## 3 Results  
The resulting optimal profile of the IFS FE model showed that unnecessary elements were removed under a stress constrain condition and a HS model was generated with jagged appearance to optimize/reduce the structural volume (Figure 2a,b). The HS model structure and high stress regions represented trends similar to the buttress pillars of the nasomaxillary and zygomaticomaxillary buttresses (Figure 6). The variation in maximum bone stress (maximum principal stress) and solid volume between the IFS and HS models was 18.3% and 75.1%, respectively (Table 1). Since the load condition was applied to the vertical force on premolars and molars, it produced a counterclockwise bending moment on the maxillary and zygomatic bones. Points 1, 2, and 3 located at the lower, middle, and upper of the frontal process received compressive stress; the minimum principal stresses (3 rd minimum principal stress) on these points were denoted to indicate the magnitude of compressive stresses. The maximum principal stresses (1 st maximum principal stress) were denoted to present the tensile stress values of points 4, 5, and 6 located at the lower, middle, upper of the zygomatic process, respectively. Table 2 showed the bone stress values corresponding to points 1 to 6. Figure 7 shows a comparison of the maximum/minimum bone stress values among the IFS model; the \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Topology Optimization** & **Volume (mm3)** & **Max. 1 st Principal stress (MPa)** \\ \hline IFS model & 112,890 & 22.37 \\ HS model & 28,093 & 26.46 \\ variation (\%) & 75.1\% & 18.3\% \\ \hline \hline \multicolumn{5}{c}{**The stress variations of 1–6 points between the HS model and IFS model**} \\ \hline  & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \hline \multirow{3}{*}{**Unit: MPa**} & \multirow{3}{*}{\begin{tabular}{c} **Compression** \\ **(minimum principal stress)** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Tensile** \\ **(maximum principal stress)** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Tensile** \\ **(maximum principal stress)** \\ \end{tabular} } \\ \cline{1-1} \cline{2-5}
**Intact model** & & & & \\ \cline{1-1} \cline{2-5}
**(IFS model)** & \(-\)6.25 & \(-\)3.13 & \(-\)4.73 & 5.62 & 6.87 & 4.32 \\ \hline
**HS model** & \(-\)6.25 & \(-\)3.21 & \(-\)4.19 & 5.14 & 6.41 & 4.31 \\ \hline
**Variation (\%)** & 0.16\% & 2.56\% & 11.42\% & 8.54\% & 6.70\% & 0.23\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The variation of maximum bone stress (maximum principal stress) and solid volume between the IFS and HS models. Figure 6: The stress distribution of the IFS model and HS model, (**a**) and (**b**) stress distributions of the IFS and HS models, respectively. High stress regions represented a similar trend as buttress pillars of the nasomaxillary and the zygomaticomaxillary buttresses. ZMC fracture repair with thin implant and traditional mini-plates. The difference between the values should be expressed as a percentage, as shown in Figure 6. Since the frontal process was subjected to compressive stress, the stress value at the 1 st to 3 rd point on each model was compared with the minimum principal stress, while the tensile stress was applied to the zygomatic process, so the stress value at the 4 th to 6 th point was compared with the maximum principal stress. A similar stress pattern occurred between the IFS model and repair with the PSBT implant, i.e., convex curves were found while connecting the maximum stress value from points 1 to 3 and points 4 to 6. However, a different corresponding curve trend was found for the repair with mini-plates from points 1 to 3. The percentage of stress variations between the IFS and PSBT implant models was from 2.75% to 26.78%, which was much smaller than the corresponding variations from 30.67% to 96.26% between the IFS model and mini-plate models (Figure 7). Figure 8 presents the intact skeleton bone stress distribution, the ZMC fracture repair with the PSBT implant and traditional mini-plates.