with a helmet.


Fig. 10.25 Computed odontoid displacement for the helmet and non-helmeted cases. The displacement

was 5.2 mm for the helmeted case for a 10 g pulse. It could exceed 10 mm for higher

inputs and cause a cord concussion which has the same effect as a cerebral concussion on the pilot.

The peaks of the +G z and the G x accelerations were coincident for this case (taken from King

et al. (1979))

Fig. 10.26 Computed

spinal cord stretch for the

helmeted and non-helmeted

case. The stretch was not

increased by much due to

the helmet. The acceleration

peaks were simultaneous


(1979))

Fig. 10.27 The computed

chin-chest contact force for

the helmeted and

non-helmeted cases. The

force is not high enough to

cause a cerebral concussion.

Again, the acceleration

peaks were simultaneous


(1979))

CHIN-CHEST F. (N) X10 2

0. 20. 40.

0.

TOGETHER

60. 120.

TIME (MS.)

W/0. HELM

W. HELMET

180. 240.

10.7 Finite Element Modeling of the Thoracolumbar Spine 343

10.7 Finite Element Modeling of the Thoracolumbar Spine

A simple FE element model of a single vertebra was developed by Hakim and King

(1979). The vertebral body had a layer of cortical bone surrounding a core composed

of trabecular bone. The posterior structure of the vertebra was also simulated,

as shown in Fig. 10.28. In those days, computing power was extremely low, and the

model had a coarse mesh simulating bilaterally symmetric loading. That is, only

Fig. 10.28 Finite element model of a single vertebra. Due to limited computational capabilities in

the 1970s, only half a vertebra could be modeled, but the facets were modeled so that they could

mate with an adjacent vertebra (taken from Hakim (1976))



static model-predicted

vertebral cortical strains

with those measured in a

vertebra. The location of

the strain gauge was

the anterior aspect of the

vertebral body at the

center of the body (taken

from Hakim (1976))

STRAIN (X10 -6 )

400 800

MA

MODEL

EXP

500

1000

LOAD (N)

1500


static model-predicted

vertebral cortical strains

with those measured in a

vertebra. The location of the

strain was the lateral aspect

of the vertebral body near

the superior endplate (taken

from Hakim (1976))

STRAIN (X10 -6 )

400 800

SL

MODEL

EXP

500

1000

LOAD (N)

1500

half of the vertebra was simulated. However, provision was made for facet loading,

and the facet geometry allowed the addition of mating facets with adjacent vertebrae.

The vertebral cortex was simulated using shell elements, and the trabecular

bone in the vertebral body was made up of brick elements. The model was subjected

to static and dynamic loading, the latter being based on the measured IVLC data

from the vertical accelerator tests. The model was validated statically using the

strain measured on the anterior and lateral aspects of the vertebral body. However,

the thickness of the cortical bone of the instrumented vertebrae was not measured,

and only a qualitative comparison could be made. Cortical strain-load plots for two

different vertebrae are shown in Figs. 10.29 and 10.30. The perfect match in

Fig. 10.29 merely indicates that the estimated cortical bone thickness was very

close to the actual thickness. King and Yang (1986) extended the Hakim model to a

model of a lumbar functional spinal unit which is a motion segment consisting of

two vertebrae and a disc. The facet mating feature was used to simulate any


Fig. 10.31 Finite element model of a lumbar motion segment with two vertebrae and a disc (taken

from King and Yang (1986))

transmission of facet load when modeling a lumbar motion segment, consisting of

two vertebrae and a disc. The facet mating feature was used to simulate any

transmission of facet load when modeling a lumbar motion segment. The disc

was modeled as a fluid and the disc pressure transducer used by El-Bohy et al.

(1989) provided the pressure data. Figure 10.31 shows the model which has

207 elements and 268 nodes. Validation was based on a comparison of predicted

and measured disc pressure for a statically applied load, as shown in Fig. 10.32. The

experimental data on disc pressure were obtained by El-Bohy who did not publish

the data. The model was used to simulate the load on the spine of a man carrying a

40 N weight in his arms, as shown in Fig. 10.7. When applied to the model, the


Fig. 10.32 Validation of the King and Yang (1986) model of a lumbar functional spinal unit,

using intradiscal pressure (taken from King and Yang (1986))

loading pattern is shown in Fig. 10.33. The symbols in this figure are defined as

follows:

Q ¼ The 40 N weight carried by the man, 400 mm in front of the center of the disc

W A ¼ Weight of the arms

W H ¼ Weight of the head

W T ¼ Weight of the torso above the lumbar segment being modeled

E ¼ Extensor muscle force

The extensor muscle force could be adjusted to keep the man in static equilibrium

while carrying the 40 N weight, or it could exert an additional moment of 15 or

30 N.m on the spine to put it in either flexion or extension. It was also necessary to

assume that the vertebrae pivoted about the center of the disc or about the center of

the spinal canal. The disc was assumed to be either normal or degenerated.

Degeneration was simulated by a decrease in the modulus of the annulus by

30 %. With two pivot points, five loading conditions (static equilibrium and two

cases each of flexion or extension), and two disc conditions (normal or

degenerated), there was a total of 20 cases that were studied by the model. The

response parameters of interest were facet load, disc bulge, nucleus pressure, and

stress in the annulus. Table 10.5 shows the predicted facet load and nucleus pressure

for the five loading cases with the functional spinal unit pivoting about the center of

the disc. Table 10.6 shows the same predicted parameters assuming that the pivot

point is at the center of the spinal canal. In this case, both the facet loads and disc

pressures were higher. It is not surprising that the facet loads were higher, but it is

not clear why disc pressure would go up. Disc bulge for normal and degenerated


Fig. 10.33 Finite element model of a lumbar motion segment subjected to a variety of loads

(taken from King and Yang (1986))

Table 10.5 Predicted facet loads and nucleus pressures for the model shown in Fig. 10.34 for the

five loading cases with the pivot at the center of the disc (taken from King and Yang (1986))

Facet load (N)

Nucleus pressure (MPa)

Net moment (N.m) Normal disc Degenerated disc Normal disc Degenerated disc

30 flexion 54 78 0.37 0.58

15 flexion 84 126 0.57 0.90

0 122 174 0.78 1.22

15 extension 157 222 0.98 1.54

30 extension 191 271 1.18 1.86

Reprinted from Frontiers in Biomechanics, ed. by G.W. Schmid-Schonbein, S.L.-Y. Woo, B.W.

Zweifach, Chapter 16, Biomechanics of the lumbar spine, A.I. King, K.H. Yang, 1986, With


Table 10.6 Predicted facet loads and nucleus pressures for the model shown in Fig. 10.34 for the

five loading cases with the pivot at the center of the spinal canal (taken from King and Yang

(1986))

Facet load (N)

Nucleus pressure (MPa)

Net moment (N.m) Normal disc Degenerated disc Normal disc Degenerated disc

30 flexion 89 127 0.58 0.91

15 flexion 143 203 0.90 1.42

0 198 279 1.22 1.92

15 extension 252 356 1.54 2.43

30 extension 306 432 1.86 2.93

Reprinted from Frontiers in Biomechanics, ed. by G.W. Schmid-Schonbein, S.L.-Y. Woo, B.W.

Zweifach, Chapter 16, Biomechanics of the lumbar spine, A.I. King, K.H. Yang, 1986, With



Fig. 10.34 Comparison of predicted disc bulge for a normal and degenerated disc with the pivot at

the center of the disc (taken from King and Yang (1986))

discs is shown in Fig. 10.34 for the case in which the vertebrae pivoted about the

disc center. The conclusions of the study were:

1. Muscular action had a profound effect on spinal compression in general and on

the facet load in particular.

2. When the spine is in extension, there is an increase in facet load, nucleus

pressure, and disc bulge

3. Disc degeneration resulted in a higher facet load, nucleus pressure, and disc

bulge.

4. Maximum stresses on the vertebral cortex were at the pedicle-vertebral body

junction.

After the US Air Force declared that seat ejection was a mature technology in the

late 1970s, research on the effects of vertical acceleration on the thoracolumbar

spine virtually stopped. Many finite element models of the spine dealing with

clinical problems continued to appear in the literature. However, recently there

has been some interest in formulating finite element models of seat ejection and its

effect on the spine. For example, Du et al. (2014) formulated a 3-D model of the

spine which was represented by an ATB model with a detailed finite element model

of the spine from T9 to L5. The individual vertebrae were simulated with a vertebral

body and posterior elements which were assigned a modulus that was much lower

than that of cortical bone. The model was used to simulate an ejection event with a

peak +G z of 15 g, a duration of 200 ms, and an onset rate of 150 g/s. However, the

model was validated against some static test data related to range of motion and

dynamic data on disc compression. The validations were comparisons of kinematic

data. Range of motion data were compared against quasi-static data provided by

Renner et al. (2007), and disc compression (displacement) data of a single disc


(T12–L1) were compared to experimental data by Race et al. (2000) who tested

discs in the bovine tail. The origin of the curves in Figure 4 of Du et al. (2014) is

unclear. Such a curve did not appear in Race et al. (2000). The model was used to

predict stresses in vertebral bodies for the normal posture and a relaxed posture.

There was a loss of lordosis in both postures, and the most evident difference was

slouching in the relaxed posture with the pelvis rotated anteriorly. The stresses in

the cortical bone and in the endplates as well as the intradiscal pressures were

higher for the relaxed posture. It is unfortunate that a simulation was not done for

the hyperextended mode described by Prasad et al. (1974).


The full story of spinal response to vertical loading has been told in Chaps. 9 and 10.

Facet load is now accepted by the biomechanics community and facet pain is being

treated clinically. However, there is still a substantial group of researchers who

choose to ignore this work, as exemplified by Du et al. (2014). It behooves the

young researcher to search the literature with care and not automatically assume

that research published over 30 or 40 years ago is not worth reading or citing.


10.1. In the study by El-Bohy et al. (1989), he simulated loading on the spine due

to body weight and a load held in his hands in front of him

[ ] (i) There was no facet load when the man was just standing erect and

not carrying a load and

[ ] (ii) The experiment demonstrated that the simulated muscle load

increased disc pressure but not facet contact pressure

[ ] (iii) The load on the spine was magnified when the man carried a weight

in front of him

[ ] (iv) The experiment demonstrated that when facet contract pressure

there was no change in disc pressure


10.2. The objective of the experiment performed by El-Bohy et al. (1989) was to

show that

[ ] (i) spinal muscles exerted a lot of load on the spine

[ ] (ii) the inferior facets bottomed out on the laminar to transmit facet load

[ ] (iii) disc pressure increased with load borne by the spine

[ ] (iv) the extensor muscles of the spine were activated when a man is

carrying a weight in front of him

[ ] (v) an increase in extensor muscle force resulted in a corresponding

increase in disc pressure


10.3. The measurement of lumbar facet load was accomplished by:

[ ] (i) Indirect means in which the facet load was deduced from measuring

the total spine load and the disc load

[ ] (ii) Indirect means in which the contact pressure between the facet tip

and the lamina was measured during quasi-static loading

[ ] (iii) Direct means, using a miniature load cell under the facet

[ ] (iv) Direct means, using a pressure sensitive mat under the facet

[ ] (v) (i) and (ii)

10.4. Based on data from quasi-static testing of lumbar motion segments, it was

found that:

[ ] (i) There is no facet loading during normal erect standing

[ ] (ii) There is facet load during normal erect standing

[ ] (iii) There is facet load when the person is carrying a 10 lb weight some

4 in. in front of his chest



10.5. When carrying or lifting a heavy object, the extensor muscles of the back are

activated. Assuming that the average eccentricity of these muscles relative

to the center of a lumbar disc is 20 mm, the estimated force on the spine due

solely to muscle action, to lift a 100 N weight, held 400 mm in front of the

disc center, is:

[ ] (i) 2 kN

[ ] (ii) 4 kN

[ ] (iii) 5 N

[ ] (iv) 10 N


10.6. When the extensor muscles are activated, the pressure in the intervertebral

discs

[ ] (i) Is decreased

[ ] (ii) Is not affected by the muscle action because there is an equal

increase in the flexor muscle force

[ ] (iii) Is increased

[ ] (iv) Is not affected by the muscle action because the facets take all the load

[ ] (v) Goes up momentarily and returns to its original state

10.7. During pilot ejection, the intervertebral load in the lumbar spine can exceed

the total inertial load sustained by the spine because:

[ ] (i) Of the high stiffness of the facets in comparison with that of the

disc

[ ] (ii) Of a drop in the load borne by the disc

[ ] (iii) Of an increase in forward flexion moment acting on the spine


[ ] (iv) Of the loosening of the ligaments during spinal compression


10.8. Towards the end of the ejection sequence, during pilot ejection, the facets go

into tension. The majority of the tensile load can be taken by:

[ ] (i) The facet capsule

[ ] (ii) The ligamentum flavum and the posterior longitudinal ligament

[ ] (iii) The interspinous and supraspinous ligament



10.9. A computer model of the spine simulating pilot ejection was developed by

Prasad and eventually improved upon by Tennyson. It has several characteristics.

Select the incorrect answer:

[ ] (i) The model has been validated against cadaveric experiments in

terms of spinal load and facet load

[ ] (ii) The model was modified to simulate living muscular response

[ ] (iii) The model is based on a finite element mesh developed by Prasad

[ ] (iv) The model is a discrete parameter model made up of masses,

springs, and dampers

[ ] (v) The model can be used for both vertical and horizontal input

accelerations

10.10. Spinal compression due to shoulder restraint systems occurs in automotive

crashes. This was discovered by the Prasad model and subsequently measured

experimentally in cadavers. The biomechanical basis for the existence

of this spine load is:

[ ] (i) Due to fact that the seat back is inclined rearward

[ ] (ii) Due to the lordosis of the lumbar spine

[ ] (iii) Due to the kyphosis of the thoracic spine

[ ] (iv) Due to the lordosis of the cervical spine

[ ] (v) Due to the elasticity in the belt material

10.11. The articular facets of the lumbar spine transmit vertical compressive load

down the spine by:

[ ] (i) Compression between the cartilaginous surfaces of the facets

[ ] (ii) Pulling on the ligamentum flavum

[ ] (iii) Contact of the tips of the inferior facet with the lamina of the

vertebra below

[ ] (iv) Transmitting the load through the spinous process

[ ] (v) Using the flexor muscles of the back

10.12. When a jet aircraft attempts to land on an aircraft carrier and misses the

deck, it ditches (crashes into the ocean) alongside the carrier. In most cases,

the pilot fails to eject before the aircraft sinks. The Tennyson spine model


predicted that there were several possible causes of injury. Select the

incorrect answer:

[ ] (i) There is contact of the odontoid process with the spinal cord,

causing cord concussion

[ ] (ii) There is stretch of the cervical cord, causing cord concussion

[ ] (iii) There is chin-chest contact, causing cerebral concussion

[ ] (iv) There is a neck shear at C1-C2 with head rotation (flexion), causing

injury to the cord

[ ] (v) There is very high linear acceleration of the head, causing cerebral

concussion


deck, it ditches (crashes into the ocean) alongside the carrier. The Tennyson

spine model studied the influence of the helmet worn by the pilots during

ditching. Assuming that the peak +G z and the peak –G x accelerations occur

simultaneous, the model predicted that

[ ] (i) The helmet had no effect on odontoid displacement

[ ] (ii) The helmet caused a significant increase in head angular

acceleration

[ ] (iii) The helmet caused the cord stretch to almost double

[ ] (iv) The helmet caused the chin-chest contact force to increase by 50%



deck, it ditches (crashes into the ocean) alongside the carrier. The Tennyson

spine model studied the influence of the helmet worn by the pilots during

ditching. General conclusions that can be reached are:

[ ] (i) Head and neck responses are not sensitive to changes in the location

of the c.g.

[ ] (ii) Injury parameters are generally more severe when the peak vertical

and horizontal accelerations occur simultaneously

[ ] (iii) Helmets tend to decrease odontoid displacement

[ ] (iv) Chin-chest contact force is the highest when the peak vertical and

horizontal accelerations occur simultaneously

[ ] (v) Cord stretch is high when the peak G z acceleration precedes the

peak G x acceleration

10.15. A computer model of the spine simulating pilot ejection was developed by

Prasad and eventually improved upon by Tennyson. It has several characteristics.

Select the correct answer:

[ ] (i) The model has not been validated against cadaveric experiments in

terms of spinal load and facet load

[ ] (ii) The model was not modified to simulate living muscular response

[ ] (iii) The model is based on a finite element mesh developed by Prasad


[ ] (iv) The model is a discrete parameter model made up of masses,

springs, and dampers

[ ] (v) The model cannot be used for horizontal input accelerations

10.16. In a frontal crash, an occupant restrained by a three-point belt

[ ] (i) can sustain a thoracolumbar vertebral fracture

[ ] (ii) cannot sustain a thoracolumbar vertebral fracture

[ ] (iii) cannot exert additional load on the seat pan

[ ] (iv) can frequently rupture his/her lumbar intervertebral disc

[ ] (v) can sustain a Chance fracture

10.17. In the quasi-static facet load confirmation experiment by El Bohy et al.

(1989),

[ ] (i) Body weight was not simulated

[ ] (ii) Facet tip pressure and disc pressure were measured using identical

pressure transducers

[ ] (iii) Rubber bands were used to simulate muscle

[ ] (iv) Facet load was deduced to be present when a person is standing and

carrying no load in the hands

[ ] (v) Facet load would be generated only when the person is carrying a

load in the hands

10.18. The articular facets of the lumbar spine:

[ ] (i) Cannot transmit vertical compressive load down the lumbar spine

[ ] (ii) Are unable to provide shear resistance to the lumbar spine

[ ] (iii) Do not make contact with the lamina of the vertebra below

[ ] (iv) Transmit vertical load through the spinous process


10.19. To escape from a disabled jet aircraft, the pilot needs to

[ ] (i) open up the canopy and quickly bale out off the side of the aircraft

[ ] (ii) activate the seat ejection system with an acceleration of about 30 g

for 300 ms

[ ] (iii) activate the seat ejection system with an acceleration of about 10 g

for 100 ms

[ ] (iv) turn the plane upside down and disconnect all belt systems so

he/she can fall out of the aircraft


10.20. After the pilot of a disabled jet has ejected and cleared the tail of the aircraft,

the following events occur

[ ] (i) A seat parachute deploys and he lands while still in his seat

[ ] (ii) He separates from the seat and his personal parachute opens immediately

even if he is several thousand meters above ground level


[ ] (iii) He separates from the seat and his personal parachute opens when

he free falls to an appropriate altitude

[ ] (iv) He separates from the seat and needs to manually open his personal

parachute whenever he feels it is safe to do so



Prob

Ans

1 (iii)

2 (ii)

3 (v)

4 (v)

5 (i)

6 (iii)

7 (iii)

8 (v)

9 (iii)

10 (iii)

11 (iii)

12 (v)

13 (v)

14 (ii)

15 (iv)

16 (i)

17 (iv)

18 (v)

19 (v)

20 (iii)

References

P.C. Begeman, A.I. King, P. Prasad, Spinal loads resulting from G x acceleration, in 17th Stapp

Car Crash Conference, SAE Paper No. 730977, Oklahoma City, OK, 1973

T. Belytschko, L. Schwer, E. Privitzer, The theory and application of three-dimensional model to

the human spine. Aviat. Space Environ. Med. 49, 158–165 (1978)

T. Brown, R. Hansen, A. Yorra, Some mechanical tests on the lumbo-sacral spine with particular

reference to the intervertebral discs. J. Bone Joint Surg. 39A, 1135–1164 (1957)

H.J. Cramer, Y.K. Liu, D.U. von Rosenberg, A distributed parameter model of the inertially loaded

human spine. J. Biomech. 9, 115–130 (1976)

References 355

C.-F. Du, L. Wang, Y.-W. Wang, Y. Fan, Spine model for application in aviation protection, in

Computational biomechanics of the musculoskeletal system, ed. by M. Zhang, Y. Fan (CRC

Press, Boca Raton, 2014)

A.A. El-Bohy, A comprehensive analysis of the facet joint in relation to low back pain. PhD

dissertation, Wayne State University, Detroit, 1988

A.A. El-Bohy, K.H. Yang, A.I. King, Experimental verification of facet load transmission b direct

measurement of facet lamina contact pressure. J. Biomech. 22, 931–941 (1989)

C.L. Ewing, D.J. Thomas, Human head and neck response to impact acceleration. Army-Navy

Joint Report. NAMRL Monograph 21, USAARL 73–1, Naval Aerospace Medical Research

Laboratory and US Army Aeromedical Research Laboratory, AD747988, 1972

J.W. Fielding, G.V.B. Cochran, J.F. Lawsing III, M. Hohl, Tears of the transverse ligament of the

atlas. A clinical and biomechanical study. J. Bone Joint Surg. 56A, 1683–1691 (1974)

J.O. Galante, Tensile properties of the human lumbar annulus fibrosus. Acta Orthop. Scand. 38

(100), 30–31 (1967)


vertebra. PhD Dissertation, Wayne State University, Detroit, Michigan, 1976

N.S. Hakim, A.I. King, A three-dimensional finite element dynamic response analysis of a vertebra

with experimental verification. J. Biomech. 12, 277–292 (1979)

J.L. Hess, C.F. Lombard, Theoretical investigations of dynamic response of man to high vertical

accelerations. J. Aviat. Med. 29, 66–75 (1958)

D.F. Huelke, G.M. Mackay, M. Andrew, Vertebral column injuries and lap-shoulder belts.

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S.W. Wiesel et al., vol 1 (Saunders, Philadelphia, 1996), pp. 74–85

A.I. King, A.P. Vulcan, Elastic deformation characteristics of the spine. J. Biomech. 4, 413–429

(1971)

A.I. King, K.H. Yang, Biomechanics of the lumbar spine, in Frontiers in Biomechanics, ed. by

G.W. Schmid-Schonbein, S.L.-Y. Woo, B.W. Zweifach (Springer, New York, 1986)

A.I. King, S.S. Nakhla, N.K. Mital, Simulation of head and neck response to Gx and +Gz

impacts, in AGARD Conference No. 253, Models and Analogues for the Evaluation of Human

Biodynamic Response, Performance and Protection, Paper 7A, AGARD-NATO, 1979

F. Latham, A study in body ballistics: seat ejection. Proc. R. Soc. B-147, 121–139 (1957)

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Editing Manual (US Department of Transportation, 2010)

D. Orne, Y.K. Liu, A mathematical model of spinal response to impact. J. Biomech. 4, 49–71

(1971)

P. Prasad, The dynamic response of the spine during + Gz acceleration. PhD dissertation, Wayne


P. Prasad, A.I. King, C.L. Ewing, The role of articular facets during + G z acceleration. J. Appl.

Mech. 41, 321–326 (1974)

A. Race, N.D. Broom, P. Robertson, Effect of loading rate and hydration on the mechanical

properties of the disc. Spine 25, 662–669 (2000)

S.M. Renner, R.N. Natarajan, A.G. Patwardhan, R.M. Havey, L.I. Voronov, B.Y. Guo,

G.B.J. Andersson, H.S. An, Novel model to analyze the effect of a large compressive follower

pre-load on range of motions in a lumbar spine. J. Biomech. 40, 1326–1332 (2007)

J.D. States, R.P. Annechiarico, R.G. Good, J. Lieou, M. Andrews, L. Cushman, G. Ingersoll, A

time comparison study of the New York State safety belt use law utilizing hospital admission

and police accident report information. Accid. Anal. Prev. 22, 509–521 (1990)

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Wright-Patterson Air Force Base, Dayton, OH, 1969

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Car Crash Conference, SAE Paper No. 760771, Dearborn, MI, 1976


S.A. Tennyson, N.K. Mital, A.I. King, Electromyographic signals of the spinal musculature

during + G z impact acceleration. Otthop. Clin. North Am. 8, 97–119 (1977)

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Washington, DC, 1989

Chapter 11

Impact Biomechanics of the Thorax

The thorax occupies the upper part of the torso and contains the lung and heart that are

enclosed by a rib cage. Of course, the lung, heart, and the great vessels are vital organs

that need to be protected from external forces but the enclosure also needs to be

expandable to assist in the respiratory function. The rib cage is capable of expanding

the thorax and can provide some protection to the thoracic organs. However, for high

speed impacts, the ribs are vulnerable to fracture. Although multiple rib fractures are

serious injuries, the fracture of a rib or two is relatively minor. But, when cadavers are

used to assess thoracic injury, rib fracture is the only measure because injuries to the

heart and lung are generally not assessable in dead tissue. Because of the variability in

human tolerance, the number of rib fractures and the number of fractured ribs cannot

be correlated to the severity of injuries to the thoracic organs.

11.1 Brief Anatomical Review of the Thorax

The thoracic cavity occupies the superior part of the torso, extending from the base

of the neck (T1) to the diaphragm which is dome shaped and is a

musculomembranous partition between the thoracic and abdominal cavities. The

rib cage is a bony and cartilaginous structure which surrounds the thoracic cavity. It

consists of 24 ribs, 12 on each side. The posterior ends articulate with the 12 thoracic

vertebrae which are also part of the rib cage. Anteriorly, the cartilaginous ends of

the first 10 ribs are attached to the sternum while ribs 11 and 12 have no anterior

attachment and are called floating ribs. Figure 11.1 shows a typical human rib cage,

viewed from an anterior direction. The ribs have a downward inclination from back

to front which is not reproduced in the Hybrid III dummy. This inclination is

reduced with age (Weaver et al. 2014). The soft tissues associated with the rib

cage consist of skin, fascia, and muscles. Together, they form the thoracic wall.

The important organs within the thoracic cavity are the lung, heart, and great

vessels. The left lung has two lobes while the right lung has three. Both lungs are



357

358 11 Impact Biomechanics of the Thorax

First rib

Transverse process of

T 1 vertebra

3

1

2

T 1

T 2

1

Manubrium of sternum

Sternal angle

Intercostal space

6

4

5

7

2

3

4

Rib (bone)

Body of sternum

8

9

5

6

10

7

11

12

T 12

Xiphoid process

of Sternum

8

9

Costal

cartilage

10

Fig. 11.1 An anterior view of the rib cage. The yellow segments are the bony parts of the ribs. The

first 10 ribs are attached to the sternum via the blue cartilaginous segments. The 10th and 11th ribs

are floating ribs and are not attached to the sternum. Note also the downward inclination of the rib

cage which is reduced with age. That is, the ribs become more horizontal with age (taken from

Carola et al. (1992)). Republished with permission of McGraw-Hill Education, from R. Carola, J.

P. Harley, C.R. Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992; permission

conveyed through Copyright Clearance Center, Inc.

enveloped by a double-layered membrane called the pleura. During respiration, air

is brought into the lung via the trachea (windpipe) which branches into the left and

right bronchi. Each bronchus then branches repeatedly and terminates in tiny

bronchioles, at the end of which are the alveoli sacs, the functional part of the

lung. Gas exchange occurs with the capillaries that surround the alveoli and the deoxygenated

blood returns to the right atrium of the heart via the pulmonary vein.

The mediastinum is the region in the thorax that contains all other organs

besides the lungs, including the heart and great vessels as well as the esophagus

(food tube), the trachea, and nerves. The heart is located behind the sternum and

slightly to the left. It is a muscular organ composed of cardiac muscle which can

contract repeatedly without resting. The heart has four compartments, two atria

and two ventricles, as shown in Fig. 11.2. The atria are located at the top of the

heart and have relatively thin walls because they are low pressure containers that

11.1 Brief Anatomical Review of the Thorax 359

Aortic arch

Ascending aorta

Pulmonary trunk

Superior vena cava

SINOATRIAL

(SA) NODE

Internodal tracts

Right atrium

ATRIOVENTRICULAR

(AV) NODE

Inferior vena cava

Descending aorta

Left atrium

Left ventricle

ATRIOVENTRICULAR BUNDLE

(bundle of His)

LEFT AND RIGHT

BUNDLE BRANCHES

CARDIAC CONDUCTING MYOFIBERS

(Purkinje fibers)

Right ventricle

Fig. 11.2 Compartments of the heart (taken from Carola et al. (1992)). Republished with permission

of McGraw-Hill Education, from R. Carola, J.P. Harley, C.R. Noback (eds.), Human Anatomy

& Physiology, 2nd edn., 1992; permission conveyed through Copyright Clearance Center, Inc.

receive blood from veins. The ventricles have thick muscular walls that can

generate high pressures to pump blood to the lungs via the right ventricle and

even higher pressures to supply blood to the entire body via the left ventricle.

Each ventricle is guarded by two valves. As shown in Fig. 11.3, the tricuspid

valve controls backflow from the right ventricle to the right atrium and the

bicuspid valve controls backflow from the left ventricle to the left atrium.

Similarly, the pulmonary and aortic semilunar valves prevent backflow from

the pulmonary artery and aorta into the right and left ventricles, respectively.

The cardiovascular system consists of an arterial system and a venous system.

For the systemic circulation, arterial (oxygenated) blood from the left ventricle is

pumped into the aorta which branches and supplies blood to the entire body,

including the heart. The arteries branch into smaller and smaller vessels until they

become arterioles which branch into capillaries. Oxygen and carbon dioxide

exchange occurs in the capillary beds. The oxygen-depleted blood enters the venous

system via venules, veins and eventually the superior and inferior vena cava which

return the blood to the right atrium of the heart. The venous blood then enters the

pulmonary circulation from the right ventricle to the pulmonary artery. It is

re-oxygenated in the capillary beds of the lung and returns to the left atrium of

the heart via the pulmonary vein. It then enters the left ventricle to begin a new

cycle of supplying oxygen to the entire body. Figure 11.4 is a diagrammatic

depiction of the systemic and pulmonary circulatory systems. Note that the anatomical

definition of an artery is a conduit for blood leaving the heart and that of a

vein is a conduit for blood entering the heart.


Aortic arch

Left pulmonary artery

Right pulmonary artery

Pulmonary trunk

Ascending aorta

Superior vena cava

Left atrium

PULMONARY

SEMILUNAR VALVE

Musculi pectinati

Right atrium

AORTIC

SEMILUNAR VALVE

BICUSPID

VALVE

Conus (infundibulum)

TRICUSPID VALVE

Chordae tendineae

Papillary muscle

Left ventricle

Trabeculae carneae

Inferior vena cava

Descending aorta

Right ventricle

Fig. 11.3 Valves of the heart (taken from Carola et al. (1992)). Republished with permission of



Arteries are muscular organs which can constrict and relax to control their

diameter. The muscles are involuntary and located in the media, the center layer

of the arterial wall. On the inside of the media is the intima which consists of a

single layer of endothelial cells supported on an elastic membrane. External to the

media is the adventitia which is composed of collagen fibers that act as a supportive

element. Veins do not have muscles and their walls are much thinner than those of

the arteries.

A word about the cardiac cycle is necessary because cardiac arrests have been

known to occur due to chest impact and these arrests are linked to the cardiac cycle.

The heart beats rhythmically under the control of a pacemaker. The sino-atrial

(SA) node initiates the action potential for the atrium to contract. The impulse then

passes through the atrioventricular (AV) node to the atrioventricular bundle which

spreads the signal to the ventricular myocardium. The nodes and the times of

conduction are shown in Fig. 11.5. These electrical activities can be detected on

the chest in the form of an electrocardiogram or EKG. It is characterized by five

waves—the P, Q, R, S, and T waves. Correlation of the EKG with other events of

11.1 Brief Anatomical Review of the Thorax 361

Head and arms

Vein

Capillaries

Artery

Capillaries

Superior vena cava

Aorta

Pulmonary

artery

Capillaries

Left

atrium

Pulmonary

vein

Right lung

Inferior vena cava

Right

atrium

Right

ventricle

Heart

Left

ventricle

Left lung

Descending aorta

Capillaries

Veins

Arteries

Internal organs

Capillaries

Legs

Fig. 11.4 Diagrammatic depiction of the systemic and pulmonary circulatory systems.

Oxygenated blood is in red and oxygen depleted blood is in blue (taken from Carola et al.

(1992)). Republished with permission of McGraw-Hill Education, from R. Carola, J.P. Harley,

C.R. Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992; permission conveyed through

Copyright Clearance Center, Inc.


Fig. 11.5 Electrical

conduction system of the

heart (taken from Carola

et al. (1992))

0.025

0

SA node

0.045 0.03 0.06

0.18

0.2

AV node

0.12

0.19

0.17

0.145

0.15

0.14

0.155 0.16

the cardiac cycle is shown in Fig. 11.6. Normal blood pressure in an artery is

120/80 mm of Hg. That is, the systolic pressure reaches a peak of 120 mmHg and in

diastole, it is 80 mmHg.

11.2 Thoracic Injury Mechanisms

As mentioned in the previous section, isolated fracture of one or two ribs is

considered to be a minor injury, albeit a very painful one. The more severe thoracic

injuries are:

1. Flail chest

2. Lung contusions

3. Hemo- and pneumothorax

4. Injuries of the heart and great vessels

11.2 Thoracic Injury Mechanisms 363

Fig. 11.6 The cardiac cycle—Correlation of mechanical and electrical events (taken from Carola

et al. (1992)). Republished with permission of McGraw-Hill Education, from R. Carola, J.P.

Harley, C.R. Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992; permission conveyed

through Copyright Clearance Center, Inc.

11.2.1 Flail Chest

Flail chest is defined by the clinical sign of paradoxical breathing. Normally, when

one takes a breath, the chest expands to allow air into the lungs. When several ribs

are fractured, especially with multiple fractures in the same rib, the chest wall is


now detached from its bony attachments and when a vacuum is created by inspiration,

the chest wall collapses inward due to the pressure difference. Wanek and

Mayberry (2004) defined significant impairment of respiratory function as fractures

of at least four consecutive ribs in two or more places and if flail chest is such an

impairment, this definition also applies to a flail chest. Blunt impact to the chest is

the principal cause of multiple rib fractures and thus, flail chest. Although its

frequency has been estimated at 5–13 % (LoCicero and Mattox 1989), it is nevertheless

a serious injury. The AIS score is 4 for a unilateral flail chest and 5 for a

bilateral flail chest. As with all rib fractures, the mechanism of a flail chest injury is

bending of the ribs which fail in tension. Chest compression is the determining

factor for rib fractures and the extent of chest compression is a function of the

impact force. Chest wall velocity also plays a role in injury severity.

11.2.2 Lung Contusion

Lung contusion or bruising of the lung is associated with chest wall trauma, such as

a flail chest or rib fractures due to blunt impact. It can also be caused by an

explosive blast. In blunt impact, the lung parenchyma (tissue) is damaged when it

impacts the chest wall, causing the alveoli sacs to break with resulting hemorrhage

and fluid accumulation. In children subjected to thoracic blunt trauma, lung contusions

can occur without signs of chest wall injury (rib fractures) because of the

flexibility of the rib cage.

11.2.3 Hemo- and Pneumothorax

Hemothorax occurs when the pleura is torn and blood accumulates in the pleural

cavity of this double-layered membrane. A large amount of blood can enter the

cavity to interfere with normal breathing by limiting the expansion of the lungs.

Pneumothorax is the accumulation of air in the pleural cavity and can also interfere

with normal breathing. In blunt trauma, a displaced rib fracture can be the cause of a

hemo- and/or pneumothorax. However, there are also cases of spontaneous pneumothorax,

the cause of which is unclear.

11.2.4 Injuries to the Heart and Great Vessels

Blunt impact to the chest can bruise the heart or stop it. A common site for cardiac

contusion is the right heart which is behind the sternum. Injuries can range from

myocardial contusion to a ruptured heart chamber to cardiac arrest. The most

common form of blunt cardiac injury (BCI) is arrhythmia which is easily detected

on an EKG. Atrial arrhythmia in the form of atrial fibrillation is a mild form of BCI.

11.2 Thoracic Injury Mechanisms 365

The more serious ventricular fibrillation requires immediate medical attention and

is described in the paragraph below. It is due to high speed impact of a blunt

projectile against the chest. Cardiac wall rupture is a high mortality BCI. The

pericardium is the last line of defense against uncontrolled exsanguination but the

pressure build-up between the external wall of the heart and the pericardium

decreases the ventricular volume and eventually collapses the ventricle, leading

to hypotension and death. This pressure build-up in the pericardium is known as

tamponade. Biomechanically, it is not clear how a blunt impact can rupture the wall

of an atrium or ventricle or even the septum between the chambers but it is likely

due to an unusual pressure build-up in one or more chambers. Heart valves can also

be damaged by blunt impact, again presumably due to large pressures generated by

the impact. More clinical details are available in Elie (2006) but biomechanical

research is somewhat sparse.

Commotio cordis or cardiac arrest due to a blunt impact is known to occur in

sports, such as baseball or hockey when a player is struck in the chest by a ball or

puck. The exact mechanism is unknown at this time but there are two theories.

When the chest is impacted, the conduction system of the heart is disrupted either

by sternal impact or by a stress wave traveling through the heart. The method for

preventing this injury is different for the two theories. If the heart is stopped by

sternal impact, all players should wear chest protectors. If, on the other hand, it is

due to a stress wave, then the only way to protect oneself is to keep a close eye on

the ball and not to let it hit the chest because chest protectors cannot prevent stress

waves from being transmitted to the heart. A more detailed discussion of commotio

cordis can be found in Chap. 19 (Sect. 19.5).

Injuries to the aorta occur in car crashes. One of the most serious is traumatic

rupture of the aorta (TRA), an injury that may not be survivable even if it occurred

in a hospital emergency room. If the driver is unrestrained and does not have an

airbag in the steering wheel, a frontal impact with a Delta V of about 72 km/h

(45 mph) can cause this injury. When the chest impacts a steering wheel frontally,

the rim is easily bent backwards and the hub of the steering wheel impacting the

chest is the mechanism of injury. This explains the use of a 15-cm (6-in.) rigid

impactor to obtain response and tolerance data for the chest. However, the fatality

rate for TRA did not decrease with the advent of belts and airbags. In fact, the trend

is upward between the years of 1947 and 1997, as shown in Fig. 11.7. The reason for

this trend is that TRA is now principally due to side impacts which are occurring at

higher Delta V’s. Field data suggest that the overall incidence of TRA is low but the

injury is almost inevitably fatal. TRA is associated with higher speed crashes but

can occur at low speeds, such as during the deployment of an airbag. The statistics

related to TRA deaths tend to be underestimated because most victims die at the

scene and not every victim is autopsied. Roughly 3 % of those that reach a hospital

survive. Because the predominant cause is side impact, TRA can occur whether the

occupant is restrained by a seatbelt or not. Research on reproducing this elusive

injury in the laboratory is discussed in Sect. 11.6. According to Katyal et al. (1997),

94 % of all TRA occurs in the peri-isthmic region which is shown in Fig. 11.8.


25

% of Aortic Rupture Cases

20

15

10

5

Trend of Injury

16

13.5

14.8

15

17.2

21

0

1

1947 1966 1979 1980 1983 1984 1997

Strassman

Greendyke

Avery et al

Hossack

Viano

Newman and

Rastogi

Katyal et al

Fig. 11.7 Fatalities due to aortic rupture as a percentage of all automotive fatalities from 1947

to 1997

Fig. 11.8 Traumatic

rupture of the aorta occurs

frequently in the periisthmic

region, just distal

to the aortic arch (taken


Brachiocephalic Trunk

Ascending

Root

Arch

Lesser

Curvature

Left Common Carotid Artery

Left Subclavian Artery

Peri-isthmic Region

Longitudinal and

Circumferential Axes

Descending

Heart

11.4 Experiments on the Thorax: Frontal and Side Impact 367

11.3 Thoracic Injury Mechanisms

The thorax contains a large amount of soft tissue and its impact response is

viscoelastic. At low velocities of impact or during quasi-static loading, the mechanism

of injury is crushing and is independent of the loading speed. This mechanism

is valid for velocities of deformation less than 3 m/s. At very high rates of

loading, such as those encountered in an explosive blast, the injury is caused by a

pressure wave that causes virtually no deformation of the thorax but can injure the

lung. This occurs at speeds in excess of 35 m/s. In automotive crashes, the speed

range is 5–30 m/s (16.4–98.4 ft/s). Thoracic impact response is viscoelastic for this

velocity range and thoracic injury is sensitive to both chest wall velocity and chest

compression. Researchers at the Biomedical Science Department of the General

Motors (GM) Research Labs arrived at this conclusion in 1985 in a landmark paper

by Viano and Lau (1985) which was the culmination of many years of research.

This was followed by a journal publication by Lau and Vaino (1986). They also

found that impact force and spinal acceleration were not good predictors of lung

injury. The discovery was made from test results on rabbits and swine. For large

chest compressions, injury was observed even at low impact speeds. However, for

large impact velocities, injury occurred even at small chest compressions (Kroell

et al. 1981; Lau and Viano 1981). This led to the formulation of the Viscous

Criterion (V*C) which states that the injury is a function of the product of the

instantaneous chest wall velocity (V) and percent chest compression (C).

11.4 Experiments on the Thorax: Frontal and Side Impact

11.4.1 Frontal Impact Experiments

The first set of data on human thoracic response to frontal impact was published by

Patrick et al. (1965) using a newly built sled funded by GM. Impact data were

acquired simultaneously for impacts to the head, chest, and knee. Each body region

impacted a surface instrumented with a load cell to measure the impact force. The

chest impacted a 15.2-cm (6-inch) diameter padded surface. To measure the

dynamic chest deflection, a metal rod was inserted into the chest from the sternum

through the thorax to emerge at the back of the cadaver. It was attached anteriorly to

the sternum and a photographic target was attached to the rear end of the rod. Its

motion would be a measure of sternal deflection. The test set-up is shown in

Fig. 11.9. Only a few cadavers were tested and the response curves for the thorax

were not typical of what was obtained by Kroell et al. (1974). One of the reasons

could be the large amount of embalming fluid that was retained in the chest. The

data were used to design the first automotive energy-absorbing steering column.

More data were acquired by Nahum et al. (1970) and Kroell et al. (1971, 1974) who

performed frontal chest impacts to the sternum of unembalmed cadavers at the


Fig. 11.9 First whole-body cadaveric tests were carried out by Patrick et al. (1965) at Wayne

State University. Embalmed cadavers were used

University of California San Diego (UCSD), using an unpadded wooden impactor.

It was 15.2 cm (6 inches) in diameter and had a 12.7 mm (1/2-inch) edge radius. The

weight of the impactor varied from 1.6 to 23.6 kg (3.5 to 51 lb) and the speed of

impact ranged from 4.0 to 13.2 m/s (9.0 to 29.6 mph). The data collected were

impact force and chest deformation as a function of time. These data were crossplotted

to yield force-deflection curves for two speeds of impact and for two

different impactor weights. Response corridors were drawn for 12 “low speed”

tests with a 19.5-kg (43-lb) impactor and 13 “high speed” tests run at 7.15 m/s

(16 mph) with a 23.1-kg (51-lb) impactor. The nominal low speed was 4.92 m/s

(11 mph) but the speeds ranged from 4.0 to 9.9 m/s (9.0 to 22.2 mph), as shown in

Fig. 11.10. The nominal high speed was 7.15 m/s but the speed range was

4.3–10.2 m/s (9.7–22.8 mph), as shown in Fig. 11.11. The proposed corridor for

this impactor/speed combination is shown as a shaded or cross-hatched region in

Fig. 11.11. Kroell et al. (1974) stated that this corridor enveloped seven tests using a

23.1-kg (51-lb) impactor at speeds between 6.7 and 7.4 m/s (15 and 16.6 mph). The

sensitivity of the thorax to velocity of impact can be seen from this figure. Impact

responses for impacts below 7.15 m/s are below this corridor while those for

impacts above 7.15 m/s are above the corridor. No scientific method was used to

create this corridor. As stated bluntly by Neathery (1974), the basis for the response

corridors was an “eyeball average” of the collected response data. The practical

application of these data was to develop an anthropomorphic test device (crash


1600

(7117)

FORCE -lb (N)

1200

(5338)

800

(3559)

400

(1779)

3

2

1

6

4

7

5

12

11

9

8

10

1 (25.4)

Curves identified as follows:

Curve No - Cadaver No/Age/Ht(in) x Mass (lb)/Striker Mass (lb) x Vel (mph)

1 − 7FF/86/66 x 83/42.5 x 9.0

7 − 11FF/60/63 x 130/43.0 x 14.1

2 − 10FF/82/63 x 95/42.5 x 11.0

3 − 6FM/83/72 x 170/42.5 x 11.5

4 − 5FM/60/73 x 190/42.5 x 11.5

5 − 9FM/73/73 x 168/42.5 x 11.5

6 − 54FF/49/64 x 82/43.1 x 15.0

2 (50.8) 3 (76.2) 4 (101.6) 5 (127.0)

TOTAL DEFLECTION - in (mm)

8 − 46FM/46/70 x 209/42.5 x 16.4

9 − 36FM/52/72 x 165/41.8 x 16.1

10 − 34FM/64/70 x 130/41.8 x 18.4

11 − 23FF/58/64 x 135/43.0 x 17.3

12 − 55FF/46/69.5 x 179/43.1 x 22.2

Fig. 11.10 Thoracic force-deflection curves for a nominal 19.5-kg (43-lb) impactor at various

velocities. Data from 12 tests are shown (taken from Kroell et al. (1974))

dummy) with a thorax that mimics this human response. Certain corrections were

made to the raw data to simulate a tensed human. The load levels were uniformly

increased 667 N (150 lb) to account for muscle tensing of a car occupant exposed to

a collision environment (Kroell et al. 1973) and the experimentally measured

sternal deflection was decreased uniformly by 12.7 mm (0.5 in.) to account for

soft tissue thickness so that the deflection would represent skeletal deformation.

Figure 11.12 shows the corrected corridors for the two impact speeds and impactor

weights, as recommended by Kroell et al. (1973) for the development of a biofidelic

dummy. The addition of 667 N (150 lb) to the plateau force to account for muscle

tension is not consistent with data obtained by Patrick (1981) who courageously

volunteered to be struck in the chest with a 10-kg pendulum to obtain live human

data on thoracic response. He underwent eight tests during which impact force and

chest deflection were measured. Six of the eight runs were tensed. Typical forcedeflection

curves were obtained. Upon closer analysis of the data, Melvin et al.

(1985) found that his response was similar to that of the flaccid cadaver. As shown


2000

(8896)

1600

(7117)

10

8

FORCE - lb (N)

1200

(5338)

800

(3559)

9

7

6

400

(1779)

1 2 3 4 5

1 (25.4) 2 (50.8) 3 (76.2) 4 (101.6) 5 (127.0)

TOTAL DEFLECTION - in (mm)

Curves identified as follows:

Curve No - Cadaver No/Age/Ht(in) x Mass (lb)/Striker Mass (lb) x Vel (mph)

1 − 53FM/75/68.5 x 170/50.6 x 11.7 6 − 63FM/53/72 x 194/50.7 x 15.5 (rigor)

2 − 45FM/64/71.5 x 141/50.7 x 11.3

3 − 60FM/66/71 x 175/50.6 x 9.7

4 − 42FM/61/72 x 120/50.4 x 10.9

5 − 64FM/72/64 x 139/50.7 x 15.5

7 − 32FM/75/67.5 x 120/50.4 x 22.2

8 − 31FM/51/72 x 165/50.8 x 22.8

9 − 24FM/65/72 x 180/50.4 x 21.6

10 − 37FM/48/70.5 x 163/50.4 x 22.0

Corridor of seven tests @ 15.0−16.5 mph from Kroell et al. (1971)

One additional test (16.6 mph) from Kroell et al. (1971)

Fig. 11.11 Thoracic force-deflection curves for a nominal 23.1-kg (51-lb) impactor at various

velocities. Data from 11 tests are shown. The corridor envelopes seven tests for impactor speeds

between 6.7 and 7.4 m/s (15 and 16.6 mph) (taken from Kroell et al. (1974))

in Fig. 11.13, the initial stiffness of the thorax is apparently the same for the cadaver

and the tensed volunteer. Figure 11.14 shows the level of the plateau force which

again is the same for cadaver and volunteer. The adjusted values shown by the dark

dots are not predictive of human response.

The effect of velocity on lung injury was apparent in the Kroell data (Kroell et al.

1974), as stated above, but was not accounted for. Lau and Viano (1981 addressed

this problem by performing a series of blunt sternal impacts on 57 anesthetized

rabbits at 5, 10, and 18 m/s. The displacement of the impactor varied from 2 to

45 mm. The animal was restrained in a supine position on a flat plate that was

instrumented with a load cell below it. A pneumatic impactor was positioned above


Fig. 11.12 Recommended thoracic response corridor for the development of a biofidelic

dummy. The original corridor for the high speed response is shown as a shaded region (taken

from Neathery (1974))

the sternum, as shown in Fig. 11.15. The impact interface was a 6.7-cm diameter

aluminum disc connected to a piston and was centered 2 cm cephalic to the xiphoid

process. The injuries were dependent on both piston velocity and displacement. The

lung was divided into two regions for injury assessment. The bronchial region was

defined as the recess of the lung forming the entrance for the bronchi, including the

immediate segment of the bronchi entering the lung, and the alveolar region was the

rest of the lung. The findings can be summarized as follows:

• At low velocities of impact (5 m/s), there was more injury to the bronchial region

of the lungs, beginning at a displacement of 21 mm.

• Alveolar injury occurred with 10 mm of displacement at 10 m/s. It was more

severe than bronchial injury until the displacement exceeded 25 mm, at which

level, the injury severities were comparable.

• Alveolar injury occurred at 2 mm of displacement at 18 m/s.

• Injury severity correlated poorly with the measured reactive force, impulse

transfer and peak pressure in the esophagus. Injury to the rib cage increased

with displacement at each velocity and at comparable displacements, the injury

was more severe at higher velocities.


7

6 Load

Apparent Initial Stiffness, S AI , kN/cm

slope=S AI

Deflection

5

4 S AI =.263+.603(v-1.3)

3

2

1

Kroell (mean cadaver values)

Patrick (volunteer values)

−STATIC LEVEL

0

2 4 6 8

Impactor Velocity, V, m/s

10 12

Fig. 11.13 Comparison of initial thoracic stiffness data for frontal impact, taken from cadavers

and a volunteer (taken from Melvin et al. (1985))

The injury picture is described qualitatively in Fig. 11.16 which is a plot of

displacement vs. velocity. Alveolar injuries tend to occur at higher velocities where

they can be likened to alveolar injuries due to blast. Thus, the two injury mechanisms

may be different. Bronchial injuries are related more to crush while alveolar

injuries are due to impact of the chest wall at speeds in excess of the speed of sound

in the alveolar tissue—a shock wave effect. The estimated speed of sound in

alveolar tissue is 15–30 m/s (Clemedson and Jonsson 1962) and the speed of

sound through the lung parenchyma is from 25 to 70 m/s (Rice 1983) compared

to 342 m/s, the speed of sound in dry air.

As mentioned above, this landmark paper by Lau and Viano (1986) led to the

Viscous Criterion, V*C. Kroell et al. (1981) impacted the thorax of domestic

swine and found the same velocity dependency. A more detailed discussion of

the formulation of the Viscous Criterion can be found in Sect. 11.7, Tolerance of the

Thorax to Impact Loading.


7

6

Load

5

F P

3.8 cm

Deflection

Plateau Force, FP, kN

4

3

F P =1+.750(V-3.73)

2

1

STATIC LEVEL

Kroell (mean cadaver values)

Kroell (adjusted values for

muscle effects)

Patrick (volunteer values)

0

2 4 6 8 10 12

Impactor Velocity, V, m/s

Fig. 11.14 Comparison of thoracic plateau force data for frontal impact, taken from cadavers and

a volunteer (taken from Melvin et al. (1985))

11.4.2 Side Impact Experiments

Early side impact tests were conducted on subhuman primates and volunteers by

military and space agencies of the Federal Government. McElhaney et al. (1971)

summarized these studies and conducted side impact tests on the head and abdomen

of subhuman primates. Stalnaker et al. (1979) conducted one of the first whole-body

cadaveric side impact tests in France. Fifteen cadavers, ranging in age from 44 to

69 years were dropped sideways onto rigid and padded surfaces from heights of

0.5–2 m. There were three configurations for rigid impacts and two for padded

impacts. Most of the rigid impacts were from a height to 1 m and the thoracic AIS

ranged from 0 to 4. The drop height for padded impacts was 2 m and the AIS range

was also 0–4. Force-deflection curves were presented for all tests. Figure 11.17

shows lateral thoracic response to rigid impact. NHTSA funded a large number of

whole-body cadaveric side impact tests, most of which were conducted at the


Fig. 11.15 Diagram of the

test set-up for sternal

impacts on rabbits using a

pneumatic impactor (taken

from Lau and Viano (1981))

Fig. 11.16 The type of

lung injury is dependent on

both impactor displacement

and velocity (taken from

Lau and Viano (1981))

University of Heidelberg, in Germany. The tests were conducted on a deceleration

sled on which was mounted a 1.1-m long bench seat. The seat was parallel to the

direction of travel of the sled and the test subject (cadaver) was seated at the rear.

The sled was stopped abruptly and the seated cadaver slid forward on the bench seat

to impact a wall instrumented with load cells that measured thoracic, abdominal,


Applied normalized force

daN

1000

155

105

500

111

104

118

Relative

deflection

0 10 20 30 40 50

%

Fig. 11.17 Thoracic response to lateral impact—whole-body drop tests onto a rigid surface (taken

from Stalnaker et al. (1979))

Fig. 11.18 Photograph of the Heidelberg side impact test set-up (taken from Kallieris et al. (1981))

pelvic, and knee load. A photograph of the set-up is shown in Fig. 11.18 (Kallieris

et al. 1981). This method is now known as the Heidelberg method for side impact

testing although it originated at HSRI of the University of Michigan (now known as

UMTRI), as described by Melvin et al. (1976). The cadavers were instrumented

with an array of 12 chest accelerometers, as shown in Fig. 11.19. The initial array of

10 was proposed by Robbins et al. (1976) and modified to an array of 12 by NHTSA

(Eppinger et al. 1978) as a universal requirement for all cadaver tests performed


HORIZONTAL, VERTICAL AND NORMAL (+AWAY)

CLAVICLE

T1

1ST RIB

4TH RIB

NORMAL

SCAPULA

PARALLEL TO BODY

(+ AWAY)

8TH RIB

PARALLEL TO BODY

(+ AWAY)

T12

VERTICAL, HORIZONTAL AND NORMAL

(+AWAY)

Fig. 11.19 The 12-accelerometer thoracic array mandated by the NHTSA for cadaveric testing

funded by the NHTSA (taken from Eppinger et al. (1978))

under NHTSA sponsorship. There were triaxial accelerometers on the back of T1

and on the back of T12, two lateral facing accelerometers on the left and right 4th

rib and two forward facing accelerometers on the left and right 8th rib. For side

impact testing, the accelerometers on 8th rib were rotated to sense lateral acceleration.

There were also side impact cadaver tests carried out in vehicles, sponsored

by the Forschungsvereinigung Automobil-technik e. V. (FAT), a German insurance

entity. The cadavers were instrumented with the NHTSA mandated chest accelerometers

and the collision velocity ranged from 40 to 60 km/h. Of the 35 cadavers

that were tested, 21 were at a collision velocity of 50 km/h. All side impact data

collected using the standard chest accelerometer array were analyzed by Eppinger

et al. (1984) who arrived at a side impact injury criterion called the Thoracic

Trauma Index (TTI), given by the following equation:

TTI ¼ 1:4*AGE þ 0:5ðRibY þ T12YÞ*MASS=165

where

AGE is the age of the cadaver in years

RibY is the higher of the measured peak lateral acceleration of Rib 4 or 8 in g’s

T12Y is the measured peak lateral acceleration at T12 in g’s

MASS is the weight of the cadaver in lb


NHTSA also had the University of Michigan develop a side impact dummy

(SID) that would provide human-like chest responses in side impact, as described

by Morgan et al. (1981). Lateral rib and spinal accelerations measured in the SID

compared favorably with cadaveric data. However, the SID chest was very rigid

and massive and did not deflect like a human chest. When impacted, the entire chest

rotated out of the way, pivoting about the dummy spine. The reason for the rotation

of the rib cage was because it was attached to the rigid spine of the dummy by a

piece of leather that was the sternum of the Hybrid II rib cage. That is, the SID was a

Hybrid II dummy with the rib cage put on backwards. Since the ribs were horizontal,

the shape of the rib cage remained the same but lead weights were attached to it

so that it had same weight as a human chest.

The relative merits of the Viscous Criterion and the Thoracic Trauma Index are

discussed further in Sect. 11.7, Tolerance of the Thorax to Impact Loading and in

Chap. 16, Side Impact.

The National Center for Injury Prevention and Control (NCIPC) of the Centers

for Disease Control (CDC) funded a side impact cadaveric study at Wayne State

University. Heidelberg type sled tests were conducted on 17 cadavers (Cavanaugh

et al. 1990, 1992). The impact wall was modified to include four rows of load cells

to measure shoulder, thoracic, abdominal, and pelvic loads. The knee load was also

measured. The first eight tests were impacts against a rigid wall and the remaining

nine were padded wall tests. The impact speeds varied from 24 to 26.8 km/h (6.6 to

10.5 m/s). The test conditions and resulting injuries are shown in Table 11.1. In the

Table 11.1 Test conditions and results of WSU side impact tests (data taken from Cavanaugh

et al. (1990, 1993))

Run

No.

Pelvic

offset

(cm)

Padding type

Padding

thickness

(cm)

Velocity

(m/s)

Injuries sustained

SIC01 15 None 0 8.9 Severe flail chest, MAIS ¼ 5

SIC02 15 None 0 9.1 Severe flail chest, MAIS ¼ 5

SIC03 15 None 0 10.5 15 mm Aortic laceration, MAIS ¼ 5

SIC04 0 None 0 9.1 Left flail chest, MAIS ¼ 4




SIC08 0 None 0 6.6 10 mm Aortic laceration, MAIS ¼ 5

SIC09 0 ARSAN 7.5 9.2 10 mm Aortic laceration, MAIS ¼ 5

SIC10 0 Soft PHC 15 8.7 3 left rib fractures, MAIS ¼ 2

SIC11 0 Soft PHC 11 8.9 3 left rib fractures, MAIS ¼ 2

SIC12 0 Stiff PHC 11 8.9 15 mm Aortic laceration, MAIS ¼ 5

SIC13 0 Soft PHC 11 8.3 5 rib fractures, MAIS ¼ 2

SIC14 0 Stiff PHC 11 9.4 18 rib fractures, MAIS ¼ 4

SIC15 0 Soft PHC 11 8.9 No injury, MAIS ¼ 0

SIC16 0 Stiff PHC 7.5 8.9 26 rib fractures, MAIS ¼ 4

SIC17 0 Soft PHC 15 8.9 2 rib fractures, MAIS ¼ 2

PHC Paper honeycomb, Stiff 19 psi, Soft 8 psi, MAIS Maximum AIS


first three tests, there was a 15-cm offset for the pelvis. That is, as the cadaver slid

towards the wall, the pelvis was stopped 15 cm from the wall by a rigid metal block

and the rest of the torso continued to impact the other wall load cells. This was done

because NHTSA tests on the side impact dummy (SID) showed that the TTI was

lower for offset impacts. However, the cadavers sustained AIS 5 injuries and the

offset tests were discontinued. The next five rigid wall tests (SIC04 through SIC08)

resulted in either a flail chest (MAIS 4) or an aortic laceration (MAIS 5), indicating

that padding was necessary to protect the chest. The first padding tried was

ARSAN, a relatively stiff foam that produced low TTI values in the SID

(Cavanaugh et al. 1992). The injuries were severe (MAIS 5). This is the second

instance in which cadaveric injuries were not consistent with TTI. The use of paper

honeycomb (PHC) was motivated by the need for a crushable material of known

strength. Foam materials with a specific crush strength had to be special ordered and

if the quantities needed were low, the cost was very high. Two grades of PHC were

used. The softer pad had a nominal crush strength of 8 psi (55 kPa) while the stiffer

one had a crush strength of 19 psi (131 kPa). It can be seen from Table 11.1 that the

stiff PHC fared no better than the rigid wall and the only effective padding was a

soft one. The inescapable conclusion is that the chest is exquisitely sensitive to

padding stiffness.

In terms of response, pendulum impacts to the cadaveric chest, abdomen, and

pelvis were conducted at Wayne State University under GM sponsorship (Viano

et al. 1989) to obtain response corridors similar to those for frontal impact obtained

by Kroell et al. (1974). Fourteen unembalmed cadavers were subjected to lateral

impact by a 15.2-cm diameter pendulum with a mass of 23.4 kg. The average age of

the cadavers was 53.8 13.9 years and the average body mass was 67.2 16.2 kg.

There were multiple impacts on each cadaver to the chest, abdomen, and pelvis, at

impact velocities of 4.5, 6.7, and 9.4 m/s (10, 15 and 20 mph). The discussion in this

section will be limited to the thorax. To obtain more data from each cadaver, the

first chest impact was at a lower velocity on the left side followed by a more severe

impact on the right. The direction of impact was 30 anterior of the lateral axis of

the cadaver and directed at the spine, as shown in Fig. 11.20. There was no rotation

of the rib cage and chest deflection was measured directly by tracking the motion of

the pendulum on high speed film. Triaxial accelerometers were mounted on T1, T8,

and T12 but not on the ribs. As a result, TTI could not be computed. The pendulum

was equipped with a uniaxial accelerometer from which the impact force could be

deduced. The following injury functions were used to assess their ability to predict

injury:

1. Viscous response, V*C(t)

2. Compression response, C(t)

3. Spinal acceleration response. G sp (t)

4. Force, F(t)

The injuries were assessed based on the number of rib fractures and damage to

the organs of the thorax and abdomen for the 16 chest impacts that were carried out.

In three of the six high speed chest impacts at 9.4 m/s, there was laceration of the


Fig. 11.20 Lateral pendulum impact test at an oblique angle, 30 anterior to lateral (taken

from Viano et al. (1989)). Reprinted from D.C. Viano, I.V. Lau, C. Asbury, A.I. King,

P. Begeman, Biomechanics of the human chest, abdomen, and pelvis in lateral impact. Accident

Analysis & Prevention 21, 553–574, 1989, with permission from Elsevier

lung, liver, diaphragm, kidney, and spleen with possible flail chest. The average

number of rib fractures at this speed of impact was 14. The MAIS ranged from 0 to

4. Also, force-deflection curves for each test could be plotted from the measured

data. These are shown in Fig. 11.21 for the three impact speeds of 4.4, 6.5, and

9.5 m/s. Logistic plots for V*C, C and G sp at T8 are shown in Fig. 11.22 with the

computed Chi square, p and r values. V*C appears to be the best predictor for side

impact injury although compression is a close second. The chest injury criteria for

all variables are listed in Table 11.2 for AIS 4 and for a 25 % probability of injury.

It was a pity that TTI was not measured in this experiment. The reason given was

that rib-mounted accelerometers would be damaged by the pendulum. However,

damage could have been prevented by attaching the accelerometer to the inside

surface of the ribs. The real reason is political and not scientific. GM and NHTSA

had a strong disagreement regarding the injury criterion for side impact. TTI was

the initial criterion for side impact in FMVSS 214, the Side Impact Standard.

However, in 2007, it was replaced by a compression criterion for the male

dummy and by a spinal acceleration (T12) criterion for the female dummy. The

SID was replaced by the second version of the European male side impact dummy,

ES-2re, and the SID IIs (female dummy). However, TTI and SID are part of the

development of side impact protection and even though they are obsolete, they

contributed to the knowledge base and to the re-affirmation of the undesirability of

directed research exercised by the NHTSA.


Fig. 11.21 Forcedeflection

curves from

lateral pendulum chest

impacts (taken from Viano

(1989)). Reprinted from D.

C. Viano, I.V. Lau, C.

Asbury, A.I. King, P.

Begeman, Biomechanics of

the human chest, abdomen,

and pelvis in lateral impact.

