# Computational Wear Prediction of TKR with Flatback Deformity during Gait
## 2 Methods  
### Finite Element Analysis Model  
The 3D CAD model of the femoral component and tibial insert of the knee artificial joint was made using SolidWorks 2020 (Solidworks Corp., Waltham, MA, USA). The femoral component was modeled as a rigid body with 4-node-shell elements and the tibial insert was modeled with 8-node hexahedral elements (See Figure 3). Meshing, analysis and post-processing were performed using ABAQUS 2016 (Abaqus, Inc., Johnston, RI, USA). Ultra-high molecular weight polyethylene (UHMWPE) was applied as the material of the tibial insert. UHMWPE material was modeled using the J-2 Plasticity model with a density of 9.4 \(\times\) 10\({}^{-10}\) tonne/mm\({}^{3}\), an elastic modulus of 1051 MPa and a Poisson's ratio of 0.46. The stress-strain data used in the J-2 Plasticity model are shown in Table 1[15]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Stress (MPa)** & **Strain** \\ \hline
12.1 & 0.00 \\
21.4 & 0.03 \\
23.8 & 0.11 \\
44.0 & 0.55 \\
92.4 & 0.98 \\
135.0 & 1.09 \\
515.0 & 1.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The stress–strain data for the J-2 Plasticity model. Figure 3: FE model of knee artificial joints. A penalty-based method was applied to define the contact between the femoral component and the tibial insert of the knee artificial joint. For the efficiency of the computational simulation, the femoral component was modeled as a rigid body [8; 10]. However, the tibial insert was modeled as a flexible body to consider wear and deformation. The friction coefficient was set to 0.04, which is the result obtained in the experiment of the previous study [11; 14; 15]. To apply the motion of the knee artificial joint during the gait cycle (see Figure 4), in the normal gait mechanism, the knee flexion-extension angle (see Figure 5a), anterior-posterior displacement (see Figure 5d), and adduction-abduction angle (see Figure 5c) applied the conditions of the modified ISO 14243-3 [14]. Furthermore, in the flatback gait mechanism, the knee flexion-extension angle (see Figure 6a, red line) applied the kinematic data obtained through the experiment on flatback patients in a previous study [2], but the anterior-posterior displacement (see Figure 5d) and adduction-abduction angle (see Figure 5d) applied the same data as for the normal gait mechanism. For the vertical force acting on the knee artificial joint, experimental data (see Figure 6b) from a previous study [2] were applied for both gait mechanisms. The anterior-posterior displacement and adduction-abduction angle data for the flatback gait mechanism could not be confirmed in a related previous study. Furthermore, a previous study comparing the kinematic data during normal gait and flatback gait also focused on the knee flexion-extension angle and the vertical force acting on the knee. Therefore, it can be inferred that the application of the data of normal gait case to the anterior-posterior displacement and adduction-abduction angle of the flatback gait case does not have a significant effect on the comparison of the two gait mechanisms. The boundary conditions and loading conditions were set according to ISO 14243-3 [26]. As shown in Figure 7, IE rotation (see Figure 5c) and AP displacement (see Figure 5d) were applied to the tibial insert as boundary conditions at a reference point located at the center of mass of the tibial insert. Medial/lateral (ML) displacement of the tibial insert was left free, and flexion-extension rotation of the tibial insert was fixed. Flexion-extension rotation was applied to the femoral component as boundary conditions and other directional degrees of freedom were fixed. All displacement conditions given to the femoral component were given to the rigid reference point of the femoral component. The loading point on the tibial insert was offset to the medial side by a distance of 0.07 times the width of the tibial insert according to ISO 14243-3 [26].