## 2 Materials and Methods
### CAD Modeling of the Tibia Assembly--Plate Tomofix Osteosynthesis after OWHTO Surgery
#### 2.1.1 Three-Dimensional Modeling of the Tibia Taking into Account the Real Structures of the Bone  
Regarding the 3D modeling of the tibia, there is a trend in the literature for using 3D bone models without taking into account the real heterogeneous structure of human bones [28; 29]. Given the use of such models, a number of important research limitations may arise. Therefore, in this research, the aim was to create the CAD model of a real human tibia, constituted as a set of several structural entities with different dimensional, geometric, anatomical and mechanical characteristics. To achieve this goal, we started from a 3D professional model of a human tibia purchased from the ZYGOTE company, a world leader in 3D anatomical modeling. Figure 1 shows this initial model, highlighting from a dimensional point of view, the total length of the tibia, measured from the tibiadar joint to the tibial spine (376 mm), its width in the tibial plateau area (78 mm) and the length of the diaphysis, which is 272 mm. Additionally, the three important areas of the bone are presented, namely, distal epiphysis, diaphysis and proximal epiphysis, respectively. The mentioned dimensions are important, being reference elements in the dimensional characterization of the tibia. Starting from these and using quantitative computed tomography (hereinafter QCT) and images or previous research [30; 31; 32; 33], it was possible to make the necessary correlations to model the real entities of which the tibia is constituted. As is known [31; 32], the 3 components of the tibia mentioned above are structurally different. The diaphysis has a tubular structure made of cortical bone, is compact, with a variable thickness. Inside this structure is the medullary cavity filled with bone marrow. The two epiphyses that form the extremities of the tibia have a heterogeneous bone structure, being formed both of the cortical bone hard to the outside, and of the trabecular or spongy bone inside. CAD modeling was performed in Catia V5R20 software, taking into account the elements mentioned above. The main stages of modeling were:  
* creating three distinct 3D models from the tibia model: distal epiphysis, diaphysis and proximal epiphysis, respectively, Figure 1;
* remodeling each of these three initial models taking into account the actual bone structure;
* assembling remodeled entities. A. CAD Modeling of the Epiphysis  
Figure 2 shows the 3D models obtained for the two epiphyses, each of which is the set of two entities corresponding to the areas of cortical and trabecular bone. In order to obtain the models for the compact cortical bone area, a spatial off-setting (from the initial model) of the external surfaces of the two epiphyses was performed. The size of the offset, which represents the thickness of the cortical bone at the level of the epiphyses, was adopted of 2.5 mm, a value taken from the literature [30]. Figure 1: Shows the 3D models obtained for the two epiphyses, each of which is the set of two entities corresponding to the areas of cortical and trabecular bone. Figure 2: Three-dimensional model of the distal and proximal epiphysis—real structure of the bone. For the modeling of the areas formed by the trabecular bone, Boolean operations were used to extract from the initial model of the previously modeled compact cortical bone entities, the extracted part (the green one in Figure 2) thus becoming the 3D model of the trabecular structure of the epiphyses. B. CAD Modeling of the Diaphysis and Metaphysis  
The diaphysis' modeling was more complex due to its variable geometry. In order to obtain the real tubular structure, a sectioning of the initial model of the diaphysis was first performed, which has a length of 272 mm, with 17 planes perpendicular to the tibia, positioned equidistantly. In the case of the real diaphysis, each of these sections is characterized by an outer and an inner contour.