## 4 Discussion  
### Full Factorial Design  
For Response 1, the cortical thickness parameter is predominant over the others. Lower cortical bone thickness causes a very significant increase in stress in the peri-implant bone. Its impact is almost twice as great as that of the implant diameter, the second most influential parameter. The implant diameter is therefore decisive compared to other parameters, whereas its range of variation is only 1 mm. For Response 2, [PERSON]'s modulus of the implant is the most influential. A physiological situation in terms of material elasticity is approached when it becomes lower. The implant diameter is also predominant in this second response. The stresses in the implant are lower with a larger diameter, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Solution**} & \multirow{2}{*}{\begin{tabular}{c} **Stress Jump** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Average** \\ **Stress (MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Taper (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Diameter** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Length** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Angle (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Implant Young’s** \\ **Modulus (GPa)** \\ \end{tabular} } \\ \hline A & 6.23 & 6.09 & 0.35 & 3.79 & 14.99 & 0.07 & 60.34 \\ B & 6.42 & 5.80 & 0.75 & 3.90 & 14.98 & 0.41 & 60.50 \\ C & 6.65 & 5.75 & 1.2 & 3.86 & 14.98 & 0.94 & 62.22 \\ D & 6.81 & 5.45 & 1.7 & 3.95 & 14.97 & 1.14 & 61.68 \\ E & 7.00 & 5.38 & 2.45 & 3.89 & 14.98 & 0.64 & 60.85 \\ F & 7.14 & 5.20 & 2.55 & 3.97 & 14.96 & 1.25 & 62.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal solutions for multi-objective optimization. Figure 7: Solutions of genetic optimization: minimization of Response 1 and Response 2.  
resulting in a decrease of the stress jump between the bone and the implant. The same trend can be seen with the length parameter but is less marked. The interactions between two variables have weakly been studied and the ranking of so many interactions has never, to our knowledge, been done before. Strong interactions were found between the geometrical parameters of the implant coupled with the thickness of the bone for Response 1. Whatever the geometrical variable, its choice has an even greater impact on the stress level when the quality of the bone is degraded. This is particularly the case for the three variables of the intrinsic geometry of the implant (taper, diameter and length). These same interactions deeply affect Response 2. The interaction between cancellous bone Young's modulus and cortical bone thickness is also significant for Response 1. The increase in stress in cortical bone with the decrease in thickness had already been shown, but it became even more important with a low cancellous bone modulus, which is also a characteristic parameter of overall bone deterioration. When the cancellous bone is less rigid, it supports less the cortical bone, which tends to deform more under the effect of loading of the implant. On Response 2, interactions between the geometrical parameters of the implant (taper, diameter and length) and its Young's modulus are also very marked compared to the others. At constant loading, these variables influence the stress levels in the implant and thus the stress jump. The two interactions between Young's modulus of the implant and bone quality parameters can also be highlighted. Indeed, an implant that is too rigid will increase the stress jump on poor-quality bone much more than on good-quality bone. This means that the choice of implant material will have significantly more impact on deteriorated bone (osteoporosis). The angle of inclination parameter exhibits limited influence regarding the main effects.