Accident Analysis &

Prevention 21, 553–574,


Elsevier

Force (kN)

5

4

3

2

1

4.4 m/s

run 17

run 29

run 36

run 40

run 41

0

0 5 10 15

Deflection (cm)

20

5

6.5 m/s

4

Force (kN)

Force (kN)

3

2

1

0

0 5

10 run 2

run 14

run 18

8

run 33

run 37

6

4

run 4

run 5

run 7

run 9

run 11

10 15

Deflection (cm)

9.5 m/s

20

2

0

0 5

10 15 20

Deflection (cm)

Probability of MAIS 4+



11.5 Thoracic Response to Frontal and Side Impact 381

CHEST

1

1

1

0.8

0.6

0.8

0.6

0.8

0.6

0.4

Chi 2 = 13.7

0.2 P = 0.00

r = 0.77

0

0 0.5 1 1.5 2 2.5 3

VC (m/s)

0.4

0.2

Chi 2 = 13.53

P = 0.00

r = 0.76

0

20 25 30 35 40 45 50

COMPRESSION (%)

0.4

0.2

Chi 2 = 10.16

P = 0.00

r = 0.75

0

0 20 40 60 80 100

G T8-γ

Fig. 11.22 Analysis of side impact data—Logistic plots for V*C, C and G sp at T8 with computed

Chi square, p and r values (taken from Viano (1989))

Table 11.2 Chest injury

criteria (data taken from

Viano (1989)) (for AIS 4

and for a 25 % probability of

injury)

Criterion

Value

V*C

1.47 m/s

C 38.4 %

G sp at T8

45.2 g

G sp at T12 31.6

F

5.48 kN

11.5 Thoracic Response to Frontal and Side Impact

Impact response of the thorax is summarized in this section. For frontal impact, the

actual data are shown in Fig. 11.23A while the adjusted corridors are shown in

Fig. 11.23B. The area under the curve is the energy absorbed during impact and is

largely a function of the plastic deformation of the thorax. It is seen that in

Fig. 11.23B, the deflections were reduced by 12.7 mm to reflect skeletal deflection

and the force was increased by 667 N (150 lb) to reflect muscular tensing of the

living human.

For side impact, Viano (1989a, b) provided thoracic response data from pendulum

impacts at three velocities. Force-deflection curves at 4.8, 6.8, and 9.7 m/s

are shown in Fig. 11.24 which indicates that there is also a considerable amount

plastic deformation of the rib cage. The force-deflection curves in frontal and side

impact are compared in Fig. 11.25. The frontal response corridor is on the left.

It can be seen that the chest is stiffer in frontal impact than in lateral impact. The

peak forces are higher and the peak deflections are lower for frontal impact than

side impact.


A Force vs Deflection B Force vs Deflection

1400

1400

1200

1200

1000

1000

Force (Ib)

800

600

Force (Ib)

800

600

400

400

200

200

0

0 1 2

Deflection (in)

0

3 4 0 1 2

Deflection (in)

3 4

Fig. 11.23 (A) Uncorrected corridor for chest response at 16 mph, (based on Kroell et al. (1974)).

(B) Corrected corridor for chest response at 16 mph with an average curve added, based on Lobdell

et al. (1973). The correction is substantial

11.6 Biomechanics of Aortic Rupture due to Thoracic

Impact

One of the most dangerous thoracic visceral injuries is traumatic rupture of the aorta

(TRA). If there is a complete rupture of the aorta, the chances of survival are

virtually none. If the adventitia is ruptured but the media is not, then it becomes a

race against time to get the victim into surgery before the media ruptures. The

adventitia is rather brittle and cannot be counted on to maintain aortic integrity. It

was also found that the most frequent site of rupture is a length of the descending

aorta called the peri-isthmic region, as shown in Fig. 11.8. The aortic isthmus is just

distal to the left subclavian artery. In order to determine the exact mechanism of the

injury, experiments using animals and cadavers have been performed over the last

half century. One of the first experiments was conducted by Roberts et al. (1966)

who impacted 20 dogs in the chest with a 9.1-kg (20-lb) impactor at speeds ranging

from 5.5 to 6.7 m/s (18 to 22 ft/s). Acute injuries found at autopsy included rupture

of the right atrium and left ventricle as well as transverse tears of the aorta. No data

were provided regarding the frequency of TRA. Coermann et al. (1972) impacted

cadavers frontally with the hub of energy-absorbing steering assemblies and

obtained aortic tears in two cadavers, one of which was proximal to the periisthmus

region and did not duplicate the real world pathology of TRA. However,

it was conjectured that the sternum shoveled the mediastinal tissues upward, putting

the aorta in tension. This theory was originally proposed by Voigt and Wilfert

(1969) and was known as Voigt’s shoveling effect. Viano and Lau (1983) reviewed

11.6 Biomechanics of Aortic Rupture due to Thoracic Impact 383

Fig. 11.24 Thoracic

response to lateral

pendulum impact (30 from

lateral) at (A) 4.8, (B) 6.8

and (C) 9.7 m/s (taken from

Viano et al. (1989)).

Reprinted from D.C. Viano,

I.V. Lau, C. Asbury, A.I.

King, P. Begeman,

Biomechanics of the human

chest, abdomen, and pelvis

in lateral impact. Accident

Analysis & Prevention 21,

553–574, 1989, with

permission from Elsevier


A

5

B

4

4

3

FORCE (kN)

3

2

1

22FM

20FM

15FM

19FM

14FF

18FM

12FF

FORCE (kN)

RUN #4

RUN #5

RUN #7

RUN #9

RUN #11

0

0

0 2 4 6 8 10 0 5 10 15

DEFLECTION (cm)

DEFLECTION (cm)

2

1

Fig. 11.25 Comparison of frontal thoracic impact response (A) with lateral thoracic impact

response (B) (Viano et al. (1989)). Reprinted from D.C. Viano, I.V. Lau, C. Asbury, A.I. King,

P. Begeman, Biomechanics of the human chest, abdomen, and pelvis in lateral impact. Accident

Analysis & Prevention 21, 553–574, 1989, with permission from Elsevier

the literature on TRA and suggested that a potential mechanism was a combination

of tension in the aorta and increased arterial pressure. Viano and Lau (1983) also

found that arterial sclerosis increased the occurrence of vascular injury by over

50 % above normal, from blunt thoracic impact. Nusholtz et al. (1985) impacted

17 live dogs and 5 post-mortem dogs to study cardiac and aortic response to frontal

sternum impacts. The live dogs were impacted at velocities of 7.6–13.0 m/s. In

terms of TRA, there were seven transverse ruptures of the ascending aorta and only

one rupture of the descending aorta. This pattern is atypical and not generally seen

in human TRA. The authors suggested that the mechanism of ascending aortic

rupture was tension in the blood vessel caused by a downward motion of the heart.

They also stated that pressure developed in the aorta during impact was not a

mechanism of injury. Cavanaugh et al. (1990, 1993) did manage to rupture the

aorta in the peri-isthmus region of the aorta in 5 of the 17 Heidelberg type side

impact sled tests. The impacts were to the left side of the cadaver. Four of the

cadavers sustained a partial tear (laceration) 10–15 mm in length while a fifth one

sustained an intimal tear. Although this was the first reported clinically relevant

aortic injury, the injury occurred in one mode of impact, a purely lateral distributed

impact, and no biomechanical data were obtained to further the understanding of

the injury mechanism. Baque et al. (2006) attached accelerometers to the right

ventricle of the heart and to the isthmus of the aorta and subjected six cadaver torsos

to free fall impacts (vertical drops) from 1 to 4 m, achieving accelerations of about

200 g in the chest. No TRA could be reproduced but the acceleration in the isthmus

of the aorta was higher than that in the ventricle. The authors hypothesized that

TRA was due to stretching of the descending aorta. At the turn of the century (early

2000s) partial funding from private parties became available to study the mechanism

of aortic rupture. Several US institutions, including Wayne State University

participated in this research project which was directed by Dr. Kennerly Digges of


George Washington University. Hardy et al. (2008) at Wayne State successfully

duplicated TRA in seven of the eight cadavers tested. This was the culmination of

many unsuccessful attempts by several investigators, including those supported by

the Digges project as well as research done at General Motors (Viano 2011) and

elsewhere (Baque et al. 2006; Forman et al. 2005).

The hypothesis was that the aorta failed in tension. In some preliminary tensile

testing of seven isolated human aortic specimens, Shah et al. (2006) obtained failure

data for the descending aorta at strain rates in the range of 12 s 1 . The failure load

averaged 92 N and failure strain was 22 %. The tears occurred in the peri-isthmic

region. These data provided information on what loading modes would be able to

cause tensile failure of the aorta in an actual chest impact.

In the whole-body tests, loading modes were selected to generate axial tension in

the isthmus or to straighten out the aortic arch during frontal, lateral, and oblique

impacts to the chest. For frontal impact and submarining, there needed to be

dorsocranial motion of the heart. For lateral impact, failure would be likely for

anteromedial motion of the heart and for oblique impact, dorsocranial and medial

motion of the heart could produce aortic tears. A detailed description of how the

cadaver was oriented for each mode can be found in the paper. The one

distinguishing feature of the experiment was to test the cadaver in an inverted

position to obtain a more realistic positioning of the heart of a seated driver. The

heart is tethered to the diaphragm and when there is no muscle tone, the diaphragm

tends to sag. Thus, the heart would be positioned more inferiorly than normal.

Inverting the cadaver would raise the heart somewhat to its normal position in a

living human. Other features of the experiment include the removal of the lower

extremities, the use of special spinal clamps to suspend the cadaver in the inverted

position with the ability to change the orientation of the torso, the use of the high

speed X-ray unit at Henry Ford Hospital, the targeting of the peri-isthmic region of

the aorta with 2-mm lead beads, perfusion of the aorta, monitoring of pressure in the

aorta and inflation of the lungs. Experimental details can be found in Hardy

et al. (2008).

A total of eight cadavers was used in the experiment, three for frontal impact,

three for side impact, and one each for the submarining and oblique impact tests.

Figure 11.26 shows the cadaver in position for a frontal impact. The torso was

rotated 40 in the sagittal plane to place the pelvis more toward the impactor and the

head farther away. This allowed the impactor to “shovel” the heart upward (toward

the head) as it is pushed rearward (toward the spine). This configuration represented

the impactor or steering column inclined at 20 from horizontal and the torso

aligned with the seatback that was inclined at 20 with respect to the vertical.

The pneumatically driven 15.2-cm diameter impactor weighed 32 kg and was

centered over the xiphoid process. Aortic rupture occurred in two of the three

tests. The side impact tests were performed with the cadavers rotated 30 from

vertical. In two tests, the arm was impacted at the mid-diaphysis of the humerus

while in a third test the impact was to the chest with the arm out of the way.

Figure 11.27 shows a direct impact to the side of the chest with the arm moved out

of the way. Aortic rupture occurred in all three tests. In the submarining test, lapbelt


Fig. 11.26 Frontal impact to the chest of an inverted cadaver by a 32-kg pendulum which

shoveled the mediastinal contents towards the head and the spine. An aortic rupture occurred

(taken from Hardy et al. (2008))

Fig. 11.27 Side impact to the chest with the arm moved out of the way, causing an aortic rupture

(taken from Hardy et al. (2008))

loading was simulated by retracting the belt with a high speed pre-tensioner. To

simulate submarining, the belt was placed at an angle of 40 from the horizontal

(transverse) plane of the cadaver. It was placed initially over the umbilicus. The

experimental set-up is shown in Fig. 11.28. An aortic rupture resulted from this test.


Fig. 11.28 Submarining test using a seatbelt that was retracted rapidly by a belt pre-tensioner. The

belt used was placed at an angle to the torso to partially simulate submarining. An aortic intimal

tear resulted from this test (taken from Hardy et al. (2008))

Fig. 11.29 Oblique impact test at the level of the xiphoid process, 30 form lateral. An intimal

tear was found after the test (taken from Hardy et al. (2008))

The last test was an oblique impact test at the level of the xiphoid process, similar to

side impact tests conducted by Viano et al. (1989), 30 anterior to lateral. This test

is shown in Fig. 11.29. An aortic intimal tear occurred in this test. In all, there were

seven aortic ruptures or tears out of the eight tests that were conducted. There were


multiple (two or more) tears in four of the tests but all tears were transverse and

were found in the peri-isthmic region of the aorta.

Based on the visualization provided by the high speed X-ray unit, there is

evidence that the aorta underwent longitudinal tension that resulted in TRA. This

tension was due to the aorta moving dorsocranially during frontal and submarining

loading. Side impact caused the aorta to move medially and anteriorly. The

descending aorta is firmly anchored to the posterior chest wall by connective tissue.

Motion of the heart, ascending aorta, and the aortic arch generates tensile loads in

the descending aorta to cause rupture.

As to why previous experiments by Viano et al. (1989) and others did not result

in TRA, the only difference between these tests and the previous ones is the

orientation of the cadaver. Although the organs in the mediastinum are tightly

packed, they still respond to gravity and a 2 g change is apparently enough-to alter

the initial stress in the descending aorta to allow it to rupture under impact.

11.7 Tolerance of the Thorax to Impact Loading

The first tolerance criterion for frontal chest impact was an acceleration criterion

based on the famous sled ride of Col. Stapp who experienced an estimated peak

chest acceleration of 45 g. This level was raised to 60 g with a 3-ms clip (see

Chap. 1) and the acceleration was to be measured at T12. Another criterion was

based on force. It was found that a steering wheel hub load of 3.3 kN was not

injurious to cadavers (Viano and King 2004). Shoulder belt loads of 7.4 kN

(1665 lb) were not injurious to belted occupants (Foret-Bruno et al. 1978). The

compression criterion was based on the work of Kroell et al. (1971, 1974). They

found that there was a linear relationship between AIS and percent compression of

the chest (Fig. 11.30):

AIS ¼

3:78 þ 19:56 C

where C is the chest compression divided by the chest depth.

This AIS is based on skeletal injuries because the tests were done on

unembalmed cadavers. Table 11.3 lists the thoracic skeletal AIS values in terms

of rib fractures. It is seen that for an AIS of 2, the chest compression is 30 %, That is,

for a 50th percentile male with a chest depth of 230 mm (9 in.), a deflection of

69 mm will result in 2–3 rib fractures. Similarly, for a 40 % deflection or 92 mm of

compression, the AIS is 4. A flail chest is predicted at this level of compression.

Neathery et al. (1975) recommended a design limit of 75 mm (3 in.) for chest

deflection. This corresponds to an AIS of 2.6. The 3-inch limit for chest compression

became a part of FMVSS 208, the Federal standard for frontal impact.

As discussed in Sect. 11.4, later studies on thoracic injury showed that thoracic

injury was also dependent on chest wall velocity. This led to a criterion that is

applicable to both frontal and lateral impact. It is the Viscous Criterion or the V*C

11.7 Tolerance of the Thorax to Impact Loading 389

Fatal 6

Critical

Survival Uncertain 5

Severe

Life Threatening

Survival Probable

4

New Data

Kroell et al. Unrestrained Back

(1971) Data

Restrained Back Data (New)

Severe

(Non-Life) Threatening 3

AIS Injury Rating

Moderate 2

Minor

1

AIS = -3.78 + 19.56

r = .730

(A&B included)

AIS = -3.52 + 19.31

r = .772

(A&B excluded)

δm

O

δm

O

19FM

19 yrs.

20FM

29 yrs.

No Injury

B

0

.1 .2 .3

.4

.5

Total Chest Deflection dm

Chest A-P Diameter O

A

Restrained

Back Data

Fig. 11.30 Empirical linear relationship between AIS and chest deflection (taken from Kroell

et al. (1974))

Table 11.3 Linear

relationship between chest

compression and AIS (based

on Fig. 11.30 above)

No. of rib fractures AIS % Compression

1 1 24

2–3 2 30

4 or more 3 35

Flail chest 4 40

Bilateral flail chest 5 45

AIS ¼3.78 + 0.1956 (% Compression)

Criterion developed by Viano and Lau (1983). The proposed values for V*C

were 1.0 for frontal impact (Viano and Lau 1988) and 1.5 for side impact

(Viano et al. 1989) for a 25 % probability of an AIS 4+ injury. This criterion is

valid for soft tissue injury and has been used for abdominal injury (Chap. 12) and

brain injury (Chap. 3).

There are other criteria for side impact. As mentioned above, NHTSA used the

Thoracic Trauma Index (TTI) for side impact in FMVSS 214 until it was amended

in 2007. This criterion was to be used together with the SID, a dummy which

lacked biofidelity. For the sake of completeness, the criteria in the former version

of FMVSS 214 are listed below. They are for a 25 % probability of an AIS 4+

injury,

TTI < 85–90 g

Pelvis

Dummy

(85 g for four-door cars and 90 g for two-door cars)

Lateral Acceleration < 130 g

SID


11.8 Modeling of Thoracic Response

One of the first known models of the thorax was developed by Roberts and Chen

(1970). It was a finite element model that provided the basic geometry and response

to static loads. The same authors formulated a dynamic model to simulate frontal

impact (Chen et al. 1974) and attempted to match the displacement data by Nahum

et al. (1970) and Patrick et al. (1965). At about the same time, Lobdell et al. (1973)

proposed a lumped parameter, one-dimensional, model of the thorax simulating

frontal impact. Figure 11.31 shows the 4 degree-of-freedom spring-mass model

mimicking the experiments by Kroell et al. (1971). The mass, m 1 , represents

the pendulum impactor while m 2 is the chest wall and m 3 is the rest of the thorax.

The values of the springs and dashpots were adjusted until the model predicted the

experimentally measured chest deflections. The governing equations are listed below:

m 1 y 1 ¼ k 12 ðy 1 y 2 Þ ð11:1Þ

m 2 y 2 ¼ k 12 ðy 1 y 2 Þ k 23 ðy 2 y 3 Þ ð11:2Þ

m 3 y 3 ¼ k 23 ðy 2 y 3 Þ þ cve 23 ðy 4 y 3 Þ þ c 23 ðy 2 y 3 Þ ð11:3Þ

where, for i ¼ 1–4,

and

0 ¼ kve 23 ðy 2 y 4 Þ þ cve 23 ðy 3 y 4 Þ ð11:4Þ

y i ¼ dy i =dt

y i ¼ d 2 y i =dt 2

Equations (11.1), (11.2), (11.3), and (11.4) are based on Newton’s second law of

motion and their derivation is left as an exercise.

c 23

k 23

m 3

m 1

k 12

m 2

kve 23 cve 23

y 1 y 2 y 4 y 3

Fig. 11.31 Lumped parameter model for frontal chest impact. (taken from Lobdell et al. (1973)).

Human impact response: measurement and simulation: proceedings by King, William Frederic;

et al. Reproduced with permission of KLUWER ACADEMIC PUBLISHERS in the format Book

via Copyright Clearance Center

11.8 Modeling of Thoracic Response 391

Table 11.4 Model parameters used by Lobdell et al. (1973)

k 12 (lb/in) m 2 (lb) k a 23 (lb/in) c b 23 (lb/in-s) kve 23 (lb/in) cve 23 (lb/in-s) m 3 (lb)

1600 1.0 60 2.3 Comp 75 1.0 60

400 12.5 Tension

a k 23 is bilinear with the change occurring at 1.3 in.

b c 23 has different values in compression and tension

Human impact response: measurement and simulation: proceedings by King, William Frederic;

et al. Reproduced with permission of KLUWER ACADEMIC PUBLISHERS in the format Book

via Copyright Clearance Center

1200

51.0 LB. 16.0 MPH

FORCE - POUNDS

800

400

EXPERIMENTAL MEAN

42.5 LB. 11.5 MPH

SIMULATION

0

0

1 2 3 4

TOTAL DEFLECTION - INCHES

Fig. 11.32 Lobdell model predictions of Kroell et al. (1971) frontal chest impacts at two different

speeds and using two different impactors (taken from Lobdell et al. (1973)). Human impact

response: measurement and simulation: proceedings by King, William Frederic; et al. Reproduced

with permission of KLUWER ACADEMIC PUBLISHERS in the format Book via Copyright

Clearance Center

With the constants shown in Table 11.4, the model predicted thoracic response

quite well, as shown in Fig. 11.32. However, this model cannot tell us much about

injury to the thoracic viscera (organs) and a more detailed finite element model of

both the rib cage and the thoracic soft tissues is needed. One such model is by Wang

(1995) who developed a full thorax model of a 50th percentile male and validated it

against side impact data. The model simulated the skeleton of the thorax, including

the rib cage, the entire spine and sacrum, using 8-noded or 6-noded solid elements.

It also simulated the thoracic organs, including the lung, the heart, major blood

vessels, the diaphragm, and pleura. For the rib cage, ribs were modeled by one layer

of solid elements and skin and muscle tissue covering it were modeled by shell

elements. Another layer of shell elements was used to model the intercostal muscles

and the pleura, inside the rib cage. The heart and lungs were modeled by solid

elements while the major blood vessels, the trachea, and bronchi were simulated by


Fig. 11.33 Frontal oblique

view of the thoracic

skeleton of the Wang (1995)

model

shell elements. The blood vessels simulated include the aorta, the superior and

inferior vena cava, the left and right brachiocephalic vein, the pulmonary trunk, the

carotid arteries, and the subclavian artery. The diaphragm was also modeled by

shell elements. The entire model consisted of 15,671 nodes, 4333 solid elements,

45 beam elements, and 11,075 shell elements. Figure 11.33 is a frontal oblique view

of the thoracic skeleton that was modeled and Fig. 11.34 shows the mediastinum

and the diaphragm. The organs of the upper abdomen were modeled by a layer of

shell elements beneath the diaphragm. As for material properties of the many

tissues of the thorax, dynamic properties were not available. For the heart and

lungs, they were assumed to have a non-linear response in compression and a linear

one in tension. The elastic modulus of cardiac muscle in compression was increased

tenfold over the static values found in Yamada (1970), as shown in Fig. 11.35. The

modulus for the lung was also increased tenfold over the data provided by Vawter

et al. (1979). In all, 21 different tissues needed to be assigned material properties in

terms of their elastic moduli, Poisson’s ratio and mass density. These assumed

values can be found in Wang (1995). To simulate large deformation responses, the

LS-DYNA 3-D explicit code was used as the solver. The contact algorithm used

was a node-to-surface type contact. Since this was a thoracic model without the rest


Fig. 11.34 Model of the

mediastinum and

diaphragm (taken from

Wang et al. (1995))

6.0E-4

5.0E-4

Stress-strain curves of Cardiac Muscle

stress, GPa

4.0E-4

3.0E-4

2.0E-4

1

1: F.E Model

2: Yamada (1970)

1.0E-4

0.0E-4

0 0.2

2

0.4 0.6

0.8 1

strain

Fig. 11.35 Stress-strain curve for heart muscle in compression used in the model (Curve1)

compared with quasi-static response obtained by Yamada (1970). The modulus was increased

tenfold (taken from Wang (1995))

of the body, it could not be validated against sled test data. Pendulum tests at 4.4

and 6.5 m/s performed by Viano et al. (1989) were used to validate the model.

Figure 11.36 shows the FE simulation of the pendulum impact. The mass of the

head, arms, abdomen, and legs was added to obtain the correct response. Both

force-deflection and force-time curves were compared. Figure 11.37 shows the

model response plotted against the side impact corridor proposed by Viano et al.

(1989) and the five impact tests that were done at 6.5 m/s. The force-time correlation

is shown in Fig. 11.38. To exercise the model, the deformation of the thorax for


Fig. 11.36 Simulation of

side impact tests performed

by Viano et al. (1989)

(taken from Wang (1995))

Fig. 11.37 Validation of the Wang (1995) model against force-deflection data from a series of

side impact tests performed by Viano (1989)


Fig. 11.38 Validation of the Wang (1995) model against force-time data from a series of side

impact tests performed by Viano (1989)

Fig. 11.39 Computed

deformation of the thorax at

the level of the lower

sternum for a 4.4 m/s lateral

impact, as predicted by the

Wang (1995) model

a 4.4 m/s impact was computed. A cross-sectional view of the model at the level of

the lower sternum is shown in Fig. 11.39. Although the validation is acceptable, the

Wang model needed improvements, such as more reliable dynamic material properties,

fracture prediction of the ribs and a more detailed modeling of muscles over

the rib cage.

To study the mechanism of aortic rupture due to a thoracic impact, Shah et al.

(2001) developed a finite element model of the aorta. The model by Wang (1995)

was modified and improved upon by simulating the aorta as a cylindrical airbag

filled with a linear fluid (water) which is incompressible. The initial pressure of the


Fig. 11.40 Modified thoracic model by Shah et al. (2001). The model is on the right. It is

compared to thoracic anatomy shown on the left. SVC stands for superior vena cava. The color

of the arrows matches that of the words below the figure (courtesy of Dr. Chirag Shah)

fluid was 16 kPa. The membrane mesh of the aorta was greatly refined so that the

wall stress could be accurately computed. The organs on the right side of the thorax

were improved because in the Wang model all impacts were on the left side. With

this improvement, the model could simulate impacts from any direction. The

number of nodes increased to 19,760 and there were 21,399 shell elements and

4163 solid elements. The improved model is shown in Fig. 11.40 which compares

the model components to the human anatomy, as identified by arrows of the same

color. The model of the thoracic aorta is shown in Fig. 11.41 which also shows the

aortic isthmus and the ligamentum arteriosum, the remnant of an artery between the

aorta and the pulmonary artery that ceases to work as a blood vessel three weeks

after birth and becomes a ligament. The material properties used were very similar

to those proposed by Wang (1995). The only major change was the density of the

aorta. It was doubled to 4.00E-06 kg/mm 3 to compensate for the lack of inertia of

the linear fluid inside the aorta.

Shah et al. (2004) extended the thoracic model to a torso model that included the

shoulder, thorax, and abdomen. The shoulder model was developed by Iwamoto

et al. (2000) and the abdomen model was developed by Lee and Yang (2001).

A rigid head and rigid lower extremities were attached to the torso to form a wholebody

human model, consisting of 126,536 elements and 94,406 nodes. It was called

the Wayne State Human Model 04-1 (WSHM04-1). Its weight was 75.3 kg. This

model was validated against several sets of experimental data, including side and

frontal impacts to the thorax. Data from lateral pendulum tests conducted by Viano

(1989) were used to validate the thoracic model at an impact speed of 6.5 m/s. The

simulation is shown in Fig. 11.42 and model results are compared to experimental


Left Common Carotid Artery

Brachiocephalic Trunk

Left Subclavian Artery

Aortic Arch

Aortic Isthmus

Aortic

Isthmus

Ascending Aorta

Ligamentum Arteriosum

Aortic Root

Aortic Valve

Mid Descending Aorta

Ligamentum

Arteriosum

Aortic Arch

Level of Hiatus

Fig. 11.41 Model of the thoracic aorta in the thoracic model by Shah et al. (2001)

Fig. 11.42 The Shah

(2007) torso model

simulating an oblique

lateral pendulum impact to

the abdomen, reported by

Viano et al. (1989). (A)

Initial set-up. (B)

Kinematics at time

of peak force


5

4

Model

Upper Bound

Lower Bound

Exp. Curves

Force (kN)

3

2

1

0

0 20 40 60 80 100 120 140 160

Deflection (mm)

Fig. 11.43 Validation of the torso model by Shah (2007) in terms of an abdominal force deflection

curve against data generated by Viano (1989)

5

Model

Exp. Curves

4

Force (kN)

3

2

1

0

0 10 20 30 40 50 60

Time (ms)

Fig. 11.44 Validation of the torso model by Shah (2007) in terms of an abdominal force-time

curve against data generated by Viano (1989)

data in Fig. 11.43 (Force-deflection curves) and in Fig. 11.44 (Force-time curves).

The correlation was acceptable. Additionally, the model was validated against

frontal pendulum impact data developed by Kroell et al. (1974). Figure 11.45

shows the frontal impact simulation and Fig. 11.46 (Figure 2.12 in Shah’s


Fig. 11.45 The Shah (2007) torso model simulating a frontal pendulum impact to the thorax,

reported by Kroell et al. (1974). (A) Initial set-up. (B) Kinematics at time of peak force

5

4

Chest frontal pendulum impact

Model

Upper Bound

Lower Bound

Exp. Curves

Force (kN)

3

2

1

0

0 20 40 60

Deflection (mm)

80 100

Fig. 11.46 Validation of the torso model by Shah (2007) against the thoracic force-deflection

curves developed by Kroell et al. (1974)


Dissertation, p. 36) shows a comparison of the force-deflection curves. Most of the

predicted response fell within the Kroell corridors. Many details of the model are

not discussed and the reader is encouraged to consult the Shah dissertation

(Shah 2007). Unfortunately, nothing was mentioned about stresses or strains in

the peri-isthmic region of the aorta for these simulations.

In addition to the models by Wang (1995) and Shah (2007), there were thoracic

models by Plank and Eppinger (1991), Huang et al. (1994a, b), Lizee et al. (1998),

and Kimpara et al. (2005). The Plank and Eppinger model was not validated and

was too compliant. There are two models by Huang et al. (1994a, b), the first being a

MADYMO model and the second a finite element model. Both were validated

against experimental data and both will be discussed in Chap. 16 (Sect. 16.4). The

model by Lizee et al. (1998) was one of the first whole-body finite element models

developed to simulate occupant response in an automotive crash. It is a first

generation model attempting to reproduce experimentally measured forces and

displacements and model predictions for the thorax were compared with experimental

data, the source of which was not provided. The model by Kimpara et al.

(2005) simulated human thoracic responses of a 5th percentile female to lateral and

oblique impact, frontal impact and high speed ballistic breast impact. Appropriate

anatomical features and material properties of tissues were used to simulate the

female thorax. The model was validated against female side impact data provided

by Viano (1989), female frontal impact data obtained by Kroell et al. (1974), and

breast ballistic impact data taken from Wilhelm (2003). Even though there were no

experimental data from a 5th percentile female, the model predictions were reasonably

close to the measured data. The need for more female cadaveric data was

highlighted by this model.


Much research has been done on thoracic response and tolerance to frontal and

lateral impact. Cadaveric testing played a pivotal role in the acquisition of crucial

data needed to define response and tolerance and in the understanding of the

mechanisms of injury. Although tolerance data for the rib cage were based largely

on rib fractures, much information on aortic rupture was also obtained through the

use of cadavers. The cadaveric response data were used to improve anthropomorphic

test devices (dummies) which have a human-like response, albeit the dummy

chest is stiffer than the human chest, especially at lower speeds of impact.

The availability of validated models should allow the automotive designer to

come up with safe and reliable airbag and belt systems at a minimal cost. The trend

towards the use of models in place of actual physical testing should be accelerated

now that models are becoming more reliable.



11.1. The three-inch chest deflection limit for frontal impact is based on:

[] (i) No rib fractures occurring for 3 in. of chest deflection

[] (ii) A 32% chest compression which corresponds to a 3 in. deflection

and an AIS of 3

[] (iii) Flail chest occurring well over 50% of the time

[] (iv) Deflection being a component of the Viscous Criterion (V*C)

[] (v) An injury severity of AIS 4 or greater

11.2. Kroell et al. (1971, 1974) tested many cadavers at the University of California,

San Diego

[] (i) The principal aim of their research was to study spinal response to

impact

[] (ii) Their results could not be used to design a human-like crash

dummy

[] (iii) The cadavers used were embalmed

[] (iv) A 12-inch diameter metal impactor was used

[] (v) None of the above

11.3. Thoracic injury due to side impact can involve many organs. Select the

correct answer:

[] (i) Rib fractures occur only on the impacted side of the thorax

[] (ii) Lung injuries can be caused by fractured ends of ribs

[] (iii) Aortic rupture can occur

[] (iv) (i) and (ii)

[] (v) (ii) and (iii)

11.4. The following statements are related to the anatomy of the thorax. Select the

incorrect statement:

[] (i) The rib cage consists of 12 pairs of ribs

[] (ii) The sternum is made up of three different bones

[] (iii) The first seven pairs of ribs are connected directly to the sternum

[] (iv) The clavicles are attached to the sternum

[] (v) There are two pairs of floating ribs

11.5. The heart has the following anatomical features. Select the incorrect

statement:

[] (i) The heart is composed of a special type of muscle known as cardiac

muscle

[] (ii) The heart has four chambers

[] (iii) The heart has 2 one-way valves

[] (iv) The pulmonary artery carries non-oxygenated blood

[] (v) The coronary arteries are branches of the ascending aorta


11.6. Direct non-penetrating impact to the sternum with a small high speed

projectile can cause the heart to go into ventricular fibrillation

[] (i) The cause has not been firmly established

[] (ii) The impact needs to occur at the instant of the P-wave in the EKG

cycle

[] (iii) Revival of victims has generally not been successful


[] (v) (i) and (iii)

11.7. The heart has the following anatomical features. Select the incorrect

statement

[] (i) Venous blood enters the right atrium from the vena cava

[] (ii) The pulmonary vein carries oxygenated blood back to the heart

from the lungs

[] (iii) The right ventricle pumps blood into the aorta

[] (iv) Blood pressure is higher in the ventricles than in the atria

[] (v) Semilunar valves control blood flow to and from the ventricles

11.8. Flail chest is a serious thoracic injury

[] (i) It is diagnosed when the chest plate retracts upon inspiration

[] (ii) It is due to multiple rib fractures but the number of ribs fractured

necessary to cause a flail chest has not been established

[] (iii) Bilateral flail chest is a life-threatening injury

[] (iv) (i), (ii), and (iii)


11.9. Injuries to the lung are seen in automotive crashes

[] (i) Laceration of the lung can occur when the lung is injured by ends of

fractured ribs

[] (ii) Hemorrhage in the lung is called a hemothorax

[] (iii) If the lung cannot maintain a vacuum because the chest wall is

punctured, the condition is a pneumothorax

[] (iv) Recovery from lung injuries is generally complete with no residual

effects

[] (v) All of the above

11.10. Aortic rupture is a life-threatening injury

[] (i) It usually occurs at sites in the isthmus of the aorta

[] (ii) One hypothesized site is the attachment of the ligamentum

arteriosum to the aorta

[] (iii) The tears are always longitudinal because the aorta is stronger in

the transverse direction




11.11. The cadaver has been frequently used to assess the effect of blunt impact to

the thorax. The possible deficiencies in using the cadaver as a surrogate are:

[] (i) Ventricular fibrillation cannot be determined

[] (ii) Flail chest cannot be firmly established

[] (iii) Lung injury from blast waves cannot be established

[] (iv) (i), (ii), and (iii)


11.12. Criteria for chest injury for frontal impact can take several forms. Select the

correct answer:

[] (i) V*C ¼ 2.0 for a 25% probability of an AIS 4+ injury

[] (ii) Thoracic trauma index (TTI) ¼ 75 g

[] (iii) T12 acceleration in excess of 60 g for less than 3 ms

[] (iv) Chest compression of 4 in.

[] (v) Chest compression of 40%

11.13. Thoracic response to frontal impact by a 152-mm diameter impactor was

obtained by Kroell et al. in the 1970s. Response corridors were obtained

from these test data

[] (i) The corridors form the basis for the design of the Hybrid III dummy

chest

[] (ii) The stiffness of the Hybrid III chest was increased slightly because

the cadaveric data did not simulate human muscular response

[] (iii) Volunteer test data provided by Patrick show that the increase in

stiffness in the living human was negligible

[] (iv) The increased stiffness of the Hybrid III chest represents an inability

to design a human-like dummy chest


11.14. Response of the thorax to static and dynamic shoulder belt loading was

studied by several investigators

[] (i) None of them used human cadaver

[] (ii) Static volunteer data were inconsistent among investigators

[] (iii) Post-mortem dynamic pig stiffness values were higher than the

dynamic volunteer data

[] (iv) (i), (ii), and (iii)

[] (v) (i) and (ii)

11.15. The following injuries to the thorax are rated as AIS 3

[] (i) Two to three rib fractures

[] (ii) Intima tear of the aorta

[] (iii) Four or more rib fractures with a stable chest

[] (iv) Lung contusion

[] (v) (iii) and (iv)


11.16. For frontal chest impact, a chest deflection of 32.6% corresponds to

[] (i) Three to four rib fractures

[] (ii) A V*C of 2.0 for a 25% probability of an AIS 4+ injury

[] (iii) A chest deflection of 3 in. in a 50th percentile male

[] (iv) (i) and (iii)


11.17. Laboratory research in impact biomechanics

[] (i) m 2 y 2 ¼ k 12 (y 1 y 2 ) k 23 (y 1 y 3 ) kve 23 (y 2 y 4 ) c 23 (y 2 y 4 )

[] (ii) m 2 y 2 ¼ k 12 (y 1 y 2 ) k 23 (y 2 y 3 ) kve 23 (y 3 y 4 ) c 23 (y 2 y 4 )

[] (iii) m 2 y 2 ¼ k 12 (y 1 y 2 ) k 23 (y 2 y 3 ) kve 23 (y 2 y 4 ) c 23 (y 2 y 3 )

[] (iv) m 2 y 2 ¼ k 12 (y 1 y 2 ) k 23 (y 2 y 3 ) kve 23 (y 3 y 4 ) c 23 (y 2 y 4 )

[] (v) m 2 y 2 ¼ k 12 (y 2 y 1 ) k 23 (y 2 y 3 ) kve 23 (y 2 y 4 ) c 23 (y 2 –y 4 )

11.18. Modeling of the thorax can have several goals. Among them are:

[] (i) Study of injury to the viscera of the thorax

[] (ii) Simulate non-automotive impact events

[] (iii) Use it to replace the Hybrid III dummy entirely

[] (iv) All of the above

[] (v) (i) and (ii)

11.19. The thoracic model developed by Wang et al. (1995) has the following

features:

[] (i) It is a finite element model capable of simulating static loading only

[] (ii) It does not simulate any abdominal organ

[] (iii) It assumes non-linear tensile and compressive response for the

heart and lungs

[] (iv) It does not simulate the thoracic spine as a column of vertebrae and

discs


References 405

11.20. Frontal response of the Hybrid III dummy in the plateau region of the forcedeflection

curve was increased to account for muscle effect in the living

human

[] (i) This increase is justifiable because the data to design the dummy

were obtained from cadavers

[] (ii) This is not justifiable because there is evidence that living human

response yields the same plateau

[] (iii) There are no volunteer impact test data to support the increase

[] (iv) There are data from several volunteers to support the increase



Prob

Ans

1 (ii)

2 (v)

3 (v)

4 (iii)

5 (iii)

6 (v)

7 (iii)

8 (iv)

9 (v)

10 (iv)

11 (iv)

12 (iii)

13 (v)

14 (v)

15 (v)

16 (iv)

17 (iii)

18 (v)

19 (v)

20 (ii)

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Chapter 12

Impact Biomechanics of the Abdomen

The abdominal organs are located under the dome-shaped diaphragm and most of

the organs have no skeletal protection. The organs directly under the diaphragm

have minimal protection from the lower ribs which have cartilaginous connections

to the sternum and are not very strong. However, these organs are vulnerable to

injury in an automotive crash and a delayed diagnosis of severe trauma can be fatal.

Thus, tolerance of the abdomen to blunt trauma is a concern for automotive safety

engineers. The topic is covered quite completely by Rouhana (1993) in a book

chapter that details almost all aspects of the biomechanics of abdominal injury. It is

recommended reading for anyone interested in the details of abdominal injury due

to blunt impact.

12.1 Brief Anatomical Review

The abdomen is a large cavity bounded by the diaphragm above and the pelvis

below. It is filled with a variety of solid and hollow organs. The solid organs are the

liver, spleen, pancreas, kidneys, adrenal glands, and ovaries (in the female). The

hollow organs are the stomach, the small and large intestines, urinary bladder, and

the uterus (in the female). The lower rib cage partially covers the liver on the right

and the spleen and stomach on the left, as shown in Fig. 12.1. A frontal view of the

organs of the torso (thorax and abdomen) is shown in Fig. 12.2. The relative

position of the abdominal organs with respect to the rib cage, spine, and pelvis

can be estimated from this figure. In particular, the approximate location of the

kidneys relative to the rib cage and the major abdominal organs can also be deduced

from it. The lower rib cage affords some protection to the upper abdominal organs,

such as the liver and the spleen. If, however, the impact is severe enough to fracture

the lower ribs, they can become as source of injury for these organs. Those in the

mid and lower abdomen have no skeletal protection.



409

410 12 Impact Biomechanics of the Abdomen

Cut edge of diaphragm

Falciform ligament

Right lobe of liver

Gallbladder

Cut edge of parietal peritoneum

Ascending colon

Right paracolic gutter

Left lobe of liver

Spleen

Stomach

Round ligament of liver

Descending colon

Transverse colon

Internal oblique (cut)

Transversus abdominis (cut)

Left paracolic gutter

Small intestine

Cecum

Psoas major

Iliacus

Inguinal ligament

Bladder

Obturator membrane

Obturator canal

Abdominal viscera (greater omentum removed)

Fig. 12.1 Front view of the organs of the abdomen (taken from Drake et al. (2008)). Reprinted

from R.L. Drake, A.W. Vogl, A.W.M. Mitchell, R.M. Tibbitts, P.E. Richardson, Gray’s Atlas of


For diagnostic purposes, the abdomen is divided into regions or quadrants, as

shown in Fig. 12.3. The top plane is at the level of the 9th rib and the lower one

passes through the 5th lumbar vertebra. The left and right sagittal (vertical) planes

pass through the mid-clavicle and divide each region into a central zone and two

lateral zones.

12.1.1 Solid Abdominal Organs

The liver is the largest of the three solid organs, located just below the diaphragm. It

weighs 1.3–1.5 kg and has two lobes. The right lobe is about six times as large as the

left. The main function of the liver is to store proteins and sugars for the body.

12.1 Brief Anatomical Review 411

Fig. 12.2 Frontal view of organs of the torso to show the relative position of the abdominal organs

in relation to the rib cage and, in particular, the position of the kidneys with respect to the other

abdominal organs (taken from Wikipedia.org and drawn by Mikal Haggstrom)


Hypochondriac

Hypochondriac

Lumbar

Epigastric

Umbilical

Transpyloric

plane

Lumbar

Hypogastric

Transtubercular

plane

Iliac

Iliac

Right sagittal

plane

Left sagittal

plane

Fig. 12.3 Quadrants or regions of the abdomen

It also forms blood cells, manufactures heparin, and secretes bile. Beneath the thin

peritoneal layer, the liver is covered by a strong fibroelastic membrane called

Glisson’s capsule. Its interior is composed of a soft parenchymal substance that is

homogeneous and easily injured. The spleen is on the left side of the upper region

between the diaphragm and the stomach and between the 7th and 9th ribs. Its weight

can vary from 40 to 400 g. It recycles old red blood cells and provides storage for

platelets and white blood cells. It has a relatively large blood supply. There is thin

capsule covering the spleen that is composed of a mixture of elastic fibers and

collagen. The thickness is less than 1 mm (Rodrigues et al. 1999). The kidneys are

bean-shaped and are located in the rear of the cavity, spanning the distance between

T12 and L3. Its length is about 115 mm. Each kidney weighs from 130 to 150 g and

12.2 Abdominal Injuries 413

the total blood flow to both organs is 25% of the cardiac output. Renal function

consists of elimination of toxins in the blood, control of blood pH, and maintenance

of normal fluid and electrolyte balance. Structurally, the kidney is protected by

a strong fibrous capsule. Its parenchyma is composed of filtering units called

glomeruli and tubules. The pancreas is located in the rear of the upper zone, in

the left central region. It is about 140 mm long and weighs approximately 90 g. Its

functions are digestive and control of glucose (sugar) level in the blood. The

pancreas has a firm rubbery consistency and has a lobulated appearance. Each

macroscopic lobule consists of many microscopic lobules or functional units with

an exocrine (duct secretion) function.

12.1.2 Hollow Abdominal Organs

The stomach is a hollow organ on the left side of the upper region. It has the shape

of the letter “J” and its size is variable. Food enters through the esophagus and exits

through the pylorus sphincter as chyme, after it is partially digested. Digestion in

the form of absorption of nutrients and minerals continues in the small intestine,

starting at the duodenum. The small intestine is about 7 m long and is coiled

arbitrarily in the central and lower part of the abdomen. The other two named

segments are the jejunum and ileum.

In the large intestine or colon, water, the remaining nutrients, and salt are

extracted over a length of about 1.5 m (5 ft). There are four segments—the

ascending, transverse, descending, and sigmoid colon.

The urinary bladder is a sac behind the pubic symphysis of the pelvis, in the

lower abdomen. When full, its major diameter is about 12 cm.

The uterus in the female is a thick-walled muscular organ in the pelvis, behind

the urinary bladder. It is pear-shaped and weighs about 35 g. Several ligaments hold

it in place.

12.2 Abdominal Injuries

In blunt impact, solid organs tend to be more frequently injured than hollow organs,

presumably because the latter can undergo large deformations without sustaining

high tissue strains. The commonly injured solid organs are the liver, spleen, and

kidney (Yoganandan et al. 2000). They can be injured in frontal as well as lateral

impacts due to contact with the steering wheel, instrument panel, and vehicular side

structures. Belt restraint systems tend to be a cause for abdominal injury which is

reduced in frequency by the use of a combination of a three-point belt and an airbag.

Leung et al. (1982) reported on French accident data involving lapbelt-induced lower

torso injuries. There were 1542 front seat occupants restrained by a three-point belt

and there were only 35 abdominal injuries in the AIS 3–5 range. Bondy et al. (1981)


provided a breakdown of abdominal injuries in vehicular occupants between the

years 1977 and 1979, based on data from the National Crash Severity Study (NCSS).

There were 1519 abdominal injuries of all severities. These injuries constituted 2.6%

of all injuries. In the AIS range of 3–5, however, abdominal injuries represented

14.6% of all injuries. For frontal impact, Bondy et al. (1981) found a total of

695 abdominal injuries (AIS 1–5) and 314 for AIS 3–5. There were 120 hepatic

injuries, 76 splenic injuries, and 58 renal injuries in the AIS 3–5 range. The digestive

tract and the urogenital organs sustained only 58 injuries in this AIS range. For all

impact directions, the steering wheel was the cause of 30% of the abdominal injuries,

mostly among unrestrained occupants. Restrained occupants sustained 7% of all

abdominal injuries and 2.6% of AIS 3–5 injuries. For a more detailed study of the

epidemiological literature on abdominal injuries, please see Klinich et al. (2008).

12.3 Abdominal Injury Mechanisms

Under compressive loading, solid organs are more at risk than hollow organs because

higher stresses are developed in solid organs for a given degree of compression. The

compressive forces are produced when contact of the abdomen is made with interior

surfaces of vehicles or with belt restraint systems. When the lapbelt rides above the

pelvic notch (the anterior superior iliac spine), it compresses the abdominal contents

behind it during a frontal crash, causing injury. If the lapbelt is worn too loosely, the

lower extremities tend to slide forward in a frontal crash. This is known as submarining

during which the lapbelt slides off the pelvis. The resulting injuries are sensitive

to the amount of compression and to the velocity of compression.

12.4 Mechanical Response of the Abdomen

Mechanical response data were obtained by various researchers for both frontal and

lateral impact. The response was elicited from cadaveric subjects and anesthetized

animals for frontal and side impact. Most of the studies involved localized impacts to

the abdomen so that a specific region of the abdomen could be targeted. For example,

impacts to the upper abdomen target the solid organs while impacts to the lower

abdomen investigate the mechanical response and injury characteristics of the intestines.

12.4.1 Abdominal Response to Frontal Impact

For frontal impact, there have been several human studies and some animal studies on

the response of the lower abdomen to impact loading, motivated by the impact of the

lower rim of the steering wheel against the lower abdomen of unrestrained drivers.

Klinich et al. (2008) summarized these studies in an UMTRI Report. The frontal

impact studies are shown in Table 12.1. Some of the studies are discussed here,

12.4 Mechanical Response of the Abdomen 415

Table 12.1 Summary of frontal abdominal tests performed using cadaveric and porcine subjects (taken from Klinich et al. (2008))

Cavanaugh et al.

(1986)

Morgan

et al. (1987)

Nusholtz et al.

(1988) Miller (1989) Hardy (2001)

Study Horsch et al. (1985)

Subjects 17 anesthetized 12 human 12 human 6 human cadavers 25 anesthetized 9 human 1 human

porcine

cadavers cadavers

porcine

cadavers cadaver

Subject Free-back Free-back Sled buck Free-back Fixed-back Free-back Fixed-back Fixedback

position

unrestrained

supine

# Tests 17 12 12 48 29 9 7 4

Wheel Rigid bar Rigid bar Wheel

Impactor Wheel Rigid bar Wheel Semi-circular

tube

Impactor Rim: Soft/stiff/rigid

Column angle:

20 /30

Spokes: vert./horiz.

25 mm diam.

32 kg (n ¼ 8)

65 kg (n ¼ 4)

Velocity 8.9 m/s 4.87–13.02 m/s 6.7 m/s

9.4 m/s

11.1 m/s

Location 5 cm below xiphoid

(level of liver)

Soft tissue

injuries

Liver lacerations Liver lacerations

Mesenteric

laceration

Rim: Stiff 18 kg Production-level

90 to body

2–3 m/s (n ¼ 43)

6.5 m/s (n ¼ 5)

25 mm diam.

48 kg

1.7–12.4 m/s 6 m/s (n ¼ 5)

9 m/s (n ¼ 4)

L3 Ribs 8–10 L2 L4 L3 (n ¼ 6)

T11 (n ¼ 3)

Liver

lacerations

Liver lacerations

Kidney

contusions

Mesenteric tear

Stomach

contusion

Diaphragm

lacerations

Jejunum

contusion

Cecum rupture

Lg. Bowel transection

Rectum rupture

Spleen transection

Jejunum transection,

laceration

Mesentery laceration,

contusion

Liver lacerations

Spleen lacerations

Diaphragm

lacerations

Cecum

lacerations

25 mm diam.

48 kg

3 m/s (n ¼ 2)

6 m/s (n ¼ 3)

9 m/s (n ¼ 2)

Shaw

(2004)

4 human

cadavers

Rim:

Stiff

64 kg

45 to

body

4 m/s

L3 T12

None None


Table 12.2 Characteristics of the cadavers used in the frontal lower abdominal impact tests

conducted by Cavanaugh et al. (1986)

Test

no.

Cadaver

no.

Sex

Age

(years)

Stature

(m)

Body

mass

(kg)

Scaling

factor,

Lamda a

Cause of death

14 458 M 56 1.82 68 1.037 Small cell carcinoma of the

lung

19 473 F 43 1.59 53 1.130 Asphyxia due to carbon monoxide

poisoning

24 525 M 57 1.87 45 1.187 Ischemic anoxic brain injury,

caustic material ingestion,

diabetes mellitus, pneumonia

28 578 F 57 1.63 75 1.002 Cardiopulmonary arrest

33 590 F 51 1.63 68 1.030 Congestive heart failure,

arteriosclerotic heart disease,

renal insufficiency

37 684 M 50 1.69 88 0.954 Cardiac arrest, massive acute

MI

41 712 F 51 1.59 55 1.115 Carbon monoxide poisoning

43 721 M 66 1.70 70 1.026 Cardiopulmonary arrest, arteriosclerotic

heart disease,

diabetes mellitus

45 731 M 58 1.76 92 0.938 Cardiac arrest

47 739 M 43 1.72 61 1.075 Cardiac arrest, end stage heart

failure, cardiomyopathy

57 751 M 64 1.84 90 0.945 Cardiac arrest

61 786 M 60 1.80 79 0.987 Atherosclerotic cardiovascular

disease

1=3

a Lamda ¼

76:0kg

Body Mass of Test Subject

Cavanaugh et al. (1986) impacted the lower abdomen of cadaveric specimens

with a 2.5-cm (1-inch) bar which was driven into the abdomen by a 32- or 64-kg

pendulum at the level of L3, in the umbilical region. The impact bar was positioned

over L3 in the umbilical region so that it did not impact the rib cage with the

cadaver seated in an erect position. The organs impacted by the bar were the head of

the pancreas, the lower portion of the kidneys and duodenum, the inferior vena

cava, and the abdominal aorta. Since L4 is the approximate level of the top of the

iliac crests, the impacting bar did not damage the pelvis. The study involved the

testing of 12 cadavers, eight males and four females. Their age range was 43–66

years and their body weight ranged from 45 to 90 kg (see Table 12.2). Frontal

impact response of the lower abdomen is shown in Fig. 12.4. There were seven high

velocity tests at impact speeds ranging from 8.54 to 13.01 m/s (average of 10.4 m/s)

and five low velocity tests at 4.87 to 7.24 m/s (average of 6.1 m/s). The impact

kinetics are shown in Table 12.3. The mean stiffness of the abdomen for the highspeed

tests was found to be 53.9 kN/m. At the lower speed, the stiffness averaged


10000

8000

FORCE (N)

5000

4000

2000

0

0 40 80 120 160 200 240

DEFLECTION (MM)

Fig. 12.4 Abdominal response to frontal impact by a 2.54-cm diameter bar (adapted from

Cavanaugh et al. 1986)

Table 12.3 Impact kinetics—lower abdominal impacts (taken from Cavanaugh et al. (1986))

Test

no.

Impactor

mass (kg)

Impactor

velocity m/s

(mph)

Impactor

momentum

(kg-m/s)

Impactor

kinetic

energy (J)

Lower

abdominal

stiffness

(kN/m)

Peak

force

(kN)

14 31.24 6.84 (15.3) 214 731 34.2 3.30

19 31.24 5.00 (11.2) 156 391 25.5 2.59

24 31.24 4.87 (10.9) 152 370 25.2 3.34

28 31.52 6.66 (14.9) 210 699 20.2 2.39

33 31.52 7.24 (16.2) 228 826 26.9 4.49

37 31.30 10.59 (23.7) 331 1755 84.0 7.45

41 63.56 8.54 (19.1) 543 2318 61.3 9.49

43 63.56 9.07 (20.3) 576 2614 72.1 9.06

45 63.56 9.79 (21.9) 622 3046 101.2 11.59

47 63.56 10.15 (22.7) 645 3274 77.6 14.33

57 31.52 13.01 (29.1) 410 2667 54.3 10.99

61 31.52 11.62 (26.0) 366 2128 63.7 8.89

26.4 kN/m and is remarkably lower than that for the high velocity group, indicating

that the response is sensitive to the velocity of impact.

In an unpublished related study (an UMTRI Report) by Nusholtz et al. (1988),

seven cadavers were struck with the lower portion of a steering wheel in the

thoraco-abdominal region. The mass of the pendulum used was 25 kg. Many of

the 83 impacts conducted were of minor severity (low velocity). There were five

high velocity lower abdominal tests in the range of 6.5–10.8 m/s. The force-

Force (N)

8000.0


6000.0 10000.0

66M006

86M016

86M026

86M042

86M052

86M062

0.0 2000.0 4000.0

0.00

4.00

8.00 12.00 16.00 20.00 24.00

Deflection (cm)

Fig. 12.5 Abdominal response to frontal impact by the lower portion of a steering wheel (taken

from Nusholtz et al. (1988))

deflection curves for these tests are shown in Fig. 12.5. There is one additional

curve in the figure for a 3.9-m/s test (Test No. 86M026) which was plotted along

with the high velocity tests. The mean stiffness of the lower abdomen was found to

be 52.7 kN/m. We cannot rely on data from one test to conclude that the abdomen is

not sensitive to impact velocity.

One study involving subhuman primates by Stalnaker and Ulman (1985) was not

included in Table 12.1. In this study, three sets of subhuman primate impact data

acquired by researchers at HSRI (now UMTRI) were analyzed. There were 42 tests

which used six different pneumatically operated impactors and four primate species—the

squirrel, vervet and rhesus monkeys, and the baboon. The impact locations

were the frontal upper, mid, and lower abdomen and left and right sides. For

the frontal lower abdomen, there were five tests using the vervet monkey at

velocities ranging from 12.07 to 15.69 m/s. The mean stiffness was found to be

23 kN/m. The mass ratio, m r , between a 50th percentile man and the vervet monkey

is 76/3.514 ¼ 21.628 and since λ ¼ m r 1/3 , λ ¼ 2.786. It can be shown that the

stiffness ratio, S r , is given by λ 2/3 . Or, S r is approximately equal to 2. Thus, the

abdominal stiffness when scaled to the human level is 46 kN/m. This value is about

15% lower than the actual measured stiffness. Note that the two measured human

stiffness values obtained by two different research groups (Cavanaugh et al. 1986;

Nusholtz et al. 1988) with slightly different impactors are amazingly close.

Stalnaker and Ulman (1985) found a correlation between injury severity and V*C

for all four primate species for abdominal impact. That is, V*C is not species

dependent and is valid for these primates which have a mass ratio of 1–25.75,

implying that V*C can probably be extrapolated to man.


Fig. 12.6 Abdominal force-deflection curves from belt impact at the level of L4, obtained from

13 of the 25 swine tests conducted by Miller (1989)

There was another animal study by Miller (1989) who loaded the abdomen of

25 anesthetized Yorkshire swine with a 5-cm wide belt across the torso at the level

of L4. The animal was supine and supported by a V-shaped frame while a yoke was

used to compress the abdomen dynamically. The belt velocity ranged from 1.6 to

6.6 m/s and the compression ranged from 6 to 70% of the depth of the abdomen.

The animals were sacrificed 60 min after the test and an autopsy was conducted to

determine the extent of injuries sustained. Each injured organ was assigned an AIS

rating. Velocity and compression were determined from an analysis of the highspeed

film taken during the impact so that the Viscous Criterion could be computed.

Abdominal stiffness was also computed. Some of force-deflection curves are

shown in Fig. 12.6. Individual stiffness values were not provided in the paper but

Rouhana et al. (1989) published stiffness data for 13 of the 25 tests done by Miller

(1989). The average stiffness was 23 kN/m. Using 43.6 kg as an average weight for

the swine, the length ratio, λ, is 1.20 and the stiffness ratio between a 50th percentile

man and swine is 1.13. Again, the abdominal stiffness scaled to the human level is

26 kN/m which is comparable to the 26.4 kN/m stiffness obtained by Cavanaugh

et al. (1986) for low velocity impacts (4.87–7.24 m/s). However, the impact

mechanisms for the two studies are very different (5 cm belt vs 2.5 cm rigid bar).

The comparison was made because there were no belt-generated stiffness data from

cadavers.


It is not clear whether scaling animal data to the human level is reliable, as can be

seen from the two examples provided above. Additional data are needed to confirm

the validity of scaling.

12.4.2 Abdominal Response to Lateral Impact

As mentioned in Chap. 11 (Sect. 11.4.2), Viano (1989) conducted a series of

pendulum side impact tests on cadavers, including abdominal impacts. As in the

thoracic impacts, the direction of impact was 30 anterior to the lateral axis of the

cadaver for the abdominal impacts as well. There were again three sets of impacts

of varying severity. The nominal pendulum velocities were 4.5, 6.7, and 9.4 m/s

(10, 15, and 20 mph) and the same procedure as that for the thorax for conducting

multiple impacts on the same cadaver was followed. Abdominal deflection was

measured directly by tracking the motion of the pendulum as there was no rotation

of the abdomen. Response in the form of force-deflection curves is shown in

Fig. 12.7. The same injury functions as those for the chest were computed. The

injuries were assessed based on the number of rib fractures and damage to

the organs of the abdomen for the 14 abdominal impacts that were carried out.

The MAIS ranged from 0 to 4. Logistic plots for V*C, C, and G sp at T12 for MAIS

4+ are shown in Fig. 12.8 with the computed chi square, p and r values. The

abdominal injury criteria for all statistically significant variables are listed in

Table 12.4 for AIS 4 and for a 25% probability of injury. Force and not V*C

appears to be the best predictor for side impact injury. No explanation was provided

by Viano (1989) regarding this anomalous finding.

FORCE (kN)

5

4

3

2

run 19

run 23

run 24

run 30

run 42

run 43

Abdomen

FORCE (kN)

5

4

3

2

run 6

run 8

run 10

run 12

FORCE (kN)

10

8

6

4

run 15

run 20

run 28

run 34

1

1

2

0

0

0

0 5 10 15 0 5 10 15 0 5 10

DEFLECTION (cm)

DEFLECTION (cm)

DEFLECTION (cm)

4.8 m/s 6.8 m/s 9.4 m/s

15

Fig. 12.7 Force-deflection curves for abdominal side impact at three impact severities (taken

from Viano (1989))

12.5 Tolerance of the Abdomen to Impact 421

1

1

1


0.8

0.6

0.4

0.2

Chi 2 = 6.12

P = 0.01

r = 0.60


Chi 1 = 4.6

P = 0.03

r = 0.48

0 0

0.5 1 1.5 2 2.5 3 25 30 35 40 45 50

VC (m/s)

COMPRESSION (%)

0.8

0.6

0.4

0.2


0.8

0.6

0.4

0.2

0

0

Chi 2 = 4.88

P = 0.03

r = 0.53

10 20 30

G sp

40 50

Fig. 12.8 Logist plots of V*C, compression and spinal acceleration at T12 with the computed

values of χ 2 , p, and r (taken from Viano (1989))

Table 12.4 Abdominal

injury criteria (for AIS 4

and for a 25% probability

of injury) (taken from Viano

(1989))

Criterion Value Chi square

V*C 2.26 m/s 6.1

C 46.8% 4.6

G sp at T12 45.6 g 4.9

F 6.87 kN 8.5

12.5 Tolerance of the Abdomen to Impact

Because of the large number of organs in the abdomen, the study of abdominal

tolerance to blunt impact is rather complex. The first study to tackle this issue was

performed by Melvin et al. (1973) who simplified the problem by impacting two

solid organs (liver and kidney) of rhesus monkeys in a materials testing machine

while they were still being perfused by the anesthetized animal. The reason why

the organs needed to be perfused was that their rupture characteristics were

dependent on the internal pressure in the organ. A rigid platen with an area of

11.6 cm 2 (1.8 in 2 ) was used to load the organs at three rates—5, 250, and 500 cm/s.

The displacement of the platen was controlled to yield a strain of 40–75%. At

higher levels of strain and strain rate, both organs were ruptured. According to the

authors, the observed injuries were clinically relevant. The applied loads were of

the order of 450 N (100 lb). A threshold for failure stress or pressure for the liver

was estimated to be about 310 kPa (45 psi). For the kidney, the threshold is higher

but no estimate was provided.

The forces applied to the abdomen in a car crash are distributed to many organs

and structures and are expected to be much higher than those described above. It is

difficult to assess the pressure or force necessary to rupture an abdominal organ

when the abdomen is impacted externally. There have been many studies on

abdominal tolerance, including those describing injury mechanisms, already mentioned

above. In both frontal and lateral impacts, there are multiple sources of injury

and multiple organs are involved. Injury sources include the steering wheel, the

instrument panel (glove compartment), belt restraints, side door, armrest, and


Table 12.5 Tolerance of the

liver to frontal impact by a

rigid impactor

Author(s) Test subject Tolerance AIS

Lau and Viano (1981) Rabbit F ¼ 0.24 kN 3

Horsch et al. (1985) Pig V*C ¼ 0.72 3

Melvin et al. (1973) Rhesus p ¼ 310 kPa 4–5

Table 12.6 Tolerance of the liver to frontal impact by a shoulder belt (based on 25 tests on

porcine subjects)

Criterion Tolerance Injury severity Remarks

Force 3.76 N AIS 4 25% probability of injury

Compression 48.3% AIS 4 25% probability of injury

F max *C max 2.0 kN AIS 4 25% probability of injury

Based on Miller (1989)

Table 12.7 Abdominal tolerance to side impact

Author Criterion Value AIS Organ Test subject

Stalnaker et al. (1975) Compression 54% L 4–5 Upper Abd. Primate & Cadaver

60% R

Rouhana (1986) VC mac 3.15 m/s 3 Liver Rabbit

Rouhana (1986) VC max 2.71 m/s R 3 Upper Abd. Rabbit

3.31 m/s L

Viano (1989) Force 6.73 kN 4 Upper Abd. Cadaver

Viano (1989) V*C a 1.98 4 Upper Abd. Cadaver

a Next best predictor of upper abdominal injury

airbag. There is more tolerance information on solid organs than on hollow organs.

Rouhana (1993) provided eight separate tables on the tolerance of various organs to

frontal and lateral impact, using data from animals and cadavers. The tables are

arranged in terms of the mechanical parameter causing the injury, such as force of

impact, compression or the Abdominal Injury Criterion (V max *C max ). Some of the

data are summarized in Tables 12.5 to 12.7.

