# Computational Wear Prediction of TKR with Flatback Deformity during Gait
## 3 Results  
### Model Validation  
A convergence study was performed to find the optimum mesh size in the tibial insert (see Figure 9). Mesh convergence was selected as the mesh size when the maximum contact pressure values were all within 5% of the following two mesh sizes [27; 28; 29; 30; 31]. The average mesh size suitable for that criterion was 1.1 mm and the number of elements was 16,376. The mesh size of the face where the femoral component contacts the tibial insert was the same as the mesh size of the tibial insert and the number of elements in the femoral part was 7102. To verify the wear simulation model performed by finite element analysis, the wear simulation results were compared with the wear results of a previous study [15]. For the finite element analysis performed, the load and displacement conditions were applied to  
Figure 8: The flow chart of the process of deriving the results of the wear depth. Figure 9: Mesh size convergence check graph. the standard of ISO 14243-3:2004 [26] to match the actual test conditions, and the results of the wear rate at 4,000,000 cycles were derived and compared. The wear rate was obtained by subtracting the mass of the tibial insert after 4,000,000 cycles of analysis from the mass of the tibial insert before performing the wear analysis. As shown in Table 2, the wear rate (8.26 mg/MC) of the finite element analysis performed in this study and the wear rate (8.66 mg/MC) of the finite element analysis performed in the previous study [15] show similar results. Therefore, it can be judged that the reliability of the model proposed in this study has been verified. However, this wear rate is larger than the experimental wear rate (2.96-7.32 mg/MC) of the previous study. This difference can be explained by not considering the viscoelastic effect in the material model used in this study. Considering the viscoelastic effect of a knee artificial joint using UHMWPE (ultra high molecular weight polyethylene) material, it was found that the contact pressure decreased by more than 10% when the compressive force was continued [32]. Since the wear depth is proportional to the contact pressure, considering the viscoelastic effect of the UHMWPE material, the wear rate will decrease as the wear depth decreases. However, since the purpose of this study is to analyze the difference in wear trends according to other gait characteristics rather than to derive an accurate wear rate, the viscoelastic effect was not considered for the simplification of the analysis model and faster analysis time. Additionally, in order to verify the finite element model, the graph of maximum contact pressure during one gait cycle was compared with the graph of the results of a previous study [11; 16; 33]. The axial force applied to the presented FE model was used the modified ISO 14243-3 [14] (see Figure 5b). As shown in Figure 10, the maximum contact pressure tendency in the previous study showed that the peak value appeared twice before the gait cycle of 20%. Next, the peak value appeared immediately after the gait cycle of 40%. Finally, decreases and the low value were maintained after the gait cycle of 60%. The maximum contact pressure graph during one gait cycle obtained as the analysis results of this study coincided with the position of the pressure peak points and the position where the value decreased compared to the graph of the maximum contact pressure of the previous study. Above all, in the graph of the previous study, the section where the value decreased significantly after 60% of the gait cycle was also well shown in the graph of the analysis result of this study. This study does not aim to verify whether the finite element model can replace the experimental model, but to compare the wear characteristics of knee artificial joints in normal and flatback gait mechanisms. Therefore, it is judged that the finite element model proposed in this study is reliable in comparing the wear characteristics of the knee artificial joint according to the gait mechanism.