## 2 Materials and Methods
### FEM Analysis for Optimization of OWHTO Geometrical Planning  
An important moment in the successful realization of the OWHTO is the creation of the correction angle, i.e., the creation of the osteotomy wedge (Figure 6b), after the realization of the cut of the osteotomy plane (Figure 6a). This can be achieved by elastic deformation of the bone with a specialized spacer [34]. In order to avoid microcracks that may appear in the CORA or in the articular area of the medial tibial plateau, it is essential to choose the correct lot of values for the 4 variables (V1, V2, V3, V4) that characterize the geometric planning shown in Figure 6.  
Figure 6: 3D modelling of the OWHTO—the parameters of the geometrical planning. For the success of this operation and a fast and efficient recovery, an optimization of the 4 variables (V1, V2, V3, V4) is required. The optimization was performed using several sets of values and a research program was prepared using the Taguchi method, Table 1. The choice of variation levels for the 4 variables (minimum and maximum values) was made according to the surgical practice, the research and clinical trials performed. Thus, values between 30 mm and 50 mm are recommended for variable V1 [35; 36]. A minimum level of 30 mm and a maximum of 40 mm were chosen for this variable. For CORA positioning, the recommended value ranges are 5-10 mm for V2 and 15-20 mm for V3 [35; 36; 37]. Consequently, for V2 the minimum level of 7.5 mm and the maximum level of 10 mm were chosen and for V3 the minimum level of 15 mm and the maximum level of 20 mm. The Taguchi method was also used to program the research, as it allows an efficient calculation of the average effects of the variables on the response sizes. The choice of the Taguchi method was also necessary due to the fact that it allows the observance of several restrictive conditions. OWHTO geometric planning optimization was conducted using finite element method (hereinafter FEM). Thus, by using FEM, the values of the following parameters were determined: equivalent stress, shear stress, displacement. The results obtained by FEM are response functions for the combinations of input sizes presented in Table 1 and allow the identification of those sets of values for which the three output sizes listed above will have the lowest values to avoid the appearance of microcracks in the tibia. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Code**} & \multicolumn{4}{c}{**Values of Variables**} \\ \cline{2-5}  & **V1, mm** & **V2, mm** & **V3, mm** & **V4, \({}^{\circ}\)** \\ \hline
1 & 30 & 7.5 & 15 & 6 \\
2 & 30 & 7.5 & 15 & 12 \\
3 & 30 & 10 & 20 & 6 \\
4 & 30 & 10 & 20 & 12 \\
5 & 40 & 7.5 & 20 & 6 \\
6 & 40 & 7.5 & 20 & 12 \\
7 & 40 & 10 & 15 & 6 \\
8 & 40 & 10 & 15 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Research design using the Taguchi method. Figure 7: 3D modelling of the OWHTO with TomoFix Medial High Tibial Plate. The known steps were taken to perform the FEM analysis. Thus, the geometric model developed in the CATIA V5R20 program and presented in Section 2.1 was imported as a geometric model using the STEP transfer standard and then discretized. Both modeled entities (cortical and cancellous) were considered to be homogeneous, isotropic and linearly elastic. [PERSON]'s modulus for the tibia was 17 GPa for the cortical, 5 GPa for cancellous bones and [PERSON]'s ratio was 0.33 [38; 39; 40]. The model was discretized (meshed) and its constraints and loads were applied (Figure 8a). As this analysis was aimed at the intraoperative creation of the osteotomy wedge, the value of the applied force was 175 N. The value was chosen taking into account the values existing in the literature between 120-200 N [36; 41]. Figure 8b shows the meshed geometric model to which the constraints and loads were applied. As can be seen, since the area of interest is the proximal one of the tibia, a section was made in the middle of the tibia and only the upper part was analyzed.