## 2 Materials and Methods
### FE Model  
The six degrees of freedom between femoral and tibial implant component were defined as follows (Figure 1): The femoral component was free to revolve around a fixed center of rotation, which coincided with the center of rotation in full extension. The tibial component was free to translate in all axes with fixed rotations. The separation of translational and rotational degrees of freedom of the tiboferomal joint in the described way led to a stable FE model without restricting the relative kinematics in any way. The flexion  
Figure 1: CAD model of the used implant components and the global coordinate system. angle was the only degree of freedom, which was predefined by the dataset. So, there remain five degrees of freedom according to the tibofemoral kinematics. The patella has six additional degrees of freedom and is only guided by its contact to the trochlear groove and four spring-elements, which modeled the function of the patellar and quadriceps tendons (Figures 1 and 2). There are two main contact areas in the knee joint which had to be taken into account. Both the tibofemoral and the patellofemoral contact areas were modeled as asymmetric augmented Lagrangian contacts. A coefficient of friction of 0.05 was used for this simulation [33; 34; 35]. To minimize computing time, the small deformation of the femoral component was neglected, and it was instead defined as rigid body. Therefore, only some contact elements on its surface were needed, instead of a fully meshed geometry [36; 37; 38]. The material properties of the PE insert and the patella component were defined by a bilinear stress-strain curve with a yield strength of 25 MPa [33]. In the first step of the calculation, the flexion angle and the standardized tibial forces \(F_{x}^{B}\), \(F_{y}^{B}\), and \(F_{z}^{B}\) in the lateral (\(x\)-axis), anterior (\(y\)-axis), and proximal (\(z\)-axis) directions, as given by [PERSON] et al. [31], were used as time-dependent input. Secondary input data were calculated from this primary data and provided as input for the FE model. The flexion angle was the only degree of freedom which was externally controlled. The given tibial forces could not directly be applied to the PE insert because the forces acting on the patellar tendon (\(F^{P}\)) and collateral ligaments (medial: \(F^{C,m}\) and lateral: \(F^{C,l}\)) and the ground reaction forces (\(F^{G}\)) had to be subtracted first. In this study, the upper indices identified the forces or moments, while lower indices specified components of vectorial variables. Forces caused by tissues, muscles, and ligaments, which are not explicitly modeled, are summarized by an additional force vector \(F^{r}\). It complements the explicit modeled forces acting on the tibia to the standardized tibial loads \(F^{B}\). This simplification allows  
Figure 2: Tibial forces (black) and their components in \(y\) (green)- and \(z\) (blue)-directions, respectively. to avoid the modeling of every single muscle and ligament, which would exceed the acceptable effort in modeling and solving for an everyday design evaluation tool without providing better results regarding implant loads and kinematics. For the ground reaction force, 490.5 N (100 kg BW divided by two legs) are applied normal to the plane of the tibial plateau. Figure 2 shows the described forces with their components in the \(y\)- and \(z\)-directions. In a frontal view, the same could be performed for the \(x\)- and \(z\)-directions. To split the standardized loads into the single forces stated above, the equilibrium of forces in the proximal (\(z\)) and anterior (\(y\)) directions from a sagittal view is set up. The described forces must replace the forces from the load data, which led to  
\[F_{z}^{B}=F^{G}+F_{z}^{r}+F_{z}^{p}+F_{z}^{C,m}+F_{z}^{C,l}\text{ and } \tag{1}\]  
\[F_{y}^{B}=F_{y}^{r}+F_{y}^{p}+F_{y}^{C,m}+F_{y}^{C,l} \tag{2}\]  
The angle of the patellar tendon is used to derive the equation for \(F_{y}^{p}\) from \(F_{z}^{p}\), which results from Equation (1).