## 2 Materials and Methods
### Finite Element Analysis and Boundary Conditions  
Abaqus/Standard version 6.19 (Dassault Systemes, Velizy-Villacoublay, France) was used to assemble all parts of the prosthesis with femur bone, in order to perform all the finite element simulations. Each model was meshed using tetrahedral elements with a size between 1 mm and 3 mm. A refinement of mesh was performed in the contact area of the internal components of the implant, and in the tibio-femoral and bone-implant interface sections to make sure that the selected mesh was the proper one to achieve the sought after results: to check the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Material Model** & **Elastic Modulus (MPa)** & **Poisson Ratio** \\ \hline CoCr & Isotropic & 240,000 & 0.30 \\ \hline UHMW & Isotropic & 685 & 0.40 \\ \hline PMMA & Isotropic & 3000 & 0.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of the implant components: CoCr = cobalt-chromium alloy, UHMWE = ultra-high-molecular-weight-polyethylene, PMMA = polymethyl-methacrylate. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Material Model**} & \multicolumn{3}{c}{**Elastic Modulus (MPa)**} & \multicolumn{3}{c}{**Poisson Ratio**} \\ \cline{3-8}  & & **E\({}_{1}\)** & **E\({}_{2}\)** & **E\({}_{3}\)** & **v\({}_{12}\)** & **v\({}_{23}\)** & **v\({}_{31}\)** \\ \hline Cortical Bone & Transversely Isotropic & 11,500 & 11,500 & 17,000 & 0.51 & 0.31 & 031 \\ \hline Cancellous Bone & Isotropic & 2130 & & & 0.30 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of the femoral bone used for all models; the third axis was taken parallel with the anatomical axis of the femur. quality of the mesh and the proper size, a convergence test was thus performed [2; 20] and is available in the Supplementary Materials. According to the previously published study [21], surface-to-surface contacts were implemented for the definition of all contacts, i.e., among the components involved in the hinge mechanism, between the insert and the femoral component of the prosthesis and between the implant and the bone. Each configuration analyzed was tested under the same total load conditions, i.e., the proximal part of the femur constrained and a total vertical compressive force of 1000 N applied to the inferior face of the tibial tray. The subdivision of this total force on the two sides of the tibial tray was then used as a parameter in order to model the different levels of varus/valgus deformities: a simplified model in the literature [11] allowed indeed to obtain the percentage of force distribution in the medial and lateral regions of the tibial component for each angle of deformity (based on the equilibrium of forces and moments in the frontal plane), and was therefore taken as reference. The percentages of force distribution in the medial and lateral compartments obtained from this mathematical model are reported in Table 3.  
These percentages were therefore used in the present study to determine the subdivision of the total force on the medial and lateral sides, and the resulting forces were applied on the respective side of the tibial tray plateau (see Figure 1), as input loads for the FE simulations. Figure 1: Load conditions applied to the model, (**A**) frontal view, reporting the direction of the forces applied; (**B**) distal view, reporting the area used for the applied force. FL = lateral force (in blue), FM = medial force (in green).