## 2 Materials and Methods
### The Numerical Simulation of the Uniplane Opening Tibial Osteotomy  
A first stage of the research is the numerical simulation by the finite element method and consists of some static analyses of the CORA area. The behavior of this area is very important because the occurrence of micro-cracks or cracks in the CORA area can have consequences on both the smooth conduct of the surgery and on a good subsequent recovery. The software used to perform the analyses is Ansys. The purpose of the performed static analyses is to determine the state of stresses in the CORA area for the uniplane opening osteotomies, taking into account the studied parameteres, namely: X\({}_{1}\)--the position of the cutting point relative to the corresponding tibial plateau (Figure 2a) and X\({}_{2}\)--the value of the required correction angle (Figure 2b). Figure 2: Analyzed geometric parameters: (**a**) position of the cutting point; (**b**) the value of the correction angle. The characteristics of the materials necessary for performing these analyses resulted from the previously conducted bibliographic study [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40]. The values for the healthy mature bone, as summarized in [41], are the following:  
* Young's modulus (E)--12 to 19 GPa for the cortical bone, 0.5 to 1.5 GPa for the spongy bone, and 0.01 to 0.015 GPa for the articular cartilage. * Poisson's ratio--0.3 to 0.35 for the cortical bone, 0.16 to 0.2 for the spongy bone, and 0.2 to 0.25 for the cartilage. * Transverse modulus of elasticity (G)--4 to 7 GPa for the cortical bone. * Fracture resistance (Rm)--115 to 125 MPa for the cortical bone. * Elongation (A)--1.4 to 2.8% for the cortical bone. * Porosity--5 to 10% for the cortical bone, 50 to 90% for the trabecular bone. * Density--1.6 to 1.9 g/cm\({}^{3}\) for the cortical bone, 0.2 to 1 g/cm\({}^{3}\) for the trabecular bone. Considering that the opening osteotomies are made in the epiphyseal tibial area, mainly characterized by spongy bone, the use of the following mechanical characteristics in the FEM analyses was agreed upon: [PERSON]'s modulus--1000 MPa, [PERSON]'s ratio--0.18. In order to ensure the intraindividual variability of the simulations, we note that, in our calculation, we used the elastic modulus, taking into account the dependency relation between the bone's density and the elastic modulus. It is already known that researchers use a high variety of dependency relations between the bone density and the elastic modulus (linear laws, exponential laws). Out of these, we considered: \(E=C\)-\(\rho^{\beta}\), where E is the elastic modulus, C is a coefficient, and \(\beta\) is an exponent whose value varies in accordance to the nature of the bone (cortical or trabecular). Namely, the dependency function used was \(E=8.92\)-\(\rho^{1.83}\)[42] for a trabecular bone subjected to a compression load. By doing so, we could estimate what the maximum value of the loads in the bone component was by simply modifying the value of the elastic modulus. The starting point for obtaining the geometrical models was a 3D model of a human tibia, a component of a professional model of a human inferior leg. The model was acquired from the ZYGOTE company, a world leader in 3D anatomic modelling. Afterwards, the modelling of the medial open wedge HTO surgery was achieved by using the Catia V5R20 software. As we sought to obtain a CAD-CAE system with a high degree of generality and applicability, the models were achieved through a parametrized and generalized modelling. In this sense, the main variables that control, from a geometric and a dimensional point of view, the surgery were defined as parameters in the 3D modelling. By doing so, a mere modification of the parameters' values allowed us to obtain the desired geometrical model. For creating this models, we took into account the steps and the geometric elements that are used in the actual surgery. The relevant elements were positioned on the tibial model (Figure 3a): CORA axis, medial cortex, and the cutting point.