ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Solving Overconstrained Kinematic in Numerical Shoulder Model using Nullspace
Optimization
C. Engelhardt, D. Ingram, P.Muellhaupt, E. Pralong, A. Farron, D.Pioletti, A.Terrier
1. ABSTRACT
A biomechanical finite element model has been set up for quasi-static analysis of the human
shoulder complex. The model is based on the anatomical male dataset of the Human Visible Project.
It includes thorax, clavicula, scapula, humerus and 16 muscles subdivided into 28 fibres spanning
over sternoclavicular, acromioclavicular and glenohumeral joint. Humeral head translations on the
glenoid cavity are allowed. Muscle forces are estimated using an inverse dynamic approach coupled
with pseudo-inverse null space optimization. To stabilize the glenohumeral joint, reaction forces
must fulfil a direction criteria. An abduction movement is simulated. Muscle forces, joint reaction
forces, cartilage loadings and humeral head translations are computed. Muscle forces, joint reaction
forces and cartilage loadings are in agreement with literature. Obtained humeral head translation are
too large compared to experimental data.
2. INTRODUCTION
The human shoulder complex allows to reach a wide workspace and to execute complicated movements.
This is possible due a complex underlying mechanical system. Over 20 muscles are spanning
over the participating bones forming three joints. Consequently the mechanical system is highly
overdetermined. Regardless the complexity, several shoulder models have been published [1][2][3]
[4][5][6][7][8][9][10]. To handle the mechanical situation, different simplifications are found in literature.
Three simplifications are commonly used: 1) The mechanical system is reduced to the glenohumeral
joint. 2) The glenohumeral joint is assumed to be a ball and socket joint. 3) The number
of muscles is reduced respectively muscles are grouped. The differences between the models lie in
the number of muscles, the technique to determine muscular forces and the simulated movements.
One of the first musculoskeletal shoulder models was published in 1978 [1]. It contains six muscles.
Their forces are computed following experimental data obtained from electromyographic measurements.
Another method to solve the indetermined problem of muscle force distribution is to use optimization
methods. Van der Helm [4] compared four optimization criteria. The minimization of the
sum of squared muscle stresses leads to a result that is in accordance with the physiological cross
section area (PCSA). The predicted load on the glenohumeral joint is 50% of the bodyweight during
abduction in the scapula plane. This model has been developed further and validated using EMG
data and in-vivo joint reaction force measurements [5]. Not only the total loading in the glenohumeral
joint is of interest but also contact area and contact pressure on the cartilage. Therefore the
ball and socket joint simplification of the glenohumeral joint is not suitable. In several experimental
studies the translation of the humeral head on the glenoid cavity cartilage has been shown [11][12]
[13][14]. So far, few models have been published that compute loading patterns on the glenoid cartilage
by taking into account the whole shoulder mechanism and humeral head translations.
Surgeons observed a shorter lifetime of prosthesis after total shoulder arthroplasty in patients, that
show unsymmetrical cartilage and bone wear. The questions arising out of this observation are:
How does a muscular imbalance influence the appearance and development of degenerative cartilage
diseases? How should prosthesis be chosen and placed in patients showing characteristic cartilage
damages? This issue motivated the set up of a new finite element musculoskeletal shoulder
model. Target specifications are to permit humeral head translation for the computation of cartilage
loading patterns and to take into account the whole shoulder girdle for the analysis of muscular coordination.