For frontal impact, the tolerance of the liver is provided in Table 12.5 in terms of

force, V*C, and pressure. There is a strong correlation of liver injury with the

Viscous Criterion (V*C) based on the work of Viano and Lau (1985). Tolerance to

shoulder belt loading is shown in Table 12.6, using data taken from Miller (1989).

For side impact, Rouhana et al. (1985) found that V max *C max was well correlated

with upper abdominal injury while Viano (1989) found that force was the best

predictor of abdominal injury, as had already been mentioned above. Table 12.7

lists some of the tolerance values for the upper abdomen (and liver), based in part on

a study by Rouhana et al. (1986) using rabbits. Rouhana (1993) has made an

excellent survey of existing knowledge on abdominal tolerance and has provided

information on the tolerance of the liver, kidney, upper abdomen, and lower

abdomen, without specifying the direction of impact. This tolerance information

is summarized in Tables 12.8, 12.9, 12.10, and 12.11. It can be seen from these

12.5 Tolerance of the Abdomen to Impact 423


liver (Rouhana 1993)

Criterion Value range Injury severity

Peak force 0.24–1.56 kN AIS > 3

V max *C max 0.75–3.15 m/s AIS > 3

Compression 16–29% AIS > 3

[V*C] max 1.2–1.24 m/s AIS > 4

Pressure 67–260 kPa AIS > 4

276–320 kPa AIS > 5

F max *C max 0.63–4.5 kN AIS > 3

Energy 36–46 j AIS ¼ 3

Reprinted from Accidental Injury, 1st edn. ed. By A.M. Nahum,

J.W. Melvin, Chapter 16, Biomechanics of abdominal trauma,

S.W. Rouhana, 1993, With permission of Springer


kidney (Rouhana 1993)



V max *C max 5.5 m/s AIS > 3

Pressure 251 kPa AIS > 3

276 kPa AIS > 4




Table 12.10 Tolerance of

the upper abdomen

(Rouhana 1993)



Compression 43.7–60% AIS > 4

V max *C max 1.8–3.8 m/s AIS > 3

[V*C] max 1.98 m/s AIS > 4





Table 12.11 Tolerance of

the lower abdomen

(Rouhana 1993)


Peak force 2.93–3.96 AIS > 3

3.76–4.72 AIS > 4

Compression 37.8–48.4% AIS > 3

48.3–54.2 AIS > 4

V max *C max 3.0 m/s AIS > 3

[V*C] max 1.40 m/s AIS > 4


216–270 kPa AIS > 4





tables that the tolerance range for some of the criteria is rather large and is not

suitable for use in the design of safety equipment. In addition to the natural

variability of biological materials, there is the variability among species and

variability due to age in humans. Criteria involving force and pressure tend to

have the most variability.

12.6 Mechanical Characterization of Abdominal Organs

For the protection of abdominal organs and to enable accurate modeling of the

abdomen, it is necessary to have actual material properties of the organs obtained

from dynamic testing. Tamura et al. (2002) conducted such a study and measured

the material properties of the porcine liver, kidney, and spleen at three different

rates of loading, using a stress relaxation test method. In order to use the data

obtained from this method, it is necessary to introduce briefly the quasi-linear

viscoelasticity theory, commonly known as the QLV theory (Fung 1972). This

theory was formulated to model the behavior of biological soft tissues which exhibit

both an elastic and a viscoelastic response to load. The theory works hand in hand

with a prescribed experiment in which the specimen is loaded rapidly and held so

that the initial stress and the relaxation of the induced stress over time can be

measured. The measured data are used to help determine five constants used in the

QLV theory so that material response to load can be characterized and a stress–

strain curve can be formulated at varying strain rates. The theory is based on a step

function load applied to the specimen but a pure step function is not achievable in

practice. Various methods have been proposed to determine the response of the

material with a finite rise time in the “step” function. Much of the theory is devoted

to the handling of the loading ramp function followed by a period of constant strain.

12.6.1 The QLV Theory

The QLV theory is commonly used to characterize biological soft tissue which

undergoes large deformations and exhibit rate sensitive viscoelastic behavior. As

mentioned above, the theory is based on experimental data collected from loading

specimens at a known rate and monitoring the stress relaxation while it is held at a

constant strain. A stress relaxation function, G(t), is defined to relate stress at any

instant of time to the stress corresponding to an instantaneous strain, as follows:

σðÞ¼Gt

t ðÞ* σ e ðÞ ε

ð12:1Þ

where σ(t) is the stress at time, t,

σ e (ε) is the stress corresponding to an instantaneous strain,

the asterisk (*) represents the convolution of G(t) and σ e (ε), and

G(t) is the reduced relaxation function given by:

12.6 Mechanical Characterization of Abdominal Organs 425

þ

Gt ðÞ¼σðÞ= t σðt 0 Þ ð12:2Þ

where t 0 ¼ the rise time of the ramp strain (see Fig. 12.9)

t 0 + ¼ any time t after t 0

Thus,

þ

Gt ð 0 Þ ¼ 1

According to the QLV theory, the stress at time, t, can be described by summing up

contributions of all past changes:

ð t

σðÞ¼

t

1

Gt ð τ

Þf∂σ e ½ετ

ðÞ=∂εgð∂εðÞ=∂τ

τ Þdτ ð12:3Þ

The term {∂σ e [ε(τ)]/∂ε} is the instantaneous elastic response and the term ∂ε(τ)/∂τ

is the strain history. Also, we can change the lower integration limit to 0 from 1

for the experimental situation.

There have been a number of proposed forms of G(t), beginning with the original

form proposed by Fung (1993). He used a relaxation spectrum and arrived at the

following form for G(t):

Gt ðÞ¼ 1 þ cE 1 ðt=τ 2 Þ E 1 ðt=τ 1 Þ =

1 þ c ln ð τ2 =τ 1 Þ g ð12:4Þ

where E 1 (x) is the exponential integral given by:

E 1 ¼

ð 1

x

ðe x =xÞdx

and

c, τ 1 , and τ 2 are material constants to be determined.

Fig. 12.9 Strain ramp of

duration t 0 with a slope ¼ α.

ε 0 ¼ αt 0 and ε ¼ αt


For the instantaneous elastic response, an exponential approximation was

chosen:

σ e ðÞ¼Ae ε

Bε 1

ð12:5Þ

where A and B are material constants.

We are, thus, left with five material constants that need to be determined, A, B, c,

τ 1, and τ 2 , for the ramp loading shown in Fig. 12.9.

To obtain a usable expression for the stress history in Eq. (12.3), we note that for

the ramp function, the strain history, ∂ε/∂t, is equal to α for t t 0 , and for t > t 0 ,itis

equal to zero. These terms are required for the determination of the stress history

from Eq. (12.3).

We also need to evaluate ∂σ e (ε)/∂ε, using Eq. (12.5):

∂σ e ðÞ= ε ∂ε ¼ ABe Bε

ð12:6Þ

and

ε ¼ αt for 0 t t 0 ;

Substituting the strain history and Eqs. (12.4) and (12.6) into Eq. (12.3) and noting

that ∂ε/∂t ¼ 0 for t > t 0 , we end up with two integrals with different limits of

integration, as follows:

For 0 t t 0 ,

ð t

σðÞ¼ABα

t Gt ð τÞe Bατ dτ ð12:7Þ

0

And, for t > t 0 ,

σðÞ¼ABα

t

As for G(t), we can represent the relaxation phenomenon by

where

and,

ð t 0

0

Gt ð τÞe Bατ dτ ð12:8Þ

Gt ðÞ¼P ðln tÞ þ Q

P ¼ c= ðc lnτ 2 c lnτ 1 Þ


Q ¼ Pð1=c γ þ lnτ 2 Þ

P and Q are positive constants and γ is the Euler constant (γ ¼ 0.5772).

Thus, in theory, algebraic expressions for σ can be found for the integrals in

Eqs. (12.7) and (12.8).

The constants, A, B, c, τ 1, and τ 2 , are determined by minimizing the parameter, S,

given by

S ¼ X n

i¼1

σ σ i i 2

where S is the sum of the squares of the differences between the theoretical values

of σ and the measured values, σ i , and n is the total number of experimental values

available. A computer program is written to accomplish this task.

12.6.2 Stress–Strain Curves for Solid Abdominal Organs

(Tamura et al. 2002)

Fresh porcine livers, kidneys, and spleens were procured from a local slaughter

house shortly after the animals were killed and brought to the lab to undergo

compressive relaxation tests at three different strain rates—0.005, 0.05 and 0.5 s 1 .

The test specimens were rectangular in shape, 20 20 10 mm, and were loaded

in the anteroposterior direction. Liver specimens were too soft to cut accurately and

were cut while frozen. A side study was done to ensure that the properties of the liver

had not changed due to freezing. To conduct the relaxation tests, the specimens were

placed on an aluminum platform and immersed in normal saline at 36 C in an

environmental chamber, as shown in Fig. 12.10. To perform the relaxation test

with a short rise time for the applied load, the loading head was placed two millimeters

above the specimen and driven into it to produce a strain of 40, 50, and 70% in the

Fig. 12.10 Photograph of

the test setup for performing

relaxation tests on solid

abdominal specimens

(taken from Tamura et al.

(2002))


liver, kidney, and spleen, respectively. The loading duration was 0.1 s and the loading

speed was 60, 70, and 90 mm/s. Force and displacement were measured and sampled

at 100 Hz. There were 10 liver specimens, 11 kidney specimens, and 9 spleen

specimens. Next, a series of rate dependent compression tests was conducted. It

was necessary to pre-condition the specimens five times at a speed of 0.5 mm/s to a

peak strain of 20, 30, and 40% for the liver, kidney, and spleen, respectively. Each

specimen was allowed to recover 100 s before the actual test was conducted. Since

Cauchy’s stress needed to be calculated, the instantaneous cross-sectional area was

computed by dividing the volume of the specimen by the instantaneous height of the

specimen, assuming that its volume remained constant. Note that Cauchy stress is

defined as:

σðt; εÞ ¼ force=deformed cross-sectional area ¼ Ft ðÞ=Aðt; εÞ ð12:9Þ

In the actual test to failure, the strain rates were 0.005, 0.05, and 0.5 s 1 . In the

relaxation tests, the strain, ε 0 ,att ¼ t 0 , was maintained constant for several hundred

seconds. Thus, from Eq. (12.2),

Gt ðÞ¼σðt; ε 0 Þ=σðt 0 ; ε 0 Þ ð12:10Þ

where 0 < t 0 < 0.1 s and t > t 0

A reduced relaxation function, G(t), obtained from liver tests, is shown in

Fig. 12.11. G(t) for the spleen and kidney are shown in Figs. 12.12 and 12.13.

Since R 2 is close to unity, we conclude that the QLV theory is suitable for the

determination of material properties of solid abdominal organs. As described in

Sect. 12.6.1 above, the five constants, A, B, c, τ 1 , and τ 2 , were determined by a

minimization procedure. These constants can be determined in the same way for the

spleen and the kidney and the material constants for the reduced relaxation function

are summarized in Table 12.12 and the material constants for the elastic response

are shown in Table 12.13. The stress–strain plots for the three organs are shown in

Figs. 12.14, 12.15, and 12.16 for all three strain rates. The tissues were also loaded

to failure in compression. It was found that the ultimate compressive strain was

independent of strain rate for all three organs, as shown in Fig. 12.17.

Fig. 12.11 The reduced

relaxation function G(t) for

the liver (taken from

Tamura et al. (2002))

G(t)

experiment theory

1

G(t) = -0.0791Ln(t) + 0.6789

0.8

R 2 = 0.9987

0.6

0.4

0.2

0

0.01 0.1 1 10 100 1000

Time (sec)




the kidney (taken from


G(t)

experiment theory

1

G(t) = -0.0791Ln(t) + 0.6821

0.8

R 2 = 0.9997

0.6

0.4

0.2

0

0.01 0.1 1 10 100 1000

Time (sec)



the spleen (taken from


G(t)

experiment theory

1

G(t) = -0.0783Ln(t) + 0.5759

0.8

R 2 = 0.9927

0.6

0.4

0.2

0

0.01 0.1 1 10 100 1000

Time (sec)

Table 12.12 Material

constants for reduced

relaxation functions (taken

from Tamura et al. (2002))

Liver Kidney Spleen

c 0.3553 0.3254 0.4244

τ 1 (s) 0.0307 0.0320 0.0079

τ 2 (s) 570.5 458.0 261.9

A 0.0791 0.0791 0.0783

B 0.6789 0.6821 0.5759

R 2 0.9987 0.9997 0.9927

Table 12.13 Material

constants for elastic response

fitted to the QLV theory


(2002))

α C D

Liver 0.005 s 1 1.677E+04 6.78

0.05 s 1 1.897E+04 6.14

0.5 s 1 1.268E+04 6.83

Kidney 0.005 s 1 9.55E+03 10.09

0.05 s 1 5.34E+03 11.78

0.5 s 1 4.84E+03 11.90

Spleen 0.005 s 1 3.54E+03 5.74

0.05 s 1 3.49E+03 5.45

0.5 s 1 3.87E+03 5.01


Fig. 12.14 Stress–strain

plots for the liver at

different strain rates (taken


Cauchy Stress (KPa)

200

150

100

50

0

0

0.1

0.005s -1

0.05s -1

0.5s -1

0.2 0.3 0.4 0.5

Nominal Strain


plots for the kidney at

different strain rates (taken


Cauchy Stress (KPa)

250

200

150

100

50

0

0

0.1

0.005s -1

0.05s -1

0.5s -1

0.2 0.3 0.4 0.5

Nominal Strain


plots for the spleen at

different strain rates. Note

the lack of strain rate

sensitivity for the spleen


(2002))

Cauchy Stress (KPa)

200

150

100

50

0

0

0.2

0.005s -1

0.05s -1

0.5s -1

0.4 0.6 0.8 1

Nominal Strain

Fig. 12.17 Ultimate strain

is independent of strain rate

at the three rates used in the

experiment (taken from


Ultimate Strain

1

0.8

0.6

0.4

0.2

Liver Kidney Spleen

0

0.005/s

0.05/s

0.5/s

12.7 Computer Models of the Abdomen 431

This study has shown that it was possible to use the QLV theory to characterize

the response of solid abdominal organs to compressive loading. Unfortunately, the

strain rates used were not high enough for abdominal impact and more experiments

at higher strain rates than those reported here are needed so that the results can be

used in an impact model of the abdomen.

12.7 Computer Models of the Abdomen

Finite element models simulating the response of the abdomen are rare. The first

one specifically designed to study the organs of the abdomen during an impact was

developed by Lee and Yang (2001). It was a 3-D model of a 50th percentile male

simulating the human abdomen and was code-named WSUHAM. The model was

validated against both frontal and side impact tests. Since the frequently injured

organs are the solid organs, the model paid special attention to the liver, spleen, and

kidneys. Hollow organs (including the large and small intestines, stomach and

esophagus) and other smaller organs such as the gall bladder, bile ducts, ureters,

rectum, and adrenal glands were modeled by three body bags that provided the

inertial properties of the organs but not their detailed geometry. The body bags also

allowed the solid organs to be properly located in the abdomen. The material

properties of the organs were taken from the literature as the study by Tamura

et al. (2002) described in Sect. 12.6 had not been completed and the strain rates used

were not high enough. It was also necessary to include in the model a portion of the

thorax, the pelvis, and lower extremities because validation of the model involves

impacts to the torso and an isolated abdominal model could not be validated.

12.7.1 Model Geometry and Material Properties

Abdominal anatomy is complex and asymmetric, with many organs of different

shapes and sizes. For example, the liver is the dominant organ of the upper abdomen

and is largely on the right side while the spleen is on the left. Thus, side impact

injuries would be different depending on the side of impact. Lee and Yang (2001)

developed the Wayne State University Human Abdominal Model (WSUHAM) and

started the modeling process by acquiring the skeletal geometry from cryosections

of the Visible Human Project which is available from the National Library of

Medicine (Bethesda, MD). The images were taken along a vertical axis at 1 mm

interval and had a higher resolution than most MR or CT scans. The male specimen

of the Visible Human Project was taller than an average male and the skeletal

dimensions were scaled down. Also, the solid abdominal organs became distorted

in the freezing process. They were reconstructed to their normal shape using data

available in the literature. The skeletal model is shown in Fig. 12.18. It includes the


Rib

Slernum

Intercostal muscle

Intercostochondral

muscle

Costal cartilage

Vertebra

Intervertebral disc

Sacrum

lliac crest

Femoral head

Femur

Ischium

Pubis

Fig. 12.18 Skeletal model for the abdominal model (taken from Lee and Yang (2001))

lower rib cage (Ribs 8–12), spine (T8-L5), pelvis, and a portion of the femur with

the femoral heads.

The liver was modeled with viscoelastic solid elements. It had two lobes, both of

which were connected to the falciform ligament which is attached to the diaphragm

and to the anterior body wall. Figure 12.19 shows this ligament between the left and

right lobes. The spleen was also modeled by viscoelastic solid elements. The

kidneys and their capsules were modeled as nonlinear viscoelastic solids. They

were also tethered to the aorta and vena cava by simulated renal arteries and veins.

In terms of other blood vessels, the model only featured the aorta and vena cava

which were connected directly to the diaphragm and modeled as elastic shell

elements. The diaphragm was modeled as an elastic membrane and the hollow

organs were modeled as body bags to transfer energy from one side to the other

during an impact. The first bag was located between the liver and the spleen to

represent the stomach. The second bag was located between the subcostal plane

(transverse plane at the level of L3) and the pelvis to represent most of the

intestines. The third bag was situated between the liver and the diaphragm in the

right hypochondriac region. It is not clear what the third bag represents


Fig. 12.19 Frontal view of

the liver. The top margin of

falciform ligament is

attached to the undersurface

of the diaphragm. Together

with the coronary ligament,

they hold the liver in the

upper abdomen

inferior vena cava

Aorta

Liver

Body bag I

Spleen

Splenic artery/vein

Renal artery/vein

Left Kidney

Right Kidney

Body bag II

(Anterior View)

(Posterior View)

Fig. 12.20 Frontal and rear views of the organs and soft tissues of the abdominal model (taken

from Lee and Yang (2001))

anatomically as there is virtually no space between the superior surface of the liver

and the undersurface of the diaphragm. Peripherally, the model is covered by

superficial muscles and skin so that it can be used to simulate direct impact by a

pendulum or an armrest. These structures were modeled as Kelvin -type elements—

a viscoelastic material modeled by a springs and dashpots in parallel. Figure 12.20

shows the front and rear views of the solid organs, body bags, and other soft tissues

of the abdominal model and Fig. 12.21 is an oblique view of the complete

WSUHAM. It is composed of 35,982 nodes and 34,956 elements. The weights of

the solid organs, body bags, and the entire body are shown in Table 12.14.


Fig. 12.21 An oblique

view of the complete


Human Abdominal Model

(WSUHAM) (taken from

Lee and Yang (2001))

Table 12.14 Weight

distribution (taken from Lee

and Yang (2001))

Segment

Weight (kg)

Liver 1.5

Spleen 0.11

Left/right kidney 0.12/0.13

Total body bags 10.7

Whole body 74.9

12.7.2 Material Properties of the Model Elements

There are many tissues in this model that need to be modeled. We will first consider

compact and spongy bones, cartilage (including intervertebral discs), muscles,

ligaments, and blood vessels. The material properties that need to be specified are

the density, Young’s modulus, and Poisson’s ratio. To reduce computational time,

Young’s modulus was not assigned for compact and spongy bone. Instead, just a

value lower than that of compact bone was used for all bones. Most of the other

information was taken from the literature, including properties of cartilage

(and intervertebral discs), muscles, and ligaments. Intervertebral disc properties

were simplified to a single modulus and a single Poisson’s ratio, ignoring the

differences in properties of the nucleus and annulus and the differences in response

in tension and compression. The properties of the falciform ligament were not


Table 12.15 Material properties of tissues used in the abdominal model by Lee and Yang (2001)

Tissue Density (kg/m 3 ) Young’s modulus (GPa) Poisson’s ratio

Ribs, sternum 2000 1.15E+01 0.3

Sacrum, femur, iliac crest 2000 1.21E+01 0.3

Costal cartilage 1500 2.50E02 0.4

Vertebrae 2000 2.65E02 0.3

Intervertebral discs 1000 1.03E02 0.45

Intercostal muscles 1000 1.03E02 0.4

Falciform ligament 1000 1.20E02 0.4

Diaphragm 1000 3.00E03 0.3

Blood vessels 1000 0.40E03 0.4

Fig. 12.22 Nonlinear

viscoelastic material model

used to simulate solid

abdominal organs (taken


E 2

E 1

h 2

available in the literature and data taken from the anterior longitudinal ligament of

the spine were used. The diaphragm and the major blood vessels were modeled by

isotropic elastic shell elements. The modulus of the diaphragm was assumed to be

much higher than that used by Wang (1995) to account for the effects of the heart

and lungs that were not modeled. For the aorta, its modulus was assumed to be

400 kPa, the maximum value cited by Viano (1983) to account for the lack of

pressurization of the vessel. The material properties of the above-mentioned tissues

used in this model are shown in Table 12.15.

For the solid abdominal organs, Tamura et al. (2002) had not generated their

material properties. Thus, the best available data were obtained from the literature.

These organs were assumed to be nonlinearly viscoelastic and the model used is

shown in Fig. 12.22. There are two elastic moduli in the model. E 1 is the nonlinear

elastic modulus of the elastic component while E 2 is the linear elastic modulus of

the viscous part. η 2 is the nonlinear viscous damping coefficient. The elastic

modulus is given by the equation:

Et ðÞ¼E 1 ð0ÞðV=V 0 Þ n 1

þ E 2 ðÞe 0

βt

where the first term represents the viscoelastic response in shear and the second

corresponds to a viscoelastic response to bulk loading, and

β ¼ ½E 2 ðÞ=η 0 2 ð0Þ

1 ð V=V0 Þ

n2


Table 12.16 Material properties of abdominal solid organs (taken from Lee and Yang (2001))

Organ E 1 (0) (kPa) E 2 (0) (kPa) n 1 n 2 Poisson’s ratio η 2 (0) (kPa)

Liver 195 100 4 0.2 0.45 15

Spleen 488 250 4 0.2 0.45 15

Kidney 352 150 10 0.2 0.45 15

where V ¼ V(t) and V 0 are the deformed and undeformed volumes and n 1 and n 2 are

material parameters.

Table 12.16 lists the material constants for the liver, spleen, and kidneys.

12.7.3 Model Validation and Predictions

Three separate sets of abdominal impact data were used to validate this model. The

side impact data generated by Viano (1989) and by Walfisch et al. (1980) and the

frontal impact data produced by Cavanaugh et al. (1986) were used.

To simulate the side impacts carried out by Viano (1989), a 23.4-kg rigid mass

(pendulum) traveling at 4.5, 6.7, and 9.4 m/s impacted the abdomen at an oblique

angle 30 forward of lateral, as shown in Fig. 12.23. The parameters that were

compared were the peak force and deflection and the Viscous Criterion, V*C. The

validation results are shown in Table 12.17. The maximum difference between the

experimentally measured and predicted peak force was 14% while that for deflection

or compression was 9%. V*C differed by as much as 19.4%. It is instructive to

study the kinematics of the torso during impact (Fig. 12.23) and the distortion of the

organs (Fig. 12.24), for a 6.7-m/s impact. The model could also compute the stress

distribution within an organ. The stress contours of the liver are shown in

Fig. 12.25. The highest stress was not at the point of contact of the chest wall

with the liver. Rather, it was in the center of the right lobe where the peak stress was

152 kPa for a 6.7-m/s impact. It occurred at 22.5 ms after initiation of the impact.

Abdominal force-time response and force-deflection response at 6.7 m/s are shown

in Fig. 12.26. The model did fairly well in predicting these responses and the plots

for the other two impact velocities are comparable to those in Fig. 12.26.

The next validation was a comparison of model predictions with cadaveric drop

tests in which the abdomen impacted a simulated armrest that had two different

heights. These were side impact tests carried out by Walfisch et al. (1980). The

model was oriented to simulate a side impact drop test and the test configuration is

shown in Fig. 12.27. There were four drop tests, two from a height of 1 m and two

from 2 m. The armrest heights were 31 and 51 mm. A comparison of peak spinal

(T12) acceleration and peak 9th rib acceleration for the four tests is shown in

Table 12.18. The differences between model and experimental results ranged

from 5.7 to 26.3%. Force-time data are compared in Fig. 12.28A, B for the 1-m

and 2-m drop heights, respectively. The predictions are reasonable.


Fig. 12.23 Kinematics of a pendulum side impact at 6.7 m/s, as predicted by the WSUHAM,

simulating impacts conducted by Viano (1989) (taken from Lee and Yang (2001))

The frontal impact data obtained by Cavanaugh et al. (1986) were also used for

validation. Recall that these were frontal impacts to the lower abdomen (at the level

of L3) by a 2.54-cm diameter rigid rod that simulated the lower part of a steering

wheel rim. The cadaver was seated upright with its legs flat on the ground. The


Table 12.17 Comparison of experimental data from Viano (1989) and predicted results by the

WSUHAM for pendulum side impact (taken from Lee and Yang (2001))

Impact velocity

(m/s)

Experiment/

Model

Peak force

(N)

Deflection

(mm)

Compression*

(%) V*C (m/s)

4.5 (4.79 0.77) Experiment 2410 490 108.3 23 32.0 6.6 0.77 0.23

Model 2510 82.72 26.2 0.84

% Difference 4.1% 23.6% 18.1% 9.1%

6.7 (6.83 0.15) Experiment 3710 480 114.3 76 36.2 1.65 1.26 0.12

Model 4221 104.3 33.0 1.47

% Difference 13.8% 8.7% 8.8% 16.7%

9.4 (9.40 0.87) Experiment 6510 1100 146.0 23.6 45.8 3.1 2.22 0.41

Model 6327 127.86 40.5 2.65

% Difference 2.8% 12.4% 11.6 % 19.4%

% Compression is the ratio of the deflection and the original abdominal width

Fig. 12.24 Distortion of abdominal organs due to a 6.7-m/s pendulum side impact as predicted by

the WSUHAM. Maximum compression occurred at about 30 ms (taken from Lee and Yang (2001))


Fig. 12.25 Stress contours in the liver at 22.5 ms into the impact by a 6.7-m/s pendulum. The peak

stress was 152 kPa (taken from Lee and Yang (2001))

Fig. 12.26 Comparison of model predicted force-time and force-deflection curves with experimental

data, for impacts at 6.7 m/s (taken from Lee and Yang (2001))

Fig. 12.27 Simulation

of a cadaveric drop test

conducted by Walfisch

et al. (1980). The abdomen

was targeted to impact a

simulated armrest (taken



Table 12.18 Comparison of experimental data from Walfisch et al. (1980) and predicted results

by the WSUHAM for pendulum side impact (taken from Lee and Yang (2001))

Drop height (m)/Armrest

height (mm) Cadaver/Model Peak T12 Accel. (G) Peak 9th rib Accel. (G)

1/31 Cadaver 30 94

Model 28.3 103

% Difference 5.7% 9.6%

1/51 Cadaver 38 124

Model 48 145


2/31 Cadaver 84 –

Model 87.9 143.2

% Difference 4.6% –

2/51 Cadaver 81 180

Model 94 195


Fig. 12.28 Comparison of force-time data for abdominal impacts (A) the 1-m drop tests and

(B) the 2-m drop tests. The experimental data taken from Walfisch et al. (1980) (taken from

Lee and Yang (2001))

simulation of the impact is shown in Fig. 12.29. Two different pendulum masses

were used—32 and 64 kg. Twelve cadavers were impacted, each only once. The

velocities of impact were 6.1 and 10.4 m/s. There were seven tests at the higher

velocity and 5 at the lower velocity. Figure 12.30 shows a comparison of model

predicted force-time curves with the force-time corridor developed by Cavanaugh

et al. (1986) for both the low and high velocity impacts. Similarly, Fig. 12.31 is a

comparison of model predicted force-deflection curves with those obtained experimentally

by Cavanaugh et al. (1986) for the two impact velocities. There appears to

be good agreement between the two sets of results.

In summary, a human abdominal model for impact has been developed and

validated against three sets of cadaveric data. The model simulated the bony

Fig. 12.29 Simulation of

frontal impact abdominal

tests by a rigid bar at the

level of L3. The impact

speeds were 6.2 and

10.4 m/s. The experimental

data were taken from

Cavanaugh et al. (1986)

(taken from Lee and Yang

(2001))

Simulated steering

wheel rim

Impact bat

6.1, 10.4 m/s

Fig. 12.30 Comparison of model predicted force-time curves with experimental corridor developed

by Cavanaugh et al. (1986). (A) is for low velocity impacts (6.1 m/s) and (B) is for high

velocity impacts (10.4 m/s) (taken from Lee and Yang (2001))

Fig. 12.31 Comparison of model predicted force-deflection curves with experimental forcedeflection

curves obtained by Cavanaugh et al. (1986). (A) is for low velocity impacts (6.1 m/s)

and (B) is for high velocity impacts (10.4 m/s) (taken from Lee and Yang (2001))


skeleton, the three abdominal solid organs—the liver, spleen, and kidney and also

simulated the abdominal hollow organs that were grouped into three separate body

bags. The validation was limited to global force-time and force-deflection response

because stress distribution in the internal organs had not been measured experimentally.

Material properties were taken from the literature and there is no

assurance a globally validated model is valid locally; that is, at the organ level.

However, the WSUHAM is the first model that can determine stresses in individual

solid organs of the abdomen.


Much information has been gathered regarding the injury patterns seen in car

crashes for the abdomen. However, the information gathered by clinicians and

accident investigators is some 20 years old and the more recent picture can be

quite different since most cars are now equipped with frontal and side impact

airbags. The research on injury mechanisms is still valid and the vulnerability of

the solid organs remains a priority in injury prevention. The disparate numbers on

injury tolerance make it difficult to design safety systems for the abdomen and it

would be helpful if these tolerances could be tightened with more research. That is,

a concerted program needs to be set up to test a large number of cadavers and/or

animals to obtain a coherent picture of the tolerance of the major organs. Unfortunately,

abdominal injuries are a small part of the injury picture and other areas of

the body have a more urgent need for research support, such as the head and neck.


12.1. The abdomen contains both solid and hollow organs. The solid organs

include:

[ ] (i) The liver

[ ] (ii) The appendix

[ ] (iii) The rectum

[ ] (iv) The uterus

[ ] (v) The colon

12.2. The abdomen contains both solid and hollow organs. The hollow organs

include:

[ ] (i) The spleen

[ ] (ii) The kidney

[ ] (iii) The small intestines

[ ] (iv) The adrenal glands

[ ] (v) The ovaries


12.3. Which of the following is incorrect?

[ ] (i) The liver is the largest organ in the abdomen

[ ] (ii) The liver is the largest organ of the body

[ ] (iii) The spleen is located on the upper left side of the abdomen

[ ] (iv) Total blood flow to the two kidneys is about 1/4 of the cardiac output

[ ] (v) The small intestines are about 7 m long

12.4. Which of the following is incorrect?

[ ] (i) The right lobe of the liver is considerably larger than the left

[ ] (ii) Solid organs are more frequently injured than hollow organs

[ ] (iii) The pylorus sphincter is between the esophagus and the stomach

[ ] (iv) In their undistended state, the wall of the uterus is thicker than that of

the urinary bladder

[ ] (v) The large intestines are divided into four segments

12.5. In the USA, a side impact to the driver’s door is likely to cause injury to

abdominal organs. Select the incorrect answer:

[ ] (i) The spleen is more likely to be injured than the pancreas

[ ] (ii) Hollow organs are less frequently injured than solid organs

[ ] (iii) The pancreas is more likely to be injured than the spleen

[ ] (iv) (i) and (ii)

[ ] (v) (i) and (iii)

12.6. In Japan, a side impact to the driver’s door is likely to cause injury to

abdominal organs. Select the incorrect answer:

[ ] (i) The liver is more at risk in comparison with drivers in the USA

sustaining the same impact

[ ] (ii) The spleen is more likely to be injured than the pancreas

[ ] (iii) The pancreas is more likely to be injured than the spleen

[ ] (iv) (i) and (ii)

[ ] (v) (i) and (iii)

12.7. Abdominal mechanical response data are available from cadavers and

animals

[ ] (i) Lower abdominal stiffness from cadaver tests is approximately

53 kN/m

[ ] (ii) Lower abdominal stiffness scaled to the human level from animal

tests is also about 53 kN/m

[ ] (iii) Abdominal stiffness in response to belt loading scaled to the human

level is mainly in the range of 30 kN/m

[ ] (iv) The use of scaling laws to obtain human abdominal response from

animal testing is not reliable

[ ] (v) Lateral abdominal stiffness was reported to be in the range of

100 kN/m but there are data that differ from this value


12.8. Tolerance of the abdomen to frontal impact has been given in terms of several

parameters. Select the incorrect answer:

[ ] (i) A peak force

[ ] (ii) A peak compression

[ ] (iii) A peak value for V*C

[ ] (iv) A peak pressure


12.9. Tolerance of the abdomen to lateral impact has been given in terms of several

parameters. Select the incorrect answer:

[ ] (i) A peak force

[ ] (ii) A peak compression

[ ] (iii) A peak value for V*C

[ ] (iv) A peak pressure


12.10. Tolerance of the

[ ] (i) Liver to impact force is in the range of 0.24–1.56 kN (AIS > 3)

[ ] (ii) Kidney to impact force is 1.82–2.14 kN (AIS > 3)

[ ] (iii) Upper/mid abdomen to impact force is 3.11–6.73 kN (AIS > 4)

[ ] (iv) (i) and (ii)

[ ] (v) (i) and (iii)


Prob

Ans

1 (i)

2 (iii)

3 (ii)

4 (iii)

5 (iii)

6 (iii)

7 (ii)

8 (ii)

9 (iv)

10 (v)

References 445

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Chapter 13

Impact Biomechanics of the Pelvis

Pelvis is the Latin word for basin. It holds the organs of the lower abdomen and is

anatomically part of the abdomen but the skeletal pelvis has a load bearing function

because it transmits the weight of the head and torso to the lower extremities via the

sacrum which is firmly attached to the pelvis. In this chapter, we will study the

biomechanics of pelvic response to impact and the injuries that result from pelvic

impact. The pelvis also plays a crucial role in restraining automotive occupants

during a crash because the lapbelt is designed to hold the torso to the seat so that it

can ride down with the car and prevent severe impacts of the head and the torso

against parts of the vehicle.

13.1 Anatomy of the Skeletal Pelvis

The skeletal pelvis is shown in Fig. 13.1. It is largely made up of the hipbone, the

three irregularly shaped fused bones—the ilium, ischium, and pubis. The fusion

occurs around a cup-shaped articular cavity called the acetabulum (hip socket)

which is situated near the middle of the outer surface of the bone. A side view of the

pelvis is shown in Fig. 13.2 in which the fusion of the three bones is clearly visible.

The ilium makes up the flank of the pelvis in the form of a broad and expanded

piece of bone extending upward from the acetabulum. The crest of ilium reaches the

level of L4 in the human and the anterior superior iliac spine (ASIS) is a protrusion

on the anterior aspect of the iliac crest which can be used to keep the lapbelt from

riding up the pelvis. That is, lapbelts need to be worn low and below the ASIS. The

ischium occupies the lower part of the hipbone, along the posterior aspect. The

ischial body is fused to the ilium and is located superiorly with respect to the ischial

tuberosity, the “sit” bone where the contact pressure with the seat can be high. The

pubis forms the other half of the lower part of the hipbone and is situated along the

anterior aspect. The pubic body is also fused with the ilium and the acetabulum

while the two pubic rami extend anteriorly across the torso to meet their



447

448 13 Impact Biomechanics of the Pelvis

Sacrum

Sacroiliac Joint

Iliac Crest

Ilium

Acetabulum

Ischium

Pubic Symphysis

Coccyx

Pubis

Fig. 13.1 Frontal view of the pelvis (taken from Gray (1973))

A

Anterior superior

iliac spine

B

Iliac crest

Anterior superior

iliac spine

ILIUM

Iliac fossa

Auricular surface with sacrum

Anterior inferior iliac spine

PUBIS

Superior ramus of pubis

Pubic tubercle

Pubic crest

Symphysis pubis

Inferior ramus of ischium

Posterior

superior

iliac spine

Greater sciatic notch

Ischial spine

Lesser sciatic notch

ISCHIUM

Ischial tuberosity

Obturator foramen

Posterior inferior iliac spine

Anterior inferior iliac spine

Junction of ilium and ischium

Acetabulum

Acetabular notch

PUBIS

Superior ramus of pubis

Pubic tubercle

Inferior ramus of pubis

Fig. 13.2 Lateral view of the right hip bone or pelvis (taken from Carola et al. (1992)).

Republished with permission of McGraw-Hill Education, from R. Carola, J.P. Harley, C.R.

Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992; permission conveyed through


counterparts at the pubic symphysis which is a cartilaginous joint on the midline.

It is amphiarthrodial, meaning that it is only slightly movable. The inferior pubic

ramus is an extension of the ischial ramus. The ischium and the pubis form a large

opening called the obturator foramen. It is mostly covered by a strong membrane

but there is an opening in the superior region through which blood vessels and

nerves pass from the pelvis into the lower extremities. The acetabulum is the hip

socket which articulates with the head of the femur (thigh bone). This is shown in

Fig. 13.3.

13.1 Anatomy of the Skeletal Pelvis 449

ILIAC CREST

ANTERIOR

SUPERIOR

ILIAC SPINE

GREATER

TROCHANTER

ACETABULUM

(HIP SOCKET)

FEMUR:

FEMORAL

SHAFT

NECK

HEAD

SUPERIOR PUBIC

RAMUS

PUBIC

SYMPHYSIS

INFERIOR PUBIC RAMUS

wb

Fig. 13.3 The acetabulum (hip socket) houses the head of the femur (thigh bone) (taken from

Nusholtz et al. (1982))

Male and female pelves differ in shape and size because the female pelvis had

evolved to facilitate childbirth. As shown in Fig. 13.4, the male pelvis is longer

(taller) and narrower than the female pelvis. The cavity between the pelvic bones is

oval in shape in the female while in the male is more heart-shaped. Because the

female pelvis is wider, the female gait is different than that of the male. Men can

walk with the legs moving in a single plane while women need to swing their leg

forward and inward, resulting in a gait with swinging hips.

Posteriorly, the two iliac bones are attached to the sacrum which is composed of

five fused sacral vertebrae that decrease in size inferiorly. A slightly oblique frontal

view is shown in Fig. 13.5. The sacrum still has the intervertebral foramina through

which nerve roots pass in the same way as in the spine. The transverse processes

have fused into a lateral mass on each side, called the sacral ala which is shown in

Fig. 13.5 and in cross-section in Fig. 13.6. Part of the sacroiliac (SI) joint is

synovial, with cartilaginous surfaces but most of the joint is held together by strong

interosseous ligaments (Fig. 13.6). There are also extrinsic ligaments on both sides

of the joint that help support it. The anterior extrinsic ligaments are the ventral

sacroiliac ligament and the lumbosacral ligament which are shown in Fig. 13.7. The

sacrotuberous ligament and the sacrospinous ligament on the floor of the pelvis are

also shown in this figure. The former extends from the sacroiliac complex to the

ischial tuberosity and can resist vertical loads that push the pelvis down relative to

the sacrum but not the vertical (+G z ) acceleration sustained by mounted soldiers

experiencing an IED explosion. The latter is a strong band between the lateral edge

of the sacrum and the ischial spine. It resists external rotation of the ischium.

Posteriorly, there are several SI joint ligaments, including the short and long

posterior sacroiliac ligaments, as shown in Fig. 13.8.

Body of fifth lumbar vertebra

Iliac crest

Anterior superior

iliac spine

Anterior inferior

iliac spine

Greater (false) pelvis

Sacroiliac joint

Sacral promontory

SACRUM

Inlet of lesser (true) pelvis

Sacrococcygeal joint

COCCYX

Symphysis pubis

Obtrurator foramen

(A) MALE

Pubic

arch

(acute or

narrow angle)

Greater (false) pelvis

RIGHT OS COXA

ILIUM

PUBIS

ISCHIUM

(B) FEMALE

Pubic arch

(oblique angle)

Symphysis

pubis

SACRUM

Inlet of lesser (true) pelvis

COCCYX

Brim of lesser (true) pelvis

Head of femur

Acetabulum

Fig. 13.4 Frontal views of the male (top) and female pelvis (bottom). The female pelvis has

evolved to facilitate childbirth (taken from Carola et al. (1992)). Republished with permission of



Fig. 13.5 A slightly oblique frontal view of the sacrum (taken from Gray (1973))

13.1 Anatomy of the Skeletal Pelvis 451

Interosseous

Ligaments

Synovial Syndesmosis

Sacroiliac Joints

Hip Bones

Fig. 13.6 Transverse section of the pelvic and sacrum, showing the sacroiliac joints which have a

synovial segment anteriorly. A large part of the joint is held together by strong interosseous

ligaments (taken from Gray (1973))

Above the sacrum is the lumbar spine which carries the weight of the upper

body. The sacrum transfers this weight to the pelvis via the two sacroiliac joints. It

can be seen from Fig. 13.6 why the range of motion of the SI joint is limited. In

pregnant women, a female hormone (relaxin) is released to relax these ligaments

and the pubic symphysis to allow the pelvis to open up a little more, enabling the

fetus to pass through pelvis. With age, the flat or planar surface of the SI joint

develops ridges and depressions to help with the weight transfer. A side view of the

sacrum and coccyx is shown in Fig. 13.9. The bones are concave forward. Finally,

below the sacrum is the coccyx, a bone consisting of three to five fused coccygeal

vertebrae. It is our vestigial tail which provides support during reclined sitting and

has muscles and ligaments attached to it for functions of the pelvic floor, such as

defecation and continence.


Fig. 13.7 Anterior ligaments between the ilium and the sacrum are shown in this figure along with

the sacrotuberous and the sacrospinous ligaments on the floor of the pelvis (taken from Gray

(1995)). Reprinted from Gray’s Anatomy: The Anatomical Basis of Medicine and Surgery, 38th

edn. by Gray, (Churchill Livingstone), 1995, with permission from Elsevier

13.2 Pelvic Injuries Due to Impact

The pelvis can be injured from frontal, lateral, and vertical (caudocephalad)

impacts. In the automotive setting, vertical (+G z ) accelerations are not commonly

experienced in crashes and separation of the sacroiliac joint due to vertical shear is

rare. Frontally, the acetabulum is at risk when the knee load is transmitted to the hip

joint, especially for the unrestrained front seat occupant experiencing a large Delta

V. An example of this would be the injuries sustained by two police officers

traveling at high speed to the scene of a crime and rearending a large truck at an

estimated Delta V of 60 km/h or 37 mph. Both officers were unrestrained and both

sustained a right acetabular fracture. The driver also sustained a fracture of the right

ischium while the passenger sustained a fracture of the right pubic bone and damage

to the right SI joint. It can be seen from Fig. 13.3 that the anteroposterior force on

the acetabulum would bend the hipbone rearward or outward causing separation of

13.2 Pelvic Injuries Due to Impact 453

Fig. 13.8 Posterior ligaments between the pelvis and the sacrum (taken from Gray (1995)).

Reprinted from Gray’s Anatomy: The Anatomical Basis of Medicine and Surgery, 38th edn. by

Gray, (Churchill Livingstone), 1995, with permission from Elsevier

the pubic symphysis, bending of the ischial ramus and causing damage to the SI

joint. Side impact of the door against the greater trochanter of the femur can cause

acetabular fractures and pubic rami fractures. The lateral load places both rami in

bending as they are anterior to the acetabulum. In orthopedic surgery, fracture

classifications are used to simplify the description of many forms of injury and to

separate the mechanically stable injuries from unstable ones. One popular pelvic

fracture classification was proposed by Tile (1988). There are three main groups.

The fractures can be stable, rotationally unstable, or vertically unstable. A fracture

is stable if locomotion is possible. A rotationally unstable fracture means that

although the pelvis can transmit vertical load to the extremities, there is disruption

of one of the SI joints or the pubic symphysis, allowing the hemi-pelvis to rotate

externally or internally. Vertically unstable fractures mean that the pelvis is not able

to transmit a vertical load down to at least one of the extremities. An example of a

rotationally unstable injury is shown in Fig. 13.10. It is called a bucket handle

fracture because the fractured pubic rami on the right side looks like a bucket

handle on X-ray. Figure 13.11 is an example of a vertically unstable pelvic fracture.

Both the anterior and posterior arches are disrupted by dislocation of the pubic


Articular process

Median sacral crest

Body

Promontory

Cornu of sacrum

Cornu of coccyx

Coccyx

Fig. 13.9 Side view of the sacrum and coccyx (taken from Gray (1973))

Fig. 13.10 Illustration of a

rotationally unstable pelvic

fracture caused by internal

rotation of the left hipbone.

It is called a bucket handle

fracture because the

fractured right pubic rami

(on the left of the figure)

provides the image of a

bucket handle on X-ray)

13.2 Pelvic Injuries Due to Impact 455

Fig. 13.11 Illustration of a

vertically unstable pelvic

fracture with disruption of

both the posterior and

anterior arches

Table 13.1 Classification of pelvic disruption (taken from Tile (1988)). Reproduced with permission

of British Editorial Society of Bone and Joint Surgery via PLSclear

Type A

Type B

Type C

Stable

A1—Fractures of the pelvis not involving the ring

A2—Stable, minimally displaced fractures of the ring

Rotationally unstable, vertically stable

B1—Open book

B2—Lateral compression: ipsilateral

B3—Lateral compression: contralateral (bucket handle)

Rotationally and vertically unstable

C1—Unilateral

C2—Bilateral

C3—Associated with an acetabular fracture

symphysis and the left SI joint. Note that the L5 and the sacral nerve roots are at risk

of being stretched or severed and neurological dysfunction is expected. Additionally,

pelvic blood vessels are frequently ruptured in unstable fractures and require

immediate surgical care to prevent death by exsanguination. In the automotive

crash environment, rotationally unstable fractures can occur in high energy crashes.

Vertically unstable fractures are rare because occupants do not experience high

vertical accelerations and lapbelt loading is generally not large enough to distract

the SI joint (Table 13.1).

Sacral fractures are not common in automotive crashes but they are seen in severe

crashes. The lumbosacral joint at L5 can be dislocated from the sacrum and the sacrum

itself can sustain vertical as well as horizontal fractures. Figure 13.12 is an example of

a U-shaped fracture. The vertical fractures usually go through the neural foramina

which act as stress risers. The horizontal fracture is usually at the S1-2 or S2-3 level.

The injury mechanism is vertical loading coupled with a forward bending moment on

the sacrum. Again sacral fractures have been classified. Denis et al. (1988)proposeda

vertical fracture scheme in which the injury severity increases as the vertical fracture

moves medially. Transverse fractures have been classified by Roy-Camille et al.


Fig. 13.12 A U-shaped

fracture of the sacrum

(1985) who based his classification on his experience treating suicidal jumpers who

land on their feet when they hit the ground. In addition to fracture, the sacrum can also

be dislocated. These injuries are not seen in automotive crashes.

13.2.1 Femoral Neck Fractures in the Elderly

A small digression is made here to discuss the issue of femoral neck fractures in the

elderly. We commonly hear the statement that Grandma fell and broke her hip

(femoral neck). What we want to examine is if this is a medical myth or true

statement. That is, did she break her hip in the fall or did she break her hip and then

fall? In automotive side impacts to the greater trochanter, femoral neck fractures are

rare and yet there is epidemiological evidence that hip fractures occur frequently

when the elderly fall to the side (Greenspan et al. 1998). Yang et al. (1996)

demonstrated experimentally that clinically relevant hip fractures could be

reproduced in cadaveric femoral specimens by simulating muscle loading by either

the iliopsoas or the gluteus medius and that the failure loads and energy to failure

were comparable to those reported by Lotz and Hayes (1990) who used a loading

scheme to simulate a fall. It was suggested that spontaneous hip fractures could

happen more frequently than originally thought. The actual cause of hip fractures

has far-reaching implications, especially for women. If the hip fractures due to a

fall, elderly women should be encouraged to wear hip pads to protect the hip. If, on

the other hand, the fracture is the cause for the fall, then it behooves all women to

store calcium in their bones so that they can live a long life without sustaining a hip

fracture. This is an example of a medical myth that will not die because, quoting the

Lancet, “The most entrenched conflict of interest in medicine is a disinclination to

reverse a previous opinion” (Lancet 2011, Vol. 377, Issue No. 9773: Cover Page).

There are many such cases in medicine and the cause of subdural hematoma had

already been discussed in Chap. 3.

13.3 Mechanical Response of the Pelvis to Impact 457

13.3 Mechanical Response of the Pelvis to Impact

In frontal impact for front seat automotive occupants, the pelvis is loaded by the

knees which transmits the compressive load into the acetabulum. The response of

the acetabulum to a load applied to its posterior wall is discussed in this section.

Side impact response has also been studied.

13.3.1 Frontal Response of the Pelvis to Impact

Although there have been many studies of frontal knee impact since the first paper

by Patrick et al. (1965), there was little information on acetabular injuries.

According to Rupp et al. (2002), the reason for the lack of information was that

the cadaveric experiments were carried out at a high rate of loading (400–3000 kN/

s) and a time lag between the application of force to the knee and onset of force at

the hip precluded the development of a large acetabular force. On the other hand,

real-world loading rates from dummy testing were below 300 kN/s and a large hip

force could develop. Alternately, one can think of an impact applied to the knee and

if the knee and femur are not fractured, then the load is transmitted to the hip socket

where a fracture can occur. These two explanations are basically equivalent. At

high rates of loading, the knee or femur (excluding the patella) fractures before the

force can be transmitted to the hip while at low rates of loading (perhaps due to

padding of the impactor) the impact can be transmitted directly to the hip. This

explains why in many knee impact tests, acetabular fractures did not occur while

knees and femurs were fractured,

In studying acetabular fractures caused by frontal impact to the knee, we need to

consider a couple of issues. The orientation of the femur relative to the acetabulum

is an important factor because the contact area between the femoral head and the

acetabular surface varies with femoral abduction/adduction as well as flexion/

extension. Rupp et al. (2002) stated that hip tolerance is expected to increase with

increased abduction because the area of contact with the acetabulum is higher in

abduction. There does not appear to be any data supporting this statement nor are

there any data comparing contact areas as a function of abduction/adduction or

internal/external rotation.

We also need to be cognizant of what types of acetabular fractures are seen

clinically because if the fractures produced in biomechanical experiments bear no

resemblance to those treated by orthopedic surgeons, there is probably something

faulty about the experiments. The authoritative source for acetabular fracture

patterns is that of Letournel (1980) who described five simple fracture types

along with five associated types, as shown in Fig. 13.13(A–J). Dakin et al. (1999)

studied the acetabular fracture patterns in front seat occupants. For frontal impact

loading via the femur the three main acetabular injuries were fractures of the

posterior wall, posterior column, and posterior wall and column—Types A, B,


Fig. 13.13 Acetabular fracture patterns as described by Letournel (1980). The simple patterns are

(A) posterior wall, (B) posterior column, (C) anterior wall, (D) anterior column, and (E) transverse

fractures. The associated patterns are (F) fractures of the posterior column with a posterior wall,

(G) transverse fracture of the posterior wall, (H) T-style acetabular fracture, (I) fracture of the

anterior column posterior hemitransverse, and (J) fractures of both columns (taken from Alton and

Gee (2014))

Pneumatic

actuator

Sled

Energy

absorbing

material

Laser Laser reflector

(ram position)

Femur Pelvis

Reaction

load

Ram impact surface

Ram

Molded knee

load cell

interface

Ram

Accelerometer

IIiac wing

support

Fig. 13.14 Impact apparatus used impact the knee and fracture the acetabulum (taken from Rupp

et al. (2002))

and F in Fig. 13.13. Injuries of lower severity involve the acetabular rim and with

higher forces, the wall of the acetabulum is fractured. With even more force, the

posterior wall and column are fractured, leading to pelvic instability.

Early work by Nusholtz et al. (1982) did not produce useful results and a clearer

understanding of acetabular injury was delineated by Rupp et al. (2002) two

decades later. The apparatus used is shown in Fig. 13.14. The pelvis was inverted

and fixed in a clamp and the line of force application was along an axis from the


A

Direction of

applied force

B

90° Direction of

120°

applied force

Top View

Side View

Fig. 13.15 Orientation of the femur with respect to the pelvis viewed from the top (A) and the side

(B). The pelvis was fixed in a clamp (taken from Rupp et al. (2002))

8

300 N/ms

6

Force (kN)

4

2

0

Fracture or peak force

10 20 30 40 50 60

Time (ms)

Fig. 13.16 Loading rates used in the acetabular fracture study by Rupp et al. (2002)

center of the femoral condyles to the hip joint center that is perpendicular to the line

connecting the left and right hip joint centers, as shown in Fig. 13.15A. The degree

of hip flexion (120 ) is shown in Fig. 13.15b. This is the standard male sitting

posture determined by Schneider et al. (1983). By fixing the pelvis, the inertial

effect of the thigh was minimized and the measured force behind the pelvis was

nearly identical to the applied force at the knee. A typical loading curve is shown in

Fig. 13.16. It is seen that the rate of loading is just above 300 kN/s and the fracture

force of 6.5 kN is identified by the reversal in slope at the 30-ms mark. Table 13.2

shows a summary of the test results. Of the 17 knee-thigh-hip (KTH) complexes

tested, 12 resulted in acetabular fractures at an average load of 6.66 kN (not

including the femoral neck fractures). All acetabular injuries involved the posterior


Table 13.2 Results of KTH testing resulting in many acetabular fractures (taken from Rupp et al.

(2002))

Test

ID

Force at

fracture

(kN)

Time to

peak

(ms)

Loading

rate

(N/ms)

Calculated

KTH stiffness

(N/mm)

Fractures

5L 5.59 13.7 361 NA a Acetabulum (“T-type fracture”),

inferior ramus

5R 5.37 15.8 303 NA a Acetabulum (transverse, posterior

wall)

6L 4.85 33.3 175 NA a Acetabulum (posterior wall)

7R 4.49 38.6 114 208 No injury

8L 7.52 33.9 417 334 Femoral neck

8R 7.87 23.5 566 534 Femoral neck

10L 6.60 29.5 326 379 Acetabulum (posterior wall),

pubic rami

12R 6.67 56.1 138 195 Acetabulum (posterior col., anterior

hemitransverse fx.) pubic rami

13R 3.34 53 93 105 Iliac wing, pubic rami

14R 4.65 36.1 146 191 Femoral neck

16R 5.59 45.7 125 197 Acetabulum (posterior wall/column),

inferior pubic ramus

17L 4.79 38.5 80 119 Acetabulum (transverse posterior

wall), inferior pubic ramus

18L 5.57 40.4 159 249 Acetabulum (posterior wall)

19R 4.04 31.3 161 NA a Acetabulum (posterior wall/

column)

22L 8.85 33.6 326 268 Acetabulum (posterior rim)

24R 3.91 34.5 144 181 Acetabulum (transverse posterior

wall), pubic rami

25L 5.67 55.3 132 189 Acetabulum (“T-type” with comminuted

posterior wall)

25R 5.87 59.2 132 177 Acetabulum (posterior rim)

26L 6.60 54.7 138 172 Acetabulum (posterior wall, anterior/superior

rim)

Mean 5.70 b 38.3 b 193 c 233 d

sd 1.38 b 11.5 b 114 c 110 d

a NA ¼ not applicable because of invalid ram displacement measurements or because a whole KTH

was not tested

b Calculated using averages of data from subjects where both left and right sides were tested and

excluding tests 7R and 13R where no hip fractures occurred

c Calculated using averages of data from subjects where both left and right sides were tested

d Calculated using averages of data from subjects where both left and right sides were tested and

excluding all tests where stiffness could not be calculated due to missing ram displacement

measurements


acetabulum with some fractures extending into the posterior column and the pubic

rami. The T-type and transverse acetabular fractures were not reported by Dakin

et al. (1999). The rates of loading for the KTH tests are shown in Fig. 13.16. Most

rates were below 300 kN/s. The stiffness of the KTH complex was found to be

233 110 kN/m. In the next series of tests, Rupp et al. (2003) studied the tolerance

of the hip in three different postures. This study will be described in Sect. 13.4. The

neutral posture is described in Rupp et al. (2002). In the adducted posture the right

angle shown in Fig. 13.15A becomes acute (some angle less than 90 ) and in the

flexed posture, the flexion angle in Fig. 13.15B is less than 120 .

13.3.2 Lateral Response of the Pelvis to Impact

The pelvis is subjected to a lateral impact by the car door during a side impact.

Pedestrians struck by cars are frequently impacted in the pelvic area laterally as

they walk across the street. There have been a few studies of lateral pelvic impact.

Viano (1989) impacted the thorax, abdomen, and pelvis laterally, using a 23.4-kg

pendulum. Pelvic response was obtained at three different impact velocities. They

were nominally 5.2, 6.7 and 9.8 m/s (nominally 10, 15 and 20 mph). Unlike the

thoracic and abdominal impacts, the direction of impact was lateral because there

was no rotation of the rib cage to contend with. There were 14 impacts to the

14 cadavers. Four of the eight tests at the high impact speed, two at the medium

speed, and four at the low speed had complete data sets. As a result, there were

sufficient data to generate force-deflection corridors only for the high and low speed

impacts, with four sets of data at each speed. These responses are shown in

Fig. 13.17. In terms of injury, there were only two pelvic rami fractures which

occurred during the high speed tests.

A

10

B

15

8

FORCE (kN)

6

4

run 21

2

run 25

run 26

run 31

0

0 5 10 15 20

DEFELCTION (cm)

FORCE (kN)

10

5

0

0

run 22

run 27

run 22

run 39

5 10 15 20

DEFELCTION (cm)

Fig. 13.17 (A) Pelvic force-deflection curves for lateral impact at 5.2 m/s and (B) at 9.8 m/s

(taken from Viano (1989))


Fig. 13.18 Hypothetical pelvic force data showing that the cumulative duration of the force in

excess of 12 kN is greater than 3 ms

There was an earlier study by Cesari and Ramet (1982) who did 60 lateral

impacts on 22 cadavers (five females) using a pendulum system. The cadavers

were unbelted and seated on a rigid seat in the driving posture. The age range was

54–85 years, the body weight ranged from 44 to 100 kg and the height ranged from

1.44 to 1.84 m. They were impacted by a 17.3-kg spherical impactor 17.5 cm in

diameter. The diameter of the sphere was 60 cm. There were five padded impact

tests. The rest was done with a rigid impactor. The impact speeds producing pelvic

injuries ranged from 22 to 50 km/h (15–30 mph). The cadavers were scheduled to

undergo multiple lateral impacts on the same side (right) until a fracture occurred.

They were X-rayed after each test. Some subjects underwent as many as five

impacts while others sustained an injury on the first test. The repeated test protocol

was justified on the basis that some of the cadavers that were impacted once

sustained fractures at lower impact severities that those that had undergone multiple

impacts. Among the 19 cadavers, there were 29 pubic rami fractures, the most

frequent fracture among all injuries. This corresponded to 32 fractures among

14 accident victims. Note that the number of rami fractures was calculated based

on the number of rami fractured. If there was a fracture of all four rami, the count

would be 4 fractures. The impact force was expressed in two different ways. In

addition to the peak force, the authors used the force level with a duration of 3 ms—

the 3-ms clip, shown hypothetically in Fig. 13.18. The reason for using the 3-ms

clip as a fracture level instead of the peak is to eliminate the effect of ringing of the

measuring devices which can present a false peak. There was a lot of scatter in the

data but the range of the 3-ms impact force was 4880–12,920 N for males and

4440–8200 N for females. As a result of this study, it was recommended by Cesari

and Ramet (1982) that the pelvic fracture load be set at 10 kN for the 50th percentile

male, using the 3-ms clip value.

13.4 Tolerance of the Pelvis 463

1.0

Probability of Hip Fx or Dislocation

0.8

0.6

0.4

0.2

0.0

0

15° Flexed,

30° Abducted

0° Flexed,

0° Abducted

2 4 6 8 10 12

Peak Force at Hip (kN)

Fig. 13.19 Probability of hip fracture or dislocation as a function of peak force at the hip.

The probability of injury increases with increased hip flexion and abduction (taken from Rupp

et al. (2009))

13.4 Tolerance of the Pelvis

Rupp et al. (2003) found that the human hip joint could tolerate a frontal impact

load of 6.1 1.5 kN, based on four pairs of tests on the knee. The hips were tested in

the neutral position, as described in Fig. 13.15A. Hip tolerance decreased by an

average of 34 4 % with 30 of flexion from the neutral position and by 18 8%

with 10 of adduction from the neutral position. Rupp et al. (2009) subsequently

developed a risk injury function for the hip joint for frontal knee loading.

The probability of fracture of the acetabulum was a function of the peak force

transmitted to the hip, the stature of the crash victim, and the hip flexion and

abduction angles. Figure 13.19 is a graphical illustration of the risk function. The

probability of fracture is increased with hip flexion and abduction from neutral. It

was hypothesized by Rupp et al. (2003) that hip tolerance is reduced with hip

flexion and abduction due to a reduction in the contact area between the femoral

head and the acetabulum. The hip joint tolerance of 6.1 N is well below that of the

femur (~10 kN) and that of the femoral condyles (also about 10 kN). Thus, the

explanation provided by Rupp et al. (2002) has validity and the posterior portion of

the hip joint is weaker than the knee or femur.

For side impact, Cesari and Ramet (1982) proposed a force tolerance value of

10 kN while Viano (1989) found that the best predictor for side impact tolerance

was pelvic deflection or compression. At a probability of 25 %, the fracture

tolerance is 27.4 %. This value appears to be high for a large and fairly rigid bone

like the pelvis but compression was the only significant parameter for lateral pelvic

impact.



In the automotive crash environment, pelvic injuries can occur in both frontal and

side impacts. For frontal impact the unrestrained occupant is likely to sustain

acetabular fractures from knee impacts into the dash. The probability of an acetabular

injury in belted occupants is low. In side impact, the pelvis needs protection

from an airbag because door intrusion is the source of both acetabular fractures and

fractures of the ilium. The more severe types of pelvic injuries, including those of

the sacrum are uncommon in automotive crashes unless the crash energy is very

high. However, these severe injuries are seen in the military environment and are

sustained by civilians who fall from a great height.


13.1. The pelvis consists of a fusion of

[ ] (i) Ilium, ischium, and pubis

[ ] (ii) Ilium, ischium, pubis, and sacrum

[ ] (iii) Ilium, pubis, and sacrum

[ ] (iv) Ilium, pubis, sacrum, and coccyx


13.2. One of the following statements is incorrect:

[ ] (i) The female pelvis is flatter and more open

[ ] (ii) The sacroiliac joint is slightly movable

[ ] (iii) The sacro-coccygeal joint is slight movable

[ ] (iv) The pubic joint is fused

[ ] (v) There is a disc between the lumbar spine (L5) and the sacrum (S1)

13.3. In a side impact, the following pelvic injuries can occur:

[ ] (i) Fracture of the superior pubic ramus

[ ] (ii) Fracture of the inferior pubic ramus

[ ] (iii) Fracture of the pelvic ring


[ ] (v) (i) and (iii)

13.4. In a frontal impact, the following pelvic injuries can occur:

[ ] (i) Separation of the sacroiliac joint

[ ] (ii) Fracture of the acetabulum

[ ] (iii) Fracture of the ischium


[ ] (v) (i) and (ii)


13.5. Pelvic response data have been obtained by various researchers. The following

types of tests have been conducted:

[ ] (i) Frontal pendulum impact to the pelvic ring

[ ] (ii) Lateral pendulum impact to the pelvic ring

[ ] (iii) Lateral sled impact involving the whole pelvis



13.6. Tolerance of the pelvis to side impact can be expressed in terms of force,

acceleration, displacement, or V*C. Which one of the following is incorrect?

