## 3 Results  
The tibial reaction moments are the main results for the validation of the described model. The comparison between simulation results and the reference values from literature is shown in Figure 5 for the load cycles corresponding to knee bend, sit down, and stand up. During weight-bearing squat, the medial tibial contact force was higher than the lateral one for low flexion angles. They showed equal values of 1350 N at the point of the zero-crossing of the varus-valgus moment at 75\({}^{\circ}\) of flexion. For higher flexion angles, the lateral contact force was the dominant one. At 30\({}^{\circ}\) (60\({}^{\circ}\), 90\({}^{\circ}\)) of flexion, the medial and lateral tibial contact forces reached 999 N (1310 N, 1373 N) and 478 N (950 N, 1700 N). Figure 5: Comparison of simulation output to the reference data for the tibial moments for knee bend, sit down, and stand up cycles. At the point of the maximum resultant tibial contact forces, the proportion of the medial contact force was 40% of the total tibial contact forces. Figure 6 shows the medial and lateral tibial contact forces for all three load cycles. For the knee bend cycle, the peak patellofemoral force was reached during the upwards movement at 91.4\({}^{\circ}\) of flexion with a magnitude of 2563 N, which is equal to 2.61 BW. The sit down cycle (stand up cycle) led to a maximum patellofemoral force of 2600 N/2.65 BW (2872 N/2.93 BW) at 84.2\({}^{\circ}\) (86.1\({}^{\circ}\)) of flexion. The main translational and rotational degrees of freedom, which are femoral AP translation and tibial rotation around its axis, were analyzed and are shown in Figure 7. The mean relative femoral AP translation was equal to the tibial translation in the opposite direction, which was directly given by the model. For the 98\({}^{\circ}\) squat, the maximum AP translation between femur and tibia was 16 mm at a flexion angle of 98.1\({}^{\circ}\). Figure 6: Tibial contact forces in medial and lateral compartment during weight-bearing squat. The tibial rotation could also be directly derived from this model by taking the femoral rotation around the tibial \(z\)-axis with a negative sign (Figure 7). A maximum tibial rotation of 8\({}^{\circ}\) was calculated at 93.6\({}^{\circ}\) of flexion (knee bend cycle). For applications without evaluation of the tibiofemoral contact, the PE insert could be simulated as a rigid body to decrease computational time by about 10% without changing kinematics in a considerable way. The averaged difference between the curves of the tibial reaction moments was less than 4%. Furthermore, taking peak patellofemoral force during the knee bend cycle as an example, this value changed by only 42 N, going from 2539 N to 2581 N when simulating the PE insert as a rigid body. The patellar kinematics were analyzed under variations of the patellar tendon stiffness between 300 N/mm and 1000 N/mm, and the initial proximo-distal patellar position was simultaneously varied in a range of \(\pm\)6 mm. The peak values of patellar flexion, spin, and tilt during the downwards movement of the knee bend are given in Figures 8-10. The maximum absolute values of patellar flexion decrease for a decreasing stiffness of the patellar tendon and for a more proximally-placed patella. The peak values of patellar spin are between 3.64\({}^{\circ}\) and 5.26\({}^{\circ}\) of lateral rotation. Figure 7: Femoral rollback of medial and lateral condyle and the axial femoral rotation for sit down, stand up, and knee bend cycle. The patellar spin increases with a weaker patellar tendon and for patellae placed more proximally. The range of peak values of patellar tilt is between 3.35\({}^{\circ}\) and 3.68\({}^{\circ}\) of medial tilt and no clear relationship to the initial patellar proximo-distal position or the stiffness of the patellar tendon can be seen.