## 2 Materials and Methods
### The Numerical Simulation of the Uniplane Opening Tibial Osteotomy
We note that, during the modelling, the cutting point was constrained so as to permanently coincide with the medial cortex and so its position can be defined relative to the tibial plateau (30, 40, 50 mm in our study). Additionally, we note that the line (depicted in blue in Figure 3a) that started from the cutting point and was perpendicular on the CORA axis defined, together with the CORA axis, the osteotomy plane. To achieve the correction, it was necessary to rotate the proximal segment of the tibia around the CORA axis (Figure 3b). The correction angle was measured between the successive positions (before and after the rotation) of the blue line (depicted in Figure 3c) that started from the cutting point and was perpendicular on the CORA axis (Figure 3c). In this way, we obtained the geometrical models that were necessary for the FEM analyses, models that were later imported in the ANSYS software. These are differentiated by parameters X\({}_{1}\) and X\({}_{2}\), to which the values listed in the table below were assigned (Table 1):  
The values assigned to variable X\({}_{1}\) were justified by the data collected from scientific literature [20, 24, 25, 26, 27, 28], which proves that, as mentioned above, this distance should not have been smaller than 30 mm, nor should it have exceeded 50 to 60 mm. Obviously, the anatomical dimensions of the bone were also taken into consideration. Consequently, the values chosen for the FEM analyzes were: 30, 40, and 50 mm. The second variable, X\({}_{2}\), was the angle at the tip of the osteotomy wedge, which was identical to the correction angle. The variable was important because the higher the correction angle was, the higher the probability of CORA area cracking was. Possible correction angles resulting from literature [20, 24, 25, 26, 27, 28] and surgical practice ranged between 4-5 degrees to 16-18 degrees. The boundaries were given by the fact that a value that was too low did not justify the surgery, and a value that was too high made the surgery impossible. Consequently, the values considered appropriate for this research were: 6, 10, and 14 degrees. As shown in Table 1, all possible combinations between the values of the two variables were considered, thus resulting in nine geometric CAD models. With respect to the degree of precision of the analyses performed by using the finite element method, we note that the network of used elements (a network of tetrahedric elements) was generated so the element size did not exceed 1 mm. Hence, the meshed model contained 861,371 finite elements \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **X\({}_{1}\) (mm)** & **X\({}_{2}\) (degree)** \\ \hline
1 & 30 & 6 \\
2 & 30 & 10 \\
3 & 30 & 14 \\
4 & 40 & 6 \\
5 & 40 & 10 \\
6 & 40 & 14 \\
7 & 50 & 6 \\
8 & 50 & 10 \\
9 & 50 & 14 \\ \hline \end{tabular}
\end{table} 
Table 1: Values assigned to the variables and their combinations. Figure 3: 3D modelling of the medial open wedge HTO surgery: (a) geometrical elements; (b) 3D rotation; (c) correction angle. connected one to another through 1,261,857 nodes. Moreover, the check mesh quality function was activated, and a 100% obsolete mesh percentage resulted. By doing so and by performing a slow type transition from the large size elements to those of a reduced size, we made sure that the error percentage did not exceed 3%, a unanimously accepted value in the scientific community. Figure 4a shows the model meshed for a cutting point located at 30 mm from the tibial plateau and a correction angle of 14 degrees. The method of applying the necessary stresses and constraints on the model (Figure 4b) considers the angular removal of the two sides of the osteotomy cut in order to achieve the osteotomy wedge at the desired correction angle. In this regard, a fixed constraint was considered, located on the side facing the joint, while the other face was subjected to a uniformly distributed stress. The static structural analysis was made when the required correction angle was reached.