[ ] (i) In terms of force, the proposed tolerance limit is 10 kN for males

[ ] (ii) In terms of acceleration, the FMVSS limit is 135 g

[ ] (iii) In terms of displacement, the proposed tolerance is 27.4% of the

pelvic width

[ ] (iv) In terms of V*C, the proposed tolerance is 1.6 m/s

[ ] (v) All of the above are incorrect

13.7. Fractures of the acetabulum can occur

[ ] (i) During a vertical (+G z ) impact, such as during seat ejection

[ ] (ii) During a side impact due to vehicular intrusion

[ ] (iii) During a frontal impact from knee loading



13.8. Acetabular fractures are seen in automotive crashes. They are the result of

[ ] (i) Frontal impact to the knee

[ ] (ii) Vertical impact to the ischial tuberosities

[ ] (iii) side impact to the wing of the ilium

[ ] (iv) side impact to the greater trochanter of the femur

[ ] (v) (i) and (iv)

13.9. Femoral neck fractures among the elderly are often attributed to a fall to the

side. From impact biomechanics, we know that

[ ] (i) In side impacts of the greater trochanter by the car door, femoral

neck fractures are infrequent

[ ] (ii) a side impact to the greater trochanter of the femur results in fracture

of one or both pubic rami

[ ] (iii) muscular activity around the femoral neck can cause it to fracture

[ ] (iv) the fall occurred after the neck had fractured

[ ] (v) all of the above

13.10. Fractures of the sacrum are rare in automotive crashes. They occur due to

[ ] (i) A pure vertical load on the pelvis


[ ] (ii) A combined horizontal anteroposterior load at L5 and a vertical

load on the pelvis

[ ] (iii) A combined vertical load on the pelvis and a bending load on the

lumbar spine

[ ] (iv) A combined horizontal postero-anterior load at L5 and a vertical

load on the pelvis



Prob

Ans

1 (ii)

2 (iv)

3 (iv)

4 (v)

5 (v)

6 (iv)

7 (v)

8 (v)

9 (v)

10 (iii)

References

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Crash Conference. SAE Paper No. 821159, Ann Arbor, MI, 1982

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associations with motor vehicle crash information. J. Trauma Acute Care Surg. 47(6),

1063–1071 (1999)

F. Denis, S. Davis, T. Comfort, Sacral fractures: an important problem retrospective analysis of

236 cases. Clin. Orthop. Relat. Res. 227, 67–81 (1988)


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Chapter 14

Impact Biomechanics of the Lower

Extremities

This chapter deals with the biomechanics of impact injuries sustained by the upper

and lower legs, or, in anatomical terms, the thigh and the leg. Injuries to the foot

will be discussed in Chap. 15. In both frontal and lateral impacts, the lower

extremities are at risk of being injured when they come into contact with the dash

or the car door. The mechanisms of injury are explored and the types of injuries are

discussed.

14.1 Anatomy of the Thigh and Leg

The thigh bone or femur is the longest bone in the body. As shown in Fig. 14.1, it

articulates with the pelvis via the hip joint proximally and with the tibia distally. As

with all long bones, the ends are wider than the central shaft but the thickness of the

cortical bone decreases towards both ends of the bone where there is more trabecular

or spongy bone (Fig. 14.2). The leg (shin) bone or tibia articulates with the

femur proximally and with the talus or ankle bone distally, as shown in Fig. 14.3.

Alongside the lateral aspect of the tibia is the fibula which is attached to the tibia by

an interosseous membrane. Proximally, the head of the fibula is attached to the

tibia, laterally under the tibial plateau. Distally, it articulates with the talus (ankle

bone). It can be seen from Fig. 14.3 that head of the fibula does not articulate with

the femur and the distal end of the fibula forms the lateral malleolus of the ankle

while the distal end of the tibia forms the medial malleolus, the two protrusions of

the ankle that are easily palpable. The estimated load carried by the fibula can vary

from less than 7–13 % of the total tibial load, depending on ankle position

(Goh et al. 1992; Takebe et al. 1984). The knee cap or patella is a sesamoid bone

that is found anterior to the femoro-tibial joint. As can be seen from Fig. 14.4, itis

triangular in shape with the base of the triangle on top and its apex pointing

inferiorly. On the underside, it has two facets that articulate with the condyles of

the distal femur. The patella is held in place by the quadriceps tendon superiorly and



469

470 14 Impact Biomechanics of the Lower Extremities

Fig. 14.1 Anterior (left)

and posterior (right) views

of the bones of the right

lower extremity. The femur

articulates with the pelvis

proximally and the tibia

distally. The tibia

articulates with the femur

proximally and with the

tarsal (ankle) bone distally

(taken from Carola et al.

(1992)). Republished with






permission conveyed

through Copyright


RIGHT PELVIC GIRDLE (os coxa)

ILIUM

Coxal (hip) joint

PUBIS

ISCHIUM

FEMUR

Tibiofemoral (knee) joint

PATELLA

TIBIA

FIBULA

Interosseous space

Talocrural (ankle) joint

TARSAL BONES

METATARSAL

BONES

PHALANGES

the patella tendon inferiorly. The anterior muscles of the thigh, the quadriceps,

insert into the base of the patella via the quadriceps tendon while the patella tendon

attaches the apex of the patella to the tibial tubercle or tuberosity, a small but

palpable protuberance on the front of proximal tibia, just below the knee joint.

Figure 14.5 is a side view of the knee showing the quadriceps and patella tendons.

Biomechanically, the patella acts to increase the moment arm of the quadriceps

muscles, thereby enabling leg extension more efficiently.

In addition to the quadriceps muscles on the anterior aspect of the thigh, there are

hamstring muscles on the posterior side which flex the leg and extend the thigh. These

14.1 Anatomy of the Thigh and Leg 471

Fig. 14.2 Anterior view of

the right femur. The

spherical femoral head fits

into the acetabulum of the

pelvis while the condyles on

the distal end roll and slide

on the two tibial plateaus

(taken from Carola et al.

(1992)). Republished with






permission conveyed

through Copyright


Greater trochanter

Head

Fovea capitis

Neck

Lesser trochanter

Shaft

Shaft

Lateral

epicondyle

Lateral condyle

Patellar surface

Medial epicondyle

Medial condyle

are the biceps femoris the semitendinosus and the semimembranosus. There are also

muscles that adduct the thigh. Some of these are shown in Fig. 14.6 which is a crosssection

of the thigh. The leg has 14 muscles, 5 extensors, 7 flexors, and 2 lateral

muscles called peroneals. The anterior muscles act to plantar flex the foot, extend the

toes, and invert the foot while the posterior muscles dorsiflex the foot, flex the toes,

and also invert the foot. The lateral muscles evert the foot. More discussion will

follow in Chap. 15 which deals with the biomechanics of foot injury (Fig. 14.7).

The anatomy of the ligaments around the knee joint is also of biomechanical

interest. The knee is a unique joint in that its motion is not constrained by bony

structures. Instead, it is held in place by four ligaments, two on either side of the

knee and two in the center of the joint. The lateral collateral ligament (LCL) and the

medial collateral ligaments (MCL) on either side of the knee provide lateral

stability to the joint, as shown in Fig. 14.8. The cruciate ligaments are located in


A

B

FEMUR

Lateral condyle

of tibia

Intercondylar

eminence

of tibia

PATELLA

Intercondylar

eminence

of tibia

Proximal tibiofibular

joint

Medial condyle

of tibia

Lateral condyle

of tibia

Head of fibula

Medial

condyle of

tibia

Head of fibula

Tibial tuberosity

TIBIA

FIBULA

Shaft of fibula

Shaft of tibia

Fibular notch

Medial malleolus

Lateral malleolus

TALUS

Talocrural

(ankle) joint

Distal tibiofibular

joint

Lateral malleolus

Medial malleolus

Fig. 14.3 Frontal view of the right tibia and fibula. In (A), the proximal and distal articulations are

shown. In (B), the location of the head of the fibula is seen in detail. It does not articulate with the

femur. Also, in (B), the distal end of the fibula is the lateral malleolus while the distal end of the

tibia is the medial malleolus (taken from Carola et al. (1992)). Republished with permission of



the center of the knee joint, forming a cross and hence their name. By being in the

center of the joint, they allow a wide range of motion while not taking up a lot of

space. The cruciates are flat but rounded in shape. They connect the tibia to the

femur and are enveloped by a synovial membrane. The anterior cruciate ligament

(ACL) is attached to the anterior aspect of the head of the tibia, in front of the

14.1 Anatomy of the Thigh and Leg 473

A

Base

B

Base

Facet

for medial

condyle

of femur

Facet

for lateral

condyle

of femur

Apex

Apex

Fig. 14.4 (A) Frontal view of the patella. (B) Rear view of the patella (taken from Carola et al.

(1992)). Republished with permission of McGraw-Hill Education, from R. Carola, J.P. Harley, C.

R. Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992; permission conveyed through


Fig. 14.5 Side view of the

femoro-tibial joint showing

the quadriceps and patella

tendons that hold the patella

in place

intercondyloid eminence and originates from deep within the intercondylar notch

of the distal femur. It is about 4 cm long and 10 mm wide. It has two principal

bands, a small anteromedial band and a bulkier posteromedial band. The former is

tight when the knee is in flexion while the latter is tight when the knee is in

extension and internal rotation. The posterior cruciate ligament (PCL) is attached

to the posterior head of the tibial plateau and originates from the roof of the

intercondylar notch and the lateral edge of the medial femoral condyle. It is also

about 4 cm in length and about 13 mm wide. It also has two bands. The

anterolateral band consists of about 65 % of the PCL and is taut with the knee in

flexion. The smaller posterolateral band is taut in extension. The ACL prevents the

tibia from sliding forward relative to the femur while the PCL prevents tibia from

sliding rearward relative to the femur.

VASTUS LATERALIS

RECTUS

FEMORIS

VASTUS INTERMEDIUS

Femur

Nerve to Vastus medialis

Saphenous nerve

VASTUS

MEDIALIS

SARTORIUS

Femoral artery in the

adductor canal

Great saphenous vein

Femoral vein

GRACILIS

ADDUCTOR

LONGUS

SEMI-

MEMBRAN

ADDUCTOR

MAGNUS

SEMITENDINOSUS

BICEPS

FEMORIS

(LONG

HEAD)

Arteria profunda

femoris

Biceps femoris

(short head)

Sciatic nerve

Posterior femoral cutaneous nerve

Fig. 14.6 Muscles of the mid-thigh viewed in cross-section. The femur is among the anterior

extensor muscles (taken from Gray (1973))

Fig. 14.7 Ligaments of the knee - The lateral and medial collateral ligaments and the cruciate

ligaments hold the knee in place. The patella has been removed and the patellar tendon has been

cut (taken from Carola et al. (1992)). Republished with permission of McGraw-Hill Education,

from R. Carola, J.P. Harley, C.R. Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992;


14.2 Injury Mechanisms of the Thigh and Leg 475

Fig. 14.8 Expanded view

of the cruciate ligaments of

the knee - The ACL is

attached to the anterior

aspect of the tibial plateau

while the PCL is attached to

its posterior aspect

14.2 Injury Mechanisms of the Thigh and Leg

The two important injury mechanisms of the thigh and leg are fracture of the long

bones and injury to the knee and ankle. Joint injuries are more disabling and more

difficult to treat.

14.2.1 Long Bone Fractures Due to Tensile Strains

For the long bones, the injury mechanism is tension because bone is weak in

tension. High tensile strains develop under bending loads and thus the mechanism

of failure is generally a bending mechanism. It should also be kept in mind that

bone is relatively brittle compared with other tissues in the body and its failure

strain ranges from 1.2 to 2.5 %. Even in torsion, it can be demonstrated that tension

is the failure mechanism. The bone shown in Fig. 14.9 is subjected to a torsional

load and the failure mode is a spiral fracture. If we consider a free body at the site of

the fracture, the horizontal shear forces are due to the applied torque. This couple

needs to be balanced by an equal and opposite couple on the vertical faces to keep it

from rotating. Figure 14.10 is an enlarged view of the free body diagram and the

shear resultants produce a tensile force at 45 deg, to the long axis of the bone,

causing the bone to fail at this angle. The result is a spiral fracture.


Fig. 14.9 Torsional load

applied to a long bone

Fig. 14.10 Free body

diagram of an element of

bone at the fracture site. The

shear resultants form a

tensile force at 45 deg to the

long axis of the bone,

causing a spiral fracture

A pure bending load on a long bone will produce a clean transverse fracture

across the bone while a greenstick fracture occurs in immature bone in which there

is a fracture on the tension side and buckling of the bone on the compression side, as

shown in Fig. 14.11. Compression of a long bone from one of its ends will produce


Fig. 14.11 Example

of a greenstick fracture

of the humerus

(Witmer et al. (2017)).

Reprinted from Sabiston

Textbook of Surgery, ed. by

C.M. Townsend Jr. et al.,

20th edn. Chapter 18,

Emergency care of

musculoskeletal injuries by

D.K. Witmer, S.T.

Marshall, B.D. Browner,


Elsevier

comminuted fractures, such as the pilon (pylon) fracture of the ankle due to a

dynamic load applied to the distal end of the tibia. Figure 14.12 shows a severe

pilon fracture with many fragments. This appears to be a compression induced

injury but it will be shown later that the fractures originate with the development of

a tensile stress in the distal tibia. In summary, tension is the principal mechanism of

bony fracture.

14.2.2 Injury Mechanisms Involving the Knee

In terms of joint injuries, the knee is the most frequently injured joint among

athletes. The ACL and the MCL are at risk and the biomechanics of their injury

in sports is discussed in Chap. 19. In the automotive crash environment, the PCL

can be ruptured if the front dash of the car is not properly designed. A vertically

oriented dash allows the tibial tuberosity to contact it and push the tibia rearward in

a frontal crash. The tuberosity only protrudes a few millimeters from the tibial

surface but it is large enough to exert high tensile strains in the PCL, causing it to


Fig. 14.12 Example of a

comminuted Pilon fracture

caused by a compressive

load applied to the distal

end of the tibia by the talus

(ankle bone)

rupture (Viano et al. 1978). Even in small cars, the dash is designed to slope away

from the knees to avoid PCL rupture. If the dash contacts other parts of the tibia, the

leg can still load the PCL and cause it to rupture (Viano et al. 1978). Thus, it is

better to load the knee and make the load go through the femur. Before the airbag

became available in all cars, it was not uncommon to see knee bolsters installed in

front of the dash to cushion the impact of the knee and to avoid contacting the tibial

tuberosity (Cheng et al. 1979). A cross-section of a 1979 Volkswagen rabbit knee

bolster is shown in Fig. 14.13.

The knee injury mechanism is of concern to automotive safety designers because

FMVSS only addresses the femoral fracture limit of 10 kN and says nothing about

preventing injury to the patella or the condyles. It is hypothesized that the type of

injury sustained by the knee depends on the type of impact. If the knee hits a rigid

dash so that contact is made with only the patella, then a stellate type patella

fracture of the type shown in Fig. 14.14 would occur. Since the impact is not

borne by the condyles surrounding the patella, the condylar notch is also fractured

by the rearward motion of the patella. This fracture is shown in Fig. 14.15. If the

dash is padded with stiff padding so that there is no condylar load, patella fracture

can be prevented but condylar notch fractures can still occur. If there is adequate

padding to distribute the load to the condyles, then knee fracture can be prevented.


Fig. 14.13 Cross-section of

a 1978 VW Rabbit knee

bolster designed to protect

the knee and to avoid PCL

rupture (taken from Cheng

et al. (1984))

Fig. 14.14 Stellate fracture

of the patella due to direct

impact against a rigid

surface. A stellate fracture

is one with central point of

injury from which radiate

numerous fissures

(Copyright may be held by

LinkedIn)

These scenarios are depicted in Fig. 14.16. If the knee remains intact, the impact

force is transmitted to the femur and onto the acetabulum which can fracture at low

loading rates, as hypothesized by Rupp et al. (2002). If the dash is heavily padded,

the knee becomes “pocketed” in the dash and shear forces in the plane of the dash


Fig. 14.15 A condylar

notch fracture is caused by

the rearward motion of the

patella into the knee joint. It

is likely to occur if the knee

load is not shared by the

femoral condyles

surrounding the patella

(Hayashi et al. 1996)

F

F

F

F

Rigid impact on the Patella

Padding distributes load to the Condyles

Fig. 14.16 Illustration of the effect of padding to distribute the knee load to the condyles and thus

prevent patella and condylar notch fractures (Hayashi et al. 1996)

bend the femur about two axes, causing a fracture of the femoral shaft. This is

shown in Fig. 14.17.

Hayashi et al. (1996) validated the above hypotheses by conducting cadaveric

knee testing. They also determined the optimal stiffness for knee padding.

The experimental set-up is shown in Fig. 14.18. The femur was cut off distal to

the greater trochanter and held firmly in a cylinder filled with a potting compound.

The rest of the leg was intact. The knee was impacted at 5 m/s by a pendulum that

was covered with padding of different stiffnesses. A 450-psi (31 kPa) aluminum

honeycomb pad (Hexcel) was used as a stiff pad and a 50-psi (345 kPa) paper


Fig. 14.17 Illustration of

large knee loads that

develop if the dash is

heavily padded, pocketing

the knee. The horizontal and

vertical shear forces in the

pocket can fracture the

femoral shaft

Fig. 14.18 Experimental set-up for knee impacts to validate the hypothesis that padding affects

the type of knee fracture and to determine the optimal stiffness of the padding to prevent knee

injury (taken from Hayashi et al. (1996))

honeycomb pad was used as a soft pad. Ten specimens from five cadavers were

used. Cadaver data and test results are shown in Table 14.1. There was one rigid

impact just to show that a patella fracture would be the result. Previous studies have

created many such fractures (Patrick et al. 1965). The rigid pad (450-psi Hexcel)

caused a split condylar fracture because it only deformed 7 mm and was not able to

distribute the load to the condyles. For the four 50-psi paper honeycomb tests, the

condyles and the patella shared the load and no fractures were observed. However,

because of the softness of the padding, there were two femoral shaft fractures due to


Table 14.1 Knee pendulum impact data from Hayashi et al. (1996)

Test

No.

Cadaver

gender

Cadaver

age

Pendulum

velocity (m/s)

Padding type

Padding

stiffness (psi)

Peak

force

(kN)

1 Male 50 5.0 None Rigid 17.4

2 Male 50 5.1 Al Hexcell 450 15.5

3 Male 66 5.0 3-in Paper HC 50 5.2

4 Male 66 4.9 3-in Paper HC 50 6.7

5 Male 45 4.8 2-in Paper HC 50 6.4

6 Male 45 5.1 2-in Paper HC 50 9.4

7 Male 61 5.0 Al Hexcel 100 9.8

8 Male 61 5.4 Al Hexcel 100 9.8

9 Male 68 5.5 Al Hexcel 100 10.5

10 Male 68 5.4 Al Hexcel 100 10.1

Al Aluminum, HC Honeycomb

Fig. 14.19 Finite element model of knee impact simulating the Hayashi experiments (taken from

Hayashi et al. (1996))

pocketing of the knee. In order to find the optimum stiffness for the knee pads, a

100-psi aluminum honeycomb pad was tested. In two of the four tests, condylar

split fractures were found along with subchondral injury to the patella and the

condyles in all tests. That is, the optimal stiffness is just below 100 psi, probably

between 80 and 90 psi (551 and 620 kPa).

A finite element model of the Hayashi experiment was developed, as shown in

Fig. 14.19. The model was first validated against data from dummy knee impacts


Fig. 14.20 Validation of the knee impact model by Hayashi et al. (1996)—(A) Comparison of

rigid impact response, (B) Comparison of response for a rigid padding impact (450 psi), (C)

Comparison of response for a 100 psi pad impact, and (D) Comparison of response for a 50 psi pad

impact (Hayashi et al. (1996))

after which it was validated against both rigid and padded cadaveric knee impacts.

A comparison of model predicted and measured impact forces is shown in

Fig. 14.20 for the rigid impact and the three padded impacts. For the rigid impact,

the model predicted a high stress concentration in the condylar notch with no load

shared by the condyles. For the 100-psi pad, the load sharing by the condyles was

about 16 %, as shown in Fig. 14.21. It can be concluded that both the experimental

results and the model prediction show that the hypothesis is valid and that the

padding needed to be soft enough to distribute some of the impact load to the

condyles. If the padding is too soft, femoral shaft fractures will occur. The optimal

stiffness appears to be just under 100 psi (689 kPa).


Fig. 14.21 Load sharing between the patella and the condyles as predicted by the Hayashi

model—The condyles share 16 % of the load if a 100-psi pad was used (taken from Hayashi

et al. (1996))

14.2.3 Injury Mechanisms Involving the Ankle

The pilon fracture described in Sect. 14.2.1 is a common injury whenever there is

footwell intrusion in a frontal collision. This injury is well known to the orthopedist

but the mechanisms involved in producing this complex fracture were unclear.

Attempts at reproducing this injury in the cadaver were largely unsuccessful.

Yoganandan et al. (1996) and Klopp et al. (1997) impacted the foot and ankle

and the most frequent fracture mode was fracture of the calcaneus (heel bone).

Kitagawa et al. (1998) were the first to reproduce pilon fractures by impacting the

sole of the foot, simulating brake pedal interaction with the lower limb during a

frontal crash. It was hypothesized that in addition to the external force from the

brake pedal, the ankle and tibia were subjected to muscular pre-loading because of

brake application. This is one of the rare occasions which require active muscle

simulation in a cadaver to perform the experiment. The test set-up is shown in

Fig. 14.22. The cadaver tibia was potted in epoxy and rigidly attached to a fixture

table so that it could resist the large forces generated to create a pilon fracture. The


Fig. 14.22 Experimental

set-up to produce a pilon

fracture in a cadaver leg

(adapted from Kitagawa

et al. (1998))

Fig. 14.23 The tendon catcher was a modified rope holder with spikes inside. However, the spikes

were not enough to hold the tendon and surgical suture was used to reinforce the assembly so that it

could resist a load of 2 kN (taken from Kitagawa et al. (1998))

tibial axis was horizontal and the bottom of the foot was impacted by an 18-kg

pendulum with the point of impact 50 mm below the tibial axis. It was critical that

the location of impact be precise because deviations would result in either a

calcaneal fracture or a failure to produce a pilon fracture. Another important part

of the experiment was the introduction of a calf muscle or Achilles tendon force

during the test. The magnitude of this force was estimated to be 2 kN based on

emergency braking tests done by volunteers. A specially designed tendon catcher

was used to grab the slippery tendon and permitted the application of up to 2 kN of

tension on the tendon without slipping. This tendon catcher is shown in Fig. 14.23.

The simulated muscle load was limited to 1.8 kN by an energy absorber (EA in

Fig. 14.22) which is a piece of metal with a tear in it and was designed to tear at a

constant force of 1.8 kN. The Achilles tendon force increased the compression in


Fig. 14.24 The measured tibial force is consistently 2 kN higher than the impact force, whether

the pilon fracture occurred or not (taken from Kitagawa et al. (1998))

Table 14.2 Of the 16 impact tests conducted there were five pilon fractures

CAD# Fimp(N) Ftib(N) Autopsy CAD# Fimp(N) Ftib(N) Autopsy

271R 5344 7801 Calc. FX 28443R 5786 7779 Calc. FX

271L 4932 8152 No FX 28443L 4890 7759 Calc. FX

242R 5969 8549 Calc. FX 28441R 4462 6738 Pilon FX

242L 5179 7620 Pilon FX 28441L 2917 5737 Calc. FX

715R 5116 7110 Pilon FX 900R 5483 8654 Calc. FX

715L 4971 7349 Pilon FX 900L 6012 8803 Calc. FX

28483R 4791 7145 Calc. FX 480R 5765 9108 Calc. FX

28483L 5306 7437 Calc. FX 480L 4996 7091 Pilon FX

the tibia and less impact force was necessary to cause the pilon fracture. This is

shown in Fig. 14.24. The results are shown in Table 14.2. Of the 16 impact tests

conducted there were 5 pylon fractures. This is the largest number of pilon fractures

attained in any test series and validates the hypothesis that an internal tibial

compression force was necessary to cause the pilon fracture. If there were no

Achilles tendon force and the external impact force was increased by about 2 kN,

and calcaneal fractures will be the result. That is, a pilon fracture requires a force of

7 kN but 2 of those 7 kN need to be internal.

In order to determine the mechanism of pilon fractures a finite element model of

the ankle joint was used to determine the stress or strain distribution within the

joint. The model selected was originally developed by Beaugonin et al. (1996) and

improved upon by Beaugonin et al. (1997). In the original 1996 model, the bones of

the foot were assumed to be rigid and in the improved 1997 model the tarsal bones

of the foot, including the talus and the distal tibia and fibula were assumed to be

linearly elastic. The metatarsal bones and the phalanges of the foot were assumed to

be rigid. Figure 14.25 shows the foot and ankle model with deformable tarsal bones

and Fig. 14.26 shows a comparison of the predicted forces with those measured


Fig. 14.25 The foot and

ankle model developed by

Beaugonin et al. (1997) was

used to simulate the impact

experiments conducted by

Kitagawa et al. (1998)

Fig. 14.26 Comparison of model predicted forces with experimental data obtained by Kitagawa

et al. (1998) for the simulation of pilon fractures (taken from Kitagawa et al. (1998))

experimentally. There is good correlation in the axial tibial force. Upon analyzing

the distribution of principal stresses, it was found that an area of tensile stress

concentration occurred, at 6 ms after impact, in the distal tibia at the junction of

plafond (the articular surface of the distal end of the tibia) with the inside surface of

the medial malleolus, suggesting that a fracture could originate there and propagate

into the distal end of the femur to result in a pilon fracture (Fig. 14.27). Although

more research is necessary to confirm this hypothesis, we can say that it fits in with

the theory that bone is weak in tension and that pilon fractures have a tensile origin

despite the fact that it was caused by a seemingly compressive load.


Fig. 14.27 Calculated first principal stress in the ankle joint. It is seen that an area of tensile stress

concentration is developed in the distal tibia at the junction of plafond (the articular surface of the

distal end of the tibia) near the inside surface of the medial malleolus, suggesting that a fracture

could originate there and propagate into the distal end of the femur to result in a pilon fracture

(taken from Kitagawa et al. (1998))

14.3 Mechanical Response of the Thigh and Leg to Impact

Biomechanical response data of the thigh and tibia to impact are needed for the

design of dummies which are used in the automotive industry to ensure that cars are

designed to comply with the FMVSS. For the femur, FMVSS 208 sets a 10 kN limit

for frontal knee impact and the response of the dummy femur should mimic that of

the human so that the vehicle is not only safe for dummies but also for its human

occupants.

14.3.1 Response of the Femur (Knee) to Frontal Impact

Patrick et al. (1967) were the first to provide response data on knee impact.

Unrestrained cadavers were placed on a deceleration sled and made to impact the

head, chest, and knees in the same test. Patrick et al. (1965) provided the first

response data on knee impact. Force-time curves were presented for the right and

left knee. The data are shown in Fig. 14.28 for historical interest. The peak values

have been written in by hand and the duration can be estimated from the vertical

timing lines that are 10 ms apart. Patrick et al. (1967) provided data from four more

cadaver tests and the raw response data were published in the form of light-beam

chart recordings similar to those shown in Fig. 14.28. A comprehensive study by

Melvin et al. (1975) revealed that the force-time curves for fractured femurs were

different from those that were not fractured. There is also a second peak in the

sub-fracture response, the reason for which was not provided. The response curves

14.3 Mechanical Response of the Thigh and Leg to Impact 489

Fig. 14.28 The first knee

response curves recorded by

Patrick et al. (1965). The

data were taken from a

whole-body cadaveric sled

test in which both knee

impact loads were measured

(taken from Patrick

et al. (1965))

are shown in Fig. 14.29. Strain data were also collected in this study. The femur was

subjected to bending because of the eccentricity of the femoral neck. The neutral

axis was found to be approximately normal to the axis of the femoral neck, as

shown in Fig. 14.30. Apparently, the lateral surface of the femur was in tension.

Additional response data of knee impact against Styrofoam and aluminum

honeycomb were obtained by Hering and Patrick (1977) to quantify knee response

against deformable materials so that dummy knee response can be tuned to human

response. The Styrofoam used was called Styrofoam DB (for Decorative Billet) and

was manufactured by Dow Chemical Co. Its density was 219–314 N/m 3 (1.4–2.0 lb/

ft 3 ). The aluminum honeycomb was manufactured by Hexcel Corporation. It had a

crush strength of 2965 % kPa (435 % psi). The crush properties of Styrofoam

DB and aluminum honeycomb are different. Styrofoam offers increasing resistance

with penetration while the Hexcel offers uniform resistance independent of the

depth of crush. Cadaver knees were set at 90 deg flexion and impacted frontally by a

52.3-kg (115-lb) pendulum at nominal speeds of 1.8 and 3.6 m/s (5.9 and 11.8 ft/s).

The response characteristics are shown in Fig. 14.31. Unfortunately, there do not


A

(lbs)

2000

(N)

(N-sec)

(lb-sec)

20

7500

75

1500

15

FORCE

1000

5000

50

10

IMPULSE

500

2500

25

5

0

0

B

(lbs) (N)

5000

5 10 15 20 25 30

TIME msec

(N-sec)

0

(lb-sec)

25

2000 100

4000

20

FORCE

3000

2000

1500

1000

75

50

15

10

IMPULSE

1000

500

25

5

0

0 5 10 15 20 25 30

TIME msec

0

Fig. 14.29 Femoral response curves for axial knee impacts. (A) Non-fracture response. (B)

Fracture response (taken from Melvin et al. (1975))

14.3 Mechanical Response of the Thigh and Leg to Impact 491

UNIAXIAL

STRAIN GAGE

TOP STRAIN

GAGE ROSETTE

Lateral

Aspect

SIDE STRAIN

GAGE ROSETTE

FEMORAL NECK AXIS

NEUTRAL AXIS

OF BENDING

Fig. 14.30 Estimate of the neutral axis for bending in femoral shaft in relation to the axis of the

femora neck, based on strain gage data. Apparently, the lateral surface of the femur is in tension

(taken from Melvin et al. (1975))

A

8000

B

8000

Mean and ± one standard deviation of

12 cadavers

Mean and ± one standard deviation of 12 cadavers

6000

6000

Knee Force (N)

4000

Knee Force (N)

4000

2000

2000

0

0 20 40 60

Knee penetration (mm)

80 100

0

0 20 40 60 80 100

Knee penetration (mm)

Fig. 14.31 (A) Knee impact response to Styrofoam DB impacts at 3.6 m/s (11.8 ft/s). (B) Knee

impact response to aluminum honeycomb impacts at 3.6 m/s (11.8 ft/s) (taken from Hering and

Patrick (1977))

appear to be any force-deflection curves for rigid knee impacts that could be used to

compare with these padded impacts.

Much of the response data cited above were acquired as part of a study to

generate tolerance data for the knee and femur. The other purpose was to compare


human response to that of crash dummies which needed to be made more human

like. Typically, response data are used to design more human-like dummies but in

the case of the knee and femur, the basic design of the knee and femur (and tibia)

was finalized before any of the response data became available. Metal rods were

used for the dummy femur and tibia to ensure they would not break during crash

testing, enabling the dummy to be tested repeatedly without damage to the lower

limbs. However, the response data are useful in the development of computer

models.

14.3.2 Tibial Response to Impact

Most of the studies on tibial response and tolerance to transverse impact were

motivated by the injuries sustained by pedestrians in a car-pedestrian impact. Thus,

the data presented were in the form of fracture force and fracture type. The work of

Pritz et al. (1975) involved vehicular front end cadaveric impacts to the whole body.

Some of the tests were to the upper tibia. Kramer et al. (1973) tested a large number

of cadavers, impacting them frontally at various location of the proximal tibia and

obtained 43 fractures. They performed 209 tests using cylindrical impactors of two

different sizes, 8.5 and 5.7 in (22 and 14.5 cm) in diameter. The response was

presented in terms of leg acceleration which was converted to force. There was

much scatter in the data and analysis proved difficult. Nyquist et al. (1985)

conducted a series of controlled impacts on denuded tibias both frontally and

laterally, using a 32-kg linear impactor. The bones were simply supported at the

two ends and the reaction force to the mid-shaft impact was measured. The bending

moment at the mid-shaft was computed by taking the product of the average

reaction force and the half the length of the tibia. There was a total of 20 tests,

11 of which were anteroposterior. The other 9 were lateromedial. The speed of

impact varied from 2.1 to 6.9 m/s and the distance between supports varied from

229 to 305 mm. Fracture occurred in each test with 12 tibias sustaining comminuted

fractures. The peak bending moment varied from 176 to 453 N.m and the computed

peak tensile stress at failure was 94 to 435 MPa, based on the measured bone crosssection

at the mid-shaft. For anteroposterior loading, the force-deflection response

was linear with an average slope of 282 N/mm. The lateromedial response was

bilinear. The initial slope was 105 N/mm and the final slope was 265 N/mm. The

reason for the bilinear response is the fibula which stiffens the bony complex at

large tibial deflections.

14.4 Tolerance of the Thigh and Leg to Impact 493

14.4 Tolerance of the Thigh and Leg to Impact

Interest in the tolerance of the thigh (femur) was stimulated by the knee load limit

imposed by FMVSS 208. Tolerance data for the tibia were acquired much later as

there was no Federal regulation governing the tibia.

14.4.1 Tolerance of the Thigh (Femur)

Patrick et al. (1965, 1967) were the first researchers to perform whole-body frontal

knee impacts on a sled to determine the dynamic failure load of femurs. The

duration of the impacts was in the 25–35 ms range. They suggested that a conservative

fracture load for the femur should be 1400 lb (6.2 kN) even though, in five

cases, the maximum applied force exceeded 2000 lb (8.9 kN). The specimens tested

were embalmed and it was subsequently found that embalmed bone was weaker

than unembalmed or fresh bone (Kress and Porta 2001). Follow-on studies were

performed by Powell et al. (1975) who found that the failure load of embalmed

femurs, subjected to pendulum knee impacts averaged 2360 lb (10.5 kN) even

though the specimens were impacted several times at lower loads prior to fracture.

The impact duration was between 10 and 20 ms. Melvin et al. (1975) tested

unembalmed cadaver femurs, using a 20.9-kg (45.9-lb) linear striker that was

padded with a 2.5 cm of Ensolite foam. The impact duration using this foam varied

from 6 to 18 ms. The experimental set-up is shown in Fig. 14.32. In the 19 padded

impacts, there were only four fractures and the failure load for the femur ranged

from 3500 to 4400 lb (15.6 to 19.6 kN), excluding data from specimens that

fractured at a screw hole, a stress riser. For the non-fractured specimens, the peak

load they sustained was as high as 5510 lb (24.5 kN).

Fig. 14.32 Knee/femur

impact set-up used by

Melvin et al. (1975) who

were the first to test

unembalmed cadaveric

knees with a linear impactor

(taken from Melvin et al.

(1975))


Both Powell et al. (1975) and Melvin et al. (1975) indicated that the femur was

subjected to high bending moments during knee impact. This statement was based

on strain gages mounted on the femur. The moment is due to the femoral neck

which renders the knee impact load eccentric with respect to the acetabulum. Since

bending can generate high tensile stresses, they can be the cause of femoral shaft

fracture. Yet the tolerance of the femur is expressed in terms of the knee impact

force, as required by FMVSS 208. It is not likely that the standard for knee impact

will change in the foreseeable future but the present criterion of 10 kN was largely

influenced by the work of Melvin et al. (1975).

14.5 Tolerance of the Leg

The studies by Kramer et al. (1973) and Nyquist et al. (1985) were actually

tolerance studies. Despite the large scatter in the failure data obtained by Kramer

et al. (1973), it was possible to arrive at a median failure load of 4.3 kN at 7.1 m/s

and 3.3 kN at 6.3 m/s. Note that median values are different for average values.

They are the center values of a range of numbers and are not affected by data

scatter. The data obtained by Nyquist et al. (1985) were more consistent and

tolerance was expressed in terms of bending moment to failure, as shown in

Table 14.3 for all tests in the first row and for AP and LM tests in the next two

rows, respectively. It is seen that the tolerance for lateromedial bending is higher

than that for anteroposterior bending. Tables 14.4 and 14.5 show the tolerance for

males and females and the difference is even more dramatic between the sexes.

However, the tolerance for lateromedial bending is consistently higher than that

anteroposterior bending. These data are useful for assessing car-pedestrian injuries

Table 14.3 Tolerance of the Tibia for Anteroposterior and Lateromedial loading for both sexes

(taken from Nyquist et al. (1985))

Direction of load

Bending moment

mean (N.m)

Bending moment

SD (N.m) Force mean (kN) Force (SD (kN)

AP & LM 308 79 4.83 1.23

AP only 300 77 4.60 1.37

LM only 317 84 4.86 1.27

Table 14.4 Tolerance of the Tibia for Anteroposterior and Lateromedial Loading for males only


Direction of load

Bending moment

mean (N.m)

Bending moment


AP & LM 317 88 4.80 1.45

AP only 304 90 4.57 1.59

LM only 330 89 5.03 1.37

14.6 The Tibia Index 495

Table 14.5 Tolerance of the Tibia for Anteroposterior and Lateromedial loading for females only


Direction of load

Bending moment

mean (N.m)

Bending moment


AP & LM 278 30 4.48 0.61

AP only 288 37 4.70 0.74

LM only 264 14 4.16 0.22

for leg-bumper impact. If we are concerned with axial compression, such as the

loading that causes pilon fractures, the tolerable load was found to be 5 kN,

according to the research done by Kitagawa et al. (1998). Unfortunately, a tolerance

of 7 kN is often cited due to the lack of attention to the difference between forces

generated externally and those due to muscular contraction.

14.6 The Tibia Index

The NHTSA has been entertaining proposals for an injury criterion for the tibia.

Mertz (1984) proposed the Tibia Index (TI) as a possible candidate at a meeting of

the International Standards Organization (ISO) which was formalized in Mertz

(2002). The tibia index is given by:

TI ¼ Mt ðÞ=M c þ Ft ðÞ=F c < 1:0

where

M(t) is the resultant bending moment acting on the tibia at time, t

M c is the critical bending moment for the tibia

F(t) is the absolute value of the corresponding axial compressive force at time, t,

and

F c is the critical compressive for the tibia.

That is, the sum of the moment and force ratios should be less than 1 for tibial

fractures to be unlikely. It is analogous to the column failure criterion due to

combined bending and compression.

The critical moment for the 50th percentile male was set at 225 N.m while the

critical compression force was set at 35.9 kN. Justification for the use of these

values was not provided by Mertz (2002). It can be assumed that the critical

moment was based on the work of Nyquist et al. (1985) although the minimum

value was 264 N.m (Table 14.5). As for the critical force of 35.9 kN, it is much

higher than the 5 kN value cited above for pilon fractures. Lower values for F c have

been suggested, such as 12 kN, and the criterion has been raised from 1.0 to 1.3

(Kuppa et al. 2001). However, the tibia can be injured in many ways and in different

regions. It is best to consider the tolerance of individual regions and not rely on an

overall criterion that is too general for application to the whole bone.


14.7 An Impact Model of the Lower Extremity

Many lower extremity models were developed in the 1990s and in the early 2000s

to address different aspects of lower limb injuries. For example, the work of

Hayashi et al. (1996) and of Kitagawa et al. (1998) has already been discussed in

this chapter. There is also a finite element model of the lower limb simulating

pedestrian impact by Takahashi et al. (2000) and a tibia mid-shaft finite element

model simulating fracture due to a frontal knee impact by Tamura et al. (2001).

Beillas et al. (1999) developed a finite element model of the foot and ankle designed

to study ligamentous injury around the ankle. In this model, the forefoot was

simulated with rigid elements because bony fracture was not part of the study.

There did not appear to be a finite element model that could be used to simulate a

variety of impacts to the lower limb until Beillas et al. (1999) developed a versatile

model that was validated against nine experimental studies ranging from

pedestrian-bumper impacts to frontal sled impacts and pendulum knee impacts.

In order to develop this model, Beillas et al. (1999) needed to obtain the

geometry of the lower limb from the pelvis down to the toes. MRI scans of an

entire cadaveric lower limb were obtained at 20-mm intervals. The limb was

scanned in sections which were aligned using anatomical landmarks to produce a

scan of the entire limb. More detailed scans were made of the knee to image the

menisci. Meshing of the lower limb was performed using Hypermesh (Altair, Troy,

Michigan). The finite element solver used was Radioss (Mecalog SA, Paris,

France). Because of the size of the model and the need to maintain a time step of

1 μs, the element size needed to be 2 mm or larger. However, the compact bone

thickness ranged from 2 to 7 mm and it was not possible to use larger elements to

properly model the compact bone. The solution was to use shell elements to

represent compact bone and to locate them along the mid surface of the compact

bone. Spongy bone and cartilage were modeled using hexahedral (brick) elements

while shell and brick elements were used to model knee ligaments. Non-linear

spring elements were used to model the 28 groups of foot and ankle ligaments. Most

of the material properties of the tissues of the lower limb were taken from the

literature. For compact bone, it was assumed to be elastic-plastic and the assumed

properties are shown in Table 14.6. Some properties have a range of values because

they vary along the length of the bone and a graded variation was introduced to

avoid sudden discontinuities. For example, the Young’s modulus of compact bone

is lower at the two ends of a long bone than at the center. There is even a larger

variation in the properties of spongy bone. Similarly, for the knee and ankle

ligaments, cartilage, the plantar (foot) pad, knee capsule, muscles and skin, different

values of Young’s modulus and viscous coefficients (where appropriate) were

assigned to them. The literature sources used in Table 14.6 and for the other tissues

can be found in Beillas et al. (1999). Joints were modeled as non-linear sliding

interfaces with a coefficient of friction of 0.01. The model is shown in Fig. 14.33.It

was based on MRI scans that were made with the knee flexed about 10 deg, as

shown in Fig. 14.33A. To configure the limb in typical driving position, it was

14.7 An Impact Model of the Lower Extremity 497

Table 14.6 List of material properties used to model bone (taken from Beillas et al. (2001))

Units Density g/mm 3 Young’s

modulus MPa

Diaphyseal

Femur/tibia

Metaphyseal

Femur/Tibia

Epiphyseal

compact

bone

Other (compact

bone

patella, fibula

and ankle)

Cancellous

bone

Poisson’s

ratio

Yield

stress

MPa

Failure

strain %

Failure

stress

MPa

0.0018–0.0021 16,000–17,500 0.3 120 3 125–135

0.0018–0.0020 12,000–15,000 0.3 80–100 3 110–130

0.0018 5000–6000 0.3 80–100 3 110–130

0.0015–0.0021 12,000–15,000 0.3 80–100 2–3 100–125

0.0013–0.00185 75–450 0.3 10 3 15

Fig. 14.33 (A–B) The

lower limb model moved

into a driving position by

applying a spring load to the

leg (taken from Beillas et al.

(2001))

Leg simplified representation

based on literature points

center of the hip (rotation only)

Sprig used to move the model

A Initial position

B Final position

necessary to position the thigh according to measurements made on seated drivers

by Schneider et al. (1983) and to rotate the leg to the position shown in Fig. 14.33B.

This was done by attaching two springs to the leg on one end and to a reference

point in the vehicle on the other to bring the leg down. A similar procedure was used

to place the model in a standing position to simulate car-pedestrian impacts.


Table 14.7 List of simulations used to validate the lower limb model by Beillas et al. (2001)

Test condition Setup Reference

Static or

dynamic

Tibia region:

Axial compression Present reanalysis S

Foot & Tibia complex (new set-up only)

Axial compression along the tibia Present reanalysis S

Femur-Knee-Tibia complex:

Horizontal impact on patella 90 knee angle Haut et al. (1995) D

Horizontal impact on patella 90 (+) knee angle Hayashi et al. (1996) D

Vertical impact on tibia 90 knee angle Banglmaier et al. (1999) D

A-P shear on tibia 90 knee angle Viano et al. (1978) D

Whole lower limb

Lateral-medial shear on proximal Standing position Kajzer et al. (1990) D

tibia

Knee bending (lateral-medial shear Standing position Kajzer et al. (1993) D

on distal tibia)

Whole body

Sled Cheng et al. (1984) D

The model was used to simulate nine different loading conditions summarized in

Table 14.7. The first two static simulations were for the replication of axial

compression tests on tibias carried out by Begeman and Aekbote (1996) and

Begeman and Paravasthu (1997a, b). Some of the tests were axial loads to the distal

tibia with the foot attached while others were tests without the foot. The original

data reported on the failure loads but, for the purposes of validating the model, the

tests were repeated using a total of 6 specimens. They were first tested with the foot

attached after which the foot was removed and the distal end of the tibia was

impacted. Force-deflection data were obtained for comparison with model predictions.

Figure 14.34 shows validation of the tests with the foot attached. The

model was similarly validated using test data without the feet. Beillas et al. (2001)

continued to validate the model against other experimental data. These include the

six data sets from Haut and Atkinson (1995) and Hayashi et al. (1996) for patella

impacts, Banglmaier et al. (1999) for rigid inferior to superior impacts to the tibia,

Viano et al. (1978) for anteroposterior loading of the tibia, and Kajzer et al. (1990,

1993) for shear and bending loads on the leg of a pedestrian to simulate lateral loads

due to bumper impact. Model results correlated fairly well with experimental data

but the match was not perfect. Details of these validation studies can be found in

Beillas et al. (2001). The final validation was to simulate a sled test conducted by

Cheng et al. (1984) to study the effect of a knee bolster on the knee and femur. The

cadaveric subject was restrained by an automatic three-point belt and a 1983 VW

knee bolster, similar to the one shown in Fig. 14.13. The simulated test set up is

shown in Fig. 14.35 which shows that the right leg is the FE leg. Kinematic results

are shown in Fig. 14.36 and a comparison of calculated and measured bolster and

femoral loads are shown in Fig. 14.37.

Foot and tibia static axial response

Force (N)

10000

Model

Exper: Hirsh & White

Exper: Huang et al

Exper:

Current study:

8000

Average (n=6)

Maximum

minimum of all specimen

minimum without specimen 152

6000

4000

2000

0

0.00 5.00 10.00 15.00 20.00

Displacement (mm)

Fig. 14.34 Validation of the foot and tibia model simulating a static load applied to the foot.

There were six tests on cadaveric specimens, one of which was osteoporotic (Test No. 152). The

model was not as stiff as the averaged data but it compared well with data from other tests

performed by Hirsch and White (1965), Huang et al. (1993) and Ker et al. (1987) (taken from

Beillas et al. (2001))

Fig. 14.35 Drawing of the

sled test set-up showing a

restrained Hybrid III

dummy seated in front of

VW knee bolster. The right

leg is a model of the human

lower limb (LLMS) (taken

from Beillas et al. (2001))


Fig. 14.36 Comparison of whole-body kinematics between sled test and model (A) and (B).

Details of skeletal contact with the knee bolster are shown in (C) while in (D) details of patella

contact with bolster are shown. These details cannot be easily visualized in a sled test but the

model is capable of showing the interaction (taken from Beillas et al. (2001))


Biomechanical research on the thigh and leg is virtually complete. With the

many contributions from a large number of investigators, there is not much left to

be done to obtain additional data. The injury mechanisms are also well defined and

understood and there are adequate tolerance data. This is one region of the body

where little additional biomechanical research is necessary to improve our knowledge

on impact injury to the thigh and leg. The one area of uncertainty is the use of

the tibial index or trying to apply it to the entire bone for different modes of impact.

It may be difficult to arrive at a universal tolerance criterion for the tibia.


A

15000

Knee Bolster Force (N)

1 Model Force in the direction of impact

2 Exper Force in the direction of impact

12500

10000

7500

5000

2500

0

B

-2500

12500

10000

Femur Force (N)

Model

Model

Model

Exper

Exper

Exper

Axial load

Medio-lateral load

Vertical load

Axial load

Medio-lateral load

Vertical load

7500

5000

2500

0

-2500

0 25 50 75 100 125 Time (ms)

Fig. 14.37 Comparison of knee impact force in the sled test using a VW knee bolster. The peak

deceleration was 35 g. (A) is a comparison of the measured and predicted force in the femur in the

direction of impact. (B) Compares the three components of force in the femur (taken from Beillas

et al. (2001))


14.1. The medial malleolus is:

[ ] (i) In the distal part of the tibia

[ ] (ii) In the distal part of the fibula


[ ] (iii) In the knee area

[ ] (iv) In the midshaft of the tibia

[ ] (v) In the midshaft of the fibula

14.2. The function of the patella is:

[ ] (i) To provide protection to the tibia

[ ] (ii) To provide a larger moment arm for the quadriceps muscles

[ ] (iii) To provide a smoother motion of the femur over the tibia

[ ] (iv) To provide an anchor for the hamstring muscles

[ ] (v) To provide a mechanism to wear out the knee joint

14.3. The femur has the following characteristics:

[ ] (i) It is the longest bone in the body

[ ] (ii) It does not have any spongy or trabecular bone

[ ] (iii) It has a spherical head at its distal end

[ ] (iv) It articulates with the fibula

[ ] (v) (i) and (iii)

14.4. Knee ligaments have the following characteristics:

[ ] (i) The anterior cruciate ligament prevents the knee from moving

posteriorly

[ ] (ii) The posterior cruciate ligament can be torn if the instrument panel

contacts the tibial tuberosity before it contacts the knee

[ ] (iii) The medial collateral ligament can be torn by an impact to the

medial side of the knee



14.5. Compact bone has the following mechanical properties:

[ ] (i) It is weak in compression

[ ] (ii) It is weak in tension

[ ] (iii) It is a brittle material



14.6. Spiral fractures in long bones occur as the result of

[ ] (i) A high bending load

[ ] (ii) A pure torsional load

[ ] (iii) The development of tensile principal stresses due to torsion




14.7. In the design of an instrument panel (IP), it is important to ensure that

[ ] (i) The first part of the knee to contact the IP is not the tibial tuberosity

[ ] (ii) The first part of the knee to contact the IP is the tibial tuberosity

[ ] (iii) The IP material is stiff, as long as it meets the 10 kN peak load

specified in FMVSS 208

[ ] (iv) The IP material is soft enough to pocket the knee during impact


14.8. In FMVSS 208, tolerance of the femur is expressed in terms of a compressive

force. Using the principles of impact biomechanics, one can say that:

[ ] (i) This is a good standard because, in frontal impacts, the femur is

loaded mainly in compression

[ ] (ii) This is a bad standard because bone does not fail in compression as

easily as it does in tension

[ ] (iii) This is a bad standard because one should use loads which cause

tensile stresses to be developed in the bone

[ ] (iv) This is bad standard because there is no consideration of torsional

loading


14.9. Tolerance of the tibia to midshaft transverse loads can be expressed in terms

of a bending moment

[ ] (i) The tibia is stronger when impacted laterally than when it is

impacted frontally

[ ] (ii) Male and female tolerance are almost the same

[ ] (iii) Only static tolerance data are available

[ ] (iv) In looking at the female data, it is seen that the female tibia is

stronger in lateral bending than in frontal bending


14.10. Tolerance of the distal tibia to pylon fracture

[ ] (i) Cannot be established because no one has done any work on this

injury

[ ] (ii) Is approximately 7 kN, taking into consideration muscle preload

[ ] (iii) Is approximately 5 kN, taking into consideration muscle preload

[ ] (iv) Is approximately 3 kN, taking into consideration muscle preload

[ ] (v) Cannot be established because this injury cannot be reproduced

experimentally

14.11. The mechanism for pylon fracture is

[ ] (i) Unknown because it has never been reproduced in the lab

[ ] (ii) Due to the development of tensile stresses in the fibula

[ ] (iii) Due to the development of tensile stresses on the inside surface of

the medial malleolus


[ ] (iv) Due to the development of compressive stresses at the distal end of

the tibia

[ ] (v) Due to the development of shear stresses in the distal end of the

tibia

14.12. Associated with pylon fractures is a split fracture of the calcaneus. The

mechanism of this fracture is

[ ] (i) Compressive failure of the trabecular bone in the calcaneus

[ ] (ii) Bending failure of the calcaneus due to tension in the Achilles

tendon

[ ] (iii) Tensile failure of the calcaneus due to tension in the Achilles tendon

[ ] (iv) Shear loading across the length of the calcaneus in the heel to toe

direction


14.13. To reproduce a pylon fracture in the laboratory, it is necessary to apply a

substantial force to the Achilles tendon, because, without this force,

[ ] (i) There would not be enough of a bending moment to fracture the

tibia

[ ] (ii) It would require too large of a compressive foot load to allow the

bones of the foot to transmit the load to the distal tibia

[ ] (iii) It would require the calcaneus to be strong enough to withstand a

high compressive load without fracturing



14.14. The Tibial Index is based on

[ ] (i) Sound biomechanical data

[ ] (ii) A simple engineering principle that things fail due to a combination

of axial load and bending

[ ] (iii) A finite element model of the tibia under axial and bending loads



14.15. The Tibial Index is

[ ] (i) Useful for preventing tibial shaft fractures

[ ] (ii) Is not applicable to the distal tibia

[ ] (iii) Is based on the use of failure data for bone in compression

[ ] (iv) Is based on the use of failure data for the tibia under bending


References 505


Prob

Ans

1 (i)

2 (ii)

3 (i)

4 (ii)

5 (v)

6 (v)

7 (i)

8 (v)

9 (i)

10 (iii)

11 (iii)

12 (iii)

13 (v)

14 (ii)

15 (v)

References

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223–228 (1992)


1973)

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A. Hirsch, L. White, Mechanical stiffness of man’s lower limbs Report 1810 S-F015 1404.

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C. Huang, H. Kitaoka, K. An, E.Y. Chao, Biomechanical evaluation of longitudinal arch stability.

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J. Kajzer, C. Cavallero, J. Bonnoit, A. Morjane, S. Ghanouchi, Response of the Knee joint in

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Y. Kitagawa, H. Ichikawa, A.I. King, R.S. Levine, A severe ankle and foot injury in frontal crashes

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G. Klopp, J.R. Crandall, G. Hall, W. Pilkey, S. Hurwitz, S. Kuppa, Mechanisms of injury and

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through vehicle design, in 19th Stapp Car Crash Conference, SAE Paper No. 751166, San

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Chapter 15

Impact Biomechanics of the Foot

This chapter deals with the biomechanics of impact injuries of the foot. In current

vehicles, foot injuries are usually the result of footwell intrusion caused by an offset

frontal impact. The force applied to the plantar (bottom) surface of the foot can

result in injury to both the midfoot and the hindfoot. In the early days of aviation,

the brake pedal in open cockpit single seaters was a round bar and there are

anecdotal records of pilots breaking their feet (midfoot) while doing a crash

landing. In the nineteenth century, French surgeon, Jacques Lisfranc de

St. Martin (1790–1847) treated injuries to the midfoot of Napoleon’s cavalrymen

when their foot got caught in the stirrups after they fell from their horse. This

serious foot injury is now named after Lisfranc.

15.1 Anatomy of the Foot and Ankle

The foot is the platform on which bipedal creatures walk. It not only supports the

weight of the entire body but also propels it during walking and running. As shown

in Fig. 15.1, the foot can be divided into a hindfoot which is made up of two of the

seven irregularly shaped tarsal bones, a midfoot consisting of the other five tarsal

bones, and the forefoot which consists of the phalanges (toes) and of five long bones

(metatarsals) that are located between the phalanges and the midfoot. The two large

bones of the hindfoot are the talus and the calcaneus. The former is the ankle bone

which articulates with the tibia and fibula while the latter is the heel bone which is

somewhat elongated in shape and serves as the anchor for the Achilles tendon in the

back of the leg. The five bones of the midfoot are the navicular, directly in front of

the talus and the medial, intermediate (middle), and lateral cuneiforms and the

cuboid all of which articulate between the metatarsals of the forefoot and the

navicular and the hindfoot. The cuboid also articulates with the calcaneus.

The forefoot is made up of five metatarsals that are classified as long bones and

of the phalanges of the foot. Each toe has three phalanges except the great toe which



509

510 15 Impact Biomechanics of the Foot

Fig. 15.1 Top view of the right foot showing all the bones of the foot (taken from Carola et al.

(1992)). Republished with permission of McGraw-Hill Education, from R. Carola, J.P. Harley,

C.R. Noback (eds.), Human Anatomy & Physiology, 2nd edn., 1992; permission conveyed through


has only two. All 26 bones of the foot are shown in Fig. 15.1. When viewed from the

side, the foot is arched, as shown in Fig. 15.2. The bones of the foot are configured

to form the arch but it is maintained under load principally by the plantar

aponeuerosis which originates at the calcaneus and inserts into the proximal

phalanges. The arch is important to energy savings during locomotion by storing

some of the energy in the foot during ground contact.

There are very few muscles in the foot. Motion of the toes is controlled by

muscles in the leg, the tendons of which are attached to the bones of the foot to

extend and flex the phalanges and to rotate the foot about the ankle, such as eversion

and inversion of the foot. Figure 15.3 shows how foot rotation about the ankle is

defined. The anterior tibialis dorsiflexes the foot while the soleus and gastrocnemius

plantar flexes the foot. As shown in Fig. 15.4, the medial muscles of the leg invert

the foot while the lateral muscles evert the foot.

15.1 Anatomy of the Foot and Ankle 511

Fig. 15.2 Side (medial) view of the bones of the left foot, showing the longitudinal arch (taken

from Gray (1973))

0 deg

Dorsiflexion

Plantar flexion

Dorsiflexion

Plantar flexion

Inversion

Eversion

Fig. 15.3 Definition of dorsiflexion, plantar flexion, inversion, and eversion of the foot

Between the hindfoot and the distal tibial-fibula complex (the medial and lateral

malleoli) there are many ligaments across the ankle joint which can be strained or

ruptured in inversion or eversion. On the lateral aspect of the ankle, there are about

a half a dozen ligaments and retinacula (fibrous bands) spanning the ankle, as

shown in Fig. 15.5. The anterior and posterior tibiofibular ligaments originate at

the tip of the lateral malleolus of the fibula and insert into two separate locations of

the distal tibia. The other ligaments are the calcaneofibular ligament and the

anterior and posterior talofibular ligaments. As their names imply, they are attached

to named bones. On the medial side, the group of ligaments is known as the deltoid

ligament which is made of three to six ligaments, depending on the anatomist

making the definition (Fig. 15.6). Their primary function is to prevent inversion


[A] Right lateral view. [B] Right medial view.

SOLEUS

SARTORIUS

GRACILIS

GASTROCNEMIUS

PERONEUS LONGUS

TIBIALIS ANTERIOR Patellar tendon

SEMITENDINOSUS

SEMIMEMBRANOSUS

Calcaneal tendon

EXTENSOR DIGITORUM

LONGUS

POPLITEUS

PERONEUS BREVIS

EXTENSOR HALLUCIS

LONGUS

PERONEUS TERTIUS

Tendon of

peroneus tertius

SOLEUS

GASTROCNEMIUS

Calcaneus

[A]

Extensor

digitorum brevis

Flexor digitorum

longus

TIBIALIS ANTERIOR

Calcaneal tendon

TIBIALIS POSTERIOR

EXTENSOR HALLUCIS LONGUS

Flexor hallucis longus

[B]

Flexor hallucis brevis

Fig. 15.4 (A) Medial muscles of the leg used to invert the foot. (B) Lateral muscles of the leg used

to evert the foot (taken from Carola et al. (1992)). Republished with permission of McGraw-Hill

Education, from R. Carola, J.P. Harley, C.R. Noback (eds.), Human Anatomy & Physiology, 2nd

edn., 1992; permission conveyed through Copyright Clearance Center, Inc.

of the ankle. According to the latest description by Hintermann and Golanó (2014),

the deltoid ligament has a superficial and deep layer. The ligaments that make up

the superficial layer are the tibiospring ligament, the tibionavicular ligament, the

tibiotalar ligament, and the tibiocalcaneal ligament. The deep layer consists of

the posterior tibiotalar ligament and the deep layer of the tibiotalar ligament. As

their names imply, most of these ligaments originate at the tip of the medial

malleolus of the tibia and insert into the talus, navicular, or calcaneus. The other

functions of the deltoid ligament are stabilization of the ankle and guidance of

passive motion.

15.1 Anatomy of the Foot and Ankle 513

Fibula

Tibia

Anterior tibiofibular ligament

Posterior tibiofibular ligament

Lateral malleolus

Posterior talofibular ligament

Anterior talofibular ligament

Lateral ligament

of the ankle joint

Calcaneofibular ligament

Dorsal talonavicular ligament

Interosseous talonavicular ligament

Superior fibular

retinaculum

Bifurcate ligament

Inferior fibular retinaculum

is attached to fibular

trochlea between fibularis

Long plantar ligament

brevis and longus tendons

Lateral talocalcaneal ligament

Fibularis longus tendon

Fibularis brevis tendon

Lateral view

Fig. 15.5 Lateral ligaments and retinacula of the ankle (taken from Drake et al. (2008)). Reprinted

from R.L. Drake, A.W. Vogl, A.W.M. Mitchell, R.M. Tibbitts, P.E. Richardson, Gray’s Atlas of


Fig. 15.6 Superficial medial ligaments of the ankle or the deltoid ligament. The tibiospring

ligament is denoted by (1), the tibionavicular ligament by (9), the superficial tibiotalar ligament

by (10), the tibiocalcaneal ligament by (14). For details, see Hintermann and Golanó (2014)


15.2 Injury Mechanisms and Tolerance

of the Foot and Ankle

In the last chapter (Chap. 14), some of the experiments on axial loading of the distal

tibia had the foot attached and a common injury to the foot was fracture of the

calcaneus. The fracture load for 50 % probability of fracture was found to be 6.2 kN

(Yoganandan et al. 1999) but there are no biomechanical studies on the stresses

developed in the cortical bone of the calcaneus. Anatomical studies suggest that the

cortical thickness of the calcaneus ranged from 2.1 to 3.1 mm (Sabry et al. 2000).

That thickness was obviously not adequate to withstand a 6.2 kN load. The

calcaneus can also be fractured by the Achilles tendon which can split it along its

posteroanterior length when the tendon force gets too large, such as during panic

braking.

Begeman and Prasad (1990) addressed the problem of ankle injuries in automotive

crashes, specifically, injuries due to dorsiflexion of the ankle, such as during

heavy braking associated with a frontal crash in which there is footwell intrusion.

The study was motivated by publications in the literature on a variety of ankle

(malleolar) fractures and ligamentous tears, seen in motor vehicle crashes (Martin

and Thompson 1986; Wilson-MacDonald and Williamson 1988; Wroble et al.

1988; O’Leary and Ward 1989; Reidelbach and Zeidler 1983; Zeidler et al.

1981). The injuries described in these papers were presumably due to high strain

rate loading on the foot and ankle which had not been simulated in the laboratory at

that time. Begeman and Prasad (1990) tested nine pairs of unembalmed cadaveric

lower legs and feet. The experimental setup is shown in Fig. 15.7. The impactor was

a 2.5-cm diameter steel bar covered with foam. It impacted a 12-mm aluminum

plate that supported two load cells that were strapped to the bottom of the foot. One

of the load cells was centered on the ball of the foot while the other was over the

heel. The tibia was fixed to a restraint box which was attached to a load cell that

measured the reaction force due to the impact. There was a significant axial force

BIAXIAL LOAD CELLS

PHOTO TARGETS

BIAXIAL LOAD CELL

PNEUMATIC IMPACTOR

TRIAXIAL LOAD CELL

Fig. 15.7 Test setup for dorsiflexion testing of the foot and ankle (taken from Begeman and

Prasad 1990)

15.2 Injury Mechanisms and Tolerance of the Foot and Ankle 515

Ankle Injury verse Peak Angle

Injury

Injury Status

No

Injury

20

40

Dorsiflexion angle (Degrees)

60 80

Fig. 15.8 The injury status in dorsiflexion changes abruptly at 45 deg of dorsiflexion, indicating

that injury would likely occur at this angle (taken from Begeman and Prasad (1990))

from the impactor which also caused the foot to go into dorsiflexion. The force and

moment data had a lot of scatter but when the injury status was plotted against the

dorsiflexion angle, as shown in Fig. 15.8, there is a clear shift in injury status at

45 deg of dorsiflexion. That is, the tolerance of the ankle in dorsiflexion is 45 deg.

There were six ankle injuries out of the 18 tests conducted. The injuries ranged from

uni- and bi-malleolar fractures to deltoid ligament avulsion and rupture.

