## 3 Materials and Methods
### Finite Element Models Proposed  
After both STL files were generated (for the healthy and Cam-type hip joints), they were imported into the [PERSON](r) software [48] for the generation of the mesh of the cortical and cancellous bone and cartilage, and their subsequent FE analysis. The mesh for both hip joints FE models was created by 4-node tetrahedral elements with linear formulation. After each FE model was generated, an analysis of sensibility was conducted. The reason for this analysis was to determine the correct size of the elements used to ensure good results at the lowest computational cost. For all the FE models, element sizes of 0.32, 0.65, 1.0, 1.2, and 1.6 mm were used. A compression test was applied for each proposed FE model, with their different sizes of proposed elements. This test consisted of the application of a load of 40 kg in the longitudinal direction of the femur (not including its rotation of this bone). All the proposed FE models with all the different mesh sizes were simulated in computers with by Xeon processor, CPU 2.2 GHz (two processors) and 128.00 GB (random access memory (RAM)). The maximum values for the von Mises stresses from all the FE models and their computational cost were obtained, and appear in Table 1. The table indicates that, as the mesh size decreased, the computational cost increased, and the difference between the von Mises stresses between each mesh sizes analyzed was smaller. For example, the von Mises stresses obtained when the mesh size was 0.65 mm hardly differed from the stresses obtained for a mesh size of 0.32 mm (0.98 MPa vs. 0.96 MPa for healthy; and 2.28 MPa vs. 2.27 MPa for Cam-type), whereas the computational cost was notably greater (2184 min vs. 1718 min for healthy; and 2319 min vs. 1987 min for Cam-type). Once the results obtained were analyzed according to the von Mises stresses and the required computational cost, a mesh size of 0.65 mm was selected to carry out the study of a healthy and Cam-type hip joint considering an alpha angle of 50\({}^{\circ}\) and the patient's body weight of 80 kg.  
Figure 5 shows the mesh that was generated with the MeshMixer software after it was imported into the Mentat-Marc(r) software, considering a mesh size of 0.65 mm. Figure 5a shows the FE model with the damaged hip joint (of the Cam-type), whereas Figure 5b,c shows, respectively and in detail, the femur and the pelvis with the cartilage. In addition, Table 2 summarizes the number of elements and nodes of the pelvis, femur, and cartilage of the healthy and Cam-type hip joints when the mesh size considered is 0.65 mm.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Element Size** & **Comp. Cost** & **von Mises** & **Comp. Cost** & **von Mises** \\
**[mm]** & **Healthy [Min.]** & **Healthy [MPa]** & **Cam-Type [Min.]** & **Cam-Type [MPa]** \\ \hline
1.6 & 1057 & 0.52 & 1177 & 1.09 \\
1.2 & 1428 & 0.77 & 1492 & 1.83 \\
1.0 & 1575 & 0.89 & 1662 & 2.14 \\
0.65 & 1718 & 0.96 & 1987 & 2.27 \\
0.32 & 2184 & 0.98 & 2319 & 2.28 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Computational cost and maximum von Mises Stress for the element sizes of healthy and Cam-type hip joint FE models.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Healthy Hip Joint**} & \multicolumn{2}{c}{**Cam-Type Hip Joint**} \\ \hline  & Elements & Nodes & Elements & Nodes \\ Pelvis & 285,785 & 66,477 & 285,649 & 66,474 \\ Cartilage & 46,285 & 13,285 & 45,849 & 13,159 \\ Femur & 186,265 & 42,121 & 186,198 & 42,105 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The number of elements and nodes of the pelvis, femur, and cartilage of the healthy and Cam-type hip joints, considering a mesh size of 0.65 mm.