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

of the ligament strain; a linear relationship is assumed when the ligament strain is larger
than 2l. At the reference (extension) position of the joint, the initial strain in a ligament
is given by the parameter r. This parameter determines the zero-load length if the
reference length Lr is known
퐿 = 퐿 /(∈ + 1)
Stiffness values were based on data reported by Shelburne and Pandy, (1997), while
reference strains in fully extended knee were set according to the numerical data of
Mommersteeg et al., (1995), and Blankevoort and Huiskes, (1991). Values of Lr are the
ones obtained from our model (Table 1).
Ligaments were treated as non-linear springs and divided in multiple bundles to analyze
their specific behavior: anterior cruciate ligament (ACL) and posterior cruciate ligament
(PCL) were simulated considering an anterior and a posterior bundle while medial
collateral ligament (MCL) was divided in anterior and intermediate bundle; the lateral
collateral ligament (LCL) was represented by a single bundle.
Ligament K [N] Lr [mm] r
ACL 1500 34.4 0.07
PCL 2600 28 -0.1
LCL 2000 56.6 0.065
MCL 2500 94.8 0.07
Table 1 - Values of stiffness (K), reference length (Lr) and initial strain (r) assumed in the model.
Quadriceps tendon wrapping on the distal femur was reproduced by using a chain of
three short cylinders that could come in contact with the femoral groove. The patella
could then slide over the trochlea, while the patellar tendon was generated with a rigid
rod connecting patella and tibial tuberosity. Quadriceps muscle was considered as a
linear actuator that could be controllable by the program.
In order to reduce the roughness of the bone surfaces obtained from MRI segmentation,
that could prevent a proper sliding of femoral condyles over the tibial plateau, the
contact surfaces were remodeled and smoothed by means of a CAD software
(Rhinoceros 4.0, McNeel, Seattle, WA, USA).
A 300 N constant vertical load (about 42% of body weight) was applied to the pelvis. A
quadriceps force was applied through the controllable linear actuator in order to sustain
the external load at a set of different knee joint angles. These angles were: 0° (full
extension), 15°, 30°, 40°, 50°, 60°, 75°, 90°.
Ligament forces and elongations, quadriceps force and tibio-femoral contact forces
were extracted from the model when a steady-state condition was achieved. Contact
forces are expressed in body weight (BW) referring to our subject BW that was 712 N
(≈72.6 Kg).
3. RESULTS
3.1 Quadriceps muscle force
Muscle force was almost nil at fully extended knee, and increased with flexion as
(2)