Repeating this experiment using the Hybrid III foot and ankle was worthwhile. It

was found that the range of motion of the dummy ankle in dorsiflexion was limited

to 30 deg and was not humanlike in its response. As a result of this finding, the

design of the Hybrid III ankle was changed to increase its range of motion. The new

foot and ankle mimicking the human ankle was designated as the Advanced Lower

Extremity I (ALEX 1) which had a dorsi and plantar flexion range of 45 deg and

an inversion/eversion range of 30 deg (Crandall et al. 1996). This required a

change in the FMVSS regulating the Hybrid III dummy, a major effort undertaken

as a result of the paper by Begeman and Prasad (1990).

The Begeman and Prasad (1990) dorsiflexion study was repeated by Rudd et al.

(2004) with better and fancier instrumentation to obtain the response and tolerance

of the ankle, using 20 cadaveric specimens. New instrumentation consisted of an

acoustic sensor to detect the instant of bony fracture and a multi-axis fibula load

cell. Figure 15.9 shows the instrumentation attached to the lower leg and Fig. 15.10

is a diagram of the test device which used a brake pedal to impact the ball of the

foot. Straps were used to keep the leg horizontal and to prevent the knee from

flexing. In terms of results, 11 of the 20 specimens sustained a bony fracture while


x

y

z

Tibia Load Cell

Accelerometer/MHD

Acoustic

Sensor

Tibia

Foot

Fibula

Fibula Load Cell

Accelerometer/MHD

Fig. 15.9 Instrumentation of the lower leg and foot used to study response and tolerance of the

ankle in dorsiflexion (taken from Rudd et al. (2004))

Fig. 15.10 Test device used to test the ankle in dorsiflexion. The foot was impacted by a brake

pedal at the ball of the foot (taken from Rudd et al. (2004))

four specimens sustained ligamentous ruptures and a majority of specimens showed

either osteochondral or cartilaginous injuries. As in the previous study, most of the

fractures involved the medial malleolus. The dorsiflexion moment ranged from 25.6

to 114.1 N.m while the axial compressive force ranged from 597 to 2562 N for

impact velocities that were mostly between 15 and 17 m/s. The dorsiflexion angle at

which fracture occurred was 40 deg. Weibull-based injury risk functions for ankle

moment and dorsiflexion angle were developed. Their respective values for a 50 %

probability of injury were 85 N.m and 51 deg. The dorsiflexion angle of 40 deg is

not too different from the 45 deg suggested by Begeman and Prasad (1990) but

Rudd et al. (2004) decided not to include the Begeman and Prasad data in a more

in-depth analysis of injury data.


Fig. 15.11 Ankle inversion

can result in sprain or

rupture of the lateral

ligaments of the ankle

Fig. 15.12 Drawing of the impact device used to apply inversion and eversion loads to the foot

(taken from Begeman et al. (1993))

Another mode of foot injury is inversion and eversion. In sports, inversion

injuries are common, leading to rupture of the lateral ligaments, as shown in

Fig. 15.11 (Garrick 1977). The medial ligaments are at risk in eversion. For the

automotive front seat occupant, footwell and brake pedal intrusion can lead to

inversion and eversion injuries. Field data have identified these injury mechanisms

in roughly half of the frontal crash ankle injuries (Dischinger et al. 1994; Morris

et al. 1997) and up to 92 % of malleolar fractures (Lestina et al. 1992). Begeman

et al. (1993) relied on injury reports in the medical literature describing a variety of

ankle injuries seen in frontal collisions and initiated a study on the response and

tolerance of the ankle to inversion and eversion. The impact device used in their

dorsiflexion studies was modified to allow an eccentric load to be applied to the

bottom of the foot. The device is shown in Fig. 15.12. The eccentricity was set at


Table 15.1 Summary of inversion and eversion ankle test data (taken from Begeman et al. (1993))

Test Tbl Fy N Tbl Fz N

Calc

Mx Nm

Angle deg

Rot

vel r/s Injury Comment

44i 230 270 9 35 – – Hybrid3

45i 650 520 12 35 – – Hybrid3

46e 250 300 22 30 29 – Hybrid3

47i 600 700 82 35 17 – Hybrid3

48e 80 360 25 37 37 None

49i 200 860 14 33 35 None

50i 130 620 35 57 21 None

51e 320 790 55 67 40 delt tear

52i 350 1000 70 62 37 None

53e 320 1300 120 52 28 None

54i 350 640 38 73/65 45 Lat mal fx

55e 250 560 18 77/58 40 delt rup

56e 240 740 40 81/50 37 med mal fx

57i 260 850 34 85/65 52 lig tears

58e 160 530 28 57/55 27 talus fx dors 13

59i 230 350 36 58/58 42 dis fib fx dors 13

60i 200 850 28 73/50 37 fib fx dors 13

61e 180 550 53 71/59 40 talus avul dors 13

62i 150 520 40 62/60 29 gr2 lat sprain plnt 13

63e 180 540 44 75/57 45 delt torn plnt 13

64e 140 800 50 71/67 27 lig rupt plnt 13

65i 300 640 21 72/65 32 lat lig rupt plnt 13

Notes: First angle value is maximum, second is at injury.

Test no. postfix—e ¼ eversion, i ¼ inversion.

50 mm from the axis of the ankle so that both inversion and eversion loads could be

applied. The calcaneus was attached to the foot plate with screws and the forefoot

was tied to the foot plate using twine. The six-axis load cell behind the specimen

measured the axial and shear reaction forces as well as the reaction moments

generated by the eccentric impact. Foot motion was monitored by high-speed

cameras running at 500 frames/s. Eighteen feet from nine cadavers were tested,

nine in inversion and nine in eversion. The ages of the cadavers ranged from 29 to

79 with an average of 63 years. There were also four tests on the foot of a Hybrid III

dummy. To study the results in detail, it is necessary to understand the coordinate

system used. The positive z-axis is defined to be along the long axis of the tibia

pointing superiorly, and the positive x-axis is in the posteroanterior direction. By

the right-hand rule, the positive y-axis is to the right. The moments due to inversion

and eversion are about the x-axis and the ankle M x as well as the forces in the tibia

can be computed from the reactions measured by the six-axis load cell, using a free

body diagram. Table 15.1 lists the results of all 22 tests. The computed joint

reactions are shown along with angle data. The first value under the angle data is

the maximum value reached while the second is the value at which injury occurred.


Table 15.2 Ankle injuries due to inversion and eversion (taken from Begeman et al. (1993))

Test Subject Mode Description

48 954L ever No injury

49 954R inver No injury


51 465L ever Partial tear ant. aspect of deltoid ligament


53 986L ever No injury

54 335R inver Transverse avul. fx of tip of lateral malleolus

55 438R ever Complete disruption of med. lig. structures: deltoid torn, med. and

post. capsule torn

56 588R ever Med. malleolar fx, avul. ant. deltoid ligament

57 588L inver Ant. talofib. lig., post, talofib. lig, and calcaneofib. lig. torn

58 673R ever Fx med. aspect of talus, fx med, aspect of calcaneous

59 673L inver Small undisplaced fx post. dist. fibula

60 607L inver Fx post. aspect of fibula, (lat. mall, fx) ant. talofib. lig. and calcaneofib.

lig. torn, disruption of the subtalar joint. Osteoporotic

61 607R ever Avul. fx of talus, talocalc. lig. torn

62 215L inver Grade 2 sprain of all lat. ligament

63 215R ever Total disruption of med. ligs (complete deltoid tear)

64 305R ever Subtalar joint disrupted all ligaments

65 305L inver Disruption of all lateral ligaments

Table 15.2 lists the injury data in more detail. Ankle injuries appeared to have

occurred, both in inversion and eversion, at about 60 deg. Unfortunately, the

authors did not perform any statistical analysis, such as a Logistic analysis of the

injury data. They also did not discuss the variation in the applied axial load and the

effect of placing the foot in dorsiflexion or plantarflexion prior to impact. However,

the mechanism of injury is pretty obvious—inversion results in injury to the lateral

aspect of the foot and eversion results in injury to the medial aspect of the foot.

Subsequent to this study, Funk et al. (2002) studied the effect of preload and

dorsiflexion on ankle inversion and eversion. This is a complex study involving data

from two laboratories, many loading conditions and a detailed analysis of the data.

An abbreviated description is provided so the results can be presented. Seventeen

cadavers were used of which 14 were from the University of Virginia and three

from CEESAR (Centre Européen d’Etudes de Sécurité et d’Analyse des Risques),

in Nanterre, France. The method of attaching the foot to the test device was similar

to that used by Begeman and Prasad (1990). The calcaneus was placed in a box and

fixed to the foot plate with Steinmann pins and epoxy resin. The forefoot was

attached to the footplate with wires and screws. The testing apparatus is shown in

Fig. 15.13. It could cause the foot to go into inversion or eversion and place the

specimen in initial dorsiflexion and in axial compression using a spring.

The magnitude of the compression was controlled by a honeycomb material. The

specimens were tested in neutral dorsiflexion (foot at 90 deg to the leg) and at


Fig. 15.13 Test apparatus for inversion/eversion tests used by Funk et al. (2002). The specimen

can be subjected to an initial axial compression as well as dorsiflexion

Table 15.3 Summary of significant ankle inversion and eversion injury data (taken from Funk

et al. (2002))

Preload Flexion Injury parameter Inversion Eversion

None Neutrally flexed Moment (Nm) 24 6 42 15

Angle (deg) 34 10 30 8

2kN Neutrally flexed Moment (Nm) 79 24 I42 100

Angle (deg) 44 14 41 14

2kN Dorsiflexed 30 deg Moment (Nm) 62 31 I40 53

Angle (deg) 33 4 40 6

30 deg dorsiflexion. The preload varied from 0 to 3 kN in 1 kN increments. The

results are summarized in Table 15.3. It can be seen from this table that axial

preload significantly increased ankle tolerance to forced inversion and eversion and

that dorsiflexion reduced the tolerance to inversion slightly. However, when compared

to the data generated by Begeman and Prasad (1990), the failure angle in

inversion and eversion is about 20 degrees lower. Whether this is due to differences

in the way the forefoot was restrained could not be ascertained. In any case, the

40-deg limit is more conservative.

There is another means of injuring the ankle—rotation of the foot about the tibial

axis. The ankle can be injured by internal or external rotation. Wei et al. (2010)

studied the tolerance of the ankle to external rotation under dynamic conditions

simulating those an athlete would experience—a low energy injury. The test setup

is shown in Fig. 15.14 The ten specimens used in the study were loaded axially

while they were rotated externally about the tibial axis. Provision was made to place

the foot in dorsiflexion or plantar flexion. For the nine dorsiflexed specimens, the

distal tip of the fibular was avulsed four times by the posterior talofibular ligament

15.3 The Lisfranc Fracture 521

Fig. 15.14 Test device

used by Wei et al. (2010) to

determine ankle tolerance to

external rotation (taken

from Wei et al. (2010))

Vertical

Linear Actuator

Plate Allowing

X-Y Adjustment

Eversion

Fixture

Load Cell

Dorsiflexion

Wedge

Rotary Actuator

while the distal fibula was fractured twice by the anterior tibiofibular ligament.

Injuries that occurred only once were distal fibular fracture, spiral fracture of the

tibia and fibula and rupture of the anterior deltoid ligaments. In plantar flexion,

there was mid-substance tear of the posterior talofibular ligament. The average

external rotation angle that resulted in these injuries was 40.7 7.3 deg and the

average torque was 69.5 11.7 N.m. Begeman et al. (1994) obtained biomechanical

data by testing 10 feet, five in internal and five in external rotation, while they

were under an axial compressive load to simulate high energy injuries seen in

automotive crashes. The foot was in neutral flexion. In external rotation, there were

two injuries, a superior lateral talus osteochondral fracture and a medial malleolar

fracture. In internal rotation, four of the five specimens were injured, involving

rupture or stretching of the talofibular ligament and the calcaneofibular ligament

and a superior lateral talus osteochondral fracture. The average maximum external

rotation angle was 50.6 deg and the average maximum torque was 30.0 N.m. The

equivalent values in internal rotation are 45.2 deg and 31.2 N.m, respectively.

Compared to the external rotation results of Wei et al. (2010), the average angle

of 50.6 deg is approximately 10 deg higher than that found by Wei et al. (2010)but

the average maximum torque is less than half of that reported by Wei et al. (2010).

It should be noted that the results reported by Begeman et al. (1994) were not peerreviewed.

One of the problems was Begeman et al. (1994) reported that the

talofibular ligament was injured but they did not specify whether it was the

posterior or the anterior talofibular ligament.

15.3 The Lisfranc Fracture

As mentioned in the beginning of this chapter, Lisfranc injuries are a group of

injuries to the midfoot. They include fractures of the metatarsal and tarsal bones,

ruptures of the Lisfranc ligament and generally the disruption of the joints between


Fig. 15.15 The Lisfranc

ligament spans the medial

cuneiform and the second

metatarsal bone (courtesy

of Dr. Brian Smith)

the mid- and forefoot. The Lisfranc ligament spans the medial cuneiform and the

proximal end of the second metatarsal bone and its rupture destabilizes the joint.

This ligament is shown in Fig. 15.15. Lisfranc injuries can occur in offset frontal

impacts but are rare in sports and home accidents. Hardcastle et al. (1982) estimated

the frequency to be one person per 55,000 and proposed a classification scheme

shown in Fig. 15.16, based on injury patterns rather than injury mechanisms which

were unclear at that time. In fact, there have been many unsuccessful attempts to

reproduce these injuries in the cadaver in order to establish the mechanism of

injury. For example, Portier et al. (1995) conducted tests to study the interaction

cadaveric feet with the brake pedal but observed only one Lisfranc injury out of the

16 sled tests conducted at speeds ranging from 14.6 to 15.8 m/s. Similarly, Rudd

et al. (1998) conducted sled tests using cadavers and dummies to study the effect of

foot placement on the brake pedal in frontal collisions at a Delta V of 16 m/s. No

Lisfranc injuries were found. There were also studies of foot injuries using accident

data. Such studies were conducted by Håland et al. (1998); Richter et al. (2001); and

Wilson et al. (2001). Many factors were identified as possible causes of foot and

ankle injuries but no specific cause could be identified. However, Crandall et al.

(1996) found that shorter drivers sustained more foot injuries than taller ones

because they tend to lift their feet during braking, plantar flexing their feet. This

was the first clue of how Lisfranc injuries might have occurred. There is also a

clinical report by Nunley and Vertullo (2002) who studied Lisfranc injuries among

athletes. After successfully treating 15 athletes with midfoot sprains, they stated

that the most common mechanism of Lisfranc complex injury in their patients

typically occurred when an axial load was sustained by the foot while it was plantar

flexed and slightly rotated. This was a second clue. However, it was not clear why

plantar flexion of the foot could result in a Lisfranc injury.

15.4 A Biomechanical Study of Foot Fracture 523

Fig. 15.16 Classification of Lisfranc fractures, proposed by Hardcastle et al. (1982), based on

injury patterns rather than mechanism of injury. Reproduced with permission of British Editorial

Society of Bone and Joint Surgery via PLSclear

15.4 A Biomechanical Study of Foot Fracture

Smith et al. (2005) initiated a study on Lisfranc injuries at about the turn of the

century and were not aware of this second clue. As a result, they initially

impacted the plantar surface of the foot with the foot in neutral flexion (plantar

nominal configuration). They conducted the first 13 tests in this configuration but

it was difficult to create a Lisfranc injury in the plantar normal configuration.


Even though they impacted them at a high speed of 16 m/s (31 mph), they were

only able to produce three Lisfranc injuries (23 % injured). Two different test

setups were used. They are Setups A and B shown in Fig. 15.17. Uptofive

separate tendons were preloaded to simulate braking, using the technique developed

by Kitagawa et al. (1998). It was concluded that this configuration was not

representative of how the foot interacted with the brake pedal in a frontal crash to

produce Lisfranc injuries. Acting on the clue provided by Crandall et al. (1996),

the feet were tested in a plantar flexed configuration, as shown in Fig. 15.17C.

The configuration can be seen more clearly in Fig. 15.18. Forty-one specimens

were tested in this configuration of which 30 tests were done with the tendons

pulled. In this configuration, there were 27 foot injuries (65 % injured) and

19 (46 %) that strictly satisfied the definition of a Lisfranc type injury. The

impact speeds varied from 1 to 15.5 m/s and injury occurred at speeds as low

as 2.8 m/s. The most common injury was metatarsal fracture which occurred in

51 % of the specimens tested. Twenty-nine percent of the feet tested sustained

dislocation and/or fracture of the tarsometatarsal joints. There were four Lisfranc

ligament ruptures and one avulsion. They occurred simultaneously with some of

the metatarsal joint injuries. In terms of injury severity and impairment, 12 feet

(34 %) were judged to have sustained permanent impairment, based on a Foot

and Ankle Severity Scale for impairment (FASS-I) proposed by Manoli et al.

(1997). There are five levels of impairment and from minimal to total impairment.

For FASS-I > 2 the patient is unable to walk and requires pain medication.

It can be seen from Fig. 15.19 that, in the plantar flexed configuration with the

toes flexed, a large compressive load is developed at the tarsometatarsal joints

causing them to fracture and/or dislocate. A comparison of the impact load for

the two configurations can be made using test data from a test in the plantar

nominal configuration at 16 m/s and one in the plantar flexed configuration at

13.5 m/s. The initial velocities differed by 2.5 m/s (about 10 %) but the peak foot

load for the plantar flexed configuration was almost three times higher, demonstrating

that the metatarsals were placed in compression in the plantar flexed

configuration. The loads causing tarsometatarsal injuries ranged from 4.5 to

14.7 kN and the impact velocity ranged from 4.5 to 15.5 m/s. The impactor

acceleration ranged from 80 to 349 g. Detailed results can be found in Smith

(2003). An observation was made regarding the effect of simulating muscle

action (pulling the tendons). The foot was more stable and did not move out of

the way of the impact. Muscle action apparently provided a more realistic

simulation of foot impact.

Logistic regression analysis was performed on the data from impacts in the

plantar flexed configuration which resulted in realistic Lisfranc injuries. For injury

analysis, this method selects injury as the binary dependent variable and finds the

best predictors (independent variables) of injury. In this case, the likely predictors

are impact velocity, foot load, and Achilles tendon force. As mentioned in Chap. 1

(Sect. 1.6.3), the probability of an injury occurring is given by Eq. 1.1.


Fig. 15.17 (A–C) The three impact devices used by Smith (2003) to create Lisfranc foot injuries.

Five tendons were preloaded to simulate braking, including the Achilles tendon


Fig. 15.18 A foot being tested in the plantar flexed configuration, simulating braking by a short

driver using the toes to press on the brake pedal (courtesy of Dr. Brian Smith)

Fig. 15.19 Comparison of impactor load on the foot in the plantar flexed (A) and plantar nominal

(B) configurations. There is effective load transmission through the metatarsals in the plantar

flexed configuration (taken from Smith (2003))


Fig. 15.20 Logistic plot of probability of injury vs. velocity of impact for tests in the plantar

flexed configuration with simulated muscle loading (tendons pulled) (taken from Smith (2003))

px ðÞ¼1 ½ þ expðα βxÞ 1 ð1:1Þ

where x ¼ response variable, such as force or acceleration

α, β ¼ Logistic coefficients

p(x) ¼ probability of an injury occurring

For each response or independent variable, values of chi square (χ 2 ) and p

(probability) provide an assessment of the goodness of fit or level of prediction.

Higher values of χ 2 and smaller p values mean that the variable is a better predictor

of injury. To perform the analysis, it was necessary to select a level of injury

severity, and, for the foot, the level selected was FASS-S 3, where FASS-S is the

Injury Severity Scale (FASS-S has six levels and, for the foot, FASS-S ¼ 3 involves

metatarsal fractures and dislocations).

When velocity was selected as the independent variable, the Logistic curve is

shown Fig. 15.20 for the runs in which the tendons were pulled. Because there was

no overlap of injury and non-injury data, it has a high χ 2 value of 38.2 and a p-value

of 0.0. The velocity for a 50 % probability of a tarsometatarsal injury is 4.6 m/s.

The Logistic curve for foot load is shown in Fig. 15.21 for which the χ 2 was 18.1

and p-value was 0.0. The foot load for a 50 % probability of a tarsometatarsal injury

is 3850 N.

We can analyze the injury tolerances described above further by examining

the sensitivity and specificity measures so that an optimal tolerance level can be

obtained. As mentioned in Chap. 1 (Sect. 1.6.3), we recall the definition of

sensitivity and specificity as follows:

Sensitivity ¼ TP= ðTP þ FNÞ ¼ TPRðTrue positive rateÞ ð1:4Þ


FOOT LOAD vs INJURY

PROBABILITY OF INJURY

1.00

0.75

0.50

0.25

0.00

0.0

FN

TN

TP

FP

20.0 40.0 60.0

FOOT LOAD N x100

80.0 100.0 120.0 140.0

Fig. 15.21 The definition of true and false positives and true and false negatives applied to a

Logistic plot for foot load. Experimental data were used to demonstrate a special case of no

overlap of injury and non-injury data along the abscissa. This is not usually the case for most

data sets (taken from Smith (2003))

Specificity ¼ TN= ðFP þ TNÞ ¼ FNRðTrue negative rateÞ ð1:5Þ

where

TP ¼ true positives

FP ¼ false positives

TN ¼ true negatives

FN ¼ false negatives

Relative to a Logistic plot, for a given probability level, there is a threshold for

injury. This is shown in Fig. 15.21 in which the plot is divided into four quadrants.

Experimental data were used to demonstrate the meaning of definition of true and

false positives and negatives.

Now, if we make a graph of Sensitivity vs. 1-Specificity for a range of thresholds,

we get a receiver operating characteristic (ROC) curve. To construct this

curve, we use the data from foot load impacts with tendons pulled, as shown in

Table 15.4. For each load, we refer to Fig. 15.22 to obtain a probability of injury

which is in the second column. Then, take for example, the eighth row in which the

foot load is 4499 N. At that level of foot load, there are 14 true positives, 1 false

negative, no false positives and 6 true negatives. The sensitivity is therefore equal to

14/(14 + 1) ¼ 0.9333 and 1-Specificity is equal to 1 [6/(0 + 6]] ¼ 0. When plotted,

this point is located on the vertical axis for 1-Specificity ¼ 0 and at 0.9333 on the

vertical axis for Sensitivity ¼ 0.9333. The probability of injury of 81.3 % is noted

for later use. To plot the entire ROC, start with the data point on the first row and

calculate Sensitivity and 1-Specificity by counting the number of TP, FN, FP, and


Table 15.4 Sensitivity and specificity analysis of foot load data with tendons pulled (taken from Smith (2003))

Injury Foot load Probability of injury TP FN FP TN Sensitivity Specificity 1-Specificity Sum

0 1819 0.00989 15 0 6 0 1.0000 0.0000 1.0000 1.0000

0 1987 0.01442 15 0 5 1 1.0000 0.1667 0.8333 1.1667

0 2108 0.01888 15 0 4 2 1.0000 0.3333 0.6667 1.3333

1 3196 0.18502 15 0 3 3 1.0000 0.5000 0.5000 1.5000

0 3207 0.18881 14 1 3 3 0.9333 0.5000 0.5000 1.4333

0 3605 0.36470 14 1 2 4 0.9333 0.6667 0.3333 1.6000

0 3909 0.53357 14 1 1 5 0.9333 0.8333 0.1667 1.7667

1 4499 0.81333 14 1 0 6 0.9333 1.0000 0.0000 1.9333

1 4865 0.90911 13 2 0 6 0.8667 1.0000 0.0000 1.8667

1 5319 0.96553 12 3 0 6 0.8000 1.0000 0.0000 1.8000

1 6693 0.99842 11 4 0 6 0.7333 1.0000 0.0000 1.7333

1 7017 0.99924 10 5 0 6 0.6667 1.0000 0.0000 1.6667

1 7129 0.99941 9 6 0 6 0.6000 1.0000 0.0000 1.6000

1 7431 0.99970 8 7 0 6 0.5333 1.0000 0.0000 1.5333

1 9000 0.99999 7 8 0 6 0.4667 1.0000 0.0000 1.4667

1 10146 1.00000 6 9 0 6 0.4000 1.0000 0.0000 1.4000

1 10317 1.00000 5 10 0 6 0.3333 1.0000 0.0000 1.3333

1 11066 1.00000 4 11 0 6 0.2667 1.0000 0.0000 1.2667

1 12376 1.00000 3 12 0 6 0.2000 1.0000 0.0000 1.2000

1 12840 1.00000 2 13 0 6 0.1333 1.0000 0.0000 1.1333

1 14787 1.00000 1 14 0 6 0.0667 1.0000 0.0000 1.0667


1.00

FOOT LOAD vs INJURY WITH TENDONS PULLED

PROBABILITY OF INJURY

0.75

0.50

0.25

0.00

0.0

2500

5000 7500 10000 12500 15000

FOOT LOAD N

Fig. 15.22 Logistic plot of probability of injury vs. foot load for tests in the plantar flexed

configuration with simulated muscle loading (tendons pulled) (taken from Smith (2003))

TN. That point will be at the very top right hand corner of the graph. As we go down

Table 15.4, the points stay on the top line for sensitivity ¼ 1 until the value of

1-Specificity is 0.5. The points now lie on a horizontal line for Sensitivity ¼ 0.9333

as 1-Specificity drops to zero. The remaining points all end up on the vertical axis

for 1-Specificity ¼ 0. The ROC is shown in Fig. 15.23. As explained in the figure

caption, we find two thresholds at 3196 and 4499 N. To find the optimum tolerance,

we find the foot load for which the sum of the Sensitivity and Specificity is a

maximum. From Table 15.4 the maximum is 1.9333 and occurs at a foot load of

4499 N which is optimum tolerance.

In Fig. 15.20, there is no overlap of injury and non-injury data. Table 15.5 lists

the sensitivity and specificity data. The ROC curve starts out at the top right hand

corner where the Sensitivity is 1.0 and 1-Specificity is also 1.0. The points then

move to the left along the line Sensitivity ¼ 1 until it reaches the top left hand

corner. It then moves down the vertical line for 1-Specificity ¼ 0, forming a square.

That is, in the rare case of a perfect fit, the ROC is a square with an area under it

equal to 1.0. The optimum tolerance or threshold occurs when the sum of Sensitivity

and Specificity is a maximum at 2.0000. It is 5 m/s with an injury probability

of 75 %.

15.5 Modeling of Foot Impact 531

1.0000

SENSITIVITY

0.9000

0.8000

0.7000

0.6000

0.5000

0.4000

0.3000

0.2000

0.1000

Second Threshold

Specificity: 1.0 = 0 False Positives

Probability: 81.3.%

Threshold Value: 4498 N

First Threshold

Sensitivity: 1.0 = 0 False Negatives

Probability: 18.5%

Threshold Value: 3196 N

0.0000

0.0000

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1-SPECIFICITY

Fig. 15.23 Receiver operating characteristics (ROC) curve for foot load with tendons pulled. The

area under the curve is 0.9667. Since there are two changes in slope of the ROC, the changes

represent a threshold value for injury. The first threshold is at 3196 N with an injury probability of

18.5 % and the second is at 4499 N with a probability of 81.3 % (taken from Smith (2003))

15.5 Modeling of Foot Impact

There have not been too many models of the foot and ankle. The first was developed

by Beaugonin et al. (1996). Its purpose was to study ankle injuries and only

ligaments were modeled by deformable elements. All the bones of the foot and

leg were assumed to be rigid but the soft tissues (ligaments and foot pad) were

deformable. The irregular shapes of the bones of the foot rendered the formulation

of the model somewhat challenging. The model was used to simulate the inversion/

eversion tests reported by Begeman et al. (1993). Special attention was paid to the

congruency of articular joint surfaces to enable the accurate prediction of the

kinematics of the ankle/foot complex. Correlation of model predictions with experimental

data on a global scale was attained. The model by Tannous et al. (1996)

assumed the calcaneus and talus to be deformable while the rest of the foot was

made up of rigid elements. They selected four tests performed by Yoganandan et al.

(1999) to validate the model. The parameters used for validation were the impactor

acceleration and the foot plate acceleration which had very little to do with the

deformation of the foot. The computed impact load did not compare well with

experimental data and the formula used to calculate elastic modulus is not the

standard one used in elasticity. Beaugonin et al. (1997) improved their 1995 model

by assuming the calcaneus, talus, navicular, and cuboid to be deformable, along

with the fibula and tibia. The rest of the bones of the foot were assumed to be rigid.

Ligaments, tendons, retinacula, and the foot pad were assumed to be deformable.

Both the original rigid model (Beaugonin et al. 1996) and the deformable model


Table 15.5 Sensitivity and specificity analysis of impact velocity data with tendons pulled (taken from Smith (2003))

Injury Impact velocity Probability of injury TP FN FP TN Sensitivity Specificity 1-Specificity Sum

0 1 0 20 0 10 0 1.0000 0.0000 1.0000 1.0000

0 1 0 20 0 9 1 1.0000 0.1000 0.9000 1.1000

0 2 0 20 0 8 2 1.0000 0.2000 0.8000 1.2000

0 2 0 20 0 7 3 1.0000 0.3000 0.7000 1.3000

0 3 0 20 0 6 4 1.0000 0.4000 0.6000 1.4000

0 3 0 20 0 5 5 1.0000 0.5000 0.5000 1.5000

0 3 0 20 0 4 6 1.0000 0.6000 0.4000 1.6000

0 4 0.00003 20 0 3 7 1.0000 0.7000 0.3000 1.7000

0 4 0.00003 20 0 2 8 1.0000 0.8000 0.2000 1.8000

0 4 0.00003 20 0 1 9 1.0000 0.9000 0.1000 1.9000

1 5 0.75 20 0 0 10 1.0000 1.0000 0.0000 2.0000

1 5 0.75 19 1 0 10 0.9500 1.0000 0.0000 1.9500

1 5 0.75 18 2 0 10 0.9000 1.0000 0.0000 1.9000

1 6 1 17 3 0 10 0.8500 1.0000 0.0000 1.8500

1 6 1 16 4 0 10 0.8000 1.0000 0.0000 1.8000

1 7 1 15 5 0 10 0.7500 1.0000 0.0000 1.7500

1 7 1 14 6 0 10 0.7000 1.0000 0.0000 1.7000

1 8 1 13 7 0 10 0.6500 1.0000 0.0000 1.6500

1 8 1 12 8 0 10 0.6000 1.0000 0.0000 1.6000

1 9 1 11 9 0 10 0.5500 1.0000 0.0000 1.5500

1 9 1 10 10 0 10 0.5000 1.0000 0.0000 1.5000

1 10 1 9 11 0 10 0.4500 1.0000 0.0000 1.4500

1 10 1 8 12 0 10 0.4000 1.0000 0.0000 1.4000

1 11 1 7 13 0 10 0.3500 1.0000 0.0000 1.3500

1 13 1 6 14 0 10 0.3000 1.0000 0.0000 1.3000

1 14 1 5 15 0 10 0.2500 1.0000 0.0000 1.2500

1 14 1 4 16 0 10 0.2000 1.0000 0.0000 1.2000

1 15 1 3 17 0 10 0.1500 1.0000 0.0000 1.1500

1 16 1 2 18 0 10 0.1000 1.0000 0.0000 1.1000

1 16 1 1 19 0 10 0.0500 1.0000 0.0000 1.0500

15.5 Modeling of Foot Impact 533

were validated against dorsiflexion test data generated by Begeman and Prasad

(1990). Both the predicted dorsiflexion angle and the impacted forces compared

welltheexperimentaldataforthedeformablemodel.Somestressanalysiswas

done on the deformable bones but injury data were not available from Begeman

andPrasad(1990) to compare the results. The lower extremity model of Beillas

et al. (1999) used the foot and ankle model developed by Beaugonin et al. (1997)

but the foot model was not exercised. Iwamoto et al. (2005) developed a lower

limb model to simulate pilon fractures. The bones in the entire foot were assumed

to be deformable but since the principal interest was in the ankle joint, the effect

of the deformability of the foot bones was not studied. The latest model is by Shin

et al. (2012). It was part of a joint research effort by a group of automotive

companies, university researchers, and the NHTSA to develop a total human

body model for use by industry and government—the Global Human Body

Model Consortium (GHBMC). Like the previous model, the purpose of developing

this model was to study the injury response of the ankle and subtalar joints.

As a result, the deformable bones in the model were the fibula, tibia, talus, and

calcaneus. The rest of the bones of the foot were assumed to be rigid. No doubt

the authors were aware of injuries to the mid and forefoot, such as Lisfranc

injuries. However, the simulation of the more distal irregular tarsal bones and

their interaction with each other and with the metatarsal bones increases the level

of complexity of the model and was not attempted. The model was validated

against four different sets of experimental data. The experiments were performed

by Wheeler et al. (2000), Begeman et al. (1994), Rudd et al. (2004), and Wei

et al. (2010). The model was validated against the measured acceleration in the

dorsiflexion tests done by Wheeler et al. (2000). The dorsiflexion data obtained

by Begeman and Prasad (1990) were not used in the validation and no reason was

given as to why the data were ignored. In axial rotation, an attempt was made to

validate the model against the data supplied by Begeman et al. (1994) who

performed static and dynamic tests in internal and external rotation. Because of

the uncertainty of whether the axis of rotation of model was coincident with that

of the subtalar joint, only a static validation was attempted. However, a momentangle

graph was presented to show the correlation of internal and external angles

of rotation with experimental data. Strangely, the graph showed a “test corridor”

when Begeman et al. (1994) only performed two static tests, one in internal

rotation and one in external rotation. The dorsiflexion study by Rudd et al.

(2004), involving the foot, leg, and thigh was simulated. Good agreement with

experimental data was obtained for this validation attempt. The predicted

moment-angle curve followed the average test data curve closely. The model

also predicted failure of the posterior talofibular ligament at a predicted

dorsiflexion angle of 37 deg as compared to the experimental average failure

angle of 38 7 deg. The external rotation study of Wei et al. (2010) was also used

for validation of the model. The model predicted a failure moment of 73.3 N.m at

39.3 deg while the model failure moment was 69.5 11.7 N.m at 40.7 7.3 deg.

Overall, the model did a good job of simulating most of the available

experimental data.



Injuries to the foot and ankle are rarely fatal. But, because these injuries are quite

disabling, much attention has been given to study the mechanisms of injury and

tolerance so that some of these injuries can be prevented. Since footwell intrusion

appears to be the main culprit, the easy solution would be to strengthen the footwell

to minimize intrusion in offset collisions. This entails adding weight to the vehicle

and is not desirable when the government is promoting gas economy. The breakaway

brake pedal was introduced some years ago but the design did not catch

on. Innovative ideas are needed to solve this problem without affecting the global

ecology.

Modeling of the foot and ankle is quite advanced as far as the hindfoot is

concerned. For the mid and forefoot, FE models do not exist to predict response

and injury. This is largely due to the difficulty of dealing with the very irregular

shapes of the tarsal bones. However, one of the most serious foot injuries is the

group of Lisfranc injuries and hopefully, someone with great expertise in finite

element modeling can simulate this group of injuries in the near future.


15.1. Cadaveric foot fractures have been reproduced in the laboratory

[ ] (i) These fractures were due solely to the application of large forces on

the brake pedal by the driver

[ ] (ii) These fractures were due to the footwell intrusion in conjunction

with brake pedal force

[ ] (iii) These fractures were due to brake pedal force and forces in the

tendons of the foot

[ ] (iv) These fractures have an unknown injury mechanism


15.2. A Lisfranc foot injury has to do with

[ ] (i) Fracture of the calcaneus

[ ] (ii) Fracture of tarsal bone

[ ] (iii) Rupture of the Achilles tendon

[ ] (iv) Fracture of the navicular bone


15.3. The mechanism for a Lisfranc foot injury is

[ ] (i) Tension applied to the metatarsal bones

[ ] (ii) Shearing at the phalangeal-metatarsal joint

[ ] (iii) Axial loading of the metatarsal head by the plantar flexed phalange

[ ] (iv) Bending of the metatarsal bones



15.4. Lisfranc injuries are more likely to occur in drivers who are short in stature

because

[ ] (i) They sit up straight in order to see the road

[ ] (ii) They plantar flex their toes to reach the brake pedal

[ ] (iii) They sit too close to the steering wheel

[ ] (iv) Their knees are up against the dash

[ ] (v) They cannot see the hood ornament

15.5. In the experiments performed by Smith et al. (2005), he was able to reproduce

Lisfranc injuries in the laboratory

[ ] (i) by impacting the foot in the plantar normal configuration at impact

speeds less than 16 m/s

[ ] (ii) by impacting the foot in the plantar normal configuration at impact

speeds ranging from 2.8 to 15.5 m/s

[ ] (iii) by impacting the foot in the plantar flexed configuration at impact

speeds at or over 16 m/s

[ ] (iv) by impacting the foot in the plantar flexed configuration at impact

speeds as low as 2.8 m/s


15.6. Lisfranc injuries can include

[ ] (i) Fracture of the phalanges of the first and second toe

[ ] (ii) Rupture or avulsion of the Lisfranc ligament

[ ] (iii) Dislocation or fracture/dislocation of the tarsal/metatarsal joints

[ ] (iv) Rupture of the deltoid ligament


15.7. The tolerance of the foot to dorsiflexion is

[ ] (i) yet to be determined

[ ] (ii) is 45 degrees

[ ] (iii) ranges from 50 to 70 degrees

[ ] (iv) is less than 30 degrees


15.8. Foot ligaments can be injured by ankle inversion and eversion

[ ] (i) The lateral ligaments are injured due to inversion

[ ] (ii) The medial ligaments are injured due to eversion

[ ] (iii) The lateral ligaments are injured due to eversion

[ ] (iv) The medial ligaments are injured due to inversion

[ ] (v) (i) and (ii)


15.9. External rotation of the foot while it is in dorsiflexion can cause ankle

injuries. These include

[ ] (i) Medial malleolar fractures

[ ] (ii) Lateral malleolar fractures

[ ] (iii) Avulsion of the anterior talofibular ligament



15.10. Automotive drivers can sustain foot injuries during an offset frontal crash.

The cause of these injuries is

[ ] (i) due to heavy braking

[ ] (ii) due to bending of the foot over the brake pedal

[ ] (iii) due to the type of shoe worn

[ ] (iv) due to the heel losing contact with the floor of the footwell

[ ] (v) due to intrusion of the footwell


Prob

Ans

1 (ii)

2 (v)

3 (iii)

4 (ii)

5 (v)

6 (v)

7 (ii)

8 (v)

9 (ii)

10 (v)

References

M. Beaugonin, E. Haug, D. Cesari, A numerical model of the human ankle/foot under impact

loading in inversion and eversion. in 40th Stapp Car Crash Conference. SAE Paper

No. 962428, Albuquerque, New Mexico, 1996

M. Beaugonin, E. Haug, D. Cesari, Improvement of numerical ankle/foot model: modeling of

deformable bone. in 41st Stapp Car Crash Conference. SAE Paper No. 973331, Lake Buena

Vista, Florida, 1997

P.C. Begeman, P. Prasad, Human ankle impact response in dorsiflexion, in 34th Stapp Car Crash

Conference, SAE Technical Paper No. 902308, Orlando, FL, 1990

References 537

P. Begeman, P. Balakrishnan, R. Levine, A.I. King, Dynamic human ankle response to inversion

and eversion. in 37th Stapp Car Crash Conference. SAE Paper No. 933115, San Antonio,

Texas, 1993

P. Begeman, K. Aekbote, R. Levine, A. King, Human ankle response in internal and external

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P. Beillas, D. Nicolopoulos, K. Kayventash, K.H. Yang, Foot and ankle finite element modeling

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J.G. Garrick, The frequency of injury, mechanism of injury, and epidemiology of ankle sprains.

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1981

Chapter 16

Side Impact

In a side impact, the struck vehicle is at a disadvantage in terms of occupant safety

because of the proximity of the side structures (e.g., the side door) to the occupant

compared to the space available to the occupant in a frontal impact. The seat belt

system is also not effective in preventing injury from a side impact. As a result,

before side impact airbags were available, the fatality rate was high even though the

speed of impact of the striking vehicle is low. In fact, in the 1990s, the annual

fatality rate for side impact was close to 10,000 before FMVSS 214 for side impact

was implemented, as shown in Fig. 16.1. However, after the standard came into full

effect in 1997, the rate showed no substantive drop. The total fatality rate was

42,013 in 1997 and it dropped from a high of 43,510 in 2005 to 32,575 in 2014. That

is, even with the introduction of active safety into our vehicles, side impact fatalities

remain unchanged and is becoming a larger part of the fatality problem. The

reasons for this anomaly are discussed in this chapter.

16.1 The Kinematics of Side Impact

When a car is T-boned or impacted on the side, the front end of the impacting

vehicle caves in the side structure of the struck vehicle and the inside surface of that

structure impacts the occupant before he/she starts to move. This scenario is

depicted in Fig. 16.2. Point 0 is the firewall of the impacting vehicle and serves

as a point of reference for the impacting vehicle. Point 1 is the front bumper which

is the first part of the striking vehicle to make contact with the struck vehicle; Point

2 is on the door skin of the struck vehicle and moves inward as the bumper crushes

the door. Point 3 is on the inside of the door and makes contact with the arm or chest

of occupant, represented by Point 4. Point 5 is a reference point for the compartment

of the struck vehicle and is located on the door on the far side. Quantitatively, the

impact is represented by a plot of the velocity of various points on the two vehicles



539

540 16 Side Impact

10000

9000

8000

7000

6000

5000

LTVs

Cars

4000

3000

2000

1000

0

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Fig. 16.1 Side impact fatality rates in the USA from 1975 to 2004. FMVSS 214 was phased into

new cars from 1994 to 1997. The rate remained unchanged in 2004 relative to the rates in

1994–1997 (taken from Kahane (2007))

Fig. 16.2 Depiction of a broadside impact

as a function of time, as shown in Fig. 16.3. The velocity of the striking vehicle is

shown on the top of the figure. Its initial velocity is 40 mph (64.4 km/h) and, in the

first 25 ms or so, it is not slowed down much as the soft side structure of the struck

vehicle collapses. The curve represents the common velocities of Points 1 and 2. In

the bottom of the figure, the velocity of the door interior (Point 3) is the solid curve

which attains a speed of almost 20 mph (32.2 km/h) in just over 20 ms when the

door makes contact with the occupant and starts deforming the chest of the

occupant. It is seen that the occupant remains stationary for the first 28 ms and

occupant velocity is represented by the dashed curve (Point 4). Lateral acceleration

of the struck vehicle is relatively low (about 8 g), taking about 50 ms to reach a

speed of 10 mph (16 km/h). Its velocity is shown by the dot-dash curve for Point 5.

16.2 Side Impact Injuries and Injury Criteria 541

40

35

STRIKING VEHICLE FIREWALL-0

STRIKING VEHICLE CRUSE

VELOCITY (MPH)

30

25

20

15

10

5

0

DOOR

INTERIOR-3

INITIAL DOOR

TO DUMMY

DISPLACEMENT

0

STRIKING VEHICLE

BUMPER & DOORSKIN-1,2

GP=46

OCCUPAHT-4

DOOR PADDING PENETRATION

AND CHEST COMPLIANCE

10 20 30 40 50 60 70

TIME (MSEC)

PADDING AND DUMMY

DEFLECTION RECOVERY

COMPARTMENT-5

80 90 1

Fig. 16.3 Vehicle kinematics in a side impact (taken from Strother et al. (1984)). Reprinted with

permission Copyright © 2017 SAE International. Further distribution of this material is not

permitted without prior permission from SAE

It should be noted that this is a rather severe side impact and that the velocity of the

striking vehicle is set at 32.6 0.5 mph (52.9 8 km/h) by FMVSS 214. The

standard was amended in 2007 (NHTSA 2007) to include an oblique pole test at

20 mph (32.2 km/h).

One of the useful inventions for measuring chest deformation was developed by

Eppinger (1989) while side impact was being intensely studied. It is called a “chest

band” which consisted of a thin strip of metal (stainless steel) instrumented with a

large number of evenly spaced strain gages. The band is wrapped around the chest

to measure the contour of the chest during an impact and is based on the theory that

the measured strain is inversely proportional to the radius of curvature (Perry and

Lissner 1955). Pintar et al. (1996) validated the chest band, confirming that it was a

reliable instrument to measure instantaneous chest contours.

16.2 Side Impact Injuries and Injury Criteria

According to the NHTSA, the distribution of side impact injuries to various body

regions in the 1977–1987 period was as follows:

Head 45 %

Chest 29 %

Neck and Spine 11 %

Abdomen 9 %

These data were published in the Federal Register, Volume 55, No. 210, 10/30/

90. In a more detailed study by Augenstein et al. (1999), the breakdown of injuries

for near side impacts at the MAIS level of 3 or higher is shown below:

542 16 Side Impact

Head/Face 24 %

Chest 44 %

Abdomen 5 %

Pelvis/Lower Ext. 14 %

Spine/Neck 4 %

Other 9 %

These data were taken from the National Automotive Sampling System (NASS).

The injury distribution has changed since 1990 and justifies the emphasis on

preventing injuries to the chest in FMVSS 214, as will be discussed below.

The frequency of impact from different angles for single and multiple vehicles is

shown in Fig. 16.4 (Viano et al. 1990). Single vehicle side impacts are usually with a

fixed object, such as a tree or a utility pole, when the car is driven too fast on a curve

and it goes off the roadway. Such crashes constitute just over 30 % of all side impact

crashes and can result in large intrusions into the passenger compartment due to the

narrowness of the impacted object. They can cause severe injuries to the near-side

occupant and FMVSS 214 was amended in 2007 to include an oblique pole test. The

majority of the side impact tests are multiple vehicle intersection crashes with an

equal frequency of left and right sided impacts. Most of these impacts are right

angled impacts with less than 10 % occurring at 30 from the purely lateral

direction. Viano et al. (1990) also commented on the fact that fatality of elderly

drivers was over-represented in multi-vehicle side impact crashes. Sixty-four percent

of near-side occupants were over 50 years of age and 36 % were over 70 in fatal

multi-vehicle impacts. Reasons for the high rate were changes in visual perception of

the speed of on-coming vehicles, loss of judgment of traffic conditions and lack of

attention. The fatality rate among elderly occupants is also high because they have a

lower probability of recovering from a severe injury. On the other hand, the younger

Fig. 16.4 Frequency of vehicular impacts by angle of impact for single and multiple vehicle

accidents. Single vehicle side impacts are usually with a fixed object, such as a tree or a utility pole

(taken from Viano et al. (1990)). Reprinted from D.C. Viano, C.C. Culver, L. Evans, M. Frick, R.

Scott, Involvement of older drivers in multivehicle side-impact crashes. Accident Analysis &

Prevention 22(2), 177–188, 1990, with permission from Elsevier

16.2 Side Impact Injuries and Injury Criteria 543

25

Percent

20

15

10

Single car frontal crash

Struck on left by another car

Deformation moderate or less

5

0

10 20 30 40 50 60 70 80 90 100

Driver age (years)

Fig. 16.5 Distribution of automotive fatalities by age. Young drivers tend to impact fixed objects

while older drivers are more involved in intersection crashes (taken from Viano et al. (1990)).

Reprinted from D.C. Viano, C.C. Culver, L. Evans, M. Frick, R. Scott, Involvement of older

drivers in multivehicle side-impact crashes. Accident Analysis & Prevention 22(2), 177–188,


driver is more frequently involved in single vehicle side impact crashes. This

statistic is demonstrated in Fig. 16.5 which shows the fatality distribution by age

for single car frontal crashes and for left-side impacts (Viano et al. (1990)). Also,

according to a NHTSA Report on NASS Passenger Car Crash Data (1982–1986),

4829 of the 12,519 occupants who sustained serious or fatal injuries in side impacts

with fixed objects were under 20 years of age and in the 20 to 40-year-old age group,

there were 6718 injuries/fatalities in side impacts with fixed objects. For the age

groups from 40 to 80+, the total was less than 1000.

In terms of injury criteria for side impact, there was a major disagreement between

NHTSA and the automotive industry on what parameter to use to assess side impact

injury to the chest in the 1990s when the side impact standard (FMVSS 214) was

being promulgated. The NHTSA sponsored a large and long-term project to determine

chest tolerance to side impact. Most of the cadaveric work was done at the

University of Heidelberg in Germany under the direction of Dr. D. Kallieris. (See, for

example, Kallieris et al. 1981; Marcus et al. 1983; Klaus et al. 1984). The data were

analyzed by NHTSA and the proposed criterion for chest tolerance was expressed in

terms of chest acceleration. Specifically, the Thoracic Trauma Index (TTI) was

defined as the average of the lateral accelerations measured at the 4th or 8th rib

and the lateral acceleration of T12 of the cadavers subjected to the Heidelberg-type

side impact, modified by the age of the cadaver, as discussed in Sect. 11.4.2:

TTI ¼ 1:4*AGE þ 0:5ðRibY þ T12YÞ* MASS=165

where

the age of the cadaver is in years

RibY is the higher of the measured peak lateral acceleration of Rib 4 or 8 in g’s

544 16 Side Impact

T12Y is the measured peak lateral acceleration at T12 in g’s

MASS is the weight of the cadaver in lb

The dummy to be used in conjunction with this index was the Side Impact

Dummy (SID) developed at the University of Michigan (Melvin et al. 1976). When

TTI is computed for the SID the formula becomes:

TTIðdÞ ¼ 0:5ðRibY þ T12YÞ

where

TTI(d) is the Thoracic Trauma Index for the 50th percentile SID

RibY is the higher of the two measured peak lateral chest acceleration in g’s.

Two accelerometers are mounted on the chest at the approximate locations of T4

and T8 because the SID has no rib cage. Most of the weight of the SID thorax is

concentrated in the chest wall which contains lead and is virtually non-deformable.

The lack of biofidelity of the SID is patently obvious

T12Y is the measured peak lateral acceleration on the dummy spine just above

the lumbar spine

The formulation of TTI was based on empirical data involving many cadaveric

side impact sled tests sponsored by NHTSA. Using the SID as the test instrument, it

was decided that the tolerance limits for side impact should be:

Chest

Pelvis

TTI < 85–90 g

Lateral acceleration < 130 g

The 85-g limit applies to four-door cars and the 90-g limit is for two-door cars.

These limits were written into the 1997 version of FMVSS 214 which was

promulgated in 1997. As mentioned above, FMVSS was amended in 2007 and

the above limits using TTI were abolished as was the SID. The new limits involve

the use of European male side impact dummy (ES-2re) and SID IIs female dummy

with the following limits for an AIS injury of 3+, except for the female pelvis for

which the injury risk is AIS 2+: The ES-2re is the second version of the European

side impact dummy modified with rib extensions (re) to prevent it from “grabbing”

the seat back while it slides along the seat.

ES-2re

Chest

Abdomen

Pelvis

SID IIs

Chest

Pelvis

Deflection < 44 mm

Force < 2.5 kN

Force < 6.0 kN

Acceleration < 82 g

Force <5.525 kN

These are the government regulations. For the chest, the automotive industry

proposed an alternate criterion called the Viscous Criterion (V*C) which is the

instantaneous product of the chest wall velocity and the lateral chest compression

ratio. This same criterion was used for frontal impact, as discussed in Chap. 11

16.3 A Cadaveric Study of Side Impact—Sled Tests 545

(Sect. 11.7). Based on research performed at Wayne State University and sponsored

by the Biosciences Department of the GM Research Labs, the proposed criterion for

side impact is V*C ¼ 1.5 for a 25 % probability of an AIS4+ injury. This result was

based on a study by Viano et al. (1989) described in Chap. 11 (Sect. 11.4.2). It was

found that the parameter V*C was the best predictor for side impact chest injury and

this criterion was promoted by the automotive industry, resulting in a major conflict

between government and industry before the 1997 version of FMVSS 214 came

into effect. There was, in fact, a public debate after one of the Stapp Conferences but

nothing was resolved as a result of this debate between government and industry.

Stapp Conferences constitute the world’s premier meetings on impact biomechanics

and the papers presented at this meeting are consistently of high quality. Eventually,

the government prevailed and the TTI became part of the 1997 FMVSS 214 for side

impact. With the newly amended 2007 FMVSS 214, the issue of TTI has become

moot but it is part of the history of side impact research and needed to be discussed.

However, the new chest criteria for FMVSS 214 are not based on V*C and it appears

that some of the old animosity still remains within the government.

16.3 A Cadaveric Study of Side Impact—Sled Tests

The CDC supported project described in Chapter 11 produced more side impact

data than those related to the chest. Recall that the Wayne State Heidelberg sled was

equipped with a wall made up of four sets of load cells that measured the forces of

impact at the shoulder, chest, abdomen, and pelvis. These data constituted the

response of these regions to lateral impact and the results were summarized by

Cavanaugh et al. (1992). They are shown in Table 16.1. High speed film data of

shoulder impact with a padded or rigid wall could not be read because the shoulder

disappears into the torso when impacted. Thus, it was not possible to analyze the

displacement of the acromion (shoulder) with respect to the rigid wall. Instead,

Irwin et al. (1993) analyzed the displacement of the contralateral (non-impacted)

shoulder which is biomechanically not too interesting. A more interesting result

was the motion of the scapular which swung out widely if the ribs were intact but

showed little motion if they were fractured. This is shown in Fig. 16.6. It is not

known if the muscles attached to the scapular and the bursae between the scapular

and the rib cage were injured when there is no rib fracture but it is likely that the

muscles attached to the scapula and the bursae between the rib cage and the

scapular sustained injury. In the same set of side impact experiments described

by Cavanaugh et al. (1990), the abdomen was also impacted. The abdominal impact

data were analyzed by Cavanaugh et al. (1996) and they found that rigid wall

impacts at 20 mph (32.2 km/h) resulted in frequent injury to the abdominal organs

and if the soft padding was used with a manufacturer’s rated stiffness 15 psi or

103 kPa (actual stiffness of 8–10 psi (55–69 kPa)), there were no abdominal organ

injuries. Future reference to soft padding in this chapter implies a stiffness of 15 psi.

Zhu et al. (1993) analyzed the pelvic injury data from the same tests and concluded

that average force is a good predictor of pelvic injury and that for a 50 % probability

546 16 Side Impact

Table 16.1 List of all 17 side impact sled tests performed by Cavanaugh et al. at Wayne State University (taken from Huang (1995))

Pelvic

Pad

MAIS to body regions

Run

No. Run date offset

(in) Wall pad thick. (in) Sled vel. (m/s) Cad No. Mass (kg) HT.

(m) Age Sex Lamda NE SH TH AB PE

SIC01 1-20-89 6 NO 0 8.9 UM6 70.5 1.76 61 M 1.021 0 2 5 2 2

SIC02 1-30-89 6 NO 0 9.1 187 49.5 1.63 64 F 1.148 3 2 5 2 3

SIC03 2-03-89 6 NO 0 10.5 188 70.0 1.75 37 M 1.023 0 0 5 0 2

SIC04 4-03-89 0 NO 0 9.1 215 57.6 1.63 69 M 1.092 3 2 4 2 2

SIC05 4-10-89 0 NO 0 6.7 216 44.0 1.72 67 M 1.194 0 0 4 0 0

SIC06 4-27-89 0 NO 0 9.0 217 61.2 1.82 60 M 1.070 0 2 4 0 2

SIC07 5-16-89 0 NO 0 6.7 206 74.8 1.70 66 M 1.001 0 2 4 0 0

SIC08 8-10-89 0 NO 0 6.6 UM12 73.9 1.62 64 F 1.005 3 2 5 3 0

SIC09 0-26-89 0 ARSAN 3 9.2 280 54.9 1.65 61 F 1.110 3 2 5 0 3

SIC10 1-17-90 0 15 PH a 6 8.7 317 62.1 1.71 60 M 1.065 0 0 2 0 0

SIC11 2-22-90 0 15,23 PH a 4 8.9 330 55.3 1.65 54 F 1.107 0 0 2 0 0

SIC12 3-01-90 0 23,31 PH a 4 8.9 335 54.4 1.43 68 F 1.113 0 0 5 0 0

SIC13 4-12-90 0 15,23 PH a 4 8.3 338 66.7 1.61 62 M 1.040 0 0 4 0 0

SIC14 7-17-90 0 15,23 PH a 4 9.4 360 55.3 1.74 72 M 1.107 3 2 4 2 0

SIC15 8-09-90 0 15,23 PH a 4 8.9 386 68.9 1.54 43 F 1.028 0 2 0 0 0

16.3 A Cadaveric Study of Side Impact—Sled Tests 547

SIC16 3 8.9 462 56.7 1.70 58 F 1.098 0 2 4 4 2

2-21-91 0 16,23 Verticel a

SIC17 6-11-91 0 15,23 PH a 8 8.9 503 93.0 1.80 65 M 0.931 0 2 2 0 0

a SIDEWALL PAD: PH SIGNIFIES PAPER HONEYCOMB

15, 16, 23, 31 ARE MANUFACTURER’S RATED COMPRESSIVE STRENGTHS IN PSI

NE ¼ NECK, SH ¼ SHOULDER, TH ¼ THORAX, AB ¼ ABDOMEN, PE ¼ PELVIS

SIC 09: PADDING 3 00 THICK 0.9 PCF CLOSED CELL FOAM ENTIRE HEIGHT OF SIDEWALL

SIC 10: 6 00 THICK 15 PSI PADDING USED ENTIRE HEIGHT OF SIDEWALL

SIC 11: 4 00 THICK 15 PSI PADDING USED AT THORAX & ABDOMEN BEAMS, 23 PSI AT SHOULDER & PELVIC BEAMS



SIC 14: ONE PIECE OF 4 00 THICK 15 PSI PADDING USED AT SHOULDER, THORAX, ABDOMEN BEAMS; 23 PSI AT PELVIC BEAM


SIC 16: 3 00 THICK 16 PSI VERTICEL USED AT THORAX & ABDOMEN BEAMS, 23 PSI HONEYCOMB AT SHOULDER & PELVIC BEAMS


SIC01–13: ARMS DOWN (ANGLE APPROXIMATELY 15 DEGREES ANTERIOR TO MID–AXILLARY LINE)

SIC 14–17: ARMS UP TO EXPOSE LEFT SIDE OF THORAX TO DIRECT IMPACT

548 16 Side Impact

Fig. 16.6 Motion of the

scapular due to a side

impact to the torso.

(A) Motion with no

rib fracture. (B) Motion

with rib fractures (taken

from Irwin et al. (1993))

A

undeformed rib

deformed rib

scapula

spine

scapular

target

B

rib before

fractures

fractures

spine

scapula

scapular

target

of pelvic fracture, the lateral impact force is 5 kN. With 100 mm of padding,

averaging in compressive strength of 124 kPa (18 psi), pelvic injuries were

prevented. It was also stated that the pelvic acceleration limit of 130 g in the

1997 FMVSS 214 was too high.

16.4 A Cadaveric Study of Side Impact—Pendulum

Impacts

In Chap. 11 (Sect. 11.4.2), the thoracic portion of the cadaveric study by Viano et al.

(1989) was described. In this section, the remainder of the study is described.

A 23.4-kg pendulum was used to impact the thorax, abdomen, and pelvis of

14 unembalmed cadavers at three different speeds. To avoid rotation of the rib

cage, the impact direction was 30 anterior of the lateral axis of the cadaver for

thoracic and abdominal impacts (Fig. 11.20) while the pelvis was impacted laterally.

The response of the abdomen is shown in Fig. 16.7 for the three speeds of

impact. The deflections at 4.8 m/s appear to be larger than those at 6.8 m/s due to

variations in cadaver size and stiffness. If the data were normalized the

16.4 A Cadaveric Study of Side Impact—Pendulum Impacts 549

Fig. 16.7 Force-deflection

curves from lateral

pendulum abdominal

impacts (taken from Viano

1989)

FORCE (KN)

5

4

3

2

run 19

run 23

run 24

run 30

run 42

run 43

4.8 m/s

1

0

0 5 10 15 20

DEFLECTION (cm)

5

4

run 6

run 8

run 10

run 12

6.8 m/s

FORCE (KN)

3

2

1

0

0 5 10 15 20

DEFLECTION (cm)

5

4

run 15

run 20

run 28

run 34

9.4 m/s

FORCE (KN)

3

2

1

0

0 5 10 15 20

DEFLECTION (cm)

550 16 Side Impact

inconsistency is improved but not totally eliminated. The ideal solution would be to

obtain more data but if that is not possible, a variety of statistical methods can be

used to draw response corridors at each impact velocity, as described in Viano

(1989). There was only one MAIS 4 injury to the abdomen due to a 9.8-m/s impact.

The injury was in the form of a lacerated diaphragm and a lacerated right lobe of the

liver. For the pelvis, response in the form of a force-deflection curve was obtained

for impact speeds of 5.2 and 9.8 m/s. These curves are shown in Fig. 16.8. It can be

10

5.2 m/s

8

FORCE (kN)

6

4

run 21

2

run 25

run 26

run 31

0

0 5 10

DEFLECTION (cm)

15 20

15

9.8 m/s

10

FORCE (kN)

5

run 22

run 27

run 32

run 39

0

0

5 10

15 20

DEFLECTION (cm)

Fig. 16.8 Force-deflection curves from lateral pendulum pelvic impacts (taken from Viano 1989)

16.5 Models of Side Impact 551

seen that pelvic deflections exceed 5 cm at 5.2 m/s and 10 cm at 9.8 m/s. It is

presumed that the motion is occurring at the sacroiliac joint. There were two pubic

rami fractures at the higher speed of impact (MAIS ¼ 2). For tolerance, logistic

analysis of the data using such predictors as V*C, C and force was attempted. For

the abdomen, it was found that V*C was the best predictor as it had the highest γ 2

value for MAIS 4+ injuries. The value of V*C is 2.26 m/s for a 50 % probability of a

MAIS 4+ injury. For the pelvis, C was the best predictor for pubic ramus fracture

with a value of 27.4 % for a 50 % probability of fracture. This result does not agree

with the sled test study by Zhu et al. (1993) who found average force to be a better

predictor than compression.

16.5 Models of Side Impact

Modeling of side impact involves the whole body and can be accomplished by

using a rigid body model, such as MADYMO, or by finite element methods which

are more complex but which may be able to predict internal organ injuries. One of

the first models was developed by Huang et al. (1994a) who modified the standard

15-link rigid body model to simulate a Heidelberg side impact test or a real-world

car-to-car side impact. The study was motivated by the fact that although 10 cm of

relatively soft padding can protect the chest, the padding brings the chest closer to

the vehicular side structure and lengthens the duration of impact. Those who

objected to the use of padding were of the opinion that padding would increase

chest injury severity. A MADYMO-type model, representing a human torso, would

be able to ascertain the benefits and shortcomings of the use of padding. The model

was validated against 13 of the 17 side impact cadaver tests performed at Wayne

State University and against the pendulum impact data published by Viano (1989).

It was then exercised to simulate a car-to-car impact, by using a variety of padding

materials to protect the occupant and by lowering the height of the window sill so

that shoulder was not able to participate in the protection of the torso. Because

impact loads were measured at the shoulder, chest, abdomen, and pelvis, four

ellipsoids were used instead of the normal three to represent the torso. Additionally,

the neck was given more flexibility by simulating it with three instead of one

segment. As a result, the MADYMO model had 18 segments. The dimensions

and weights of these segments were selected to model a 50 th percentile male. A

frontal view of the side impact MADYMO model is shown in Fig. 16.9. Extra

features were built into the model to calculate V*C and TTI. Figure 16.10 shows

mini-models built into each of the four segments with two small masses, M1 and

M2. The mass, M1, is a contact ellipsoid just inside the ellipsoid (segment) and its

motion is tracked as the body segment penetrates the padding or rigid wall. Its

displacement and velocity yield V*C. However, for the chest, the model generated

the total chest deflection but the experimental data were expressed in terms of

deflection of the half thorax. To resolve the discrepancy between model and

552 16 Side Impact

Fig. 16.9 MADYMO

model of a 50th percentile

male simulating side

impact. It has 18 rigid body

segments. 1 for the head,

3 for the neck, 4 for the

torso, 4 for upper

extremities, and 6 for the

lower extremities (taken

from Huang (1995))

Fig. 16.10 Mini-models

used in the side impact

model by Huang (1995)

to calculate the Viscous

Criterion and TTI

experimental data, data from the chest band was used to compute the half deflection,

given by the equation:

Half Body Compression ¼ 0:65 ½Delta ðL1Þ þ L3=147

where

Delta (L1) is the deflection of the thorax, in mm

L3 is deflection of the padded surface, in mm

and

147 is the lateral half depth of the chest in mm


The chest deflection on the struck side is 65 % of the total chest deformation.

