## 3 Results
### Patellefemoral Joint  
The forces around the knee extensor mechanism exhibited peaks during the momentum transfer phase of the chair-rising movement at about 90\({}^{\circ}\) of knee flexion. Peak values of the quadriceps muscle force, quadriceps tendon-to-femur force, and PF compressive force for all the simulated PE insert thickness cases are shown in Figure 4, and their variations with regard to the reference case are summarized in Table 1. Interestingly, the PF compressive force followed an opposite trend than the compressive force on the TF side,  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Reference PE Insert Thickness 9 mm**} \\ \hline \multicolumn{2}{c}{\(-\)**4 mm**} & \multicolumn{2}{c}{\(-\)**2 mm**} & \multicolumn{2}{c}{**+2 mm**} & \multicolumn{2}{c}{**+4 mm**} \\ \hline  & **Average** & **Peak** & **Average** & **Peak** & **Average** & **Peak** & **Average** & **Peak** & **Difference** \\  & **Difference** & **Difference** & **Difference** & **Difference** & **Difference** & **Difference** & **Difference** & **Difference** \\ \hline
**Tibiofemoral** & & & & & & & & & \\
**joint** & & & & & & & & & \\ MCL force & \(-\)89\% & \(-\)75\% & \(-\)59\% & \(-\)47\% & +100\% & +51\% & +251\% & +106\% \\ LCL force & \(-\)100\% & \(-\)100\% & \(-\)83\% & \(-\)73\% & +210\% & +106\% & +554\% & +223\% \\ PCL force & \(-\)53\% & \(-\)41\% & \(-\)31\% & \(-\)23\% & +43\% & +29\% & +104\% & +67\% \\ Compressive & \(-\)21\% & \(-\)7\% & \(-\)9\%\% & \(-\)4\% & +17\% & +8\% & +44\% & +21\% \\
**Patellofemoral** & & & & & & & & & \\
**joint** & & & & & & & & \\ Quadriceps & +4\% & 0\% & +1\% & 0\% & 0\% & 0\% & \(-\)1\% & 0\% \\ muscle force & & & & & & & & \\ Quadriceps & & & & & & & & \\ tendon-to-femur & \(-\)30\% & \(-\)28\% & \(-\)15\% & \(-\)15\% & +15\% & +17\% & +29\% & +33\% \\ force & & & & & & & & \\ Compressive & +3\% & +7\% & +3\% & +3\% & \(-\)3\% & \(-\)3\% & \(-\)8\% & \(-\)7\% \\ force & & & & & & & & \\ \hline \hline \end{tabular} Data are presented as average and peak percentage difference over the chair-rising simulation for each 2 mm PE insert thickness change relative to the reference case.  
\end{table}
Table 1: Changes in muscle, ligament, and joint compressive forces due to tibial PE insert thickness variations.  
Figure 3: Peak ligament and compressive forces on the tibiofemoral (TF) joint at varying PE insert thicknesses during a chair-rising simulation. From left to right: MCL force, LCL force, PCL force, and TF compressive force. Results are displayed relative to the reference case (gray filled marker).  
indicating a peak decrease of 0.1 BW and 0.3 BW when PE insert thickness was varied from 9 mm to 11 mm or 13 mm, respectively. In contrast, simulation of thinner tibial PE inserts, relative to the reference case, resulted in a slightly increased peak PF joint compressive force by 0.1 BW (\(-\)2 mm) and 0.3 BW (\(-\)4 mm). The force-angle curves of the knee extensor mechanism structures are provided in Appendix A.  
Changes in PE insert thickness affected the patellar proximal-distal translation and medial-lateral rotation, with a minimal effect at full knee flexion (Figure 5). The patella shifted by 0.8 mm distally for every 2 mm incremental change of the PE insert thickness, from 9 mm (reference) up to 13 mm, and about 0.8 more proximally for each 2 mm decrement relative to the reference thickness. Compared to the reference case, the patella was rotated 0.4 and 0.7 mm more medially with 11 mm and 13 mm PE insert thicknesses, respectively and, accordingly, 0.4 and 0.1 mm more laterally with a 7 mm and 5 mm PE insert thickness, respectively.