# Identification of Surgical Plan for Syndesmotic Fixation Procedure Based on Finite Element Method
## 3 Results  
After completing the FE analysis of each type of syndesmotic screw, the data were outputted, as shown in Figures 4 and 5. Tables 5-8 show the analysis of the maximum von Mises stresses and syndesmosis widening results. Figure 3: Loading conditions applied to the finite element (FE) model: (**a**) compressive force, (**b**) tangential force, and (**c**) fixed support. Figure 4: **The von Mises stresses of the syndesmotic screw and adjacent bone at screw level of 25 mm with three cortical bones purchased: (a) titanium screw with a diameter of 3.5 mm, (b) stainless steel screw with a diameter of 3.5 mm, (c) titanium screw with a diameter of 4.5 mm, (d) stainless steel screw with a diameter of 4.5 mm. **  
Figure 5: The von Mises stresses of the syndesmotic screw and adjacent bone at screw level of 25 mm with four cortical bones purchased: (**a**) titanium screw with a diameter of 3.5 mm, (**b**) stainless steel with a diameter of 3.5 mm, (**c**) titanium screw with a diameter of 4.5 mm, and (**d**) stainless steel screw with a diameter of 4.5 mm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Diameter (mm)**} & \multirow{2}{*}{**Level (mm)**} & \multicolumn{2}{c}{**Maximum von Mises Stress (MPa)**} & \multicolumn{1}{c}{**Syndesmosis**} \\ \cline{3-5}  & & **Screw** & **Adjacent Bone** & **Widening (mm)** \\ \hline
3.5 & 10 & 611.60 & 206.07 & 0.6722 \\
3.5 & 15 & 574.21 & 179.42 & 0.4707 \\
3.5 & 20 & 550.93 & 161.62 & 0.1095 \\
3.5 & 25 & 577.37 & 142.97 & 0.0117 \\
4.5 & 10 & 370.49 & 202.59 & 0.1526 \\
4.5 & 15 & 368.86 & 139.03 & 0.1179 \\
4.5 & 20 & 344.13 & 170.35 & 0.0682 \\
4.5 & 25 & 372.05 & 115.01 & 0.0891 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Maximum von Mises stresses and syndesmosis widening: titanium with four cortical bones purchased. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Diameter (mm)**} & \multirow{2}{*}{**Level (mm)**} & \multicolumn{2}{c}{**Maximum von Mises Stress (MPa)**} & \multicolumn{1}{c}{**Syndesmosis**} \\ \cline{3-5}  & & **Screw** & **Adjacent Bone** & **Widening (mm)** \\ \hline
**3.5** & **10** & 346.58 & 192.24 & 0.4217 \\
3.5 & 15 & 345.39 & 177.06 & 0.1504 \\
3.5 & 20 & 325.30 & 158.60 & 0.1292 \\
3.5 & 25 & 312.16 & 126.25 & 0.0752 \\
4.5 & 10 & 310.08 & 206.35 & 0.2123 \\
4.5 & 15 & 310.96 & 128.06 The maximum von Mises stress is the maximum stress acting on the engaged syndesmotic screw and adjacent bone of the screw. This stress was measured by applying a load to the tibia. The values of the maximum von Mises stresses, listed in Tables 5-8, show that the stresses decrease with an increase of the screw level from 10 to 25 mm. Figures 6-11 show the graph of the stress results at the syndesmotic screw and adjacent bone of the screw, to facilitate the understanding of the stress trend for the remaining parameters. Figure 6 shows that the maximum von Mises stress of the stainless steel screw is lower than that of the titanium screw. As shown in Figure 7, the stress is lower for a diameter of 4.5 mm compared with that for a diameter of 3.5 mm. The maximum von Mises stresses are slightly lower for cases wherein three cortical bones are penetrated compared with other cases, as shown in Figure 8.  
Figure 6: Analysis of the maximum von Mises stresses of the syndesmotic screw in terms of the syndesmotic screw material for screws with diameters of: (**a**) 3.5 mm penetrating three cortical bones, (**b**) 3.5 mm penetrating four cortical bones, (**c**) 4.5 mm penetrating three cortical bones, and (**d**) 4.5 mm penetrating four cortical bones. Figure 8: Analysis of the maximum von Mises stresses of the syndesmotic screw in terms of the number of penetrated cortical bones for: (**a**) titanium screw with a diameter of 3.5 mm, (**b**) titanium screw with a diameter of 4.5 mm, (**c**) stainless steel screw with a diameter of 3.5 mm, and (**d**) stainless steel screw with a diameter of 4.5 mm.