## 2 Materials and Methods
### Finite Element Method Analysis  
On ANSYS 2022 (Canonsburg, PA, USA), models of the bones (with and without supports), and femoral cartilage from each subject were imported to understand the influence of OA defects onto the cartilage mechanical properties through computational  
Figure 2: Three-dimensionally printed functional model of the knee joint (femur, tibia and femoral cartilage) during the mechanical evaluation. analysis. Here, the different parts were assembled into a single model, and the material properties, loads and boundary conditions were assigned. Five different materials were chosen during the simulation: _Cartilage Literature_, _Bone Literature_, _Printed Cartilage Soft_, _Printed Cartilage Medium_ and _Printed Bone_. From a biomechanical standpoint, articular cartilage can be effectively represented as an elastic isotropic material during dynamic loading [26]. This is because the loading time of interest, corresponding to that of a fully extended leg touching the ground, is much shorter than the viscoelastic time constant of cartilage, which is 1500 s [27]. This approximation proves accurate for short-term cartilage response as demonstrated by [PERSON] et al. [28], who proved that there are no significant changes in the cartilage contact response shortly after loading. Cartilage behaves as an incompressible material in its short-term (instantaneous) response (\(v\approx 0.5\)), while it reflects characteristics of a compressible material in its long-term response (\(v\approx 0\)) [29]. Therefore, in order to capture the intermediate behavior observed during physiological walking, which falls between the instantaneous and long-term responses to functional loads, a Young's modulus of 5 MPa and a Poisson's ratio of 0.45 were chosen to represent the cartilage behavior [30; 31; 32]. We assessed the impact of bone properties on cartilage with a FEM analysis. We assigned the materials _Printed Bone_ and _Bone Literature_ to the bones and then evaluated the results. Despite the substantial difference in stiffness values between the two materials, the observed variations in stress and strain within the femoral cartilage were close to 1%. Therefore, since the influence of bones properties on cartilage was minimal, we decided to model the bones as an isotropic linear elastic material with a Young's modulus of 17,000 MPa and a Poisson's ratio of 0.31 [33] in order to avoid unnecessary computational costs as confirmed in the literature [31; 34]. Elastic properties of the designed materials are reported in Table 2.  
The connections between femur-cartilage and cartilage-tibia were defined as bonded [35] due to a partially mineralized zone between that secure cortical bone and the articular cartilage by anchoring the collagen fibrils of the deep zone to the subchondral bone [1]. Due to the simplification applied to the model, by excluding menisci and tibial cartilages, a pinball region was set to compensate for the gap between the tibia and femoral cartilage. The asymmetric behavior and the augmented Lagrange formulation were used for handling contacts. In the analyses, flexo-extension and varus-valgus rotations were constrained for the femur in order to analyze the knee joint in full extension. The tibia was constrained on the lower surface with a fixed support. A compressive force of 1150 N was applied perpendicularly to the upper surface of the femur, which matches the force acting during a gait cycle for a full extension position [36] (Figure 3, Left). The values of Equivalent Elastic Strain [mm/mm] and Equivalent (von Mises) Stress [MPa] for the femoral cartilage were exported, and the stress-strain graphs were created to analyze the joint behavior with different material properties. The first FEM analyses on both subjects were carried out by assigning the _Soft_ and _Medium_ materials to the femoral cartilages and the _Printed Bone_ (_VeroWhite_) material to the bones, using their native geometry.