## 2 Materials and Methods
### Shape Analysis for Parameter Detection  
In order to measure parameters, we performed 3D surface reconstruction from magnetic resonance imaging (MRI) scans of 261 female femoral surfaces based on quality assured manual segmentations of the distal femur bone. The segmentations were part of the previously published OAI-ZIB dataset [22]. For further technical details, we refer the reader to that publication. We calculated the point-wise mean shape, a standard procedure in statistical shape modeling [23], and performed an error-minimizing cylinder fit to the condyle region with respect to the contact points obtained by virtually mimicking the flexion-rolling of the distal femur bone (see Figure 4a,b). The radius of the determined cylinder serves as parameter \(r_{madi}\). Taking the center line of the fitted cylinder as the (flexion) axis, we intersected the medial condyle region with a plane deflected by \(15.32^{\circ}\) and adapted the resulting intersection curve to the load-bearing cartilage interface by restriction to the segment connecting the two points of maximal curvature. The parameter \(l_{madi}\) could then be defined as the Euclidean distance between these points (see Figure 4c). In contrast to most studies in which the condylar radius is determined by considering the condyles as independent spheres [24; 25], this study fitted a cylinder around the flexion axis of both condyles. This approach was chosen because ISO 14243-1:2009 also takes the flexion axis into account when both condyles contact the tibial plateau. Furthermore, in the study by [PERSON] et al. [24], only very small differences between the radii of the medial and lateral condyles of a human knee joint were determined (on average 0.1 to 0.2 mm, accompanied with high standard deviations), although the condyles were considered individually as spheres. As these are very small differences, we assume that the use of a cylinder in the determination of the radius is suitable. The parameters used are summarized in Table 1.  
This resulted in a constant value of \(E/(1-v^{2})=14.56\) N/mm\({}^{2}\) for the bearing materials cortical bone on cartilage with the material parameters after insertion in Equation (2). This resulted in the following equation for the physiological contact pressure:  
\[p_{H}=\sqrt{\frac{F_{madi}\times 14.56\ N/mm^{2}}{2\ \pi\times 20.58\ mm\times 25.29\ mm}} \tag{3}\]  
In order to determine the force for the rolling-sliding test bench, Equation (1) had to be modified according to the force and the determined natural contact pressure with the geometric data and the material data of the samples to be tested. The geometric parameters \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Meaning** \\ \hline \(F\) & 0.17 to 2.6 kN & Axial force according to ISO 14243–1 [15] \\ \(F_{meli}\) & 0.12 to 1.82 kN & Axial force that is transmitted via the medial \\  & & \multicolumn{1}{c}{} & \\  & & \multicolumn{1}{c}{} & \\  & & \multicolumn{1}{c}{} & \\  & & \multicolumn{1}{c}{} & \\ \end{tabular} \
\begin{tabular}{c} \(r_{madi}\) \\  & 20.584 mm & Cylinder radius/radius of the condyle \\  & & Length of contact of the cylinder with the \\  & & \multicolumn{1}{c}{} & plane/cartilage surface \\  & & \multicolumn{1}{c}{} & \\  & & \multicolumn{1}{c}{} & \\ \end{tabular}
\begin{tabular}{c} \(E_{A}=E_{cortical bone}\) \\  & 17,000 N/mm\({}^{2}\) & [PERSON]’s modulus of cortical bone [26] \\  & 0.3 & [PERSON]’s ratio of cortical bone [26] \\  & 12 N/mm\({}^{2}\) & [PERSON]’s modulus of cartilage [20] \\  & 0.42 & [PERSON]’s ratio of cartilage [20] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used to determine the physiological contact pressure in the medial knee joint. Figure 4: Algorithmic estimation of condyle radius and width. (**a**) Contact points of simulated flexion movement on the distal femur; (**b**) optimal cylinder fitted to the contact points; and (**c**) curve along and through the medial condyle approximating the describing contact for a flexion angle of \(15.32^{\circ}\).