Computational Modeling of Knee Biomechanics

A 3D non-linear finite element (FE) knee model was developed from the computed tomography (CT) and MRI images of a healthy 36-year-old male subject.^{23 (link),24} The contours of the bony structures (including the femur, tibia, fibula, and patella) and the soft tissues (the ligaments and menisci) were reconstructed from the CT and MRI images, respectively. This computational knee joint model has been established and validated in previous studies.^{23 (link),24} The bony structures were modelled as rigid bodies.^{25 (link)} All major ligaments were modelled with non-linear and tension-only spring elements.^{26 (link),27 (link)} The force-displacement relationship based on the functional bundles in the actual ligament anatomy is shown in Table I.^{28 (link)}The forces across the components of the knee joint were calculated as follows:
$f\left(\epsilon \right)=\{\begin{array}{c}\frac{k{\epsilon }^2}{4{\epsilon }_1},0\le \epsilon \le {\epsilon }_1\\ k\left(\epsilon -{\epsilon }_1\right),\epsilon >2{\epsilon }_1\\ 0,\epsilon <0\end{array}$
$\epsilon =\frac{l-l_0}{l_0}$
$l_0=\frac{l_r}{{\epsilon }_{\text{r}}+1}$
where f(ε) is the current force, k is the stiffness, ε is the strain, and ε₁ is assumed to be constant at 0.03. The ligament bundle slack length l₀ can be calculated by the reference bundle length l_r and the reference strain ε_r in the upright reference position.
Contact conditions were applied between the femoral component, PE insert, and the patellar button in TKA. The coefficient of friction between the PE material and metal was chosen to be 0.04 for consistency with previous explicit FE models.^{24 ,29 (link)} Contact was defined using a penalty-based method with a weighting factor. As a result, contact forces were defined as a function of the penetration distance of the master into the slave surface. The PE insert and patellar button were modelled as an elastoplastic material (Table II).²⁴ The femoral and tibial components were fully bonded to the femur and tibia bone models, respectively. All implant components were modelled as linear elastic isotropic materials (Table II).²⁴ Surgical simulation for TKA was performed by two experienced surgeons (Y-GK and KKP). A neutral position FE model was developed according to the following surgical preferences: default alignment for the femoral component rotation was parallel to the transepicondylar axis with the coronal alignment perpendicular to the mechanical axis and the sagittal alignment at 3° flexion with a 9.5 mm distal medial resection. To develop the malrotation models, ten different malrotation cases were considered with respect to the neutral position: neutral, internal and external 2°, 4°, 6°, 8° and 10° malrotations (Fig. 1). The tibial default alignment was rotated 0° to the anteroposterior axis, the coronal alignment was 90° to the mechanical axis, and the sagittal alignment was 5° of the posterior slope with an 8 mm resection below the highest point of the lateral plateau. The implant used was the Genesis II Total Knee System (Smith & Nephew, Inc., Memphis, Tennessee).
To evaluate the effect of internal and external malrotation on the femoral component of the TKA model, the stance-phase gait and squat loading conditions were applied to both the tibiofemoral and PF joint motions.^{30 (link)-32 (link, link)} The FE model was analysed using ABAQUS software (version 6.11; Simulia, Providence, Rhode Island). The results for the maximum contact stress on the PE insert were assessed, and the patellar button pressure and collateral ligament forces were evaluated in both internal and external malrotation conditions.