To calculate TTI, the mass, M2, was embedded in each segment and was part of

a viscoelastic model shown in Fig. 16.10. Its acceleration in the shoulder segment

was assumed to be that of the 4th rib and its acceleration in the abdominal segment

was assumed to be that of the 8th rib. As for the acceleration of T12, it was assumed

that it was the same as the acceleration of the abdominal segment.

The model by Huang et al. (1994a) was primarily validated against the

Heidelberg-type sled test data obtained by Cavanaugh et al. (1993). It was also

validated against the pendulum side impact data by Viano (1989). Figure 16.11

shows a comparison of the thoracic impact force against a rigid wall with and without

the 15-cm pelvic offset. The predicted force was lower than the measured force with a

pelvic offset and was slightly higher than the measured force against a rigid wall.

The MADYMO model was not as supple as the cadaver which allowed the thorax to

translate horizontally after the pelvis was stopped and strike the wall with a force

larger than that predicted by the model. A similar comparison is made for padded

Fig. 16.11 Validation of the side impact model by Huang et al. (1994a) against sled test data from

Cavanaugh et al. (1990). (A) Pelvic offset test against a rigid wall. (B) Flat rigid wall (Fig. 16.11B

was taken from Huang (1995))

554 16 Side Impact

Fig. 16.12 Validation of the side impact model by Huang et al. (1994a) against sled test data from

Cavanaugh et al. (1990). (A) Impact test against soft paper honeycomb padding. (B) Impact test

against Arsan foam padding (Fig. 16.12A was taken from Huang (1995))

impacts. The thoracic force was validated for impacts using the soft (15-psi) paper

honeycomb (PHC) padding in Fig. 16.12A and Arsan padding in Fig. 16.12B.Arsan

is a rigid foam padding that gave good TTI results when it was impacted by SID but

produced disastrous results in a cadaver. Additional validations were conducted using

chest compression and rib acceleration. These can be found in Huang et al. (1994a).

Validation of the model against pendulum impacts is shown in Fig. 16.13 in the form

of force-deflection curves for thoracic and abdominal impact. Because of the controversy

regarding the validity of TTI as an injury criterion, this model was provided at

no charge to anyone who wanted to use it to check out their side impact safety design.

The data set was given to the developers of MADYMO for distribution to anyone

who asked for it.


Fig. 16.13 Validation of the side impact model by Huang et al. (1994a) against pendulum impact

data from Viano et al. (1989). (A) Thoracic force-deflection curves. (B) Abdominal forcedeflection

curves (Fig. 16.13A was taken from Huang (1995))

The Huang et al. (1994a) model was used in a parametric study to investigate the

effects of the loss of air space between door and occupant if padding were used. The

study also looked at the effects of padding stiffness, strengthening the side door

structure, lowering of the window sill and the insensitivity of TTI. In order to

simulate a door impacting an occupant, it was necessary to re-configure the model

so that an intruding door would impact a stationary occupant. Two “typical” side

door velocity profiles were selected. One was called the GM profile because it

appeared in a 1989 issue of Search (Volume 24, #3), a GM publication, while the

other was called the Deng profile because it appeared in a paper by Deng et al.

(1988). These profiles are shown in Fig. 16.14. The Deng profile has a higher initial

velocity (12.1 vs. 8.6 m/s) and a longer duration than the GM profile but the Deng

struck velocity is much lower. These velocities are, of course, dependent on the

masses of the two interacting vehicles. For the purposes of this study, the following

criteria of injury to the chest are used:

556 16 Side Impact

Fig. 16.14 Side impact door velocity profiles used in a parametric study of the Huang et al.

(1994a) model. (A) The GM velocity profile. (B) The Deng velocity profile (taken from Huang

(1995))

Limit for C 40 %

Limit for V*C 1 0 m/s

Limit for TTI 85 g

The V*C limit is actually 1.5 for side impact but the discussion that follows is

based on the 1.0 limit for V*C, as described in the paper.


16.5.1 Effect of Air Space

This study compares the effect of the initial air space between the occupant and the

door. If there is no space, it basically simulates an occupant sitting right up against

the door before the side impact. The model predicted that if the initial (first) peak is

larger than the second (common velocity of both vehicles), 0.1 m of space was

beneficial in terms of C and V*C but not in terms of TTI. However, without

padding, all injury criteria were exceeded. This is shown in Table 16.2 for Runs

19 and 20. If, in the unlikely event that first peak is lower than the second (Runs

24 and 25), 0.1 m of air space lowered V*C and TTI but not C.

16.5.2 Effect of Padding

During the early days of side impact protection, an argument was put forth against

the use of padding because the occupant would be impacted for a longer period of

time as the padding would be right up against the torso of the occupant. Table 16.3

shows the results of the effects of a soft padding (15 psi PHC) and a stiff padding

compared to the case of no padding at all. It is seen that the soft padding was

beneficial to the occupant while a stiff padding (Arsan) was detrimental to the

thorax. These results are consistent with experimental observations. All three

criteria were lower with the use of the soft PHC pad.

Table 16.2 Model predictions of the effect of air space on the near-side occupant (based on

Huang (1995))

Effect of air sapce

Impact

conditions Run no. C (%) V * C (m/s) TTI (g’s)

Velocity (m/s)

Profile 1st 2nd Peak

No space unpad 19 54.9 3.26 155 Deng’s 12.1 6.0

0.1 m space 20 45.8 2.03 186

unpad

No space unpad 24 39.1 1.37 105 Reduced GM 7.3 8.6

0.1 m space

unpad

25 43.0 1.19 85

Table 16.3 Model predictions of the effect of padding on the near-side occupant (based on Huang

(1995))

Effect of air sapce

Velocity (m/s)

Impact conditions Run no. C (%) V * C (m/s) TTI (g’s) Profile 1st 2nd Peak

0.1 m space unpad 15 42.8 1.19 144 GM 10.8 8.6

No space 0.1 m 16 37.2 0.79 88 GM 10.8 8.6

15/23PH

No space 0.1 m

ARSAN

17 43.6 1.68 104 GM 10.8 8.6

558 16 Side Impact

Table 16.4 Model predictions of the effect of a reduction in door velocity on the near-side

occupant (based on Huang (1995))

Effect of reduction in door velocity

Impact

conditions Run no. C (%) V * C (m/s) TTI (g’s)

0.1 m space

unpad

Velocity (m/s)

Profile 1st 2nd Peak

20 45.8 2.03 186 Deng’s 12.1 6.0

30 37.8 0.85 96 Reduced 8.6 6.0

Deng’s

15 42.8 1.19 114 GM 10.6 8.6

25 43.0 1.19 85 Reduced GM 7.3 8.6

16.5.3 Reduction in Door Velocity

One of the ways to mitigate side impact injuries is to strengthen the door and thus

reduce its intrusion velocity. Table 16.4 shows the effect of an approximate 30 %

reduction in door velocity for both velocity profiles. In Runs 20 and 30, the

reduction of the initial peak of the Deng profile brought about a uniform reduction

in all three criteria lowering the predicted values of C and V*C below the injury

threshold. However, for the GM profile, the reduction is not effective, except for

TTI (Runs 15 and 25). It appears that the peak values of C and V*C are determined

by the peak door velocity, whether it is the first or second. But, for TTI, its peak

value is dependent on the first peak. Since in Run 25, the first peak is lower than the

second and the values of C and V*C are unchanged, we can conclude that there is

no need to strengthen the door ad infinitum and the best we can do is to limit the first

peak velocity to that of the second peak.

16.5.4 Loss of Shoulder Engagement

To increase visibility for the occupants, the designer can lower the window sill

height or raise the height of the seats. In either case, there is a loss of shoulder

engagement with the door during a side impact. Table 16.5 compares the computed

values of C, V*C, and TTI for three situations; namely, no padding, soft padding,

and reduced door velocity. It shows that C, V*C, and TTI are exceeded without soft

padding and padding with a stiffer door (reduced door velocity) is necessary to

protect the near-side occupant completely.

We conclude from model results that the padding can be used for side impact

protection but it needs to be soft and should not bottom out. When applied to side

impact airbags, the initial pressure should be low and the bag should not be vented

so that it does not bottom out. Moderate strengthening of the side structure is

recommended and doors with low window sills need to be strengthened and fully

padded.


Table 16.5 Model predictions of the effect of loss of shoulder engagement on the near-side

occupant (based on Huang (1995))

Loss of shoulder engagement

Velocity (m/s)

Impact

conditions

Run

no.

Thorax force

(kN)

C

(%)

V * C

(m/s)

TTI

(g’s)

Profile

1st

2nd

Peak

With Shd 15 2.9 42.8 1.19 114 0.1 m space, unpad

No Shd 35 3.9 54.2 1.55 108 GM 10.6 8.6

With Shd 16 2.0 37.2 0.79 88 No space, 0.1 m 15/23 PH

No Shd 36 3.6 51.7 1.19 83 GM 10.6 8.6

With Shd 31 1.9 35.8 0.79 71 No space, 0.1 m 15/23 PH

No Shd 46 2.3 40.5 0.79 68 Reduced

Deng’s

8.6 6.0

Huang et al. (1994b) also developed a simplified finite element model of side

impact to predict injury parameters, such as C, V*C and TT1 and to study the

interaction of the body with protective padding. It modeled the rib cage and the

spine but the thoracic and abdominal organs were not individually modeled.

Instead, they were modeled as solid elastic elements attached to the rib cage and

abdominal wall by dampers. Thus, this simplified model could not be used to study

the injury to the viscera. Just as in the MADYMO model described above, the model

was validated against sled and pendulum test data. However, the interesting part of

the study was the simulation of a sled-to-sled side impact experiment designed to

mimic a car-to-car impact in the laboratory. Two sleds were used. The stationary

target sled contained the seated test subject (cadaver) and the moving (bullet) sled had

an instrumented car door mounted on its leading edge. When the sleds made contact,

the door would impact the cadaver, simulating a realistic side impact. This was a

difficult experiment to conduct because the bullet sled tended to pitch as it impacted

the target sled but the rear supports of the bullet sled were not designed to allow it to

pitch. As a result, only two tests were conducted and unfortunately most of the sensor

data were lost due to recording equipment malfunction. The only data available for

validation of the model were those of chest deformation measured by a chest band. A

comparison of chest deformation profiles for one of two tests is shown in Fig. 16.15.


Protection of occupants is difficult because there is not much room between the

door and the occupant. The problem was complicated by the promulgation of an

ineffective side impact standard in the 1990s. FARS data in Fig. 16.16 show that

despite the standard, side impact fatalities show no decrease in the years after the

standard came into full effect in 1997. Instead of cooperating with industry, the

NHTSA railroaded the standard through over industry objections and was

560 16 Side Impact

Fig. 16.15 Comparison of computed and measured chest deformation profiles of one of the two sled-to-sled tests carried out by Huang et al. (1994b)


6,000

U.S. Side Impact Fatalities

(FARS 1995-2003, w/o rollover)

5,000

Fatalities

4,000

3,000

2,000

Near Side

Far Side

1,000

1995 1996 1997 1998 1999 2000 2001 2002

Calendar Year

2003

Fig. 16.16 US side impact fatalities from 1995 to 2003 stayed constant despite the promulgation

of FMVSS starting in 1994. The total number of occupant fatalities during this period varied

between 33,064 and 34,108 (taken from NHTSA FARS Data)

eventually proven to have promulgated a faulty standard, using the TTI and the

SID. It was revised in 2007 when both the TTI and the SID were abolished, a silent

admission of an error in judgment that cost thousands of lives. The stubborn and

autocratic attitude of the NHTSA regarding this standard led to a most regrettable

decision which should not be allowed to occur in a democracy.

The research performed by Wayne State University with support from General

Motors and the CDC has contributed to a better understanding of side impact injury

mechanisms while researchers supported by NHTSA proclaimed the virtues of TTI.

Because of the opposition of Wayne State to the use of TTI and SID in FMVSS

214, research support for the University was cut off by the NHTSA in the 1990s.

The agency was able to do this because it did not rely on a panel of independent

experts to judge the merits of the proposed research and preferred to fund and direct

the research themselves. Hopefully, the new 2007 FMVSS 214 will be better than

the old one but it is still not based on the best research available.


16.1. In side impact, the following statement is valid:

[] (i) Neck injuries are rather frequent

[] (ii) The EUROSID dummy is very human-like

562 16 Side Impact

[] (iii) The thorax is not sensitive to the stiffness of side door airbags and

padding

[] (iv) Aortic ruptures can occur

[] (v) Rib fractures do not occur on the non-impacted side of the thorax

16.2. In side impact, the most frequently injured body region is

[] (i) The head

[] (ii) The neck

[] (iii) The chest

[] (iv) The abdomen

[] (v) The upper extremities

16.3. Protection of elderly occupants in a side impact is important because

[] (i) Elderly drivers run into people all the time

[] (ii) Elderly drivers are more frequently involved in intersection type

crashes than younger drivers

[] (iii) Elderly occupants tend to not recover as well as younger occupants

after they are injured

[] (iv) (ii) and (iii)


16.4. Single vehicle side impacts are frequently due to

[] (i) Reckless driving on the part of young drivers

[] (ii) Poor handling on the part of elderly drivers

[] (iii) Skidding into telephone poles that should not have been there

[] (iv) The weather only


16.5. Side impacts occurring in intersections are frequently due to

[] (i) Drivers running red lights

[] (ii) Elderly drivers with reduced capacity to judge the speed of

on-coming vehicles

[] (iii) Skidding of cars into an intersection


[] (v) (i) and (ii)

16.6. Several injury criteria for the chest have been proposed for side impact.

Select the incorrect answer:

[] (i) Thoracic Trauma Index (TTI)

[] (ii) Viscous Criterion (V*C)

[] (iii) Average Spine Acceleration (ASA)

[] (iv) Chest Injury Criterion (CIC)

[] (v) Chest Compression (C)


16.7. Results from tests conducted by Viano (1989) show that for side impact to

the abdomen:

[] (i) The value of T12 spinal acceleration for a 25% probability of an

AIS 4+ injury is about 80 g

[] (ii) The value of V*C for a 25% probability of an AIS 4+ injury is

about 1.0 m/s

[] (iii) The value of C for a 25% probability of an AIS 4+ injury is about

44%

[] (iv) The value of peak impact force for a probability of an AIS 4+ injury

is about 4 kN


16.8. Dr. Cavanaugh conducted 17 cadaveric side impact experiments, using the

Heidelberg type sled. He wanted to:

[] (i) Determine the mechanical response of the thorax to a side impact

[] (ii) Determine the tolerance of the thorax to a side impact

[] (iii) Determine the optimal stiffness of padding for side door structures

[] (iv) (ii) and (iii)


16.9. Cavanaugh et al. (1990) found that padding can reduce injury severity due to

a side impact. Select the incorrect statement:

[] (i) Four-inch thick paper honeycomb with a crush strength of 8 psi had

the best results—MAIS averaged 2.3

[] (ii) Offset unpadded impacts in which the pelvis was stopped 6 in.

before the rest of the torso was effective in reducing MAIS

[] (iii) Unpadded impacts produced high values of AIS consistently

[] (iv) Paper honeycomb padding stiffer than 8 psi was not able to prevent

severe thoracic injuries

[] (v) Arsan, a padding which yielded low values of TTI for the Side

Impact Dummy (SID) caused severe injuries in the cadaver

16.10. The following findings refer to the side impact test results reported by

Cavanaugh et al. (1990). Select the incorrect answer:

[] (i) Aortic ruptures occurred in cadavers in unpadded as well as padded

impacts

[] (ii) The Heidelberg test impact duration is much longer than that of

pendulum impacts conducted by Viano (1989)

[] (iii) When soft (8-psi) padding was used, the maximum value for V*C

was about 1.0 m/s

[] (iv) When stiff (19 psi) padding was used, the maximum value for chest

compression (C) was in excess of 50%

[] (v) For rigid wall impacts, the peak upper sternal acceleration in the

antero-posterior direction was in the range of 50–80 g

564 16 Side Impact

16.11. The chest band invented by Eppinger (1989) has the following characteristics.

Select the correct answer:

[] (i) It consists of a thin strip of steel with lots of strain gages attached to it

[] (ii) It is based on the principle that strain is inversely proportional to the

radius of curvature

[] (iii) It needs to be calibrated twice, once while it is flat and once while it

is wrapped around the chest

[] (iv) The curvature data are adjusted using the strain data from the first

and last strain gage of the band


16.12. Based on the 17 cadaver tests done at WSU by Dr. Cavanaugh, which of the

following parameters is the best predictor for side impact injury?

[] (i) Thoracic trauma index (TTI)

[] (ii) Viscous Criterion (VC max )

[] (iii) Average Spine Acceleration (ASA10, corrected for age)

[] (iv) Compression (C max )

[] (v) Lateral Spine Acceleration (T12 y )

16.13. In evaluating the results of a Logistic analysis, the parameters of significance

are χ 2 , p, and r 2 . Which of the following statements is true?

[] (i) χ 2 should be as low as possible

[] (ii) p should be as close to unity as possible

[] (iii) r 2 should be as close to zero as possible



16.14. When comparing the proposed injury criteria for side impact, using data

published by Viano (1989) and by Dr. Cavanaugh, we find that:

[] (i) The recommended criterion for V*C is the same, namely 1.0 m/s

[] (ii) The recommended criterion for chest compression is the same,

namely 31%

[] (iii) The recommended criterion for TTI is the same, namely 140 g

[] (iv) The recommended criterion for V*C is different

[] (v) The recommended criterion for TTI is different

16.15. The Wayne State Side Impact MADYMO Model was:

[] (i) Never validated against any cadaver data

[] (ii) Was validated against volunteer data

[] (iii) Was not validated against pendulum impact data obtained by Viano

et al. (1989)

[] (iv) Was validated against cadaver data obtained by Cavanaugh et al.

(1990)

[] (v) Was validated against field accident data


16.16. Validation of the Wayne State Side Impact MADYMO Model was done by:

[] (i) Comparing model predictions with measured thoracic impact force

[] (ii) Comparing model predictions with measured abdominal impact

force

[] (iii) Comparing model predictions with measured pelvic compression

[] (iv) Comparing model predictions with measured sternum acceleration

[] (v) Comparing model predictions with measured parameters for rigid

impacts only

16.17. The Wayne State Side Impact MADYMO Model was exercised to study the

effects of adding padding or air space between the occupant and the side

door structure. It was found that:

[] (i) Padding is not helpful, even if its stiffness is low

[] (ii) Arsan padding preferred by the SID is also very beneficial to the

human

[] (iii) The effect of adding air space does not dependent on the shape of

the door velocity pulse

[] (iv) If stiff padding is used, it is the same as using no padding at all


16.18. The Wayne State Side Impact MADYMO Model was exercised to study the

effects of strengthening the side door structure and of engaging the shoulder

during a side impact. It was found that:

[] (i) The stiffer the door the better it is able to provide protection to the

near-side occupant

[] (ii) Peak values of TTI are dependent on the speed of the struck vehicle

(second peak)

[] (iii) Without shoulder engagement, peak thoracic force and compression

tend to increase for a rigid side door

[] (iv) In padded impacts, shoulder engagement does not play a large role

in decreasing peak thoracic force and compression

[] (v) Without shoulder engagement it is only necessary to use soft

padding for the thorax and abdomen

16.19. In the side impact pendulum test series conducted by Viano et al. (1989)on

the thorax

[] (i) The impacts were purely lateral impacts

[] (ii) The impactor mass was 14 kg

[] (iii) The impactor diameter was 152 mm

[] (iv) Chest deflection was measured by a string potentiometer


16.20. The chest band developed by Eppinger is

[] (i) Useful in side impact

[] (ii) Very difficult to use and calibrate

566 16 Side Impact

[] (iii) Measures chest deformation at a single level of the chest

[] (iv) Assumes that the thoracic spine does not deform



Prob

Ans

1 (iv)

2 (i)

3 (iv)

4 (i)

5 (v)

6 (iv)

7 (iii)

8 (iv)

9 (ii)

10 (ii)

11 (v)

12 (iii)

13 (v)

14 (iv)

15 (iv)

16 (i)

17 (iv)

18 (iii)

19 (iii)

20 (v)

References

J. Augenstein, E. Perdeck, J. Bowen, J. Stratton, M. Singer, T. Horton, A. Rao, K. Digges,

A. Malliaris, J. Steps, Injuries in near-side collisions. 43rd Annual Proceedings/Association

for the Advancement of Automotive Medicine, Barcelona, Sitges, 1999

J. Cavanaugh, T. Walilko, A. Malhotra, Y. Zhu, A. King, Biomechanical response and injury

tolerance of the pelvis in twelve sled side impacts. in 34th Stapp Car Crash Conference. SAE

Paper No. 902305, Orlando, Florida, 1990

J. Cavanaugh, Y.J. Zhu, Y. Huang, A.I. King, Performance and mechanical properties of various

padding materials used in cadaveric side impact sled tests SAE Paper #920354. Society of

Automotive Engineers, Inc., Warrendale, 1992

J.M. Cavanaugh, Y. Huang, Y. Zhu, A.I. King, Regional tolerance of the shoulder, thorax,

abdomen and pelvis to padding in side impact SAE Paper #930435. Society of Automotive


References 567

J. Cavanaugh, T. Walilko, J. Chung, A. King, Abdominal injury and response in side impact. in

40th Stapp Car Crash Conference, SAE Paper No. 962410, Albuquerque, New Mexico, 1996

Y.C. Deng, Design considerations for occupant protection in side impact: a modeling approach, in

32nd Stapp Car Crash Conference, SAE Paper No. 881713, 1988

R. Eppinger, On the development of a deformation measurement system and its application toward

developing mechanically based injury indices. in 33rd Stapp Car Crash Conference, SAE paper

No. 892426, Washington, DC, 1989

Y. Huang, A. King, J. Cavanaugh, A MADYMO model of near-side human occupants in side

impacts. J. Biomech. Eng. 116(2), 228–235 (1994a)

Y. Huang, A. King, J. Cavanaugh, Finite element modeling of gross motion of human cadavers in

side impact. in 38th Stapp Car Crash Conference. SAE Paper No. 942207, Ft. Lauderdale,

Florida, 1994b

Y. Huang, Automotive side impact protection—biomechanical issues. Ph.D. Dissertation, Wayne

State University, Detroit, Michigan, 1995

A.L. Irwin, A.I. King, Y. Zhu, J.M. Cavanaugh, T.J. Walilko, Displacement responses of the

shoulder and thorax in lateral sled impacts. in 37th Stapp Car Crash Conference, San Antonio,

Texas, 1993

C.J. Kahane, An evaluation of side impact protection. FMVSS 214 TTI(d) improvements and side

air bags NHTSA Report No. DOT HS 810 748. Washington DC: Department of Transportation.

National Highway Traffic Safety Adminstration, 2007

D. Kallieris, R. Mattern, G. Schmidt, R.H. Eppinger, Quantification of side imnpact responses and

injuries. in 25th Stapp Car Crash Conference, SAE paper #811009, San Francisco, California,

1981

G. Klaus, R. Sinnhuber, G. Hoffman, D. Kallieris, R. Mattern, Side impact—a comparison

between dummies and cadavers, correlations between cadaver loads and injury severity. in

28th Stapp Car Crash Conference, SAE Paper #841655, Chicago, Illinois, 1984

J.H. Marcus, G. Schmidt, R. Mattern, D. Kallieris, R.H. Eppinger, R.M. Morgan, Human response

to and injury from lateral impact. in 27th Stapp Car Crash Conference, San Diego, California,

1983

J. Melvin, D. Robbins, R. Stalnaker, Side impact response and injury. in 6th International Tech

Conference on Experimental Safety Vehicles (ESV), Washington, DC, 1976

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side impact. in 40th Stapp Car Crash Conference, SAE Paper No. 962412, Albuquerque, New

Mexico, 1996

C.E. Strother, G.C. Smith, M.B. James, C.Y. Warner, Injury and intrusion in side impacts and

rollovers. SAE Paper No. 840403, 1984

D. Viano, Biomechanical responses and injuries in blunt lateral impact. in 33rd Stapp Car Crash


D.C. Viano, I.V. Lau, C. Asbury, A.I. King, P. Begeman, Biomechanics of the human chest,

abdomen, and pelvis in lateral impact. Accid. Anal. Prev. 21(6), 553–574 (1989)

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multivehicle side-impact crashes. Accid. Anal. Prev. 22(2), 177–188 (1990)

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based on a cadaveric test series. in 37th Stapp Car Crash Conference. SAE Paper No. 933128,

San Antonio, Texas, 1993

Chapter 17

Car-Pedestrian Impact

Road users who are not protected by the vehicular structure of an automobile are

particularly vulnerable in a crash situation. These road users include pedestrians,

bicyclists, motor cyclists, and people riding in non-motorized vehicles, such as

horse-drawn carriages and the like. By far, the largest group of vulnerable road

users is the pedestrian who travels in close proximity to automobiles and, in fact,

often cross the roadways and are at high risk of being impacted by these vehicles.

The most effective way of protecting the pedestrian is to separate vehicular and

pedestrian traffic, especially in busy urban areas, by the use of overpasses and

underpasses at intersections. These are costly solutions and are not available at most

intersections, even in highly developed countries of North America and Europe.

Strict enforcement of traffic regulations regarding pedestrians in intersections is

helpful but many are still injured or killed.

17.1 Epidemiology of Car-Pedestrian Impact

In the USA, slightly under 5000 pedestrians are killed each year by automobiles

despite efforts on the part of car designers to reduce the front end lethality of cars

(NHTSA 2012). In 2012, most of the fatalities occurred in urban areas (73 %), in

clear or cloudy weather (89 %) and during nighttime hours (70 %). Seventy percent

of the fatalities occurred at non-intersections. Pedestrians aged 65 and over

accounted for 20 % of all fatalities and their fatality rate was 2.17 per 100,000

population. Males accounted for 69 % of the pedestrians killed (2.13 per 100,000

population) while the female rate was 0.91 per 100,000 population. Alcohol

involvement among drivers amounted to 17 % of the total. In large urban areas,

the highest fatality rates per 100,000 population occurred in Detroit (3.99), Oklahoma

City (3.34), and Albuquerque (3.24). The lowest rates were found in Boston

(0.79), Baltimore (0.97), and Louisville/Jefferson, KY (0.99).



569

570 17 Car-Pedestrian Impact

Pedestrian fatalities are much higher in countries with high population densities,

such as China and India but the rate may not be necessarily higher because of the high

population density. The pedestrian fatality rate was 68,000 in China and 18,700 in

India, in 2015, according to estimates made by the World Health Organization

There is also a serious problem regarding the need for the accident investigator

to fully understand the mechanics of car-pedestrian impact and for the researcher to

study the entire impact event instead of just concentrating on the interaction of the

pedestrian with the vehicles. Many fatalities are due to head injuries and it is more

than likely that a high percentage of these fatal injuries were sustained when the

head contacted the roadway. However, accident investigators could find no evidence

of head contact with the roadway because head impact with the roadway

leaves no dents. They have been attributing all head injuries to contact with stiff

components of the front end of the car, such as the A-pillar, windshield, presence of

stiff engine components directly under the hood or the stiff surface at the hood/fender

junction. These are locations on the vehicle where evidence of impact could be found.

In fact, pedestrian standards being promulgated in Europe concentrate on head impact

with the hood and leg impact with the front bumper. It is true that there is very little

experimental evidence of head/ground impact in the studies that have been conducted

thus far because most car-pedestrian experiments are generally terminated after the

test subject (cadaver) completes its impact with the hood and/or the windshield.

However, modeling of these events shows that severe head/ground impacts can occur

at vehicular speeds in excess of 40 km/h (25 mph) for US cars and that if the hood

height is high, such as in an SUV, the speed necessary to cause a fatal head/ground

impact is even lower than 40 km/h. The momentum imparted to the lower part of the

body of the pedestrian can be high enough to cause the pedestrian to do a cartwheel

above the car and the victim ends up sliding off the hood head first, sustaining a

severe head injury. This phenomenon was studied by Tamura (2010); Kendall et al.

(2006); Gupta and Yang (2013), but so far it has not gained much traction with the

powers to be who write standards for pedestrian safety. I have personally been

involved in the modeling of a pedestrian hit by an SUV with a 1-m hood height.

The SUV was traveling at 27.2 km/h (17 mph) when it struck the pedestrian who

walked into the roadway from behind a truck traveling in the opposite direction. The

pedestrian sustained a fatal head injury. The kinematics are shown in Fig. 17.1,based

on the ATB model, a rigid link model similar to MADYMO. The throw distance of

34 ft (10.4 m) matched the distance estimated by the investigating police officer.

Lower extremity injuries are common because the lower extremity is first body

segment contacted. Bumper heights vary but are unfortunately at the level of the

knee for most people. Because injuries to the knee involve soft tissues, such as the

knee ligaments, they are more difficult to treat compared to bony fractures. Car

designers have not been able to lower the bumper height substantially in current

vehicles even though they are much smaller and shorter than those in the 1960s. The

excuse given in those days was that the long overhang of the front end required a

higher bumper so it would not scrape the ground when the vehicle encounters an

upslope. However, currently, with smaller cars and shorter overhangs, the bumper

height has not been reduced substantially.

17.2 Car-Pedestrian Impact Experiments 571

Fig. 17.1 Simulation of an actual pedestrian impact by an SUV with a high hood (1 m) at 27.2 km/

h (17 mph). The momentum imparted to the lower part of the body caused the pedestrian to

cartwheel and strike the ground head first. The pedestrian sustained a fatal head injury

17.2 Car-Pedestrian Impact Experiments

In the literature, there are several reports of car-pedestrian impact experiments

involving the use of whole-body cadavers. One of the first experiments was

performed by Krieger et al. (1976) who used a full-size passenger car to impact a

series of six cadavers and a 95 th percentile dummy at speeds ranging from 15 to

25 mph (24 to 40 km/h). The objective of this NHTSA-sponsored study was to

determine the kinematics of all body segments and to use the data to validate a rigid

link model (ATB model) simulating car-pedestrian impact. The cadavers were

instrumented with 53 accelerometers in an attempt to describe the kinematics of

the body segments of the cadavers during the impact. It was because of this project

that the three-dimensional method of measuring angular acceleration was developed

(Padgaonkar et al. 1977). Nine accelerometers were used to measure the linear

and angular accelerations of certain body segments, including the head. Because

bone screws were used to attach accelerometer mounts to the skeletal structure of

the cadaver, it was difficult to assess injury severity because the presence of screw

holes in bones constitutes stress risers and could be a source of fracture. Thus,

injury was not recorded in this study.

Figure 17.2 shows a schematic of the car-pedestrian test setup, including the

location of the cameras. The test subject (cadaver) was made to stand at the impact

location and its motion was monitored by seven cameras. After the impact with the

vehicle, it was tracked by a lateral camera until it came to rest on the ground. This

was the only known test series that tracked the test subject until it stopped sliding on

the ground. Figure 17.3 shows the pedestrian (cadaver) in the sled area where the


Fig. 17.2 Schematic of the test setup for a car-pedestrian experiment conducted by Krieger et al.

(1976)

Fig. 17.3 The pedestrian (cadaver) was tested in the sled area where it was subjected to a side

impact by the front end of passenger vehicle. Out of five tests conducted, there was one frontal

impact (based on Krieger (1976))


Fig. 17.4 This figure

shows the cadaver in

position for impact. It was

held upright by a harness for

a left-sided impact. The left

knee was prevented from

buckling by taping a 1-cm

diameter wooden dowel rod

across it. Just before impact,

the harness was released

and at impact with the

bumper, the dowel broke to

allow the knee to flex.

Under the impacted leg, a

load cell measured the

ground reaction force which

was substantial (based on

Krieger (1976))

impact took place. A close-up of the cadaver in position for impact is shown in

Fig. 17.4. The cadaver was held upright by a quick release harness that was released

about 25 ms before impact. The impacted leg (in this case, the left leg) was made to

carry the weight of the body by the use of a 1-cm wooden dowel taped across the

lateral aspect of the knee. A load cell under the left foot measured the change in

ground reaction force during impact. Because of the extensive instrumentation, the

weight of the cables became a problem. A special harness was used to carry the

weight of the cables and was suspended on an overhead track so that it could move

with the cadaver as it was propelled by car. The vehicle used was a full-size

passenger vehicle, a 1973 Chevrolet, shown in Fig. 17.5. In addition to the installation

of accelerometers on virtually every body segment, careful anthropometric

measurements were made on each body segment of every test subject and, after the

test, the cadaver was frozen in its natural position and body segments were

dismembered to determine their individual weights, three-dimensional mass

moments of inertia and locations of the centers of gravity while they were still in

a frozen state. Impact kinematics of the pedestrian for a side impact start with

bumper contact with the impacted leg followed by impact with the other leg. The

front end then accelerates the lower extremities and pelvis in the direction of

vehicle travel, causing the rest of the torso to flex over the hood. At about that

time, the cadaver begins to rotate onto its back as the legs are thrown up into the air.

The extent of leg motion depends on the speed of impact. Below 40 km/h, the body

slides up on the hood towards the windshield but stays on the hood and if the car is


Fig. 17.5 The vehicle used for pedestrian impact was a 1973 full-size Chevrolet. The cadaver was

impacted by the left side of the vehicle where the bumper was straight (no curvature, bends) (taken

from Krieger (1976))

braked to a stop, it slides off the hood feet first. At or above 40 km/h, there is enough

momentum imparted to the lower extremities and pelvis to cause the entire body to

cartwheel over the hood and the body can hit the ground head first. Fatal head

injuries are due to this cartwheeling phenomenon and points to the importance of

reconstructing these impacts to determine the speed of the impacting vehicle.

Accident investigators who are unaware of this biomechanical knowledge attribute

all head injuries to impact with the front end of the car, such as the hood, cowl,

windshield, A-pillar and fender and have misled the rule makers to concentrate on

the testing of head/hood impacts. Figure 17.6 shows the initial head/hood impact at

24 km/h (15 mph) of a lateral pedestrian impact, before the cadaver rolled onto its

back. As part of this study, there were also five duplicated tests carried out on a 95th

percentile dummy.

Data from two of the six cadaver tests were not usable. The first cadaver was

embalmed and its kinematics would not be the same as the unembalmed specimens.

In one other test, the harness failed to release and the data were meaningless. Some

of the cadaveric data from the remaining four cadaver tests are shown in Fig. 17.7.

Axial ground reaction force data are shown in Fig. 17.7A. Prior to the test, there is a

small pre-load as most of the weight of the cadaver was borne by the harness. Upon

harness release, most of the weight of the cadaver was registered by the load cell

and, at impact, a large compressive force was measured by the load cell (almost

750 N) before the foot was lifted off the ground. This load is presumably due to an

increase in the effective length of the lower limb. The foot rotates onto its medial

(inner) edge and the medial femoral condyle tends to separate from the medial tibial

plateau, resulting in a momentary increase in leg length before the loss of foot/


Fig. 17.6 Instant of

cadaveric head/hood impact

of a left-sided 24-km/h

(15-mph) car-pedestrian

impact (based on Krieger

(1976))

A

B

(X10 1 )

75.00

RUN NO.: C03

PEAK

Z COMP

(X10 1 )

15.00

RUN NO.: LLL

FILTER 500 HZ.

C03

C02

FOOT L. C. (N)

-25.00 25.00

C

IMPACT

PRE-LOAD

DIRECTION OF DOWNWARD FORCE

(GRAVITY)

0.00 10.00 20.00 30.00 40.00

TIME (MS) (X10 1 )

D

LIN ACC Y (G)

-15.00 0.00

0.00 20.00 40.00

TIME (MS)

60.00 80.00

LIN ACC Y (G)

-25.00 25.00 75.00

RUN NO.: HEAD

FILTER 500 HZ.

0.00

10.00

C03

C02

20.00 30.00 40.00

TIME (MS) (X10 1 )

(X10 3 )

ANG ACCX (RAD/S/S)

-30.00 -10.00 10.00

RUN NO.: LUL

FILTER 500 HZ.

Cadaver

Dummy

0.00 20.00 40.00

TIME (MS)

C03

D10

60.00 80.00

Fig. 17.7 Sample data from car-pedestrian experiments by Krieger et al. (1976). (A) Ground force

reaction under impacted leg. (B) Impacted lower leg lateral acceleration from two cadaveric tests

at about the same velocity. (C) Lateral head acceleration for the same two tests. (D) Cadaver and

dummy head angular accelerations are compared, using tests run at the same speed of 24.1 km/h

(15 mph)


ground contact. The lateral acceleration of the impacted lower leg is shown in

Fig. 17.7B for two different cadavers impacted at about the same speed (23–24 km/

h) but the peak measured accelerations differed considerably and so did the

acceleration time histories. The same variations are seen in the lateral head accelerations

of the same cadavers (Fig. 17.7C). The head angular acceleration at hood

impact of a dummy test is compared with that of a cadaver test in Fig. 17.7D. The

speed of the impacting vehicle was the same (24.1 km/h or 15 mph) but the dummy

was taller and its head acceleration was much higher than that of the cadaver. The

main lesson learned from these tests is the randomness of pedestrian impact,

especially when it comes to acceleration of individual body segments. However,

global motion of the body is not as variable and cartwheeling at speeds of impact in

excess of 40 km/h can be expected to occur when pedestrians are hit by passenger

cars with a square front end. Sloping front ends and lower hood heights can

preclude cartwheeling at 40 km/h.

Lower limb injuries due to car-pedestrian impact were studied by Pritz et al.

(1975) who mocked up a vehicular front end on the leading edge of a sled and

impacted 15 unembalmed cadaveric subjects laterally. Although it was possible to

brake the sled at impact, it was not possible to simulate the downward pitch of the

front end. In some tests simulating panic braking, the bumper height was lowered.

Tests were conducted with the normal rigid bumper and front end as well as with

padded bumpers and hoods (with lowered front ends) to investigate the injury

reduction effect of padding. Since this was an injury study, the only cadaverborne

instrumentation used was a triaxial pelvic accelerometer mounted on S2.

Other data collected included the horizontal and vertical ground reaction forces and

impact forces at the bumper and hood edge. Impact speeds ranged from 11 to

28 mph (17.7 to 45.1 km/h).

Due to bumper impact, the typical injuries were supracondylar fractures of the

femur and comminuted fractures of the proximal tibia. When the bumper was

lowered 6 in. (15 cm), the injuries were restricted to the tibia and fibula, sparing

the knee. When the bumper was lowered and padded, injuries appeared to be less

severe and were localized in the tibia and fibula. Again, knee injury was minimal.

The large vertical ground reaction force generated as a result of impact with the

knee appeared to be responsible for tibial plateau fractures. Impact of the unpadded

hood edge to the pelvis resulted in fractures of the pubic rami and of the greater

trochanter. There is fracture of the inferior portion of the ilium and slight separation

of the sacroiliac joint. The transverse processes of L4 and L5 were also fractured on

the impacted side. Lowering the hood height resulted in an absence of pelvic

injuries.

It was concluded that lowering the height of the front end would reduce injury

severity in the lower body region of an impacted adult pedestrian. However, head

velocity almost doubled with the lowered profile. It is also surprising that the

cartwheeling effect at 28 mph was not observed or mentioned.

There have been numerous other experimental studies involving the impact of entire

cadavers by a vehicle or a simulated front end of a vehicle. Kam et al. (2005) provided a

summary of cadaver tests conducted in the past, such as the work of Bourret et al.


(1979); Cesari et al. (1980); Farisse et al. (1981); Heger and Appel (1981); Ashton et al.

(1983); Cavallero et al. (1983). The latest full-scale car-pedestrian study was conducted

by Kerrigan et al. (2007) under GM sponsorship.

The paper by Bourret et al. (1979) is apparently the first in a series of six

reporting on a collaborative European study. The first study involved the Marseille

Medical University, ONSER, a government laboratory now known was INRETS,

and Citroen, a French automobile manufacturer. The aim of the study was to

examine the effect of vehicle speed and front end profile on the severity of

pedestrian injuries in a car-pedestrian impact. “Touring” type vehicles were used

(small sedans) at impact speeds varying from 5 to 40 km/h. Braking at 0.7 g was

simulated at impact and the cadaver was impacted either laterally (right side) or

frontally. In this report, 15 cadavers were tested at speeds ranging from 10 to 25 km/

h. Vehicle data included speed at the instant of impact, characteristics of braking

and points of impact on the vehicle. New parts were used for each impact. Cadaver

instrumentation was limited to the use of photo targets at selected locations and

documentation of the motion of the cadaver throughout the impact, including its

final position on the ground. X-rays and necropsy were done to document injuries

which were not described. No injury data or kinematic data were provided.

Cesari et al. (1980) is a continuation of the Bourret et al. (1979) paper but the

study was incomplete at the time the paper was written. This paper analyzed

cadaver tests performed at 10, 20, 25, and 40 km/h (6.2, 12.4, 15.5 and 25 mph)

based on 31 cadaver tests. Two standard production vehicular front ends and one

modified front end were used. The modified front end enabled simultaneous contact

of the bumper and hood with the pedestrian. Sixteen of the 31 tests were frontal

impacts. The rest were lateral impacts. In terms of injury, there was no injury at

10 km/h in the four tests conducted (two frontal and two lateral). At 20 km/h, there

were minor head injuries (AIS 2) and knee level lower extremity fractures in the

three frontal impacts. Injuries were more severe for lateral impacts. Two of the

three sustained AIS 4 injuries which included a femoral neck fracture, pelvic rami

fracture and a C6 vertebral body fracture as well as a perforated liver by the xiphoid

process. The third cadaver was not injured. At 25 km/h, there were seven frontal

tests and 6 lateral tests. Two of the frontal tests resulted in no lower limb injuries.

There was one case of a C5/6 fracture and one case of a temporal bone skull

fracture. Laterally impacted cadavers sustained more severe injuries than those

impacted frontally with an AIS range of 2–5. There were rib fractures with

associated liver injuries. All eight cadavers impacted at 40 km/h (four frontal and

four lateral) sustained severe injuries with a maximum AIS of 5. They sustained

multiple injuries including two skull fractures, lower limb fractures, and multiple

rib fractures. For the head injuries at 40 km/h, the authors made an interesting

statement. The fractures appeared to be caused by contact with the vehicle but they

are significantly reduced if a ground protection device is provided. This is an

indirect confirmation that skull fractures are more likely due to contact with the

ground, especially at 40 km/h, at which speed the pedestrian does a cartwheel over

the hood and slides off the car head first, if the hood height is high enough. Head

velocity at impact with the hood or windshield was found to be 6–69 % higher than


the impact speed of the car in frontal impacts. For lateral impacts, the head velocity

was mostly less than the vehicle velocity, varying from 79 to 136 %. The modified

front end changed the head impact location on the hood but not the injuries.

The paper by Farisse et al. (1981) appears to be the continuation of the work

reported in Bourret et al. (1979) and Cesari et al. (1980). The work was done in the

same laboratory in Marseille but the paper reported on 58 cadaver tests, 30 frontal

and 28 lateral, using three unspecified vehicles at speeds ranging from 6.25 to

24.25 mph (10 to 39 km/h). Injuries to the lower extremities were analyzed in detail.

The paper was more concerned with treatment and prognosis.

Heger and Appel (1981) reported on the reconstruction of two car-pedestrian

impacts using cadaveric subjects. It is the second progress report. The first report

was on the reconstruction of the first such impact (PED 1). It appeared in the

proceedings of the 6th ESV (1978). In this paper, Case PED 2 was reconstructed by

testing 4 cadavers (and 3 dummies) to reconstruct the impact of a 73-year-old

female pedestrian struck by a Peugeot traveling at approximately 40 km/h.

The exact speed of the reconstructed test was not stated but it was close to

40 km/h. The experimental trajectory was plotted up to point of head contact with

the windshield but data were collected up to the point of rest on the ground. Thus,

head, chest, and pelvic accelerations were measured for primary (hood) impact and

secondary (ground) impact. Even though the speed was close to 40 km/h, the head

acceleration for hood (windshield) contact was higher than that for ground contact.

That is, the pedestrian might not have done a cartwheel over the hood because of the

shape of the Peugeot front end. The kinematics of the pedestrian were not

described. For PED 3, it was a 45 km/h impact at which three cadavers were used

to reconstruct the impact. The trajectories of the head, chest, and pelvis were plotted

until head impact with the windshield. No mention of cartwheeling was made and

head impact with the hood (windshield) was more severe than that with the ground.

The height of the hood was not mentioned. This was an incomplete study as more

tests were planned and a follow-up paper was found. This work is by Ashton et al.

(1983) and is described next.

The study by Ashton et al. (1983) was also part of the European effort to

investigate methods to reduce pedestrian injury severity. Pedestrian impacts by

five Morris cars were studied in detail. The speed of impact was estimated to be

between 14 and 18 m/s (30–40 mph) but the ages of the victims varied widely—

from 12 to 76 years. The elderly pedestrians succumbed to their injuries but the

younger ones survived. Two of the impacts were reconstructed experimentally at

the same laboratory in Marseilles, using three cadavers for each of the two cases—

Case BU135 and BU465. To reconstruct Case BU135, the cadaver was struck on

the right side and the measured head acceleration was generally higher due to

vehicle contact than ground contact. The kinematics of the cadaver were not

described and it is not known if it cartwheeled over the hood. However, in one of

the tests, the head acceleration on ground contact was higher than that with the

vehicle. For Case BU465, the pedestrian was struck on the left side and head

acceleration was more severe due to contact with the vehicle than with the ground.

In both cases, the injuries found in the cadavers were surprisingly similar despite


biological variations among the test subjects. They all sustained femoral fractures

and five of the six sustained tibial fractures. None had pelvic or skull fractures but

all had rib fractures and three had cervical spine injuries. The authors also developed

a 2-D pedestrian model which was validated by comparing the location of

head contact on the hood or windshield observed in the cadaver tests. It is seen that

the principal concern was head contact with the vehicle. If cartwheeling did not

occur at these high speeds, the only explanation is that the hood height of European

cars is lower than US cars.

The issue of hood height was indirectly addressed in the study by Cavallero et al.

(1983) which appeared to be the last paper in this series of reports on the simulation

of car-pedestrian impacts using cadavers. Figure 17.8 shows the front end profiles

Fig. 17.8 The six front end profiles used in the car-pedestrian study by Cavallero et al. (1983).

The pedestrian is a 50th percentile dummy. Reprinted with permission Copyright © 2017 SAE

International. Further distribution of this material is not permitted without prior permission from

SAE


of the six vehicles tested in this study in which 50 cadavers were used. Eight

cadavers were used for each vehicle model, four for frontal impact and four for

lateral impact. However, for one vehicle, five cadavers were used for each impact

direction. The impact speed selected was 32 km/h (20 mph) because injuries always

occurred at this speed and the most severe injuries were at the AIS 4 level. The

vehicle masses varied from 635 to 1350 kg. The AIS was used to quantify the

injuries observed after impact. It was found that that the average AIS for frontal and

lateral impact was the same—3.2. The bumper caused a similar number of lower

limb injuries to the femur, knee, tibia/fibula, and ankle for all six models. For the

head, the speed of contact with the hood, cowl or scuttle (space between the hood

and the windshield), or windshield is higher than the impact speed for frontal

impacts and about the same as the impact speed for lateral impacts. Most of the

contacts were with the windshield (35/50), followed by the cowl (12/50). The

location of impact on the vehicle was a function of the height of the test subject.

For head contact with the ground, there was no cartwheeling as the impact speed

was well below 40 km/h. Thus, the severity of head/ground impact was random

depending on the attitude of the body as it hit the ground. The authors were unsure

as to what design changes were necessary to reduce pedestrian injuries. The

weight of the impacting vehicle had no effect on the injuries or kinematics of

the pedestrian.

Kerrigan et al. (2007) tested seven cadavers in a full-scale car-pedestrian impact

experiment, using a mid-sized sedan traveling at 40 km/h (25 mph). The focus of

the experiment was the interaction of the pedestrian with the vehicle and the

cadaver was not permitted to interact with the ground following impact with the

vehicle. The cadaver was only instrumented with photo targets so that its motion

can be captured by video cameras running at 250 frames per second. No accelerometers

were used and no impact forces were measured. It was not meant to be an

injury study but the cadaver was prevented from impacting the ground and a

significant portion of the data was lost. This is particularly unfortunate because

the impact speed selected was near the critical speed at which the pedestrian could

cartwheel over the car and sustain fatal head injuries by hitting the ground head

first. The video data were analyzed extensively in an effort to predict the location of

head impact on the hood or windshield. Considering the fact that only one vehicle

front end profile was used at one impact speed, the results of this study have limited

value.

17.3 Modeling of Car-Pedestrian Impact

The experiments described in the above section lead one to conclude that pedestrian

kinematics and injuries are highly variable as they depend on many parameters,

such as front end geometry, vehicle speed, pedestrian orientation at impact and

pedestrian stature. Since it is not possible to design a front end to minimize injuries

17.3 Modeling of Car-Pedestrian Impact 581

Fig. 17.9 Inverted X-ray

cassette with three load cells

attached forming an

isosceles triangle. Lead

markers were used to

identify the centroid of the

triangle, as shown in

Fig. 17.10 (based on

Krieger (1976))

for the entire population of pedestrians, the next best thing is to develop computer

models so that the manufacturer can use it to predict pedestrian kinematics and

injuries and tailor their front end designs to minimize injury.

The first car-pedestrian impact model was developed by Padgaonkar et al.

(1977) who also attempted to validate the model using the data obtained by Krieger

et al. (1976). The model was based on the ATB gross motion simulator which is

basically a linked structure of rigid bodies. The ATB program requires a lot of input

data and since it was decided that each experiment was to be validated by the

model, data from each test subject were collected, including body segment dimensions,

inertial properties, locations of cg’s and contact characteristics.

To determine the cg location of a body segment, X-rays were used in conjunction

with a three-load cell system, shown in Fig. 17.9. The load cells formed an

isosceles triangle under an X-ray cassette and were programmed to give the same

output. The cassette shown in Fig. 17.9 is upside down. During testing, the cassette

was flipped over and the body segment was placed on top of the cassette and moved

around until all three load cells yielded the same output. An overhead X-ray was

taken with the body segment in that position and the cg would be directly over the

centroid of the isosceles triangle formed by the load cells. Figure 17.10 shows how

the cg of the pelvis is located. The body segment was rotated about the other two

axes to establish the 3-D coordinates of the cg. A rigid frame made out of

magnesium, to keep its weight to a minimum, was used to hold the body segment

so that it could undergo orthogonal rotations. The weight of the segment was the

sum of the three load cell readings. The frame was also used to determine the mass

moments of inertia of the body segments through the use of a trifilar pendulum,

shown in Fig. 17.11. The pendulum was supported on three wires that were hung

from the ceiling via three load cells that were programmed to yield the same output.

In this way, the position of the frame holding the body segment could be adjusted on

the pendulum until all three load cells yielded the same output. In this position, the

cg of the segment and frame was directly over the center of the pendulum and the

period of oscillation was measured with the segment and frame in that position. The

frame was rotated 90 twice to measure the other components of the moments of


Fig. 17.10 Locating the cg of the pelvis in the antero-posterior view. The cg is at the intersection

of the hash marks which is the centroid of the isosceles triangle formed by the three load cells

(taken from Padgaonkar (1976))

Fig. 17.11 The circular

object is the trifilar

pendulum that is suspended

from the ceiling by three

wires. The rectangular

frame is used to hold body

segments in a fixed

orientation so that inertial

properties can be measured

by orthogonal rotations.

Both the pendulum and the

rectangular frame are made

of light weight magnesium

(taken from Krieger (1976))

inertia. The use of the magnesium frame was necessary to enable orthogonal

rotations but it caused a small error in the measurements because its weight and

inertia were also included in the measurement. For accuracy, it was possible to

measure the mass moment of inertia of the empty frame and calculate the values of

the segment alone without the frame. The off-axis terms of the inertial tensor were

also measured. For details, see Krieger et al. (1976).

The ATB program also needed force-deflection data and the two major contacts

of the vehicle with the pedestrian were the impact of the head against the hood and


Fig. 17.12 Test setup for

head drop tests on the hood

to provide force-deflection

data for the ATB model. A

dummy head is shown

facing the hood which is

below it (based on Krieger

(1976))

Fig. 17.13 Schematic of the test setup for lower leg drop tests on the bumper to provide

force-deflection data for the ATB model. The impact force was measured by load cells below

the bumper and leg kinematics were recorded on high speed film (taken from Krieger (1976))

the bumper against the lower leg. Drop tests were conducted to measure these

contact characteristics. Figure 17.12 shows a setup for head impact with the hood

while Fig. 17.13 shows the setup for leg impact with the bumper. Figure 17.14


Fig. 17.14 Dynamic forcedeflection

curves for lower

leg impact with the bumper

at different impact speeds

(taken from Krieger (1976))

shows a series of force-deflection for dummy lower leg/bumper impact at different

impact speeds.

Validation was carried out in stages. First, experiments of head and leg impact

were modeled and validated. Figure 17.15A shows a comparison of the

x-component (posterior-to-anterior) head linear acceleration from a drop test experiment.

The notch in the predicted head acceleration could not be explained. In

Fig. 17.15B, a comparison is made of the pitch of the head which was initially at

about 20 . The model over predicted the pitch by about 30 at the end of the

experiment. For the dummy leg drop test, there was a good match of the roll angle

throughout the test, as shown in Fig. 17.16. The x-axis angular accelerations of the

dummy leg are compared in Fig. 17.17 and the match is acceptable. In the

simulations of car-pedestrian impacts, it was difficult for the model to predict

accurately the accelerations of body segments. Reasonably good predictions were

made for the dummy z-axis (superior-to-inferior) head acceleration, as shown in

Fig. 17.18. The x-axis (posterior-to-anterior) head acceleration in one of the

cadaver tests also yielded a good match, as depicted in Fig. 17.19. The correlation

between the predicted and measured z-axis (superior-to-inferior) acceleration for a

cadaver test is out of phase as shown in Fig. 17.20. It appears that the matching of

displacements is much easier than that of accelerations. The primary reason for this

is the fact that the measured accelerations are body-fixed and if the predicted and

measured angular displacements do not match, then the acceleration components

along the body-fixed axes would also not match.


A

LIN ACC X (G)

90.00 -10.00 10.00 30.00

B

.00

RUN NO.: DN34HEAD

30.00

RUN NO.: DN34HEAD

60.00

TIME (MS)

90.00

EXPT.

MODEL

120.00

YAW-MOD

PITCHMOD

ROLL-MOD

PITCHEXPT

ANG DISP (DEG)

-30.00 30.00

.00

30.00

60.00

TIME (MS)

90.00

120.00

Fig. 17.15 Validation of single-segment impacts (A) Comparison of the x-axis (postero-anterior)

head acceleration for a cadaveric head dropped onto the hood of the test vehicle. (B) Comparison

of the predicted and measured pitch of the head in the same drop test (taken from Padgaonkar

(1976))

Oblivious of the experimental work of Krieger et al. (1976) and the model by

Padgaonkar et al. (1977); Ishikawa et al. (1993) published a simulation of

car-pedestrian impacts, using an unspecified crash victim simulator similar to the

ATB model or the MADYMO model. Experimental cadaveric data collected at the

Hanover Medical University were used to validate the model. The model was

validated against 10 full body car-pedestrian impacts which were conducted at

25, 32, and 40 km/h (15, 20 and 25 mph). The simulation terminated upon head

contact with the vehicle. Much effort was expended to obtain the needed cadaver

anthropometry and data for contact, joint stiffness, and tolerance of many body

segments. The model-predicted that the gross motion of the pedestrian, while in


RUN NO.: DN16-RLL

MODEL

EXPT.

ROLL (DEG)

-160.00 -80.00 .00

.00

30.00

60.00 90.00 120.00

TIME (MS)

Fig. 17.16 Validation of single-segment impacts—Comparison of predicted and measured roll

angle of the lower leg during a leg drop test onto the bumper of the test vehicle (taken from

Padgaonkar (1976))

ANG ACCX (RAD/S/S) (X103)

-20.00 -10.00 .00

.00

RUN NO.: DN16-RLL

30.00

60.00

TIME (MS)

EXPT.

MODEL

90.00 120.00

Fig. 17.17 Validation of the pedestrian model for single-segment impacts—Comparison of the

x-axis (postero-anterior) angular acceleration of the right lower leg during a leg-bumper impact

(drop test) (taken from Padgaonkar (1976))

contact with the vehicle, was generally similar to that observed in the tests,

Fig. 17.21 shows a comparison of the gross motion of the pedestrian for a 39-km/

h test. The hood height of the two vehicles used was between 0.85 and 0.875 m but

there was little indication that the cadaver or the model was about to perform a

cartwheel over the car.


30.00

RUN NO.: D10-HEAD

EXPT.

MODEL

LIN ACC Z (G)

-30.00 .00

.00

15.00 30.00 45.00 60.00

TIME (MS) (X10 1 )

Fig. 17.18 Validation of the pedestrian model—Comparison of the head z-axis (superior-to

inferior) linear acceleration of a dummy car-pedestrian impact (taken from Padgaonkar (1976))

120.00

RUN NO.:C03-HEAD

EXPT.

MODEL

LIN ACC X (G)

-40.00 40.00

.00

15.00 30.00 45.00 60.00

TIME (MS) (X10 1 )

Fig. 17.19 Validation of the pedestrian model—Comparison of the head x-axis (postero-anterior)

linear acceleration for a cadaveric car-pedestrian impact at 24.1 km/h (15 mph) (taken from

Padgaonkar 1976)

Meissner et al. (2004) studied the effect of pedestrian stance and vehicle type on

pedestrian kinematics over the hood of the car for a 40 km/h impact. The

MADYMO model was used but the model predictions were not validated. The

kinematics of the torso depended on whether the struck limb was forward or

backward. They were also different if both feet were together. Had the authors


RUN NO.: C06-LT

EXPT.

MODEL

20.00

LIN ACC Z (G)

-20.00 .00

.00

40.00

80.00

TIME (MS)

120.00 160.00

Fig. 17.20 Validation of the pedestrian model—Comparison of the lower torso z-axis (superiorto-inferior)

linear acceleration for a cadaveric car-pedestrian impact at 37.3 km/h (23.2 mph)

(taken from Padgaonkar (1976))

Fig. 17.21 Validation of

the pedestrian model by

Ishikawa et al. (1993). The

vehicular impact speed was

39 km/h (24.2 mph) and the

hood height was between

0.85 and 0.875 m (2.79 and

2.87 ft). The simulation was

terminated upon head

contact with the vehicle

(taken from Ishikawa et al.

(1993))


continued the simulation till ground contact they would have arrived at more

interesting results, such as severe head impact with the ground.

There are several other models of car-pedestrian impact. For example, Yang

et al. (2000); Van Rooij et al. (2003); Teng and Le (2009) were only interested in

the interaction of the pedestrian with the car. However, recently, interest in pedestrian/ground

impact was shown by Tamura (2010) and Gupta and Yang (2013) who

used models to quantify the effect of head contact with the ground. Tamura (2010)

used the THUMS finite element model to simulate pedestrian impact with an SUV.

The model predicted high HIC values and high head angular accelerations, even at

vehicular impact speeds of 25 km/h (15.5 mph) as well as at 40 km/h. Of course,

pedestrian impact severity depends on a large number of variables and not all

impacts at those speeds will result in a direct impact of the head on the ground.

However, when the pedestrian cartwheels over the car, the probability of a direct

head impact with the ground is considerably higher than if the pedestrian slid off the

hood feet first. Tamura’s (2010) results were confirmed by Gupta and Yang (2013)

who used the MADYMO model to represent the pedestrian and a finite element

model to simulate four different mid-size car front ends and four different SUV

front ends. The profiles are shown in Fig. 17.22. They go from a square shape to a

sloping profile. The pedestrians used in the simulations were a mid-size male and a

small female. A square profile tends to cause the pedestrian to cartwheel over the

car and end up striking the ground with the head. A sloping profile for a mid-size

car, on the other hand, resulted in no head/ground impact. It was concluded that

irrespective of the shape of the front end, impact with the high hood of the SUV

Fig. 17.22 The eight front end profiles used by Gupta and Yang (2013) to simulate car-pedestrian

impact. According to the Gupta-Yang model, for SUV profiles, regardless of the shape, there was

secondary head to ground impact at an impact speed of 40 km/h (taken from Gupta and Yang

2013)


would inevitably result in a secondary head impact with the ground at an impact

speed of 40 km/h.

Countermeasures introduced thus far for pedestrian protection have not worked

very well. One of the proposed methods is to pop the rear of the hood at impact to

reduce the severity of head/hood impact. Gupta and Yang (2013) simulated the

popped up hood and found a decrease in HIC from 1298 to 633 for a small female

impacted by a mid-size car with a square profile (Profile 2) at 40 km/h. However,

she ended up with a secondary head/ground impact. The use of airbags that deploy

from the front end at impact has been suggested but they have not been installed in

any vehicle at this time. Innovative solutions are needed urgently because there

does not seem to be viable solution available to effectively protect the pedestrian.


The only reliable countermeasure to reduce pedestrian fatalities is to keep motorized

traffic and pedestrians away from each other. Efforts to make the front end of

cars less aggressive have so far been unsuccessful. Safety regulators may also be

ignoring the significant problem of ground contact after the collision. There is now

enough evidence to say that SUVs with a high hood are a major threat to pedestrians.

The high hood imparts sufficient angular momentum to the lower part of the

body to allow it to cartwheel over the car and there is a high probability that head

will hit the ground. Gupta and Yang (2013) have shown that lowering the hood of

SUVs is necessary and, in fact, for passenger cars, a sloping hood would prevent

cartwheeling at 40 km/h although it may result in a higher velocity impact of the

head on the hood. This may explain why European research does not mention

cartwheeling and European safety regulators concentrate on reducing head injury

severity due to impact with the front end of the car.


