## 3 Results  
An FE model was developed, taking into account the physiological conditions resulting from the loads produced by the hamstrings, gastrocnemius, and quadriceps muscles on the knee range of movement. To investigate the quadriceps tendon and the lateral retinaculum isolated action in patellar instability, different loading cases were performed, reducing the quadriceps tendon intensity force at 90% and unbalancing the lateral retinaculum at 90 N. Figure 6 shows the stress-contour maps evaluated for a healthy knee, (a) configuration, without patellar instability induced, and an unhealthy one, (b) configuration, obtained with a force of 90 N applied to the lateral retinaculum, while the medial is loaded with 100 N, and a quadriceps tendon force reduced by 10%. As can be seen from Eq., the von Mises stress is higher in configuration (b), about 79 MPa instead of 53 MPa found in configuration (a), which is a percentage difference of 49%. Table 1 shows the maximum stress peaks on  
Figure 4: Model muscle forces: (**a**) hamstrings; (**b**) gastrocnemius; and (**c**) quadriceps. Figure 5: _Loading setup of numerical FE model:_ (**a**) X-Y planar view of the numerical model detailed with bony and soft components, with reference to a balanced retinaculum condition; (**b**) coordinates of points 1 and 2 where loads were applied, with reference to the origin; (**c**) Y-Z planar view of the numerical model detailed with bony and soft components, with muscular loads applied to points 1 and 2, with angles of application; (**d**) mechanical properties of the FE parts. the FE models. The results confirm the obvious variances in the femur and patella with respect to the two configurations studied, with differences of 49% and 30%, respectively. It can be argued that the patellar tendon is subjected to the higher stress in (b) configurations and the percentage difference is 43%, followed by the posterior cruciate ligament with 34%. Different considerations must be made for the displacements, which show significant differences only for the patella translations. In configuration (a), its displacement is approximately 5 mm, while in configuration (b) it is 14 mm. Figure 7 shows a detailed comparative Eq. von Mises contour map of the patella. As has already been said, important differences were obtained in terms of stress, evidenced by the significant contact area shown by the unhealthy configuration. The patella right upper part is the contact area, which cannot structurally withstand this type of stress, such as the femur. The displacements obtained are 5 mm in (a) and 14 mm in (b). In addition, a reaction force of 60 N was evaluated in patella for (a) configuration at 45\({}^{\circ}\) of knee flexion, and 130 N for (b). The ageing stresses in the elastic components of the model (i.e., ligaments and cartilage) are represented in Figures 7 and 8 and Table 2. Soft tissues are fundamental for the absorption of the incremental stress caused by the patella's non-physiological position, specifically the patellar tendon is subjected to a higher stress of 43%, while in the PCL, the difference is approximately 34%. This, of course, depends on the forces at work: the patella translates laterally while the tendons try to correct its position. Similarly, both the lateral and medial collateral ligaments undergo an increased load of 19% and 23% respectively. On the other hand, the femoral and tibial cartilages are subjected to 25% and 21% more stress, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Eq. Von Mises Stress**} \\ \hline
**Bony Parts** & **Healthy [MPa]** & **Unhealthy [MPa]** & **Difference [\%]** \\ \hline Femur & 53 & 79 & 49\% \\ Tibia & 37 & 47 & 27\% \\ Fibula & 22 & 26 & 18\% \\ Patella & 30 & 39 & 30\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Stress values calculated on the bony parts and percentage difference. Figure 6: Eq. von Mises contour maps for healthy and unhealthy configuration. Figure 8: Eq.