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

first simulation uses data provided by the “Grand Challenge Competition to Predict In-
Vivo Knee Loads” [1]. The Grand Challenge data set includes implant and bone
geometries, motion, ground reaction forces, electromyography (EMG) as well as
measured knee loading. The second simulation embeds a previously validated cadaver
based knee model within a musculoskeletal model of a subject of similar height and
weight as the cadaver donor.
3. METHODS
3.1 Knee Models
Multibody computational models of the natural and prosthetic knee were created in
MD.ADAMS (MSC Software Corporation, Santa Ana, CA). The techniques used to
develop and validate the natural knee model have been previously described [3, 4].
Geometries (bone, cartilage, menisci, and ligaments) for the natural knee were derived
from magnetic resonance images (MRI) of a fresh frozen cadaver. After imaging, the
cadaver knee was mounted in a dynamic knee simulator (Kansas Knee Simulator,
University of Kansas, Lawrence, KS) with loads reproducing a walk cycle applied.
Measured bone kinematics from these tests were used to validate the force-displacement
relationships of the computational model by comparing them to predicted kinematics for
the identically loaded model. Geometries for the prosthetic knee came from data
provided by the “Grand Challenge Competition to Predict In-Vivo Knee Loads” [1].
In the multibody knee models ligament bundles were represented as onedimensional
non-linear springs. The natural knee model included two bundles for the
anterior cruciate ligament (ACL) and posterior cruciate ligament (PCL) and three
bundles for the medial collateral ligament (MCL) and lateral collateral ligament (LCL).
The prosthetic model included three bundles for both the MCL and LCL and one bundle
for the PCL. Stiffness parameters for ligament bundles came from the literature and the
zero-load lengths (lengths at which ligament bundles first become taut) were derived
from experimental measurements of cadaver joint laxity. Zero-load lengths for the
prosthetic knee were estimated based on multiple cadaver studies performed in our lab.
As described in Guess, Liu et al. [3], medial and lateral tibia plateau cartilage
geometries of the natural knee were divided into multiple hexahedral rigid bodies.
Each cartilage element was connected to tibia bone with a fixed joint located at the
center of each tibia cartilage-bone interface. A deformable contact constraint was
defined between each tibia cartilage element and the femur cartilage geometry. The
contact model used for all articulating surfaces in the knee was defined as:
n
F kδ
B(
δ )
c = + δ
(1)
where Fc is the contact force, δ is the interpenetration of geometries, δ is the velocity of
interpenetration, k is a spring constant, n is the compliance exponent, and B(δ) is a
damping coefficient. A similar method was used to section the tibia polyethylene insert
where the insert pieces were rigidly attached to the tibia tray and deformable contacts
defined with the metal femur component.
For the natural knee, multibody models of the menisci were created by radially
sectioning the lateral and medial menisci geometries. The sectioned meniscus rigid
body elements were connected to neighboring elements by a 6x6 stiffness matrix.
Values for the stiffness matrix parameters were derived through an optimization process
that minimized the displacement error between identically loaded finite element and
multibody menisci models [4]. Deformable contacts using Eq. 1 were defined between
each meniscus element and the femur cartilage. In addition, a deformable contact was