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

joint. The purpose of this study is to develop an effective tool that could be useful to
analyze ligaments, muscular behavior and contact forces in patients affected by joint
diseases and to help planning a proper positioning of prosthetic components in total
knee arthroplasty.
2. MATERIALS AND METHODS
A magnetic resonance imaging (MRI) scan (Siemens Medical Systems, T1 weighted, 1
mm slice thickness) of a fully extended leg of a Caucasian male (age=42 years,
height=1.76 m and weight=72.6 Kg) was made. MRI image processing software (Amira
5.3.3, Visage Imaging, Inc., San Diego, CA, USA) was used to generate 3D models of
pelvis, femur, patella, tibia and fibula. A multibody dynamics-based model (Fig. 1) was
generated using a commercial modeling software (Working Model 3D, MSC.Software
Corp., Santa Ana, CA, USA). The pelvis was constrained to translate along a vertical
axis and the femur was connected to the pelvis through a spherical joint representing the
hip. The ankle was modeled as a two joint system: a) talo-crural joint, cylindrical,
mediolaterally oriented, to permit dorsi-plantar flexion; b) sub-talar joint, cylindrical,
anteroposteriorly oriented, to permit inversion-eversion. The foot was fixed on the floor.
The knee joint was just defined by the contact between femoral condyles and tibial
plateau, and was constrained by forces due to anterior and posterior cruciate ligaments,
lateral and medial collateral ligaments, patellar tendon and quadriceps tendon. The
attachment points of ligaments and tendons were derived from our MRI images with the
help of anatomical atlas.
Fig. 1 - Multibody dynamics-based model of the lower limb and detail of the knee joint.
According to the work of Blankevoort and Huiskes, (1991), ligaments were assumed to
be elastic with a non-linear force-strain relationship described by a piece-wise function
0.25푘 ∈
푓 =
/∈ 푘(∈ −∈ )
0
0 ≤∈≤ 2 ∈
∈> 2 ∈
∈< 0
where f is the tensile force, k is the ligament stiffness and is the strain in the ligament
calculated from its length L and the zero-load length L0. The l parameter is assumed to
be 0.03. If the ligament strain is less than 2l the ligament force is a quadratic function
(1)