17.1. Pedestrian fatalities in the USA, due to impacts by automobiles

[] (i) Average about 5000 a year

[] (ii) Average about 10,000 a year

[] (iii) Average about 15,000 a year

[] (iv) Average about 20,000 a year

[] (v) Average about 25,000 a year


17.2. The pedestrian population most at risk

[] (i) Live in farming communities

[] (ii) Are over the age of 65

[] (iii) Do not have a driver’s license

[] (iv) Are either deaf or blind


17.3. The most effective way of reducing pedestrian injuries on our streets and

highways is to

[] (i) Warn drivers to slow down at busy intersections

[] (ii) Impose large fines on jay walkers

[] (iii) Keep pedestrians away from vehicular roadways

[] (iv) Change intersections to roundabouts

[] (v) Add more traffic lights

17.4. The automobile can be designed to be less aggressive against pedestrians.

Select the incorrect answer

[] (i) More attention should be paid to bumper design such as lowering

the bumper to below knee level

[] (ii) We are unable to solve the problem of head impact with the ground

after the pedestrian is hit

[] (iii) The prevention of head injury in head/hood contact is an important

issue

[] (iv) Head injuries tend to be less severe for smaller cars with shorter

hoods

[] (v) The use of airbags mounted on bumpers has not been tested on the

road

17.5. The first full-scale pedestrian testing project was carried out at Wayne State

University in the early 1970s

[] (i) Cadavers were not used in this test series

[] (ii) Dummies were not used in this test series

[] (iii) Both cadavers and dummies were used in this test series

[] (iv) The car used consisted of only the front end, mounted on a sled

[] (v) The car used was of foreign (non-US) manufacture

17.6. One of the objectives of the WSU pedestrian project in the early 1970s was to

[] (i) Determine the causes of injury to the pedestrian

[] (ii) Determine the kinematics of the pedestrian during a car/pedestrian

impact

[] (iii) Establish a fatal speed of the automobile

[] (iv) Determine the severity of head and leg injuries

[] (v) Determine the effects of alcohol on pedestrian injuries


17.7. To conduct a cadaveric test, simulating a car/pedestrian impact, the cadaver

was made to stand on one leg

[] (i) This is to simulate a drunk staggering in the street

[] (ii) This is to simulate a pedestrian walking across the street

[] (iii) This is to simulate a child kicking a football in the street

[] (iv) This is to simulate someone getting off a street car

[] (v) This is to simulate someone roller blading on the street

17.8. To test a human surrogate (dummy or cadaver) as a pedestrian, it is made to

stand on one leg

[] (i) The best method is to lift one foot off the ground just before impact

[] (ii) The best method is to stiffen the knee by using bandages or braces

[] (iii) The best method is to have someone hold up the cadaver and get out

of the way just before impact

[] (iv) The best method is to use a small wooden stick (dowel) to prevent

knee flexion

[] (v) The best method is to permanently prevent knee flexion by pinning

the knee so that it cannot rotate

17.9. When a normal-sized adult pedestrian is hit by the front end of a car

traveling at 20 km/h, he/she will

[] (i) Do a complete cartwheel on the hood of the car

[] (ii) Fly over the roof of the car and end up behind the car

[] (iii) Go through the windshield of the car and end up in the driver’s lap

[] (iv) Bend at the hip or pelvis so that the head and torso come into

contact with the hood

[] (v) Get bounced away from the car by the bumper and the torso never

touches the hood

17.10. When a normal-sized adult pedestrian is hit by the front end of a sedan

traveling at 40 km/h, he/she will



[] (iii) Hit the cowling in front of the windshield or the windshield of a small

car

[] (iv) Hit the ground head first

[] (v) (i), (iii), and (iv)

17.11. When an adult pedestrian is hit by an SUV with a high hood of about 1 m, at

40 km/h (25 mph)

[] (i) The pedestrian is bounced off the front end and does not bend over

the hood

[] (ii) The pedestrian does a cartwheel over the hood and hits the ground

head first


[] (iii) The pedestrian usually survives the impact

[] (iv) The pedestrian flies over the roof of the car


17.12. When the bumper contacts the lower extremity laterally, in a car/pedestrian

impact,

[] (i) The bumper causes the knee to bend laterally

[] (ii) An additional compressive force is generated in the lower leg in the

form of a ground reaction force

[] (iii) The medial collateral ligament is at risk of being ruptured


[] (v) (i), (ii), and (iii)

17.13. To validate a model simulating car/pedestrian impact, the matching of linear

accelerations of individual body segments is difficult because

[] (i) The accelerometers have inadequate frequency response

[] (ii) The accelerometers are body fixed and if the angular displacement

does not match, the acceleration will not

[] (iii) The accelerations need to be measured relative to the inertial frame



17.14. When a normal-sized adult pedestrian is hit by the front end of an SUV with

a hood height of 1 m and traveling at 20 km/h, he/she will



[] (iii) Hit the cowling in front of the windshield or the windshield of a

small car

[] (iv) Hit the ground head first


17.15. Sloping hood lines are common in European cars. Using these cars to impact

cadavers or dummies do not cause the test subject to cartwheel over the

hood, even at speeds in excess of 40 km/h. One possible reason for this is

[] (i) The bumpers are too soft

[] (ii) The low front end imparts a lower angular momentum to the lower

part of the pedestrian

[] (iii) The front end is too soft

[] (iv) The cars are too narrow

[] (v) The wheel base is too short



Prob

Ans

1 (i)

2 (ii)

3 (iii)

4 (iv)

5 (iii)

6 (ii)

7 (ii)

8 (iv)

9 (iv)

10 (v)

11 (ii)

12 (v)

13 (ii)

14 (v)

15 (ii)

References

S. Ashton, D. Cesari, J. Van Wijk, Experimental reconstruction and mathematical modelling of

real world pedestrian accidents SAE Paper #830189, UMTRI-48288 A18. Society of Automotive


P. Bourret, J. Farisse, B. Seriat-Gautier, R. Larousse, P. Billault, M. Ramet, D. Cesari,

C. Cavallero, Experimental study of injuries observed on pedestrians. in 4th International

IRCOBI Conference on the Biomechanics of Trauma, UMTRI-42962 A22, Bron, 1979

C. Cavallero, D. Cesari, M. Ramet, P. Billault, J. Farisse, B. Seriat-Gautier, J. Bonnoit, Improvement

of pedestrian safety: influence of shape of passenger car-front structures upon pedestrian

kinematics and injuries: evaluation based on 50 cadaver tests SAE Paper #830624, UMTRI-

48288 A19, 1983

D. Cesari, M. Ramet, C. Cavallero, P. Billault, J. Gambarelli, G. Guerinel, J. Farisse, B. Seriat-

Gautier, P. Bourret, Experimental study of pedestrian kinematics and injuries. in 5th International

IRCOBI Conference on the Biomechanics of Impact, Birmingham, 1980

J. Farisse, B. Seriat-Gautier, J. Dalmas, N. Daou, P. Bourret, C. Cavallero, D. Cesari, M. Ramet,

P. Billault, M. Berthommier, Anatomical and biomechanical study of injuries observed during

experimental pedestrian-car collisons. in International Research Council on the Biomechanics

of Injury Conference, 1981

V. Gupta, K.H. Yang, Effect of vehicle front end profiles leading to pedestrian secondary head

impact to ground. Stapp Car Crash J. 57, 139 (2013)

A. Heger, H. Appel, Reconstruction of pedestrian accidents with dummies and cadavers. in 8th

International Technical Conference on Experimental Safety Vehicles, UMTRI-46767 A59,

Berlin Technische Universitaet, Institut fuer Kraftfahrzeuge, Germany FR, 1981

References 595

H. Ishikawa, J. Kajzer, G. Schroeder, Computer simulation of impact response of the human body

in car-pedestrian accidents. in 37th Stapp Car Crash Conference, SAE Paper No. 933129, San

Antonio, Texas, 1993

C. Kam, J. Kerrigan, M. Meissner, C. Drinkwater, D. Murphy, J. Bolton, C. Arregui, R. Kendall,

J. Ivarsson, J. Crandall, Design of a full-scale impact system for analysis of vehicle pedestrian

collisions SAE Paper #2005-01-1875. Society of Automotive Engineers, Inc., Warrendale,

2005

R. Kendall, M. Meissner, J. Crandall, The causes of head injury in vehicle-pedestrian impacts:

comparing the relative danger of vehicle and road surface SAE Paper 2006-01-0462. Society of

Automotive Engineers, Warrendale, 2006

J.R. Kerrigan, J.R. Crandall, B. Deng, Pedestrian kinematic response to mid-sized vehicle impact.

Int. J. Veh. Saf. 2(3), 221–240 (2007)

K.W. Krieger, Full scale experimental simulation of pedestrian-vehicle impacts. Ph.D. Dissertation,

Wayne State University, Detroit, Michigan, 1976

K.W. Krieger, A.J. Padgaonkar, A.I. King, Full-scale experimental simulation of pedestrianvehicle

impacts, in 20 th Stapp Car Crash Conference, SAE Technical Paper No. 760813,

Dearborn, MI

M. Meissner, L. van Rooij, K. Bhalla, J. Crandall, D. Longhitano, Y. Takahashi, Y. Dokko,

Y. Kikuchi, A multi-body computational study of the kinematic and injury response of a

pedestrian with variable stance upon impact with a vehicle SAE Paper #2004-01-1607, 2004

NHTSA, Pedestrians Report No. DOT HS 811 888. National Highway Traffic Safety

Adiminstration, Washington, DC, 2012

A.J. Padgaonkar, Validation study of a three-dimensional crash victim simulator for pedestrianvehicle

impact. Ph.D. Dissertation, Wayne State University, Detroit, Michigan, 1976

H. Pritz, C. Hassler, J. Herridge, E. Weis, Experimental study of pedestrian injury minimization

through vehicle design. in 19th Stapp Car Crash Conference, SAE Paper No. 751166, San

Diego, California, 1975

A. Tamura, A Numerical Study of Traumatic Brain Injury Due to Ground Impact in an

SUV-Pedestrian Crash Using Full-Scale Finite Element Models. in ASME 2010 International

Mechanical Engineering Congress and Exposition, Vancouver, British Columbia, 2010

T.-L. Teng, T.-K. Le, Development and validation of a pedestrian deformable finite element

model. J. Mech. Sci. Technol. 23(8), 2268–2276 (2009)

L. van Rooij, M. Meissner, K. Bhalla, J. Crandall, D. Longhitano, Y. Takahashi, Y. Dokko,

Y. Kikuchi, The evaluation of the kinematics of the MADYMO human pedestrian model

against experimental tests and the influence of a more biofidelic knee joint. in 5th MADYMO

Users Meeting of the Americas, Troy, Michigan, 2003

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simulation of car-pedestrian impacts. Traffic Inj. Prev. 2(2), 131–149 (2000)

Chapter 18

Biomechanics of Automotive Safety

Restraints

There is an advertising poster put out in 1940 by the now defunct Packer Motors

that suggested an unusual way for the right front passenger to protect him/herself

before an impending crash. The ad suggested that the passenger in the “dead man’s

seat” curl up in the footwell to ride out the crash. This is possible for a small person

in a large car but it is not a practical suggestion because by the time the passenger

manages to get into the footwell, the crash would have occurred already. The more

practical form of protection is the use of automotive restraint systems. There are

two forms of safety restraints. Seatbelts constitute the active restraint system which

requires the occupant to actively participate in its use. There are forms of automatic

(passive) seatbelts but so far their use has been limited. The most popular form of

passive restraint is the airbag which is deployed at the time of the crash, hence the

name passive restraint. Both systems afford good protection for the occupant but

when used together, they are very effective in mitigating injuries and preventing

fatalities. The biomechanics behind the use of these restraint systems is the subject

of this chapter.

18.1 Effectiveness of Restraints in Frontal Impact

Since frontal crashes were, and still are, the most frequent type of crash, protection

of the occupant in a frontal crash was the first to be provided by automakers.

Johannessen (1984) wrote a detailed history behind how the lapbelt was invented

initially to keep occupants of horse-drawn carriages and later automobiles from

being ejected due to excessive bouncing while travelling over rough roads. Then it

was used in open cockpit aircraft to keep the pilot from falling out when the plane

flew upside down. These early belts were made of leather and were not replaced by

Nylon webbing till the 1950s and 1960s. Other improvements include the metal-tometal

buckle designs, the non-locking retractor and the automatic-locking retractor.

It was not until 1968 when all cars manufactured and sold in the USA were



597

598 18 Biomechanics of Automotive Safety Restraints

equipped with seatbelts, lapbelts in all seating positions plus shoulder straps in front

outboard seats. In the mid-1970s, thinner polyester webbing replaced the Nylon

webbing, allowing longer belt loops to be used and stored in the vehicles. The

current three-point belt was made possible by this change in belt material. An

interesting summary of the history of the seatbelt from 1885 to 1983 was provided

by Johannessen (1984) and is shown in Fig. 18.1.

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1885

1910

1922

1926

1935

1940

1949

1955

1961

1963

1965 1964

1967

1969

1971

1979

1983

1966

1968

1970

1972

1975

Seat belt used on horse-drawn vehicles to prevent ejection

Leather seat belt used on U.S.Army Plane No.1 to prevent ejection

Seat belt used by Barney Oldfield in his race car

Seat belts required in open-cockpit commercial airplanes

Factory-installed seat belts advocated by C.J.Strickland,

Founder and President of Automobile Safety League

Cornell Aeronautical Laboratory initiated the Automotive

Crash Injury Research (ACIR) program

Factory-installed seat belts offered by Nash

Factory-installed seat belts offered by Ford

SAE issued Standard J4

American Seat Belt Council (ASBC) was formed to establish and

monitor industry standards

(Model Year 1964) Car manufacturers installed seat belts in front

outboard seating positions in all new cars (delete option)

SAE issued Standard J4a

Mandatory installation of front outboard seat belts in new

cars sold in 23 states

(Model Year 1965) Car manufacturers installed seat belts in

front outboard seats in all new cars, with no delete option

SAE issued Standard J4c

(Model Year 1967) Car manufacturers install seat belts in rear

outboard seating positions in all new cars

First production installations of emergency-locking retractors,

in Shelby-American GT 350 and GT 500

Wisconsin appellate court allows “Seat Belt Defense”

FMVSS 208 takes effect, requiring seat belts in all forwardfacing

seating positions and shoulder straps in front outboard

seating positions

California appellate court allows “Seat Belt Defense”

Australia (Victoria) adopts mandatory seat belt use law

FMVSS 208 amended to require passive restraints, effective 1973

(later deferred)

TRANSPO 72 held in Washington, D.C.

Volkswagen displayed seat belt system with pretensioner

Continuous-loop system introduced on Cadillac Seville

First production tension-relieving device on shoulder strap

New York superior court allows “Seat Belt Defense”

Coleman Decision regarding passive restraints

First “19-City” study of seat belt usage

Dual-spool retractor introduced on Chevrolet light trucks

Dual-spool retractor with manual look-up of lap belt retractor

introduced on Corvette

Fig. 18.1 History of the seatbelt from 1885 to 1983 (taken from Johannessen (1984)). Reprinted

with permission Copyright © 2017 SAE International. Further distribution of this material is not

permitted without prior permission from SAE

18.1 Effectiveness of Restraints in Frontal Impact 599

The history of the seatbelt showed that its usage increased with the aid of

legislation and public campaigns but its effectiveness was determined from accident

statistics and biomechanical testing. After much analysis, the NHTSA arrived

at a best estimate for the effectiveness of the manual lapbelt. Against AIS 2–5

injuries, its effectiveness was 25–35 % and against fatalities, it was 30–40 %

(Table IV-4a, NHTSA 1984). In this context, effectiveness is defined as a percent

reduction in fatalities or injuries when a restraint system is used, in comparison with

the unrestrained occupant.

The biomechanical principle behind the effectiveness of the lapbelt is the ride

down effect on the occupant. An unrestrained occupant would continue to move

forward at the pre-crash speed with torso erect while the car is brought to a sudden

stop by the crash. Thus, the chest of the occupant would impact the steering wheel

(for the driver) or the instrument panel (for the right front passenger) at almost the

pre-impact speed, sustaining a variety of severe injuries to the head, chest, and

lower extremities. The head will impact the windshield and penetrate it in older

(pre-1966) vehicles, causing disfiguring facial injuries as the head comes back into

the vehicle. On the other hand, the lapbelted occupant slows down with the vehicle

(rides down) and any occupant impact with the vehicle would be at a much lower

speed. Lapbelted front seat occupants are still at risk for a head injury because the

lapbelt cannot prevent torso flexion and the head will very likely hit the steering

wheel or instrument panel. However, it is will not hit the windshield. Submarining

can occur if the lapbelt is not worn properly. It should be worn over the anterior

superior iliac spine of the pelvis (Fig. 13.2) to avoid abdominal and spinal injuries.

As for the lower extremities, the unrestrained front seat occupant will sustain tibial

and femoral injuries, such as a tibial plateau fracture as the knee impacts the sloping

dash and is jammed between the dash and floor and an acetabular fracture due to axial

load transmitted from the knee to the hip. Femoral fractures can also occur if the knee

is pocketed in the dash and experiences shear loading perpendicular to the femur.

This shear load at the knee puts the femur in bending and causes it to fracture at the

mid-shaft across a plane normal to the femoral axis. The knees can still impact the

dash for a lapbelted occupant, especially if the lapbelt is loosely worn. But the loads

are greatly reduced and severe lower extremity injuries are not likely to occur.

Ejection from a vehicle involved in a collision causes severe head and neck

injuries and is frequently fatal. Before better door latching mechanisms were

invented, the lapbelt was the first safety device that could prevent ejection.

For the rear seat occupant, use of the lapbelt has a double benefit. It not only

allows the rear seat occupant to ride down with the vehicle but it also prevents

him/her from being thrown into the back of front seat, causing injury to the front

seat occupant. The lapbelt will not prevent head injuries to the rear seat occupant.

For occupants restrained by a lap-shoulder (three-point) belt, the estimated

reduction in AIS 2–5 injuries is 45–55 % and in fatalities, it is 40–50 %. Of course,

this reduction is dependent on the severity of the crash and the extent of intrusion

into the passenger compartment. The driver is not immune from a head impact with

the steering wheel. Nils Bohlin of Volvo invented the three-point belt in 1958 and

patented it in 1959. Since Volvo insured its own vehicles, Bohlin was privy to all


the injury data involving Volvo vehicles. He stated in 1967 (Bohlin 1967) that

three-point belted occupants survived crashes at speeds below 60 mph (96.6 km/h).

This was confirmed by a laboratory study by Patrick et al. (1974) who reconstructed

128 Volvo accidents involving 169 occupants at barrier equivalent velocities (BEV)

from 2 to 53 mph (3 to 85 km/h). The BEV is defined as the barrier impact speed of

the crashed vehicle that is needed to absorb the same amount of energy as it did in

the actual crash (Cheng et al. 2005). Cadavers were used in these tests and only

14 of them had AIS 3 injuries. There were no AIS 5 injuries or fatalities in the study.

The addition of a cross-chest belt to the lapbelt improved the ride down and

lessened the severity of head impact of the driver on the steering wheel. However,

the diagonal belt can cause rib and sternal fractures, especially among the elderly.

The ultimate strain for ribs is known to decrease by 50 % after age 60 (Kemper et al.

2005). That is, ribs become more brittle with age and are more susceptible to

fracture when loaded by the diagonal belt. This was confirmed by a study by

Zhou et al. (1996) who demonstrated that the reduction in injury tolerance from

the “young” age group to the “elderly” age group was approximately 20 % for

frontal blunt impact to the chest and as much as 70 % for belt loading. The belt

system was improved to prevent snapping of the neck in severe frontal collisions by

adding a load limiter to the diagonal belt. Also, a pretensioner was added to the lap

portion of the belt to load the pelvis first before the diagonal belt loads the chest so

as to reduce chest deflection. In a report issued by NHTSA (Report No. DOT-HS-

809-563 by Walz (2003)), the combination of load limiters and pretensioners

reduced HIC by 232 and chest deflection by 10.6 mm for front seat occupants,

based on dummy testing. The pretensioner can also reduce submarining.

In severe impacts, ring fractures of the skull were known to occur without a load

limiter, such as in the case of NASCAR driver Dale Earnhardt. Another side effect

of the three-point belt is the development of compressive loads in the spine when

the lordotic thoracic spine tries to straighten and lengthen when the chest is pushed

up against the shoulder belt, as described in Chap. 10, Sect. 10.5. Osteoporotic

belted occupants are at risk for thoracolumbar wedge fractures or even burst

fractures. Rear seat occupants are better protected with a three-point belt and all

cars built after 1989 are equipped with at least two outboard three-point belts.

For a more complete protection of the front seat occupants, the airbag acts to

protect the head from impact with the steering wheel and other relatively stiff

vehicular surfaces, such as instrument panel and A-pillar. It was surprising to find

that crash statistics continued to show minor head injuries of AIS 1–2 in belt

restrained occupants protected by an airbag (Huber et al. 2005). The biomechanical

cause for these minor head injuries is unknown and it is not clear what the

automotive industry can do to resolve this issue. The airbag can also restrain the

upper torso in tandem with the shoulder belt. If the belt is adjusted properly, it can

help reduce the number of rib fractures. It was shown by Høye (2010) that the use of

the airbag in conjunction with the three-point belt was statistically beneficial to the

occupant in a frontal crash. When used without the three-point belt system, the

airbag is not as effective because the occupant can slide off to one side of the bag

and impact the A-pillar or the instrument panel. Additionally, without the belt,

18.1 Effectiveness of Restraints in Frontal Impact 601

Fig. 18.2 Four-point belt systems proposed by Rouhana et al. (2003). The standard three-point

belt is shown in (A), the X4 cross-chest belt is shown in (B) and the V4 belt is shown in (C)

ejection is still a possibility. Thus, the three-point belt is considered by the automotive

industry as the primary restraint and the airbag is called a supplemental

restraint system (SRS) to be used in conjunction with the belt system.

The airbag, however, is not without its side effects. The out-of-position occupant

who is too close to the airbag as it deploys can be injured. The airbag comes out of

its casing at a very high speed and the resulting bag slap can cause both head and

chest injuries. It is a good idea to maintain at least 25 cm (10 in.) of space between

the front of the chest and the center of the steering wheel. Another potential hazard

is the noise generated by the airbag as it deploys. There is research on cats which

suggests that airbag noise can cause a partial temporary and/or permanent loss of

hearing in humans, especially for ears that are susceptible to loud noises (Morris

and Borja 1998; Price and Kalb 1999).

The lowered thoracic tolerance in the elderly has prompted Rouhana et al.

(2003) of Ford Motor Company to design and test a couple of four-point restraint

systems. These are shown in Fig. 18.2 along with the standard three-point belt

(on the left). The cross-chest X4 belt is simply a lapbelt with two diagonal belt and

the V4 harness-type belt is similar to that used by flight attendants on most

commercial aircraft. It is easy to slip on and off. Rouhana et al. (2003) conducted

MADYMO modeling of the belt systems and performed sled tests using dummies

and cadavers to evaluate the relative merits of the two four-point belt systems in

comparison with the standard three-point belt that was equipped with a load limiter

and a pretensioner. Cadaveric testing revealed that although the cross-chest X4 belt

provided more constraint for the torso, it tended to cause more chest compression

and increase injury risk compared to the V4 system which did not load the chest as

much because the loads were transferred to the clavicles and the pelvis. The V4

system reduced chest deflection by as much as 50 % which is associated with a 5- to

500-fold reduction in thoracic injury risk. Submarining was avoided by using a

lapbelt pretensioner and double load limiters for the shoulder belts. The side effects

were lumbar, sacral, and pelvic injuries. The system is obviously not ready for

production as many other issues need to be resolved, including possible risk of

injury to the neck by the in-board harness due to a far-side lateral impact and

potential for injury to the fetus of a pregnant occupant due to the fact the belt buckle

has to be located over the center of the abdomen.


One injury that belt and airbag restraints cannot prevent is head injury due to an

underride collision. This occurs when a light vehicle (car) impacts the rearend of a

truck with a high cargo bed and with its rear wheels located 1 m or more in front of

its rear underride guard. Since 1998, the back surface of the rear wheels of trailers is

required to be no more than 12 in. (30 cm) in front of the rear surface of the truck so

that even if the underride bumper failed, the penetration of the hood of a small car

going under the truck would not cause decapitation of its front seat occupants. In

any case, it is not a good idea to be driving behind a tractor-trailer on the freeway.

For more details, please consult Blower and Woodrooffe (2013) which was

published in March 2013.

18.2 Effectiveness of Restraints in Side Impact

If the struck vehicle is moving or if the impact is not purely lateral, there is likely to

be an acceleration or deceleration component in its direction of travel and the

restraint systems discussed in Sect. 18.1 above will help to keep the occupants in

place. They do not afford any side impact protection and injuries resulting from

intrusion of the side door or structure of the vehicle needs to be dealt with. Research

by Cavanaugh et al. (1992, 1993) showed that to protect the thorax of a near-side

impact occupant, a soft padding with a crush strength of about 10 psi (69 kPa) is

needed. The data were derived from cadavers that were usually advanced in age so a

slightly stiffer pad would be acceptable. This means that, for airbags, the initial

stiffness of the bag when contacted by the occupant should also be in this same

range. Furthermore, the pad or the airbag should not be allowed to bottom out

because when it does, the thorax experiences a large force. The unvented airbag is a

natural way to increase its stiffness as it is compressed.

In terms of its history, the side airbag was first installed in the 1995 Volvo, using

a bag manufactured by Autoliv, Inc. The first side airbags were for torso protection

and were deployed below the side window sill. At present, there are curtain bags

that protect the head as well as torso bags. The curtain bags are usually deployed

from above the roof rail and the torso bags are deployed from the outer edge of the

seat back. Braver and Kyrychenko (2004) found that side airbags in 1997–2002

model year cars were effective in reducing injuries, especially for the near-side

occupants. However, the head airbag is an important component of the protective

system. There have also been few out-of-position injuries, especially for children.

It is noteworthy that side impact airbag was introduced without a specific

mandate by the government to install them. In fact, it was mentioned in Chap. 15

that the original side impact standard using the Thoracic Trauma Index (TTI) was

not predictive of side impact injury and it was replaced in 2007 by a revised

standard that really had no scientific basis either except that it harmonizes the US

standard with the European standard. The new FMVSS 214 calls for the use of the

Eurosid ES-2re male dummy and the SID-IIs female dummy. For both the moving

18.3 Effectiveness of Restraints in Rear Impact 603

dynamic barrier (MDB) test at 35 mph (56 km/h) and the moving pole test at

20 mph (32 km/h), the ES-2re dummy must meet the following requirements:

Head HIC 36 1000

Chest Deflection of any rib 44 mm (1.65 in.)

Abdomen Total force 2500 N (562 lb)

Pelvis Pubic symphysis force 6000 N (1350 lb)

For the SID-IIs, the requirements are:

Head HIC 36 1000

Spine Resultant lower spine acceleration 82 g

Pelvis Sum of acetabular and iliac pelvic forces 5525 N (1244 lb)

There is no chest deflection requirement, pending further research.

In the MDB test, the ES2-re is seated in the front seat on the impacted side and

the SID-IIs dummy is in the rear seat on the same side. For the pole test, either

dummy can be used, seated in the front seat on the impacted side. More details are

available in NHTSA’s final rule on FMVSS 214 (NHTSA 2007). A drawing of the

ES-2re dummy is shown in Fig. 18.3 and a photograph and drawing of the SID-IIs

are shown in Fig. 18.4. Justification for the use of the two dummies in FMVSS

214 can be found NHTSA Notice of Preliminary Rulemaking (NPRM) (Kuppa

2004) and in the Federal Register dated December 8, 2004 (2004)

18.3 Effectiveness of Restraints in Rear Impact

In most rearend impacts, fatal or life-threatening injuries rarely occur. In some

victims, long term head, neck, shoulder, and back pain can occur. However, in most

people, the neck pain is transient and minor in nature. The only countermeasure

available in our cars is the headrest which was mandated by the Federal government

under FMVSS 202 for all passenger cars manufactured after 1/15/69. The standard

was upgraded in 2004 and it became final in 2011. The main goal of the upgrade

was to limit the “backset” or the distance between the back of the occupant’s head

and the front of the headrest be limited to 55 mm (2.2 in.) because research has

shown that proximity of the head to the headrest in the driving position can reduce

the severity of the whiplash injury. As was shown in Chap. 8, the injury can occur in

the first 100 ms of impact and it is necessary to have the head as close to the

headrest as possible before the impact. Thus, the shear hypothesis for injury is valid

and the best way to prevent it is to have the head up against the headrest during the

impact. Field data from Jakobsson et al. (1994) confirmed this hypothesis.

To review the kinematics involved, let’s consider what happens to the driver of a

car that is sitting at a red light and is rearended by a distracted driver. The struck

vehicle is accelerated forward and the driver is pushed forward by the seat back.


Fig. 18.3 A drawing of the ES-2re dummy. ES-2 stands for the second version of the European

side impact dummy and the letters re indicate that the dummy was modified by the addition of a rib

extension in the rear to prevent the spine from catching on the seat back during a side impact

(courtesy of Mr. Michael Jarouche, Humanetics Innovative Solutions, Inc.)

However, the head lags behind because the headrest is generally too far behind the

head. As a result, the head and neck go into extension, stretching the neck flexors

and compressing the neck extensors. Since this is an accident situation, the neck

muscles would be contracting and the flexors can be injured while they are

contracting and being stretched. However, the pain should last for only a few

days with no long term sequelae. Since neck pain due to whiplash is usually in

the back of the neck, the source of pain is not of muscular origin. Lu et al. (2005)

have shown that the pain emanates from the cervical facet capsules which contain

nociceptors that fire when stretched. The stretching is due to relative motion

between adjacent cervical vertebrae when the lagging head is brought forward by

the torso. Thus, if shear forces are not developed in the neck, there will be no facet

capsule stretch and no whiplash injury.

From the clinical point of view, there is research by Lord et al. (1996) who used

percutaneous radio frequency waves to destroy the nerve endings in the facet

capsule to relieve chronic neck pain in whiplash patients. This is not a permanent

18.4 Types of Rollovers 605

Fig. 18.4 A photograph

(A) and an engineering

drawing (B) of a SID-IIs

dummy, showing its five

ribs and asymmetric chest.

The dummy can only be

impacted on one side (left)

because the ribs have been

lengthened to reduce lateral

chest stiffness and are

anchored to a block on the

right side (courtesy of

Mr. Michael Jarouche,

Humanetics Innovative

Solutions, Inc.)

solution to the facet pain problem as the nerve roots will grow back and the pain

will return in about 9 months to a year. However, it does demonstrate the validity of

the work of Lu et al. (2005) and that of the shear hypothesis for whiplash.

18.4 Types of Rollovers

Although newer car models (2012 and later models) have electronic stability

control (ESC) and are virtually impossible to rollover on level ground, there are

still many other driving situations which can cause a rollover. Generally, rollovers

are relatively low speed events but they are the most dangerous type of vehicular

crash, as evidenced by the high fatality rate among the occupants involved. In 2014,

only 2.0 % of the vehicles crashes resulted in rollovers but the death toll was 6839

or 32.5 % of all occupant fatalities (Kahane 2014). Prior to 2012, the number of

occupants killed in rollover crashes was much higher. For example, in 2005, 11,519

occupants died in rollover crashes and 2.6 % of the crashes was rollovers. One of

the reasons for this high fatality rate is that rollover crashes are violent, complex,

and random in nature, involving multi-directional linear and angular accelerations,

a variety of initiation mechanisms, complicated vehicle deformations and multiple

vehicle-to-ground and occupant-to-vehicle contacts. Also, prior to the installation

of rollover curtain airbags, similar to those for side impact, and prior to the


Table 18.1 Types of rollover

initiation (based on NHTSA

(2001))

1 Trip-over

2 Flip-over

3 Turn-over

4 Climb over

5 Fall-over

6 Bounce-over

7 Collision with another vehicle

8 End over end

9 Other initiation type

10 Unknown

Fig. 18.5 Examples of rollover due to a trip-over. It occurs when the lateral motion of the vehicle

is resisted by an opposing force, inducing a roll moment. The surface is deformed by the wheels

(taken from NHTSA (2010))

widespread use of belt restraints, ejection through a side window is a common mode

of fatality and/or serious injury.

For a better appreciation of rollover crashes, it is necessary to understand the

mechanisms that can initiate a rollover. The rollover types are listed in Table 18.1.

Some of these types are described graphically in Figs. 18.5, 18.6, 18.7, 18.8, 18.9

and 18.10 which were taken from General Vehicle (GV) section of the 2010

version of the manual of the National Automotive Sampling System (NASS) for

recording crash data (NHTSA 2010). The active safety system that provides

electronic stability is able to prevent a turn-over shown in Fig. 18.7. All other

modes of rollover cannot be controlled by ESC. Videos of some tripped rollover

events can be accessed via https://www.safercar.gov/Vehicle-Shoppers/Rollover/

Types-of-Rollovers.


Fig. 18.6 Examples of rollover due to a flip-over. It occurs when the vehicle mounts a guard rail

or steep hillside and rolls back towards the side of the guardrail or slope from which it came (taken

from NHTSA (2010))

Fig. 18.7 Example of a rollover due to a turn-over which is caused by centrifugal forces generated

by a sharply turning or rotating vehicle when resisted by normal surface friction, including

pavement, gravel, grass, or dirt. No furrowing, gouging, deformation, curb or any physical

obstruction of the surface occurs at the point of the trip as opposed to a trip-over (taken from

NHTSA (2010))


Fig. 18.8 Example of a rollover due to a climb-over. The vehicle climbs up and over the fixed

object which needs to be high enough to lift the vehicle off the ground. It then rolls over to the

opposite side of the impacted object (taken from NHTSA (2010))

Fig. 18.9 Example of a fall-over in which the vehicle is on a slope steep enough to cause its cg to

fall outside of the wheelbase (taken from NHTSA (2010))

There are many methods to simulate a rollover experimentally. Popular methods

include rolling over into a ditch (Fig. 18.11A), conducting the SAE J2114 dolly test

by using a dolly arrestor (Fig. 18.11B), using a sled to initiate a curb trip

(Fig. 18.11C), launching one side of a vehicle onto a ramp to initiate a corkscrew

rollover (Fig. 18.11D) and using a sled to initiate a soil trip (Fig. 18.11E), as

described by Parenteau et al. (2003).


Fig. 18.10 Example of a

bounce-over. The vehicle

rebounds off of a fixed

object, such as a guardrail,

and overturns, as a result

(taken from NHTSA

(2010))

Fig. 18.11 (A–E) Various laboratory test methods to simulate vehicular rollovers (taken from

Parenteau et al. (2003)). Reprinted from C.S. Parenteau, D.C. Viano, M. Shah, M. Gopal, J.

Davies, D. Nichols, J. Broden, Field relevance of a suite of rollover tests to real-world crashes and

injuries. Accident Analysis & Prevention 35(1), 103–110, 2003, with permission from Elsevier


18.5 Rollover Crash Injury Statistics

Most of the AIS 2–6 injuries sustained in a rollover were due to trip-over crashes.

Hu (2007) compiled the injury information in Table 18.2 using NASS data from

NHTSA (2005). Since trip-overs occurred over 60 % of the time, it would be natural

for us to study this type of rollover in greater detail and seek preventative measures.

But, rollovers are difficult to reproduce in the laboratory to yield consistent results

because a large number of variables are involved and because of the random nature

of rollovers. One way to tackle the problem is to use computer modeling to predict

occupant response because a large number of impact scenarios can be simulated at a

fairly low cost compared to the experimental staging of these events.

In terms of body regions that are commonly injured, Hu (2007) has also

compiled a list from NHTSA (2005) for belted and unbelted occupants involved

in rollover crashes. The injury information for belted occupants is shown in

Table 18.3 which shows that the most frequently injured body regions are the

head, chest, and neck, at all injury levels. Similarly, for unbelted occupants who

were not ejected, the most frequently injured regions for AIS 3–6 injuries were also

the head, chest, and neck, as shown on the right side Table 18.4. Thus, it would be

logical to analyze in greater detail the injured anatomical regions of these three

body segments.

For the head, the injuries or the injured anatomical structures are shown in

Table 18.5. For belted occupants, the highest percentage of injury is loss of

consciousness (LOC) which is less severe than brain injury, the most common

injury sustained by unbelted occupants. The most common type of brain injury

sustained by both the belted and unbelted occupants was subarachnoid hemorrhage,

as shown in Table 18.6.

The predominant chest injuries for belted and unbelted occupants were to the rib

cage and internal organs, mostly in the form of rib fractures and lung injury. The

distribution of chest injuries is shown in Table 18.7.

Table 18.2 Distribution of

rollover crashes by initiation

type for MAIS 2 to 6 injuries

(taken from Hu (2007))

Rollover initiation type

Number

of vehicles Percent

Trip-over 814 60.3

Collision with another vehicle 168 12.5

Bounce-over 131 9.7

Flip-over 68 5.0

Fall-over 67 5.0

Climb-over 43 3.2

End-over-end 28 2.1

Turn-over 16 1.2

Other rollover types 14 1.0

Total 1349 100.0

18.5 Rollover Crash Injury Statistics 611

Table 18.3 Injury distribution for belted occupants by body region (taken from Hu (2007))

AIS 2 to 6 injuries

AIS 3 to 6 injuries

Body region

Number Percent Number Percent

Head 321 30.0 163 37.9

Chest 138 12.9 107 24.9

Neck 95 8.9 38 8.8

Forearm 46 4.3 25 5.8

Thigh 19 1.8 19 4.4

Abdomen 66 6.2 18 4.2

Leg (lower) 39 3.6 16 3.7

Arm 21 2.0 14 3.3

Pelvic 47 4.4 13 3.0

Back 57 5.3 5 1.2

Other regions 221 20.7 12 2.8

Total 1070 100.0 430 100.0

Note: The percentage numbers for the top three injured body regions are highlighted in bold

Table 18.4 Injury distribution for unbelted occupants by body region (taken from Hu (2007))

AIS 2 to 6 injuries

AIS 3 to 6 injuries

Body region


Head 213 29.6 142 42.3

Chest 116 16.1 90 26.8

Neck 47 6.5 28 8.3

Abdomen 65 9.0 19 5.7

Thigh 17 2.4 17 5.1

Forearm 24 3.3 15 4.5

Arm 13 1.8 5 1.5

Back 58 8.1 5 1.5

Leg (Lower) 15 2.1 5 1.5

Face 36 5.0 4 1.2

Other regions 116 16.1 6 1.8

Total 720 100.0 336 100.0

Note: The percentage numbers for the top three injured body regions are highlighted in bold

As for the neck, the most frequent injury was vertebral fracture without cord

injury for both the belted and the unbelted occupant. Cord injury for the unbelted

occupant was almost 11 % and 7.4 % for the belted occupant. These data are shown

in Table 18.8. Vertebral dislocation occurred less frequently than spinal cord injury.

The implication is that roof crush is not likely to cause cervical cord injury or

quadriplegia. It is also interesting to look at the relationship between head and neck

injury. As shown in Table 18.9, the number of head injuries with neck injury was

not the same as the number of neck injuries with head injury or vice versa. That is,


Table 18.5 Distribution of head injury by injury type or anatomic structure (taken from Hu

(2007))

Belted

Unbelted

Injury


LOC 135 42.1 72 33.8

Brain injury 120 37.4 107 50.2

Skeletal 45 14.0 32 15.0

Skin 15 4.7 1 0.5

Vessels 3 0.9 – –

Nerves 2 0.6 – –

Whole area 1 0.3 1 0.5

Total 321 100.0 213 100.0

Note: The highest percentage of injury is in bold

Table 18.6 Types of head

injuries sustained by

occupants in a rollover


Belted

Subarachnoid hemorrhage

26 (14.0%)

Closed vault fracture

18 (9.7%)

Scalp laceration

10 (5.4%)

Intraventriclar hemorrhage

9 (4.8%)

Basilar skull fracture

8 (4.3%)

Unbelted

Subarachnoid hemorrhage

27 (19.1%)

Intraventriclar hemorrhage

8 (5.7%)

Cerebrum multiple contusion

6 (4.3%)

Subdural hematoma

5 (3.5%)

Cerebrum laceration

5 (3.5%)

Table 18.7 Distribution of chest injuries among rollover occupants (taken from Hu (2007))

Belted

Unbelted

Type of anatomic structure Number Percent Number Percent

Skeletal 72 51.4 56 46.3

Internal organs 57 40.7 55 45.5

Vessels 10 7.1 10 8.3

Whole area 1 0.7 0 0

Total 140 100.0 121 100.0

Note: The percentage for the most frequently injured thoracic regions are in bold

multiple head injuries can occur with one neck injury and vice versa. The rate of

head injury with neck injury was 16.2 % and 10.8 % for belted and unbelted

occupants, respectively, indicating that there is not a strong correlation between

head and neck injury. Further analysis revealed that no predominant type of head

18.6 Experimental Simulation of Rollover Crashes 613

Table 18.8 Distribution of neck injuries among rollover occupants (taken from Hu (2007))

Belted

Unbelted

Specific anatomic structure


Vertebral fracture without cord injury 80 84.2 36 78.3

Cord injury 7 7.4 5 10.9

Vertebral disiocation without fracture and cord injury 5 5.3 4 8.7

Disc injury 3 3.2 — —

Nerve root injury — — 1 2.2

Total 95 100 46 100

Note: Percentage values for the most frequent injuries are in bold

Table 18.9 Relationship between head and neck injury among rollover occupants (taken from Hu

(2007))

Belted

Unbelted

Injury type


Head injury Head injury with neck injury 52 16.2 23 10.8

Head injury without neck injury 269 83.8 190 89.2

Total head injury 321 100 213 100

Neck injury Neck injury with head injury 34 35.8 18 39.1

Neck injury without head injury 61 64.2 28 60.9

Total neck injury 95 100 46 100

injury occurred concomitantly with neck injury. On the other hand, vertebral body

fractures occurred frequently with head injuries in belted occupants but not with

unbelted occupants. It appears that belted occupants tend to stay more upright relative

to the vehicle and are more likely to sustain cervical compression from impact with

the roof or roof rail. This is not to say that neck injury with quadriplegia cannot occur

in any given rollover but the probability of that happening is relatively low.

18.6 Experimental Simulation of Rollover Crashes

There have been many experiments involving dummies and, occasionally, cadavers

and volunteers to simulate rollover crashes. One of the principal objectives of the

tests was to study the vertical head excursion during a rollover because of the risk of

severe neck injury due to roof crush. The occupant was restrained by a three-point

belt to reduce kinematic variability and a secondary objective was the ability of the

belt system to protect the head and neck of the occupant.

Head excursion is defined as head displacement relative to the seat. Moffatt and

James (2005) defined four categories of head excursion. They are inverted static


Fig. 18.12 Rollover test data using a Hybrid III dummy in a Chevrolet Malibu show that the neck

load peaked well before the roof crushed (taken from Bahling et al. (1990))

excursion, rotational excursion, impact excursion, and seat belt anchor excursion.

The sum of the first three excursions is the occupant excursion and the fourth

accounts for the roof crush. A typical value for inverted static excursion is 100 mm

while that of rotational excursion and impact excursion is 50 mm each, resulting in

a total excursion of 200 mm. The available vertical headroom depends on the sitting

height of the occupant but typically it is about 100 mm. Thus, if we assume the

occupant to remain upright with respect to the seat during the rollover, the inevitable

result is neck compression and neck bending. However, in a typical rollover,

the occupant slides sideways with respect to the seat and the head and neck are not

subjected to an axial impact by the roof. It was also shown by Bahling et al. (1990)

that the dummy neck load peaked well in advance of the roof crush and that any

neck injury was the result of the occupant “diving” into the roof or roof rail before

any crush occurred. The test results are shown in Fig. 18.12. It can be concluded

that roof stiffness does not play a part in head injury as the head would be in contact

with a roof that is already on the ground and the head injury would essentially be

due to ground contact.

For a more detailed discussion on the various methods used in the automobile

industry to perform rollover testing, the reader is referred to Chou et al. (2005) who

reviewed the literature on test methods used in the development of rollover occupant

protection systems.

18.7 Modeling of Rollover Crashes

Since experimental simulation of rollovers is both difficult and costly, the use of

computer models to study rollovers is not only relatively inexpensive but also

practical because many simulations may be needed to accurately duplicate a

18.7 Modeling of Rollover Crashes 615

given rollover event. Many models are available to perform the simulation but few

have been actually validated against experimental data. Chou et al. (1998)

conducted a review of computer models simulating rollover. There were four levels

of complexity, beginning with a two-dimensional rigid body model of an airborne

vehicle impacting the ground. This was followed by several unvalidated 2-D rigid

body vehicle models connected to a suspension system with and without the

inclusion of tire compliance. These models were followed by 3-D simulations

which used rigid body software already available for occupant impact simulation,

such as the ATB or the MADYMO program. In these simulations, the vehicle was

assumed to be non-deformable and the models studied the kinematics of the

occupant during rollover. Occupant motion in some of the models compared

favorably with test data but the major limitation was inability to predict the

deformation of roof structures which can play a major role in neck injury. The

last level of complexity was to use FE methods to simulate both the occupant and

the vehicle. Several FE models of actual vehicles have been developed There are at

least three known FE models of actual vehicles used by the NHTSA to study the

response of the roof to quasi-static loading. The vehicle models are of a 1998 Dodge

Caravan, a 1998 Chevrolet S-10 pick-up truck and a 2002 Ford Explorer SUV

(NHTSA 2005). The FE model of the Ford Explorer was developed by NHTSA in

collaboration with the Federal Highway Administration to study frontal impact.

This model was used by Hu (2007) to study the various factors related to rollover

injuries. It was re-meshed by Hu (2007) to reduce the number of elements from over

235,000 to about 90,000 so that it can be used to simulate a long duration rollover

without incurring excessive computing costs. The model was validated by comparing

the predicted roof crush with data obtained from testing under FMVSS

216 which is a quasi-static roof test. Hu (2007) used this vehicular model in

combination with a whole-body dummy model to simulate rollovers. The model

set-up is shown in Fig. 18.13. It assumes that during a rollover, the side airbag

curtains are deployed and that the occupant (driver) is restrained by a three-point

belt. Data from four different tests on the Ford Explorer were used to validate the

model. They were the FMVSS 216 quasi-static test, the SAE J2114 dolly test, the

curb trip test, and the corkscrew test. These tests are shown in Fig. 18.14 and were

conducted by Autoliv of North America for Ford Motor Co.

Simulation results of vehicle kinematics, using the Hu (2007) model, are compared

with experimental data in Figs. 18.15, 18.16, 18.17, and 18.18. The FMVSS

216 static test results and the predicted loads are shown in Fig. 18.15. The test

consisted of the loading of a corner of the roof by a rectangular plate, 30 by 72 in

(76.2 by 182.9 cm), at a 25-deg angle with respect to the horizontal, applied to the

roof rail, as shown in Fig. 18.4A and at a 5 angle with respect to the horizontal,

applied to the front header. The correlation between model prediction and test

results is favorable. Simulation of an SAE J2114 dolly test is shown in Fig. 18.16,

with validation of vehicle kinematics. The curb trip rollover is shown in Fig. 18.17

in which the model predictions are compared with test results. In Fig. 18.18, a

corkscrew rollover is simulated and the computed and measured vehicle kinematics

vehicle kinematics are also compared.


Fig. 18.13 Modeling rollover with a belted Hybrid III dummy occupant (taken from Hu (2007))

Fig. 18.14 (A–D) Tests used to validate the rollover model by Hu (2007)

Since the Hu (2007) model was able to simulate vehicular occupants during a

rollover, computed head accelerations and neck loads could be compared with

experimental data as well. The lateral and vertical head acceleration of a nearside

dummy head are compared against SAE J2114 rollover test results in

Fig. 18.19 while the head impact location and timing are compared in Fig. 18.20

for the same test. For the far-side occupant in this test, the vertical head acceleration

and axial neck force are compared in Fig. 18.21. In Fig. 18.22, the head impact

location and timing are compared in the same SAE J2114 dolly rollover test for the

far-side occupant. Validation of the curb-trip rollover simulation is shown in


40.0k

35.0k

Test

Simulation

30.0k

Loan (N)

25.0k

20.0k

15.0k

10.0k

5.0k

0.0

0 20 40 60 80 100

Roof Deformation (mm)

Fig. 18.15 Comparison of predicted and measured loads for the quasi-static FMVSS 216 test


Fig. 18.23 in which the head accelerations of the near-side dummy head are

compared. Head impact location and timing for the near-side occupant in this test

are compared in Fig. 18.24 and the vertical acceleration and axial neck load of the

far-side occupant are compared in Fig. 18.25. A comparison of the head impact

location and timing for this curb-trip test for the far-side occupant is shown in

Fig. 18.26. These results highlight the capability of the Hu (2007) model to simulate

the SAE J2114 dolly and the curb-trip rollovers. There are, of course, limitations

in the Hu (2007) study. Only dummy occupants were simulated and dynamic

roof crush could not be validated as no experimental data were available to measure

this crush.


The currently available protection for the automotive occupant is summarized in

this chapter with respect to frontal, lateral, and side impacts and rollovers. The

airbag is playing a large role in protecting the occupant against frontal, lateral, and

rollover crashes. The headrest issue for whiplash protection has finally been

resolved by a government regulation based largely on the research done at

Wayne State University. More safety improvements will come along but, for

now, the automobile is adequately equipped with safety features to minimize

occupant injuries. The one flaw in the entire system is the requirement to buckle

the seatbelt manually. For occupants who do not wear belts, they are unable to avail

themselves of all the protection provided by the manufacturers.


(A) Simulated vehicle motion

50

Test

Simulation

Test

Simulation

Angular velocity (degree/s)

Lateral acceleration (g)

Vertical acceleration (g)

-50

-100

-150

-200

-250

-300

-350

-400

-450

0

0.0 0.2 0.4 0.6 0.8 1.0

Time (s)

(B) Vehicle angular velocity

10

1.2 1.4 1.6 1.8 0.4 0.6 0.8 1.0

Time (s)

5

0

-5

-10

1.2 1.4 1.6 1.8

(C) Vehicle lateral acceleration

8

4

0

-4

-8

0.4 0.6 0.8 1.0

Time (s)

Test

Simulation

1.2 1.4 1.6 1.8

(D) Vehicle vertical acceleration

Fig. 18.16 Simulation of an SAE J2114 dolly test—Comparison of model predictions with test results. The simulated vehicular motion is shown in (A) while

the computed vehicular angular velocity, lateral acceleration and vertical acceleration are compared with test data in (B–D), respectively (taken from Hu

(2007))



50

0

Test

Simulation

Test

Simulation

Angular Velocity (degree/s)

Lateral Acceleration (g)

Vertical Acceleration (g)

-50

-100

-150

-200

4

2

0

-2

-4

-6

8

6

4

2

0

-2

-4

Test

Simulation

-250

-8

-6

-300

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0

Time (s)


Time (s)


-10

-8

1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)


Fig. 18.17 (A–D) Simulation of a curb trip. Comparison of model predicted kinematics with experimental data (taken from Hu (2007))



100 Test

Simulation

50

Test

Simulation

Angular Velocity (degree/s)

Lateral Acceleration (g)

Vertical Acceleration (g)

0

-50

-100

-150

-200

0.0 0.2 0.4 0.6 0.8 1.0

Time (s)


16

14

12

10

8

6

4

2

0

-2

-4

1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0

Time (s)


6

4

2

0

-2

-4

Test

Simulation

1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (s)


Fig. 18.18 (A–D) Simulation of a corkscrew rollover with comparison of model prediction with experimental data (taken from Hu (2007))


A

80

Head Lateral Acceleration (g)

60

40

20

0

-20

Test

Simulation

0.3 0.4 0.5 0.6 0.7 0.8

Time (s)

B

Head Vertical Acceleration (g)

25

20

15

10

5

0

-5

Test

Simulation

-10

0.3 0.4 0.5 0.6 0.7 0.8

Time (s)

Fig. 18.19 Comparison of measured and predicted dummy head accelerations in an SAE J2114

dolly rollover test for the near-side occupant. (A) Lateral acceleration. (B) Vertical acceleration


Fig. 18.20 Comparison of head impact location and timing in an SAE J2114 dolly rollover test for

the near-side occupant (taken from Hu (2007))

A

Vertical Head Acceleration (g)

20

Test

Simulation

15

10

5

0

-5

-10

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Time (s)

B

Axial Neck Force (N)

4000

3000

2000

1000

0

-1000

0.3 0.4 0.5

Test

Simulation

0.6 0.7 0.8 0.9 1.0

Time (s)

Fig. 18.21 Comparison of measured and predicted dummy data in an SAE J2114 dolly rollover

test for the far-side occupant. (A) Vertical head acceleration. (B) Axial neck force (taken from Hu

(2007))


Fig. 18.22 Comparison of head impact location and timing in an SAE J2114 dolly rollover test for

the far-side occupant (taken from Hu (2007))

A

B

Head Lateral Acceleration (g)

60

50

40

30

20

10

0

-10

Test

Simulation


15

10

5

0

-5

-10

-15

Test

Simulation

-20 -20

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Time (s)

Time (s)

Fig. 18.23 Comparison of measured and predicted dummy head accelerations in a curb-trip

rollover test for the near-side occupant. (A) Lateral acceleration. (B) Vertical acceleration


Fig. 18.24 Comparison of head impact location and timing in a curb-trip rollover test for the nearside

occupant (taken from Hu (2007))


A


80 Test

Simulation

12000

60

10000

40

20

0

-20

B

Axial Neck Force (N)

8000

6000

4000

2000

0

Test

Simulation

-40

0.0 0.2 0.4 0.6

Time (s)

-2000

0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Time (s)

Fig. 18.25 Comparison of measured and predicted dummy data in a curb-trip rollover test for the

far-side occupant. (A) Vertical head acceleration. (B) Axial neck force (taken from Hu (2007))

Fig. 18.26 Comparison of head impact location and timing in a curb trip rollover test for the

far-side occupant (taken from Hu (2007))


18.1. The provision of airbags in automobiles is a method of injury control. It is

[] (i) A form of environmental control

[] (ii) A form of behavioral control

[] (iii) A form of benevolent dictatorship

[] (iv) A violation of our human rights

[] (v) A Big Brother approach which is inconsistent with personal freedom

18.2. The use of the lap-shoulder belt as an occupant restraint has been shown to

be

[] (i) Marginally effective in reducing fatalities and injury severity

[] (ii) Quite effective in reducing fatalities and injury severity

[] (iii) Not effective in reducing fatalities and injury severity


[] (iv) A cause for many serious injuries due to “side effects”

[] (v) Hazardous to occupants who are tall and heavy

18.3. A driver who is properly restrained by a lap-shoulder belt is involved in an

offset frontal crash. Assuming that the driver is not out of position,

[] (i) He/she will sustain a moderate/severe head injury if the car is

equipped with a driver side airbag

[] (ii) He/she will not sustain a vertebral fracture, even if he/she is elderly

and osteoporotic

[] (iii) He/she will not impact his/her knees against the instrument panel,

regardless of his/her height

[] (iv) He/she will not sustain any foot and ankle injuries, even if there is

footwell intrusion


18.4. Unrestrained occupants involved in a full frontal crash are likely to sustain

[] (i) Severe brain injuries

[] (ii) Severe internal chest injuries

[] (iii) Severe abdominal injuries

[] (iv) Severe lower extremity injuries


18.5. To provide optimal protection for the occupant of an automobile, the

designer should ensure that

[] (i) Both belt and airbag restraints are provided

[] (ii) Compartment integrity be preserved to the maximum extent

possible

[] (iii) Instrument panels be padded with a very soft restraint


[] (v) (i), (ii), and (iii)

18.6. The effect of airbag noise on human hearing

[] (i) Has never been studied

[] (ii) Has been studied and found to have a permanent effect on human

hearing

[] (iii) been studied and found to have a temporary effect on human

hearing

[] (iv) Has been studied and found to have no effect on human hearing

[] (v) Has been studied and found to cause deafness in humans

18.7. A suitable human surrogate for the testing of the effects of noise on hearing

is the cat. In order to conduct a test on cats, it is necessary to

[] (i) Obtain a pre-exposure audiogram to determine its hearing threshold

[] (ii) Obtain a pre-exposure electrocardiogram to determine its ability to

withstand the shock


[] (iii) Obtain several post-exposure audiograms to determine any shift in

its hearing threshold



18.8. Chance fractures occur in lap-belted occupants seated in the rear of an

automobile because

[] (i) The lap belt angle with respect to the horizontal is usually over 45

[] (ii) The lap belt is usually worn properly, at or below the anterior

superior iliac spine

[] (iii) The lap belt slides over the pelvis and becomes a fulcrum for the

lumbar spine to flex over it

[] (iv) The lap belt load is high enough to cause separation of the sacroiliac

joint

[] (v) The lap belt is not wide enough to prevent submarining

18.9. For side impact protection,

[] (i) Side door padding need to have a crush strength in excess of 19 psi

[] (ii) Side torso airbags need to have an initial stiffness of no greater than

10 psi

[] (iii) A four-inch air space between the side door and the torso of the

occupant is more than adequate

[] (iv) Use the cheapest type of Styrofoam for side door padding

[] (v) It is more than adequate if the requirements of FMVSS 214 are met

18.10. The best way to design a headrest which can minimize whiplash-induced

injuries is to:

[] (i) Use a dummy with a seven-segment cervical spine

[] (ii) Design a headrest which can mechanically move forward during

the impact

[] (iii) Place the headrest as close to the head as possible

[] (iv) Make all seat backs rigid so they will not break upon impact


18.11. In rollover crashes, the most frequent cause of death or severe injury is:

[] (i) Severe roof crush

[] (ii) Total or partial ejection from the vehicle

[] (iii) Compression-flexion neck injuries due to head impact with vehicular

interior structures



18.12. To prevent partial ejection of occupants in a rollover, one of the solutions is


[] (i) To change the side window glass to a high penetration resistant

glass used in windshields

[] (ii) To provide a stiff curtain airbag for each side window so that the

head cannot get past the window sill

[] (iii) To eliminate all side windows and sun roofs

[] (iv) To have only one seat in the center of each row of seats so that no

belted occupant can reach out past the window sill

[] (v) To lower the center of mass of the car so that it cannot rollover

18.13. The neck is frequently injured in rollover crashes. The most frequent injury

is cervical vertebral fracture without cord injury. The reason why this is a

frequent injury is

[] (i) There is a lot of whipping of the neck in a rollover crash

[] (ii) Roof crush causes neck compression

[] (iii) The occupant dives towards the roof rail causing the head to impact

the roof rail

[] (iv) The occupant’s head hits the roof when the vehicle is upside down


18.14. The rollover model by Hu (2007)

[] (i) modeled both the vehicle and the occupant

[] (ii) used a MADYMO model for the occupant and a finite element

model for the vehicle

[] (iii) was validated against static roof crush data

[] (iv) can only be used to simulate either the driver or the right front

passenger


18.15. There are several types of rollovers. They are difficult to reproduce experimentally

because

[] (i) vehicular motion is complex and random

[] (ii) rollovers have different initiation mechanisms

[] (iii) can involve multiple rolls

[] (iv) the vehicle undergoes multi-directional linear and angular

accelerations



Prob

Ans

1 (i)

2 (ii)

3 (v)

4 (v)

(continued)

References 627

Prob

Ans

5 (iv)

6 (iii)

7 (v)

8 (iii)

9 (ii)

10 (iii)

11 (v)

12 (ii)

13 (iii)

14 (v)

15 (v)

References

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Chapter 19

Biomechanics of Sports Injuries

19.1 Overview of Sports Injuries

Sports-related injuries are rarely fatal but are very common. They are more

common in contact sports, such as American football, but are also seen in

non-contact sports, such as basketball and baseball. The knee is the most commonly

injured body region in sports because the joint is not well protected by bony

structures and is heavily used. However, catastrophic injuries can occur due to

impacts to the head, neck, and chest. Examples of such injuries include fatal heart

injuries in baseball, head injuries in football (soccer), baseball and basketball and

knee injuries in jogging and tennis. The topics covered in this chapter are mild

traumatic brain injury in American football, catastrophic neck injuries due to crown

impacts, cardiac injuries due to sternal impacts, and knee injuries due to a lateral

impact.

19.2 Mild Traumatic Brain Injury in American Football

19.2.1 What is Mild Traumatic Brain Injury?

With improved helmet design for football players, fatal or catastrophic brain

injuries continue to occur but are relatively rare. Head injury related fatalities

averaged over 12 per year in the three decades from 1945 to 1974. In the last

decade (2005–2014) they averaged three per year (Kucera et al. 2015). However,

there are many more head injuries, especially mild traumatic brain injury (mTBI).

Each year, an estimated 1.365 million visits to the emergency room with 275,000

hospitalizations are due to TBI resulting from physical activities, including sports.

The estimated number of annual concussions is 1.6–3.8 million (Daneshvar et al.

2011). Most of these injuries are mild, even among amateur and professional



629

630 19 Biomechanics of Sports Injuries

Table 19.1 Scores for Glasgow Coma Scale (based on Teasdale and Jennett (1974))

Scores for Glasgow Coma Scale

Test Response Score

Eye opening test (E)

Spontaneous Open eyes on own E4

Speech Open eyes when asked in a loud voice E3

Pain Open eyes when pinched E2

Pain Does not open eyes E1

Best motor response (M)

Command Follows simple commands M6

Pinch Pulls examiner’s hand away M5

Pinch Pulls body part away M4

Pain Flexes body inappropriately M3

Pain Body becomes rigid in an extended position M2

Pain Has no motor response M1

Verbal response (V)

Speech Correct conversation—Oriented to time and location V5

Speech Seems confused or disoriented V4

Speech Understandable but words make no sense V3

Speech Make unintelligible sounds V2

Speech Makes no noise V1

football players. We define the level of TBI by the use of the Glasgow Coma Scale

(GCS) which uses three sets of responses from the victim—eye opening response,

motor response, and verbal response, to assess the severity of the TBI. These

responses are listed in Table 19.1. The scores for the three tests are summed.

That is the Glasgow Coma Score (GCS) ¼ E + M + V. The maximum score is

15 and that implies no injury. The minimum score is 3 which indicates maximum

injury. The “accepted” classification of mTBI refers to individuals who have a

GCS > 12 on admission, loss of consciousness or post-traumatic amnesia <20 min

and hospitalization <48 h. This definition can include anyone with a history of head

impact. Some clinicians exclude skull fracture and brain stem and cortical contusion

while others include a brief loss of consciousness (less than 20 min but not

zero). A GCS of 15 is excluded as well. There are variations to this definition, such

as those proposed by the Mild Traumatic Brain Injury Committee of the Head

Injury Interdisciplinary Special Interest Group of the American Congress of Rehabilitation

Medicine (MTBIC 1993) or the US Army classification of blast-induced

TBI by Ling et al. (2009).

There are many symptoms associated with mTBI. They can occur days to weeks

after head impact and include progressive neuropsychological changes, such as

lethargy, fatigue, irritability, difficulty concentrating, and forgetfulness. These

changes in behavior cause unpleasant situations at home and at work, leading to

divorce and becoming unemployed. However, diagnosis of the severity of mTBI is

difficult because objective clinical evidence is either absent or unable discriminate

19.2 Mild Traumatic Brain Injury in American Football 631

its severity. An accepted method of assessment is neuropsychological testing of the

victim. It consists of a battery of tests to quantify the mental state but the method is

not foolproof. The results can only be compared to the responses of the general

population and there is usually no psychological testing prior to an injury. Additionally,

psychological depression can produce symptoms which mimic mTBI, such

as lack of concentration, loss of memory, and irritability. Individualized baseline

testing is being introduced to football and hockey where concussions are relatively

more frequent. At the beginning of a season, athletes are asked to take a baseline

test which is computerized and assesses the reaction time, memory capacity, and

speed of mental processing as well as executive functioning of the brain. The test

scores are compared to those of a post-concussive test to determine what changes in

mental status have occurred. Details of such tests can be obtained from the Sports

Concussion Institute (www.concussiontreatment.com/baseline-testing.htr). These

tests tend to increase the awareness of concussion for athletes, parents, and coaches.

One possible deficiency is for the athlete to deliberately do poorly in his/her

baseline test so that the score of a post-concussive test will not look as bad and

he/she may be allowed to continue to participate in the game.

19.2.2 The American Football Helmet

The helmet used in American football belongs to a class of helmets designed for

repeated impacts as opposed to crash helmets used by racecar drivers and motorcyclists

for protection against a single heavier impact. The basic difference between

the two types is the lining under the shell. Sports or repetitive use helmets have an

energy absorbing liner that deforms during impact but quickly returns to its original

shape while the liner in crash helmets is crushed and permanently deformed to

absorb more energy than helmets used in sports. Newman (2002) detailed the

evolution of helmets and described the original football helmet as a soft leather

hat, some of which were lightly padded. The molded plastic shell was introduced in

1939 by Riddell which also invented the suspension helmet that used an ingenious

arrangement of straps to keep the shell separated from the head. This type of helmet

was first used by the NFL in 1949. The suspension helmet was gradually replaced

by a liner made of closed cell rubberlike foam which was able to absorb more

energy. Ventilation holes were provided to keep the head from getting too hot while

wearing the helmet. The original design and helmet standard was based on this

design which did not cause a skull fracture in a test of six different helmets (Snively

1957). The idea of using the helmet to prevent concussion had not surfaced at that

time and when we now complain that concussions continue to occur in football, the

reason given is that the design and standard for football helmets were to prevent

skull fractures and not concussions. The search of more efficient energy absorbing

materials continues in an effort to improve the liner but, for severe impacts, it is

uncertain whether it is possible to avoid a concussion if the amount of space

available for the liner remains the same (Newman 2015). It is undesirable to


make the helmet any larger than it is now for several reasons, such as more

opportunities for helmet-to-helmet contact and higher rotational acceleration during

contact because of its larger radius.

