## 2 Materials and Methods
### Adjustment of Load Pattern  
According to ISO 14243-1 [15], forces between 0.17 and 2.6 kN occur in the human knee during the normal gait cycle. In the rolling-sliding test bench, tests were carried out with a cylindrical test wheel, which is considerably narrower than a knee condyle. Therefore, in order to achieve a roll-slide movement under physiological forces, the force specified by the ISO standard needed to be reduced. In addition to the different geometries, the differences in material properties, such as the elasticity of the bearing partners, also needed to be taken into account. Furthermore, it is important to consider that only one knee condyle is represented in the roll-sliding test bench. According to [PERSON] et al., 70% of the axial force is transmitted with the medial condyle and 30% with the lateral condyle [19]. Hence, the spacer material was tested by simulating loading at the medial condyle.  
In order to determine the force to be transferred between the two articulating surfaces, A and B, taking into account the geometry and material properties, the formula for the contact pressure according to Hertz (Equation (1)) was chosen, with consideration of the material parameters (Equation (2)) for the case of a cylinder (A) on a plane (B):  
\[p_{H}=\sqrt{\frac{F}{2\ \pi\ r\ l}\ \times\ \frac{E}{1-v^{2}}} \tag{1}\]  
\[\frac{E}{1-v^{2}}=\left(\frac{1-v_{\rm A}^{2}}{E_{\rm A}}+\frac{1-v_{\rm B}^{ 2}}{E_{\rm B}}\right)^{-1} \tag{2}\]  
To calculate the forces for the roll-slide test rig, the physiological contact pressure in the human knee joint must first be determined. Therefore, the maximum axial force from ISO 14243-1 was considered. For the medial condyle, a maximum force of 2.6 kN resulted in an axial maximum force \(F_{medial}\) of 1.82 kN. The knee spacer material tested in this study was developed for the treatment of knee joints with progressive osteoarthritis. Patients often suffer from a severe lesion of the femur cartilage down to the surface of the subchondral bone. Therefore, the contact model of cortical bone (femoral site) on cartilage (tibial site) was chosen for the determination of the contact pressure. The Young's modulus and Poisson's ratio of cortical bone, which were articulated against cartilage, were chosen as parameters to test the material properties of the bearing materials. [PERSON] and [PERSON] determined variable properties for long- and short-term loaded cartilage [20]. To ensure that the worst-case scenario is covered, we used the higher value for the short-term loaded cartilage to calculate the contact pressure on the articulating surface. Since progressive osteoarthritis often results in a joint space narrowing accompanied by meniscal extrusion, the meniscus was not taken into account for the calculation of the contact pressure [21]. To determine the radius and width of the medial condyle, it is necessary to ascertain the flexion axis according to the ISO norm. Since the knee does not have a fixed center of rotation and the flexion axis shifts to anterior with increasing flexion, this axis needs to be approximated for the determination. For an accurate determination, both parameters were measured at maximum force. According to ISO 14243-1, this occurs at 15.32\({}^{\circ}\) of flexion [15].