19.3 Acute Subdural Hematoma (ASDH)

The most likely cause of ASDH was discussed in Sect. 3.4 of Chap. 3. One of the

hypotheses states that the formation of ASDH is due to the rupture of cortical

arteries in the subdural space and that this rupture is due to the in-bending of the

skull from head impact and due to its rebound after the impact. However, for a

helmeted head, local skull in-bending is not likely to occur and the hypothesis is

apparently unable to explain the formation of ASDH for a helmet-to-helmet or a

helmet to ground impact. If we study the epidemiology of ASDH among football

players we find that ASDH occurs most frequently in teenager (below the age of 18)

football players and we recall that in young skulls, the bones of the skull are not

fully fused, allowing them move more freely with respect to the brain. Thus, it is

hypothesized that an impact to the helmet of sufficient magnitude can result in

deformation of the immature skull and create enough tension in the subdural space

to rupture a cortical artery. Although this is a hypothesized injury mechanism, it is

at least more logical than the bridging vein rupture theory which is hydrodynamically

untenable. Research is needed to demonstrate the validity of this hypothesis

which can be the topic of a PhD dissertation or for a grant application.

19.4 Sports-Related Catastrophic Neck Injuries

Catastrophic neck injuries which have the potential of causing quadriplegia are seen

in many sporting activities (Langer et al. 2008). In addition to football (Thomas

et al. 1999), catastrophic neck injuries occur in ice hockey (Tator et al. 1998), rugby

(Quarrie et al. 2002), snowboarding (Levy and Smith 2000), skiing (Tarazi et al.

1999), and diving (Schmitt and Gerner 2001). Such occurrences are rare compared

to the number of athletes participating in the sport. Over 1.5 million athletes

participate in football from high school to the professional level. From 1971 to

1975, the National Football Head and Neck Injury Registry compiled 259 cervical

fracture/dislocations and 99 cases of quadriplegia (Torg et al. 1979). The injury

occurs when the head and helmet are used to tackle an opposing player. This is

known as spearing which was outlawed in 1976 by the National Collegiate Athletic

Association (NCAA) Football Rules Committee and the high school football

governing bodies. This led to a 70 % drop in the rate of cervical injuries in high

school athletes (Torg et al. 1990). The football helmet protects the head but it also

gives the player a false sense of security leading to him tackle with his head. There

have been attempts to insert a support between the helmet and the shoulder to

19.5 Fatal Arrhythmias in Baseball Impacts 633

protect the neck but the shoulder is not rigid enough to prevent a neck injury. The

mechanism of these catastrophic neck injuries is forward flexion of the neck

coupled with neck compression from the helmet impact, exacerbated by the forward

momentum of the following torso. Details of this flexion-compression injury were

explained in Sect. 7.2 of Chap. 7. Pre-flexing the neck prior to load application is a

key reason for the injury because in a flexed neck, the vertebral bodies are aligned

to carry compressive load efficiently and when the tolerable load is exceeded or the

load causes the neck to bend, then fracture and/or fracture dislocation is the result.

If there is a burst fracture, the fragments of the posterior vertebral body are

propelled rearward, impacting the dura of the spinal cord and causing neurological

dysfunction. In a fracture/dislocation, there is subluxation of the superior vertebral

body over the one below it. The anterior lip of the lower vertebra is chipped off

and the spinal canal space is compromised by the presence of the posterior

structures the upper vertebra. Again, the result is neurological dysfunction, including

quadriplegia.

19.5 Fatal Arrhythmias in Baseball Impacts

Baseball is a non-contact sport and is a relatively safe sport compared to basketball,

in terms of game-related injuries. For the millions of children between the ages of

5 and 14 who play this game, they suffer over 100,000 acute injuries each year. In

terms of fatalities, 3 or 4 of these children die each year from ball impact, based on

data collected by the Consumer Protection Safety Commission (CPSC), an agency

of the Federal Government. From 1973 to 1995, the CPSC recorded 68 ball-impact

related deaths (Mueller et al. 2001). The deaths were due to an impact of the ball to

the chest which resulted in an irreversible disruption of the regular heart rhythm as

the ventricles went into fibrillation or standstill. Even with on-the-spot CPR,

virtually no one survives this impact. This arrhythmic phenomenon is known as

commotio cordis but the exact cause of this injury has not been established. The

problem is worth studying in greater detail because it has applications in other areas

of injury control. There is anecdotal evidence that high-speed slap injuries from a

deploying airbag can produce the same result and the subject is of interest to

researchers in the automotive industry. Similarly, blunt impact to the chest by

non-lethal weapons (rubber bullets) can also result in commotio cordis (Cooper

et al. 1982).

A study was conducted at Wayne State University to analyze 24 cases of sportsrelated

fatalities that occurred between 1973 and 1983 (Viano et al. 1992). Twentythree

of the victims were playing baseball and 22 of them were children between the

ages of 5 and 14. The 23 victims were struck in the chest by a baseball. There was a

single case of a lacrosse a fatality.

The positions played by the victims were as follows:


Pitcher hit by batted ball 8

Batter hit by pitch 6

Batter running bases 3

Catcher 2

Goalie (Lacrosse) 1

Spectator 2

Unknown 2

Total 24

Autopsies were conducted in 19 cases. One abnormal heart condition was found

but no other injuries were apparent. In 14 cases, immediate CPR was administered

without success. It was concluded that the deaths were due to cardiac arrhythmia

(commotio cordis). A team of experts was assembled to discuss the possible

mechanism of commotio cordis. The following possible causes of death were

suggested:

Disruption of the electrical conduction system of the heart leading to lethal cardiac

arrhythmia, such as ventricular fibrillation or ventricular standstill

Vagal stimulation causing syncope and heart failure

Loss of conductivity of the pre-cordial conducting system

Ventricular tachycardia due to reentry, leading to ventricular fibrillation. Reentry is

a phenomenon in which the propagating impulse continues to stimulate the heart

after normal activation. It is one mechanism that re-excites the heart repeatedly,

causing fibrillation.

So far, there has been no known research to ascertain which of these mechanisms

could be the cause or causes of impact-related ventricular fibrillation. However, the

work of Cooper et al. (1982) and of Kroell et al. (1986) demonstrated that acute

ventricular fibrillation does occur in chest impact, especially when the impact is

timed to occur at the time of the T-wave in the EKG cycle which is shown in

Fig. 11.6. The T-wave occurs at the end of an electrical cardiac cycle and represents

a period of repolarization for the cardiac muscle cells after they have “fired.”

Cooper et al. (1982) provided an example of an acute ventricular fibrillation in a

59-kg pig that was struck with the end of a rubber bullet which was a plastic (PVC)

cylinder, 3.7 cm in diameter, 10 cm in length, and weighing 0.14 kg. The dramatic

change in EKG is shown in Fig. 19.1. The measured chest wall displacement was

5.7 cm or the chest compression (C) was 19.4 %. There was a non-displaced sternal

fracture but no cardiac rupture and the measured peak ventricular pressure was

Fig. 19.1 Acute ventricular fibrillation in a pig due to a non-penetrating impact by a rubber bullet

travelling at an estimated speed 50 m/s and striking the sternum which was fractured (taken from

Cooper et al. (1982))

19.5 Fatal Arrhythmias in Baseball Impacts 635

17 kPa (2.5 psi). Cooper et al. (1982) did a total of 47 tests with three different

impactors at speeds ranging from 20 to 74 m/s. The pigs sustained cardiac (ventricular

and atrial) ruptures, cardiac contusions, ventricular tachycardia and fibrillation.

The fibrillation can occur subsequent to an episode of tachycardia, due to a

rupture or acutely immediately after the impact. The acute form of fibrillation is the

most serious because it usually does not recover normal rhythm (See Fig. 19.1).

This usually occurs when the heart is struck at the time of the T-wave in the EKG

cycle which apparently is a vulnerable period for ventricular fibrillation. Kroell

et al. (1986) studied cardiac impact as part of their research on chest protection in

frontal impacts. They used a much larger impactor (4.9 kg, 150 mm in diameter)

and a higher impact speed of up to 30 m/s. The animal model was the male domestic

swine weighing approximately 55 kg. The tests were conducted with the animal

suspended horizontally in a net and the sternum was impacted from below, as

shown in Fig. 19.2. The main purpose of the study was to show that both chest wall

velocity and deflection played a role in injury severity in frontal impact and that the

Viscous Criterion was valid. The experiments yielded injury results which included

severe injuries to the heart, including cardiac rupture, cardiac contusion, and

ventricular fibrillation. Out of the 23 specimens tested, 11 experienced ventricular

fibrillation, and out of those eight were acute. In five of the eight cases, the impact

occurred during the T-wave interval of the EKG. None of the eight survived. More

recently at the Tufts Medical School, Link et al. (1998) repeated the swine tests by

impacting them in the chest with a wooden baseball at 30 mph (48 km/h), first to

establish the vulnerable period for fibrillation and then to quantify this period. It

was found that when an impact occurred in a 15-ms interval, just before the peak of

the T-wave, during cardiac repolarization, acute ventricular fibrillation was consistently

produced. The effect of impactor size was studied by the same group at Tufts.

Kalin et al. (2011) impacted swine with two wooden spheres and a flat wooden

cylinder. The spheres were 42 mm (1.65 in.) and 72 mm (2.83 in.) in diameter, the

latter being of the same size as a baseball. The flat round surface also had a diameter

of 72 mm. A series of nine impacts was conducted on each of the 16 swine tested,

using the three impactors. The impact was timed to hit the chest in the vulnerable

period (21.1 6.9 ms before T-wave peak). The small sphere caused the highest

number of fibrillations (9/48) while the flat object was not able to cause any.

The reported research so far brings up more questions than answers. Is commotio

cordis due to a contusion injury to the heart or a disruption of the electrical

conduction system in the heart? Is the vulnerability period in advance of the

T-wave an indication of a problem with conductivity? Why is a smaller sphere

able to cause more fibrillations than a larger sphere? These questions need to be

answered if effective methods of prevention can be implemented. Link et al. (2008)

commented on the failure of chest protectors to prevent acute fibrillation in baseball

and lacrosse and recommended continued efforts to find an effective chest protector.

However, if commotio cordis is due to a disruption of the electrical conduction

system of the heart, caused by the shock of the impact, then a whole new line of

research needs to be followed. Clues that the problem may be electrical can be

deduced from the T-wave vulnerability and from the fact that the heart is more


Dorsal

Posterior

Floor Level

Bushing

Ventral

215 kN Steel

Invertube

Anterior

150 mm Dia Striker Plate

4.9 kg Striker Mass

To Anesthesia

Machine

Preset Striker Displacement

from Animal Contact to

Invertube Contact

Frame

Bushing

64.7 kN Aluminum

Invertube

Pneumatic Accelerator

(See Ref. [4])

Lower Chamber

Fig. 19.2 Experimental set-up used by Kroell et al. (1986) to study porcine thoracic response and

injury, including cardiac injuries

vulnerable to the impact of a smaller sphere which produces a more intense pressure

wave. This situation may be analogous to the mTBI caused by blast overpressure.

That is, pressure waves can cause injury to the nerve tissue. Research into better

methods of resuscitation is also needed.

19.6 Ligament Injuries in Football 637

19.6 Ligament Injuries in Football

As mentioned at the beginning of this chapter, the knee is the most frequently

injured joint in sports. A brief review of its anatomy is perhaps helpful, especially

its ligamentous anatomy. Functionally, the four ligaments along with the knee

capsules are the structures that hold the tibia to the femur. Figure 19.3 is a cutaway

view of the posterior of the left knee in which all four ligaments are shown. At the

center of the joint are two ligaments that form a cross, hence the name cruciate

ligaments. The anterior cruciate ligament (ACL) prevents the tibia from moving

anteriorly with respect to the femur while the posterior cruciate prevents the tibia

from moving posteriorly with respect to the femur. There is much interest in the

ACL which is more frequently injured than the PCL (see Chap. 14, Sect. 14.2.2 for

an automotive related PCL injury). Anatomically, the ACL originates on the

posterior medial surface of the lateral condyle of the femur and inserts into the

anterior aspect of the tibial plateau, as shown in Fig. 19.4 (Mall et al. 2013). It is

made up of two bundles, the anterior medial (AM) and the posterior lateral

(PL) bundle. The two bundles are functionally distinct. The PL bundle is taut

when the knee is extended and the AM bundle is lax. The reverse is true when

the knee is flexed. Thus, there is a length change with flexion and extension in both

Fig. 19.3 Posterior view of the left knee. The medial (or tibial) collateral ligament is subjected to

tensile loading when the knee is impacted laterally on its lateral aspect (taken from Gray (1973))


Fig. 19.4 (A) Proximal insertion locations of the ACL. (B) Distal insertion locations of the ACL.

PL is the posterior lateral bundle and AM is the anterior medial bundle (taken from Mall et al.

(2013)). Reprinted from N.A. Mall, A.S. Lee, B.J. Cole, N.N. Verma, The functional and surgical

anatomy of the anterior cruciate ligament. Operative Techniques in Sports Medicine 21(1), 2–9,


bundles. Injury to the ACL can occur without anything contacting the knee. A receiver

in football can be running down the field, stops and turns to catch the ball. In the

process, the PM bundle of the ACL in the extended knee can rupture. Similarly, if

the bindings on a ski are on too tightly and the ski slows down or stops when it

encounters a bare spot, the knee goes into extension and the ACL can rupture. A

significantly higher rate of ACL rupture among female athletes engaged in basketball

and soccer, compared to male athletes, has been reported (Arendt et al. 1999). The

exact causes have not been identified but they are likely to be multifactorial.


When the knee is hit laterally the medial collateral ligament (MCL) as well as

the ACL is at risk of being ruptured. This is caused by clipping in American football

which is forbidden by the rules. It can also occur in soccer in a slide tackle in which

a player slides alongside an opposing player to try to wrestle the ball away from

his/her opponent. Since the femoral condyles are not constrained laterally by bony

structures, an impact to the lateral aspect of the knee causes it to bend medially,

placing the MCL in tension. The ideal way to prevent this injury is to use a knee

brace which can prevent knee valgus (knock-knee). However, a reinforcing band on

the medial aspect of the knee can interfere with running and the next best thing is to

place the band on the lateral aspect of the knee where its effectiveness as an MCL

protector is greatly diminished. The brace also needs to be worn tightly but that is

difficult because the thigh is tapered and the brace tends to slip down and become

ineffective. In fact, the issue became a quandary for the orthopedist or sports

medicine physician who gets blamed whether he/she recommends the use of the

brace or not. The American Academy of Orthopedic Surgeons has taken the

position of not making any recommendations on knee bracing for athletes (AAOS

Document #1124, retired 2008).

In terms of research, McDavid, Inc., a knee brace manufacturer, sponsored a

project to study MCL strain during a lateral impact with the knee protected by a

knee brace. The brace had the protective band on the outside. The purpose of the

study (Begeman et al. 1987) was to determine the strain in the MCL while it was

protected by the laterally reinforced brace. Since the medial aspect of the knee was

not covered by the brace, it was possible to expose the MCL and observe how it

stretched during an impact to the lateral aspect of the knee. The MCL was painted

dark green to remove glare and five to six white targets were painted on the anterior

and posterior borders of the ligament. A total of eight cadaveric knees were used,

ranging in age from 17 to 75. The legs were preloaded to 863 N (194 lb) through the

femur to simulate the body weight of an average football player and a padded

impactor, 20.3 cm (8 in.) in diameter and weighing 74 kg (163 lb) was used to

simulate the padded shoulder of a tackler. In an impact, the entire body weight of

the tackling player is not thrown up against the knee. The speed of impact ranged

from 1.5 to 2.7 m/s. The experimental set-up is shown in Fig. 19.5 and a close-up of

the MCL is shown in Fig. 19.6. In the first test the MCL was partially torn (avulsed)

but in all subsequent tests it was completely torn, four at the tibial attachment and

three at the femoral attachment. A high-speed camera was used to record the motion

of the targets and a mercury strain gage spanning the entire length of the MCL was

used to measure its overall strain. A foil-type strain gage was placed on the cortical

bone of the femur near the proximal insertion point of the MCL to monitor the force

developed in the MCL The strain gage was calibrated after the experiment by

applying a static tensile load to the MCL so that the measured strain could be

translated to ligament load. This load was measured in four of the eight specimens

tested. However, strain in the MCL was measured in all eight tests. The strain data

(in percent strain) for the distal, middle, and proximal MCL along both the anterior

and posterior borders are shown in Table 19.2. The failure loads, strain rate, and

stiffness are shown in Table 19.3 for the four tests in which the loads could be


Fig. 19.5 A braced

cadaveric knee ready for a

lateral impact (taken from

Begeman et al. (1987))

recovered. The overall strain rates and loading rates for the specimens tested are

shown in Table 19.4. For the four tests for which load data were available, it was

possible to plot the force-deflection curves and compare them with quasi-static data

obtained by Kennedy et al. (1976). These curves are shown in Fig. 19.7. They

appear to represent the response of a viscoelastic material that is stiffer when loaded

dynamically. However, if the stress-strain curves are plotted, the viscoelastic effect

disappears, as shown in Fig. 19.8. There are a couple of reasons for this phenomenon.

First, when the knee is bent laterally, the femoral condyle compresses the

knee cartilage which is strain rate sensitive. Therefore, the force-deflection curve of

the MCL reflects this viscoelastic effect. However, the stress-strain curve of is

independent of force and deflection and the data show that at high strain rates, the

MCL is not strain rate sensitive. The reported strain rates are higher than what was

generally available in the literature at the time the work was done. Subsequently,

Crisco et al. (2002) confirmed the loss of strain rate sensitivity in the MCL at

traumatic rates of loading as did Koh et al. (2004) for shoulder ligaments.


Fig. 19.6 Medial aspect of

a braced knee, showing the

MCL which was stained

dark green and targeted with

two rows of white targets,

one along the anterior

aspect and the other along

the posterior aspect of

the MCL (based on

Begeman et al. (1987))

Table 19.2 MCL strains due to lateral impact (values in percent strain) (taken from Begeman et

al. (1987))

Test No. 01 No. 02 No. 03 No. 04 No. 05 No. 06 No. 07 No. 08

Section/ A P A P A P A P A P A P A P A P

Side

Distal 8 7 3 8 3 8 13 8 10 14 11 10 8 11 11 6

Middle 10 1 6 9 4 5 10 13 12 7 11 10 18 12 4 7

Proximal 21 13 9 8 13 6 13 11 12 14 NA 16 17 8 19 1

Overall 12 11 12 8 10 8 11 11 11 11 12 11 15 12 9 5

A Anterior border of the MCL, P Posterior border of the MCL

Table 19.3 MCL failure loads, strain rate and stiffness (taken from Begeman et al. (1987))

Test

no.

Load

(N)

Strain rate (%/s) Strain rate (%/s) Stiffness (N/mm) Stiffness (N/mm)

Anterior Posterior Anterior Posterior

1 2200 300 220 404 375

2 2060 375 200 307 343

3 1050 333 267 164 204

7 2060 652 400 445 480


Table 19.4 Overall strain rate and loading rate for the MCL tests conducted (based on Begeman

et al. (1987))

Test # 1 2 3 4 5 6 7 8

Strain rate (%/s) 260 288 300 367 220 171 566 371

Loading rate (mm/s) 136 170 150 172 100 52 135 82

Fig. 19.7 Dynamic and static response of the MCL in terms of force-deflection. The static data

were obtained from Kennedy et al. (1976) (based on Begeman et al. (1987))

Fig. 19.8 Dynamic and static response of the MCL in terms of stress-strain. The static data were

obtained from Kennedy et al. (1976) (based on Begeman et al. (1987))



Impact injuries are not limited to those sustained in automotive crashes. Sportsrelated

injuries are an example of how biomechanics can be applied to understand

and mitigates them. There are other forms of impact injury, such as those sustained

in falls and assaults, but prevention of such injuries is more difficult.

In sports, the avoidance of catastrophic injuries and those with long-term

sequelae is the first priority. These include spinal cord related neck injuries,

commotio cordis, and brain injuries. More research is needed in neck protection

which is both effective and non-obstructive to the athlete. It is difficult protect the

neck and at the same time allow it to have its natural range of motion. As for

commotio cordis, the research thus far may have been misdirected towards a search

for an effective chest protector. Here again, the old adage is applicable: You cannot

prevent an injury if you do not know its cause. It is recommended that research be

directed towards the effect of impact (or a pressure wave) on the electrical conduction

system of the heart. It goes without saying that football needs a better helmet,

one designed to prevent concussion rather than skull fracture. Whether a good

energy absorbing material can be found and made to fit in the limited space between

the head and the helmet remains to be seen.

It is also interesting to note that biological soft tissue exhibits a viscoelastic

response when deformed slowly but become insensitive to strain rate at high rates

of loading. Material science research may be able to explain the reason for this

change in response.


19.1. In sports, the athlete can sustain a variety of injuries. Select the statement

that is not true:

[] (i) Athletes in contact sports are more at risk for injury than those in

non-contact sports

[] (ii) Non-contact sports athletes can also sustain serious injuries

[] (iii) In American football, mild traumatic brain injury is quite common

[] (iv) Baseball is a safe sport because it is a non-contact sport

[] (v) The knee is the most frequently injured body part in sports

19.2. Mild traumatic brain injury is defined:

[] (i) By a Glasgow Coma Score of 12 or higher

[] (ii) By a period of unconsciousness not exceeding 20 min

[] (iii) Hospitalization of less than 48 h




19.3. Assessment of the severity of mild traumatic brain injury is done by

[] (i) Putting the patient through a battery of neuropsychological tests

[] (ii) Assessing eye-hand coordination if pre-injury test results are

available

[] (iii) Determining how irritable the patient is when confronted with an

unpleasant situation


[] (v) (i) and (ii)

19.4. The claim of a mild traumatic brain injury is difficult to refute because:

[] (i) The patient can easily fake memory loss and irritability

[] (ii) Symptoms of clinical depression are similar to those of a mild

traumatic brain injury

[] (iii) There is no quantitative method of measuring loss of cognitive

function

[] (iv) The patient can conveniently claim he/she does not recall the head

impact, thus demonstrating post-traumatic amnesia


19.5. A properly validated brain injury model can be used to aid in the assessment

of the severity of a mild traumatic brain injury

[] (i) It can be used to compute brain strain throughout the brain for an

event of known impact severity

[] (ii) Maximum strain levels can be associated with impact severity, such

as linear and angular acceleration

[] (iii) Maximum strain levels can be associated with clinical observations

of symptoms of mild traumatic brain injury

[] (iv) (i), (ii), and (iii)


19.6. Disabling neck injuries occur in several forms of sports. In American

football, horseback riding, and cycling, the predominant form of neck injury

resulting in paralysis is:

[] (i) Tension-extension

[] (ii) Compression-extension

[] (iii) Tension-flexion

[] (iv) Compression-flexion

[] (v) Axial rotation and lateral bending

19.7. Impacts to the chest by a high-speed projectile, such as a pitched or batted

ball, can cause a fatal arrhythmia of the heart:

[] (i) This is due to disruption of the conduction system in the heart

[] (ii) This happens when the impact occurs just before the p-wave of the

EKG cycle


[] (iii) This cannot happen to adults

[] (iv) This can be prevented by a catcher’s vest

[] (v) The cause of the arrhythmia is well known

19.8. Impacts to the lateral aspect of the knee, while the leg is weight bearing, can

result in:

[] (i) Fracture of the patella

[] (ii) Rupture of the posterior cruciate ligament

[] (iii) Rupture of the medial collateral ligament

[] (iv) Rupture of the lateral collateral ligament

[] (v) Fracture of the tibia

19.9. Testing of the medial collateral ligament under impact conditions revealed

that:

[] (i) Its failure load ranged from 1000 to 2200 N

[] (ii) The strain rates ranged from 170 to 370 %/second

[] (iii) The load-deflection curves were rate dependent

[] (iv) The stress-strain curves were not rate dependent


19.10. When the chest is impacted by blunt high-speed objects, such as a baseball,

[] (i) the heart can go into atrial fibrillation

[] (ii) the blood pressure can rise rapidly

[] (iii) the heart can go into ventricular fibrillation

[] (iv) one of more chambers of the heart can be ruptured

[] (v) the EKG remains normal


Prob

Ans

1 (iv)

2 (iii)

3 (v)

4 (v)

5 (iv)

6 (iv)

7 (i)

8 (iii)

9 (v)

10 (iii)


References

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women. J. Athl. Train. 34(2), 86–92 (1999)

P.C. Begeman, The effect of the McDavid knee guard on knee injuries in lateral impact at the knee

joint. McDavid Report, (1986)

P.C. Begeman, J. Kopacz, W.N. Hardy, R.S. Levine, A.I. King, Strains and forces in the human

medial collateral ligament during lateral impacts, in 1987 ASME Applied Mechanics

Bioengineering, and Fluids Engineering Conference, vol 84, ASME, AMD, New York, 1987,

pp. 233–236

G. Cooper, B. Pearce, M. Stainer, R. Maynard, The biomechanical response of the thorax to

nonpenetrating impact with particular reference to cardiac injuries. J. Trauma Acute Care Surg.

22(12), 994–1008 (1982)

J.J. Crisco, D.C. Moore, R.D. McGovern, Strain-rate sensitivity of the rabbit MCL diminishes at

traumatic loading rates. J. Biomech. 35(10), 1379–1385 (2002)

D.H. Daneshvar, C.J. Nowinski, A.C. McKee, R.C. Cantu, The epidemiology of sport-related

concussion. Clin. Sports Med. 30(1), 1–17 (2011)


Philadelphia, 1973)

J. Kalin, C. Madias, A.A. Alsheikh-Ali, M.S. Link, Reduced diameter spheres increases the risk of

chest blow-induced ventricular fibrillation (commotio cordis). Heart Rhythm 8(10),

1578–1581 (2011)

J. Kennedy, R. Hawkins, R. Willis, K. Danylchuck, Tension studies of human knee ligaments.

Yield point, ultimate failure, and disruption of the cruciate and tibial collateral ligaments.

J. Bone Joint Surg. Am. 58(3), 350–355 (1976)

S.W. Koh, J.M. Cavanaugh, J.P. Leach, S.W. Rouhana, Mechanical properties of the shoulder

ligaments under dynamic loading. Stapp Car Crash J. 48, 125–153 (2004)

C.K. Kroell, T.R. Perl, C.Y. Warner, S.D. Allen, Inter-relationship of velocity and chest compression

in blunt thoracic impact to swine II, in Proccedings of the 30th Stapp Car Crash

Conference, San Diego, CA, 1986

K. Kucera, D. Klossner, B. Colgate, R. Cantu, for American Football Coaches Association,

NCAA, National Federation of State High School Associations, National Athletic Trainers’

Association, Annual Survey of Football Injury Research: 1931–2013 (American Football

Coaches Association, National Collegiate Athletic Association, National Federation of State

High School Association, National Athletic Trainers’ Assocation, Chapel Hill, NC, 2015)

P.R. Langer, P.D. Fadale, M.A. Palumbo, Catastrophic neck injuries in the collision sport athlete.

Sports Med. Arthrosc. Rev. 16(1), 7–15 (2008)

A.S. Levy, R.H. Smith, Neurologic injuries in skiers and snowboarders. Semin. Neurol. 20(02),

233–246 (2000)

G. Ling, F. Bandak, R. Armonda, G. Grant, J. Ecklund, Explosive blast neurotrauma.

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M.S. Link, P.J. Wang, N.G. Pandian, S. Bharati, J.E. Udelson, M.-Y. Lee, M.A. Vecchiotti,

B.A. VanderBrink, G. Mirra, B.J. Maron, An experimental model of sudden death due to

low-energy chest-wall impact (commotio cordis). N. Engl. J. Med. 338(25), 1805–1811 (1998)

M.S. Link, C. Bir, N. Dau, C. Madias, N.M. Estes, B.J. Maron, Protecting our children from the

consequences of chest blows on the playing field: a time for science over marketing. Pediatrics

122(2), 437–439 (2008)

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cruciate ligament. Oper. Tech. Sports. Med. 21(1), 2–9 (2013)

MTBIC, Definition of mild traumatic brain injury. J. Head Trauma Rehabil. 8(3), 86–87 (1993)

F.O. Mueller, S.W. Marshall, D.P. Kirby, Injuries in little league baseball from 1987 through 1996:

implications for prevention. Phys. Sportsmed. 29(7), 41–48 (2001)

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and prevention, ed. by A.M. Nahum, J.W. Melvin, 2nd edn. (Springer, New York, 2002),

pp. 303–323

J. Newman, Design and testing of sports helmets: biomechanical and practical considerations, in

Accidental injury: Biomechanics and prevention, ed. by N. Yoganandan, A.M. Nahum,

J.W. Melvin, 3rd edn. (Springer, New York, 2015), pp. 755–768

K.L. Quarrie, R.C. Cantu, D.J. Chalmers, Rugby union injuries to the cervical spine and spinal

cord. Sports Med. 32(10), 633–653 (2002)

H. Schmitt, H.J. Gerner, Paralysis from sport and diving accidents. Clin. J. Sport Med. 11(1),

17–22 (2001)

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GA, 1957)

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27(2), 177–180 (1999)

C.H. Tator, J.D. Carson, V.E. Edmonds, Spinal injuries in ice hockey. Clin. Sports Med. 17(1),

183–194 (1998)

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B.E. Thomas, G.M. McCullen, H.A. Yuan, Cervical spine injuries in football players. J. Am. Acad.

Orthop. Surg. 7(5), 338–347 (1999)

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cinematographic analysis of football-induced cervical spine trauma. Am. J. Sports Med. 18(1),

50–57 (1990)

D.C. Viano, D.V. Andrzejak, A.I. King, Fatal chest injury by baseball impact in children: a brief

review. Clin. J. Sport Med. 2(3), 161–165 (1992)

Chapter 20

Epilogue

20.1 We Have Come a Long Way

The human race has been living with accidental injury and death since its beginning.

Injury prevention was a personal issue that was learned through personal

experience or that of elders. Even in the modern-day medical school, injury

prevention is not only not taught but also not considered preventable as other

diseases. The high fatality rate due to automotive collisions in the 1960s prompted

congressional action which finally brought injury prevention to the attention of the

public and attracted researchers in the field of epidemiology to look for preventative

measures. However, researchers in impact biomechanics had been aware of the

need for prevention some two decades earlier. It turns out that preventative methods

using behavioral control are not as effective as those using environmental control.

In automotive safety, behavioral control means driving at a safe speed, responding

to changing road conditions, and not drinking and driving. Automotive environmental

control includes airbags, padded interiors, headrests, and crushable vehicular

structures. Biomechanics played and continues to play a large role in the design

of many components of environmental safety control because the underlying causes

of injury must be properly understood and the design should not have injurious side

effects. The padding used to protect the knees of front seat occupants is a prime

example. Its stiffness and thickness protect the knees but do not cause femoral

fractures.

From an overall point of view, the safety features available in a modern-day

vehicle represent an evolution of over many decades. Over this period, the gradual

improvements made were based on biomechanical research by universities, the

automotive industry and the Federal government. If a 2017 model year vehicle is

compared to a 1957 model year vehicle, vast differences can be found, some of

which are very obvious. The 1957 model does not have three-point belts, is not

equipped with frontal and side airbags, and does not have a headrest or a padded

interior. In fact, the interior has many protruding appurtenances, such as knobs for



649

650 20 Epilogue

tuning the radio and for controlling the headlights, the temperature in the car and the

blower, protruding door handles and window cranks as well as the cigarette lighter.

These were all injury producing objects that have all been replaced by touch buttons

or are now hidden so that they are no longer injurious. Of course, safety comes with

cost and part of the reason for the high price of cars is the built-in safety features.

Less obvious changes involve the crushable design of the vehicular frame and front

and rear ends, strengthened side doors, the collapsible steering column, and the use

of high penetration resistant glass for windshields. Advances have also been made

in active safety. Stability control to prevent rollovers and sensing of an impending

frontal collision are features available in many car models.

There is no question that the automotive industry has come a long way in

improving the safety of the vehicle it produces. The fatality rate has been dropping

since the early part of this century and the fatality rate per 100 million miles

traveled is now very close to 1.0 whereas it was about 5.0 in 1957, as shown in

Fig. 1.1. This is strong evidence that biomechanical research has provided car

designers the necessary information to design safe cars and that the automotive

industry has done an outstanding job in improving vehicular safety. Hopefully this

trend will continue so that the injury and fatality rate can be further reduced.

The use of computer models to predict human response to impact is an almost

indispensable component of impact biomechanics research. Once validated, a

computer model can be used to study a variety of impact scenarios that cannot or

would be difficult and costly to simulate experimentally. An example of such an

impact would be a side impact to a vehicle which then rolls over and does a few

quarter turns. The motion of occupants inside this vehicle would be difficult to track

pencil [psi]

25

20

15

10

5

0

0 0.01 0.02 0.03 0.04 0.05 0.06

time [s]

Fig. 20.1 A typical Friedlander wave

20.2 What is Next for Impact Biomechanics? 651

and the sources of their injuries would be almost impossible to isolate. However, a

computer model would be able to predict all impacts to every body region for each

occupant. This would require finite element modeling of both the vehicle and the

occupants and the computation time required to run the model would not be trivial.

In terms of the human occupant, the development of a global human body model

that has been validated against experimental data is almost complete. It is being

developed under the auspices of the Global Human Body Model Consortium

consisting of automotive companies, universities, and NHTSA.

20.2 What is Next for Impact Biomechanics?

It appears that there is now adequate information available to car designers to

produce a relatively safe car. Research in impact biomechanics is now shifting to

the study of specialized populations or topics. There is current interest in the

response and tolerance of children and the elderly. Although it is almost impossible

to secure cadaveric specimens of children, work is proceeding using whatever

tissue that is made available to the researchers. Since most cadavers are in the

elderly group, it is not difficult to establish response and tolerance levels for the

elderly population. The difficulty is that current response and tolerance data are

taken from the elderly population and there is no clear-cut way to establish the

levels of response and tolerance for the elderly.

A new area of impact biomechanics research is the study of the effects of blast on

foot soldiers and occupants of military vehicles. For the foot soldier, there have

been many reports of mild TBI among those exposed to blast overpressure from

improvised explosive devices (IED). These blasts are of short duration (up to about

10 ms) and the waveform resembles that of the Friedlander wave, shown in

Fig. 20.1. It is basically a shock wave that has very steep front (short rise time)

and decays exponentially. Since the soldier could be knocked down or propelled

some distance by the blast wind that follows the shock wave, it is not always clear

whether the mTBI is due to the blast wave or a subsequent head impact with the

ground or a wall. Gurdjian et al. (1954) showed that the passage of short duration

blast wave from a fluid percussion device produced concussion in dogs. Kallakuri

et al. (2017) performed blast overpressure studies on anesthetized swine and found

injury to both the white matter and gray matter of the swine brain. The mechanism

of injury has not been established and it is important to find the level of human

tolerance so that effective countermeasures can be implemented. For occupants of

military vehicles, an underbody blast accelerates the vehicle vertically upward

imparting large +G z accelerations to both the feet and the pelvis. These occupants

sustain lower extremity injuries as well as pelvic and spinal fractures. Research is

underway to understand the injury mechanisms and to find methods to protect these

occupants.

Modeling of blast related injuries has also been attempted. However, many of

these models are unvalidated. Kalra et al. (in press) have developed a validated

652 20 Epilogue

model of the swine brain subjected to blast overpressure. Although the model tends

to predict an intracranial pressure higher than the incident overpressure, the measured

pressures were consistently lower than the incident pressure. Theoretically,

the intracranial pressure inside the skull should be higher than the incident pressure

because as the pressure wave passes from air into bone (denser medium) the

pressure in the skull is increased and when it passes through the skull into the

brain, the pressure drops but it should still be higher than the incident pressure.

Reasons for this mismatch between model and experimental data are being sought.

It was felt that if there was air around the pressure sensor due to insertion, the

measured pressure could be lower.

Looking into the future, there is much potential for the study of impact injury at

the cellular level both due to blunt impact and due to blast. The effect of pressure on

the brain has been shown to produce neuronal as well as axonal injury. The effect of

shear on the brain produced concussive effects and, by deduction, shear is a

mechanism of injury. Demonstration of cellular injury due to shear would be an

important contribution to the understanding of rotational brain injury;

Similarly, modeling of impact injury at the cellular level would enhance our

understanding of the effect of impact on the cell. Since the cell is small, the

development of cellular models will be difficult because the finite element model

may be too coarse for the cell. It may be possible to do a series of models going

from the macroscopic scale to the microscopic but this may take some time to

accomplish.

In conclusion, there is much work left to be done in the field of injury biomechanics

and a fertile imagination can lead to areas of study that have so far not been

thought of. Nevertheless, there are still unanswered questions in impact biomechanics

at the macroscopic level which need to be studied. The reader is encouraged

to explore these areas and continue the pioneering work of those who have gone

before them.

References



Neurology 4, 674–681 (1954)

S. Kallakuri, A. Desai, J. Mathei, E. Dawe, K. Feng, T. Saif, X. Jin, C.Y. Chen, L. Zhang,

J.M. Cavanaugh, A.I. King, Neuronal injury and glial changes are hallmarks of open field

blast exposure in swine frontal lobe, PLOS-ONE, 12(1), e0169239, doi 10.1371/journal.pone.

0169239 (2017)

A. Kalra, F. Zhu, K. Feng, T. Saif, S. Kallakuri, X. Jin, K.H. Yang, A.I. King, Development and

validation of a numerical model of the swine head subjected to open field blast (In press)

Index

A

Abbreviated Injury Scale (AIS), 14, 15

Abdomen

abdominal injury criteria, 421

cadaveric drop test, 439

characteristics, cadavers, 416

diaphragm, 409

distortion, abdominal organs, 438

experimental data, 438, 440

finite element models, 431

force-deflection curves, 419, 420, 441

force-time curves, 440, 441

frontal abdominal tests, 415

frontal impact, 414–420

hollow abdominal organs, 413, 431

injuries, 413, 414

kidneys, 409

lateral impact, 420

liver, 433

logist plots, 421

lower abdominal impacts, 417, 423

material

constants, 429

properties, 435

mechanical

characterization, 424–431

response, 414–420, 443

mechanisms, 414

model

elements, 434–436

geometry and material properties,

431–433

validation and predictions, 436–442

nonlinear viscoelastic material model, 435

organs and soft tissues, 433

organs of torso, 409–411

QLV theory, 424–427

quadrants or regions, 412

reduced relaxation functions, 429

rib cage, 409

side impact, 443

skeletal model, 432

solid abdominal organs, 409–413

solid and hollow organs, 442

strain ramp, 425

stress contours, 439

stress–strain curves, 427–431

stress–strain plots, 430

tolerance, 421–424, 444

kidney, 423

liver, 423

ultimate strain, 430

upper abdomen, 423

weight distribution, 434

WSUHAM, 431

Acetabular fractures, 457

Acetabulum, 448

Acute subdural hematoma (ASDH), 94,

97, 632

Acute ventricular fibrillation, 634

Advanced lower extremity I (ALEX 1), 515

Aircraft ditching, 339–341

American Football Helmet, 631, 632

American Society of Mechanical Engineers

(ASME), 7

Angular acceleration, 197

accurate and reliable alternate method, 177

angular displacements, 167

angular velocity, 163, 166, 167, 176

calibration


A.I. King, The Biomechanics of Impact Injury, DOI 10.1007/978-3-319-49792-1

653

654 Index

Angular acceleration (cont.)

curve, 170

data, 165

vomputed angular displacements, 174

Criteria, Validation, 161, 162

3-D motion, 153

effect of errors, 172–174

error analysis, 173, 174

filtered accelerometer data, 165

hypothetical data, 162

linear accelerometers, 159, 160, 175

low-frequency response, 171

measurement, 160, 161, 169–175

mechanism, 80–83

raw (unfiltered) accelerometer, 165

rotation vector, 167, 168

sled impact data, 163–168

triaxial accelerometers, 176

Wayne State method, 156–159, 161–169

Ankle, 484–487

Anterior column (AC), 56

Anterior cruciate ligament (ACL), 472, 637,

638

Anterior superior iliac spine (ASIS), 447

Anterior wedge fractures, 283

Anthropomorphic test devices (ATD), 11

Aortic rupture

acute injuries, 382

adventitia, 382

aorta and arterial pressure, 384

aortic isthmus, 382

cadaver, 388

experimental set-up, 386

frontal impact and submarining, 385

heart, 385

hypothesis, 385

side impact, 388

US institutions, 384

whole-body tests, 385

Arachnoids, 95, 96

Articulated total body (ATB), 25

Astrocytes, 45

Automotive crashes, 311

Automotive restraint systems, 597

Automotive safety restraints

airbag, 597, 600, 601

BEV, 600

cadaveric testing, 601

cross-chest X4 belt, 601

frontal crashes, 597

instrument panel and A-pillar, 600

lapbelt, 599

lowered thoracic tolerance, 601

metal-to-metal buckle designs, 597

occupant, 599

osteoporotic belted occupants, 600

rear impact, 603–605

ring fractures, 600

rollovers types, 605–608

seatbelts, 597–599

side impact, 602, 603

snapping, 600

three-point belt system, 601

tibial and femoral injuries, 599

V4 system, 601

Automotive Safety Standards, 8, 9

Axial vertical compression, 208

B

Barrier equivalent velocities (BEV), 600

bilateral controlled cortical impact, 92

Biomechanics, 4–6, 8

acceleration-time curve, 14

AIS, 15

ATB model, 26

automotive fatalities, 29

cadavers, 28

computer modeling, 31

contact force-time curves, 13

dramatic drop, 4

finite element (FE) method, 25

hip joint, 11

human tolerance, 14–20, 30–32

injury mechanisms, 10

laboratory research, 31

logistic curve, 18

lumped parameter model, 24

MADYMO model, 25, 29

mathematical model, 22–24

model validation, 27, 28

NFL, 17

optimal tolerance, 21

predictors of tolerance, mTBI, 18

regional road traffic deaths in 2010, 4, 5

response to impact, 11–13

rigid body rotation, 29

ROC, 20

spring-mass or lumped parameter model, 24

stress-strain curve, 23

technology assessment, 21–28

Wayne State Tolerance Curve, 7

whole-body models, 24

Blast related injuries, 651

Blood-brain barrier (BBB), 46, 90

Blunt cardiac injury (BCI), 364

Index 655

Body-fixed frame (BFF), 153

Brain injury

anatomy, 38–42

arteries, 41

astrocytes, 45, 46

biplanar X-ray setup, 55

blood-brain barrier, 45

blunt impact, 66–69, 72

bones, 37

brain lacerations, 49

brain tissue damage, 47–49

cadaver head impact data, 53, 58

center of gravity (cg), 41

cerebral meninges, 38, 39

cerebrum and hindbrain, 40

concussion, 47, 48

contusion, 48–49

diffuse axonal injury, 48, 72

finite element models, 129–130

and head, 36–45

head impacts, linear and angular

acceleration, 52

head kinematics, 59

HIC, 67

human skull, 65, 66, 73

Hybrid III dummy, 54

Hybrid III head, 54

intracerebral hemorrhage, 49

intracranial pressure data, 52

mechanisms, 49

microtubule, 44

neurofibrils, 43

neuroglia, 42, 45

neurons, 42

nissl substance/bodies, 43

node of Ranvier, 43, 44

neutral density, 57

oligodendrocytes, 45

PAC, 62

pia-arachnoid complex, 60

shear stress, 51

skull to fracture, 65, 67

superior sagittal sinus and bridging

veins, 38

visualization, brain response, 54–59

Wayne State Tolerance Curve (WSTC), 67

Brain lacerations, 49

Brain tissue damage, 47–49

Burst fractures, 283, 311, 313

C

Cadaveric data, 325

Cadaveric knee, 480, 483, 493, 639, 640

Cardiac cycle, 363

Car-pedestrian impact

accelerometers, 573

AIS, 580

angular acceleration, 571

ATB program, 582

cadaver tests, 572–574, 576, 592

case BU135 and BU465, 578

C5/6 fracture, 577

countermeasures, 590

2-D pedestrian model, 579

dynamic force-deflection curves, 584

eight front end profiles, 589

epidemiology, 569, 570

fatal head injuries, 574

head/hood impacts, 574

head velocity, 577

human surrogate (dummy/cadaver), 592

inverted X-ray cassette, 581

kinematics, 578

L4 and L5, transverse processes, 576

linear accelerations, 593

lower limb injuries, 576

MADYMO model, 587

modeling, 580–590

ONSER, 577

pedestrian (cadaver), 571

simulation, 571

single-segment impacts, 585, 586

six front end profiles, 579, 580

supracondylar fractures, 576

test setup, 572, 583

three-load cell system, 581

THUMS finite element model, 589

trifilar pendulum, 581, 582

validation, 584–588

whole-body cadavers, 571

xiphoid process, 577

X-rays and necropsy, 577

Catastrophic neck injuries, 208, 632, 633

Center for injury prevention and control, 2

Centers for Disease Control (CDC), 377

Central nervous system (CNS), 38, 71

Centre Européen d’Etudes de Sécurité

et d’Analyse des Risques

(CEESAR), 519

Cerebral contusion, 48

Cerebral spinal fluid (CSF), 38, 71

Cervical disc ruptures, 235

Cervical spine, 201, 206

2-D finite element model, 224

3-D discrete parameter model, 223

3-D FE model, 224

compression, 221, 222

656 Index

Cervical spine (cont.)

3-D discrete parameter model, 223

2-D finite element model, 224

experimental studies, 213–217

extension and flexion, 219–221

fracture/dislocation, 234

Kleinberger model, 224

mechanisms, 208–213

neck injuries, 208

shear, 223

tension, 222

three-dimensional neck model, 224–230

Chest band, 564, 565

Chronic pain syndromes, 243

Compression-flexion injuries, 208, 210, 232

Computer models, 236

Consumer Protection Safety Commission

(CPSC), 633

Continuum models, 333

Controlled cortical impact (CCI)

method, 90, 135

Cortical vessels, 96

Curb trip, 619

D

Degrees of freedom (DOF), 25

Diagrammatic depiction, 361

Diffuse axonal injury (DAI), 43, 70–72,

89, 111

Discrete parameter models, 333

3-D neck model, 224

Dorsal root ganglion (DRG), 244, 245

3-D partial cervical spine model, 225

Drop test device, 180, 181

Dura mater, 95

Dynamic cortical deformation (DCD) method,

90, 135

Dynamic Response Index (DRI), 330

E

Electrical conduction system, 362

Electromyographic signals (EMG), 251, 314

Electronic stability control (ESC), 605

Epilog

automotive environmental control, 649

automotive industry, 650

computer models, 650

Friedlander wave, 650

impact biomechanics, 649, 651, 652

injury prevention, 649

safety features, 649

ES-2re dummy, 604

Extensor muscle, 325

F

Facet contact pressure, 321

Facet pressure sensor and test, 320, 326

Fatal arrhythmias, baseball, 633–636

Federal Government, 8, 9, 373

Federal Motor Vehicle Safety Standards

(FMVSS), 7, 9, 93, 94

Finite element (FE) modeling, 105,

113, 236

ATB model, 348

cortical strain, 344

degeneration, 346

extensor muscle force, 346

functional spinal unit, 346

intradiscal pressures, 349

loading pattern, 345

lumbar motion segment, 345

quasi-static data, 348

seat ejection, 348

structure, 343

trabecular bone, 344

Flail chest, 363, 364

Fluid percussion method, 50, 51

Focal brain injuries, 135–145

Foot

ankle bone, 509

ankle injuries, 519

ankle inversion, 517

anterior and posterior tibiofibular

ligaments, 511

anterior tibialis dorsiflexes, 510

automotive drivers, 536

biomechanical Study, 523–530

cadaveric foot fractures, 534

calcaneus, 514, 518, 519

cuboid, 509

deltoid ligament, 511, 512

distal fibula, 521

distal tibia, 514

dorsiflexion, 514, 515, 536

hindfoot, 509

injury vs. foot, 530

injury vs. velocity, 527

inversion and eversion, 517–520, 531

lateral ligaments and retinacula, 513

lateral muscles, 512

ligamentous ruptures, 516

ligaments, 535

lisfranc

Index 657

foot injury, 534

fractures, 521–523

injuries, 535

ligament, 522

malleolar fractures, 517

medial

ligaments, 517

muscles, 512

model, 531–533

plantarflexion, 521

ROC, 531

sensitivity and specificity analysis, 529, 532

superficial medial ligaments, 513

test device, 521

test setup, 514, 520

tibia, 514

tibiotalar ligament, 512

Football Rules Committee, 632

Force-deflection curves, 549, 550

Ford Motor Company, 8

Fortran program, 335

Four-point belt systems, 601

Frontal impact experiments

alveolar injuries, 372

binjuries, 372

bronchial region, 371

chest, 367

corrected corridors, 369

eyeball average, 368

force-deflection curves, 369

lung injury, 370

plateau force, 370

pneumatic impactor, 370

test set-up, 367

Viscous Criterion, 372

G

General vehicle (GV), 606

Glasgow coma scale, 630

Glial fibrillary acidic protein (GFAP), 45

Global Human Body Consortium (GHBC), 130

Global Human Body Model Consortium

(GHBMC), 533

H

Hangman’s fracture, 213

Head excursion, 613

Head impact jerk (HIJ), 184

Head impact power (HIP), 184

Head impact telemetry (HIT), 188

Head injury riterion (HIC), 7

Head injury research

Al-Bsharat model, 121–124

angular acceleration mechanism, 80–83

arachnoids, 95, 96

ASDH, 94, 97, 100

biomechanical mechanisms, 98–102

border cell layers, 101, 102

brain injury, 104

brain model, 113–118, 120, 125, 126, 128

brain motion, 77, 87, 88

brain stretch-strain data, 86

bridging cortical artery, 97

CCI experiments, 138

computer models, animal brains, 130–145

contrecoup pressure, 116

controlled cortical impact method, 92, 106

cortical vessels, 96

coup pressure, 115

DAI, 89

DCD, 135–145

2-D models, 132, 134

2-D porcine models, 133

dura mater, 95

dynamic cortical deformation

method, 90, 106

elastoplastic characteristics of facial

bone, 126

epidemiology, 97, 98

experimental research, 83–92

FE model, 91, 105, 113, 114, 137, 146

fluid percussion device, 80

focal brain injuries, 90–92, 135–145

head acceleration and intracranial

pressure, 77

head tissue, 114

hourglass energy, 130

human head tolerancet, 92–94

inhomogeneous brain model, 117

intracranial pressure data, 127

linear acceleration mechanism, 78, 79, 104

linear and angular acceleration, 87, 104

marmarou weight-drop device, 89

neutral density accelerometers

(NDA), 84, 106

pendulum impact force, 115

photoelastic pattern, 81

predicted coup and contrecoup

pressures, 119

pre-finite element models, 111–113

rat model, 137

relative brain motion, 144

stress-stretch curve, 142

tolerance curve, 82

658 Index

Head injury research (cont.)

two-dimensional parasagittal models, 141

two-dimensional swine model, 131–135

visualization, brain Motion, 84–88

WSUBIM, 126–129, 147

Head kinematics, 229, 230

Henry Ford Hospital, 385

High acceleration whiplash testing, 246

High-speed X-ray data, 274

Horizontal acceleration, 338–341

Human brain tolerance, 198

Human neck geometry, 225


I

Improvised explosive device (IED), 7, 50, 651

Indy racecars, 198, 199

Inertial reference frame (IRF), 153

Injury and injury prevention, 2

Injury assessment reference values (IARV), 9,

93, 196

Injury biomechanics, 652

Instrumented cadaver, 256

Insurance Institute for Highway Safety (IIHS),

272

Interspinous ligament, 205

Intervertebral disc load cell (IVLC), 202, 203,

237, 292, 308–311, 330

Intracerebral hemorrhage, 49

Intractable neck pain, 273

J

Jefferson fracture, 208, 209

K

Knee, 477–483

L

Lap-belted occupants, 625

Lap-shoulder belt, 623, 624

Lateral collateral ligament (LCL), 471

Ligament injuries, football, 637–640

Ligamentum flavum, 205

Linear acceleration mechanism, 78, 79

Linear accelerometer, 159, 160

calibrating Accelerometers, 170, 171

cross talk, 169

frequency response, 169

Lisfranc fracture, 521, 522

Lissner medal, 7

Logistic analysis, 564

Loss of consciousness (LOC), 610

Lower extremities

thigh and leg

acetabulum, 494

ankle, 484–488

anterior muscles, 470, 471

anterior view, right femur, 471

anterolateral band, 473

anteroposterior and lateromedial

loading, 494, 495

bones, 470

cadaver femurs, 493

cadaver leg, 485

condylar notch fracture, 480

condyles, 469, 484

distal tibia to pylon fracture, 503

femoral response curves, 490

femoro-tibial joint, 469, 473

femur, 488–492, 502

fibula, 469

finite element model, 482

FMVSS 208, 503

foot and ankle model, 487

foot and tibia model, 499

greenstick fracture, 477


knee, 477–483

femur, 493

ligaments, 502

pendulum impact data, 482

ligaments, 471, 475

lower extremity, 496–498

lower limb model, 497, 498

material properties, 497

muscles, 474

neutral axis, 491

patella, 473, 484

pelvis, 469

pylon fracture, 504

quadriceps and patella tendons, 470

right tibia and fibula, 472

spiral fractures, 502

stellate fracture, 479

styrofoam DB impacts, 491

tendon catcher, 485

tensile strains, 475–477

tibia tndex (TI), 495, 504

tibial force, 486

tibial response, 492

tolerance, 494, 495

trabecular/spongy bone, 469

VW knee bolster, 501

whole-body kinematics, 500

Index 659

Lucite calvarium, 49

Lumbar spine injuries, 201, 297–303

commentary, 303–304

data, 328

diaphragm, 320

diaphragm-type pressure, 320

disc degeneration, 323

facet contact pressure, 321

facet load path, 319

Hakim’s Research, 295–297

intervertebral disc, 319

limb flailing, 289

L3–L5 segment, 320

45 N eccentric weight, 321

Newton-meter, 328

Prasad’s Research, 291–295

quasi-static loading, 319

spinal segment, 320

strain-gauge diaphragm, 321

Tennyson’s Research

abdominal pressure, 297–299

in vivo muscular response, 299–303

thoracolumbar spine, 288, 290

T12–L2 segment, 320

t-test, 322

vertebra, 320

Vulcan’s Research, 291

Lumped parameter spinal models, 331, 332

Lung contusion, 364

M

MADYMO model, 25, 196, 400, 552, 564, 565

Maximum thoracic AIS (MAIS), 16

Medial collateral ligaments (MCL), 471, 477,

639–642, 645

Microglial cells, 45

Mild rearend collision, 273

Mild traumatic brain injury (mTBI), 7, 35,

179, 197, 198

American Football Helmet, 631, 632

diagnosis, 630

GCS, 630

head injury, 629

individualized baseline testing, 631

symptoms, 630

TBI, 629

Minor traumatic brain injury, 198

Moving dynamic barrier (MDB), 9, 602

N

National Academy of Engineers, 8

National Automotive Sampling System

(NASS), 542, 606

National Center for Injury Prevention and

Control (NCIPC), 35, 36, 377

National Collegiate Athletic Association

(NCAA), 632

National Crash Severity Study (NCSS), 414

National Football League (NFL), 17, 18,

179, 198

National Highway Traffic Safety

Administration (NHTSA), 3, 68,

271, 377

National Institute of Standards and Technology

(NIST), 164

National Institutes of Health (NIH), 111

National Library of Medicine, 431

45 N eccentric weight, 321

Neck drop test, 216

Neck injury

multi-faceted problem, 234, 235, 273

spinal cord, 201

spinal/vertebral column, 201–207

thoracolumbar spine, 201

whiplash, 274

Neutral density accelerometers (NDA), 84, 106

Neutral density targets (NDTs), 56, 86

Node of Ranvier, 44

Notice of Preliminary Rulemaking

(NPRM), 603

Nucleus, 203

O

Odontoid process/dens, 206

Oligodendrocytes, 45

P

Paper honeycomb (PHC), 378, 554

Pelvis

acetabular fracture, 458, 459, 465

acetabulum, 448, 449, 452

amphiarthrodial, 448

anterior extrinsic ligaments, 449

anterior ligaments, 452

anteroposterior force, 452

bones, 447

bucket handle fracture, 453

cavity, 449

classification, 455

coccyx, 451, 454

femoral neck fractures, 456, 465


fractures, 453

acetabulum, 465

sacrum, 465

frontal response, 457–461

660 Index

Pelvis (cont.)

frontal view, 448

hip fracture/dislocation, 463

hipbone, 447

horizontal fracture, 455

hypothetical force-time curve, 462

iliac bones, 449

interosseous ligaments, 449

KTH testing, 460

lateral response, 461, 462

lateral view, 448

oblique frontal view, 449

orientation, femur, 459

orthopedic surgery, 453

posterior ligaments, 453

sacroiliac (SI) joint, 449

sacrotuberous ligament, 449

sacrum, 449–451, 454

tolerance, 463

transverse

fractures, 455

section, 451

unstable pelvic fracture, 454, 455

U-shaped fracture, 455, 456

Pia-arachnoid complex (PAC), 38

normal traction, 60, 61

shear, 62, 63

Plank and Eppinger model, 400

Posterior column (PC), 56

Posterior cruciate ligament (PCL), 473

Prasad model, 313

Q

Quadriplegia, 209, 234

R

Real-world brain injuries

angular acceleration, 186

brain responses model, 181

drop test device, 181

estimation, tolerance levels, 187

exemplar vehicles, 191

HIC, 186

ICP contours, 182, 183

Indy car crash data, 195

left-hand drive vehicle, 192

linear acceleration, 186

logistic regression analysis, 183–186

model-predicted values, 187

mTBI, 179

NFL study, 181, 188, 189

racecar safety and crash severities, 194, 195

simulation, 183–188

stereophotogrammetric methods, 180

strain and strain rate, 181, 185

strain contours, 182, 183, 191

triaxial linear accelerometer, 181

vehicular crashes, 189–193

vehicular deceleration pulse, 195

WSUHIM, 196

Receiver operating characteristics

(ROC), 20, 531

Rollover crashes

belted occupants, 610–613

bounce-over, 609

climb-over, 608

experimental simulation, 613, 614

fall-over, 608

flip-over, 607

head and neck injury, 611–613

injury statistics, 610–613

MAIS 2–6 injuries, 610

modeling, 614–617

turn-over, 607

unbelted occupants, 610–612

Ruan model, 120

Runge–Kutta method, 156

S

SAE J2114 dolly test, 618

Scalp lacerations, 46

Seat ejection

aircraft, 329

cockpit, 329

IEDs, 329

jet aircraft, 328

leg restraints, 329

limb flailing injuries, 329

survival pack, 329

zero-zero capability, 329

Side impact

air space, 557

automotive fatalities, 543

chest band, 541

chest compression and rib acceleration, 554

computed and measured chest deformation

profiles, 560

Deng profile, 555

door velocity, 556, 558

fatality rates, 539, 540, 542

FMVSS, 544

GM profile, 555

injuries, 541

Index 661

kinematics, 539–541

MADYMO-type model, 551

mini-models, 552

NHTSA, 543, 561

padding, 557

pendulum impacts, 548–551, 565

RibY, 544

rigid body model, 551

shoulder engagement loss, 558, 559

single and multiple vehicles, 542

sled tests, 545–548

T12Y, 544

V*C, 545

validation, 553–555

viscoelastic model, 553

Side impact dummy (SID), 377, 544

Side impact experiments

cadavers, 375, 376, 378

chest injury criteria, 379


Heidelberg method, 375

injury functions, 378

pendulum impacts, 378

protection, 625

SID, 377

triaxial accelerometers, 376, 378

Viscous Criterion, 377

thoracic trauma index, 377

SID-IIs dummy, 605

Sloping hood lines, 593

Spinal compression, 250

Spinal cord

anatomy, 244

neurophysiology, pain, 244, 245

Spinal ligaments, 237

Spine simulating vertical acceleration, 331

Sternocleidomastoid (SCM), 252

Stress–strain curves, 427–431

Supplemental restraint system (SRS), 601

Supraspinous ligament, 205

T

Temporal mandibular joint (TMJ), 37

Tennyson spine model, 341

Tension extension injuries, 212

Thoracic force-deflection curves, 369, 370

Thoracic spine, 201

Thoracic trauma index (TTI), 389, 543, 602

Thoracolumbar spine, 333–338

anatomy, 281, 282

anterior wedge fractures, 283

burst fractures, 283

dislocations and fracture-dislocations, 285

hyperextension injuries, 286

rotational injury, 286

tolerance, 304–307

two-dimensional model

AIS 3+, 338

automotive crash environment, 336

computer program, 337

data, 333

elements, 334

horizontal crash, 338

hyperextended modes, 335

kyphotic thoracic spine, 337

near-frontal crashes, 337

validations, 335

Thorax

aortic isthmus, 396

aortic rupture, 395, 402

arteries, 360

atria, 358

atrioventricular (AV) node, 360

automotive crashes, 402

cardiac cycle, 360

cardiovascular system, 359

carotid arteries, 392

chest deflection, 401

chest injury, 381, 403

cross-sectional view, 395

diaphragm, 392, 393

dynamic model, 390

EKG, 360

elastic modulus, 392

endothelial cells, 360

FE simulation, 393

finite element model, 390

flail chest, 363, 364, 402

force-deflection curves, 380, 381

force-time correlation, 393

frontal chest impact, 404

frontal oblique view, 392

gas exchange, 358

heart, 360, 401

aorta, 384

great vessels, 364, 365

lung, 357

hemo- and pneumothorax, 364


Kroell corridors, 400

lateral pendulum impact test, 379

ligamentum arteriosum, 396

linear fluid, 396

linear relationship, 389

Lobdell model, 391

662 Index

Thorax (cont.)

LS-DYNA 3-D explicit code, 392

lumped parameter model, 390

lung contusion, 364

lung injury, 374

mechanisms, 367

mediastinum, 358, 392, 393

model parameters, 391

Newton’s second law, 390

oblique impact test, 387

oxygen and carbon dioxide exchange, 359

peak forces, 381

pleura, 358

pulmonary and aortic semilunar valves, 359

rib cage, 357, 358, 391

rib fractures, 357

seatbelt, 387

side impact tests, 377, 381

sino-atrial (SA) node, 360

spring-mass model, 390

stress-strain curve, 393

subclavian artery, 392

test set-up, 374

thoracic aorta, 397

thoracic cavity, 357

thoracic viscera, 391

tolerance, 388

torso model, 396–399

venous blood, 359

ventricular fibrillation, 402

Wang model, 395

Three-dimensional neck model, 224–230

Tibia Index (TI), 495

Transduction, 245

Traumatic brain injury (TBI), 7, 35

Traumatic rupture, 366

Traumatic rupture of the aorta (TRA), 365, 382

Turnbuckles, 323

T-wave, 634

Two-Dimensional Swine Model, 131–135

U

University of California San Diego (UCSD),

367

University of Heidelberg, in Germany, 373

Unrestrained occupants, 624

US Air Force (USAF), 330, 348

US Army Aeromedical Research Lab

(USAARL), 220

US and Global Statistics, 2–4

U-shaped fracture, 455, 456

V

Vehicle miles traveled (VMT), 3

Vertebral/spinal canal, 202

Vertical acceleration, 338–341

Viscous Criterion (V*C), 544

W

Wayne State Human Model 04-1

(WSHM04-1), 396

Wayne State method, 156–159, 161–169, 181

Wayne State Tolerance Curve (WSTC), 6, 17,

66–69, 77, 93, 189

Wayne State University, 378

Wayne State University Brain Injury Model

(WSUBIM), 125–128

Wayne State University Human Abdominal

Model (WSUHAM), 431, 434

Wayne State University neck model, 236–238

Whiplash pain

BioRID neck vertebrae, 265

cadavers, 253, 254, 257

capsular strain estimation, 263

cervical spine kinematics, 254

head acceleration data, 258

HFH19 and HFH20, 258

hyperextension hypothesis, 246

inertial reference frame, 258

low-speed rear impact, 254

muscle hypothesis, 246, 247

neck, 271

pinching hypothesis, 248

pressure hypothesis, 248

seat pan load, 258

seatback angles, 265

shear hypothesis, 249, 250

sled acceleration and velocity, 258

time-consuming process, 255

triaxial accelerometer, 256

upper neck moment (M y ), 258

volunteers, 251–253

Whiplash-induced injuries, 625

Whole-body cadaveric tests, 368

WSU pedestrian project, 591

X

X-ray cinematography, 253

Y

Yellow ligament, 205

The Biomechanics of Impact Injury

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