# Identification of Surgical Plan for Syndesmotic Fixation Procedure Based on Finite Element Method
## Materials and Methods
### Finite Element Analysis  
We conducted the FE analysis using the ANSYS 2019 R1 software. We imported the 3D models of the ankle and screw into the ANSYS program and inputted various biomechanical parameters for the model analysis. The results of the analysis are discussed herein. The parameters, which were inputted to the program to obtain desirable results, include the material property, contact condition, meshing style, and load condition. In this study, material properties were assigned to the cortical bone, cancellous bone, ligaments, and syndesmotic screw. As titanium and stainless steel were selected as the two types of screw materials, the properties of each material were inputted. The materials were assumed isotropic, nonlinearly elastic and plastic, and homogeneous. Tables 2 and 3 list the properties of the various materials [10; 11; 13; 14; 15; 16; 17; 18; 19]. In the case of titanium and stainless steel, the exact characteristics of the material should be reflected. Therefore, the stress-strain curve of each material was used for the analysis [20; 21]. With regard to the contact condition, we need to set the relationship between the two bones and that between a bone and the syndesmotic screw. The contact between the tibia, fibula, talus, and calcaneus was set for the bonded friction condition, and the friction coefficient was set to 0.1 [19]. Similarly, the contact between the screw and a bone was set for the friction condition, and the friction coefficient was 0.7 [22; 23]. In this study, the screw thread was simplified for ease of analysis. However, this was contrary to more accurate interpretation; thus, screw characteristics were considered in the contact between the screw and bone. Screw characteristics such as thread diameter, core diameter, thread pitch, and thread angle were in accordance with the standard metallic medical bone screw (F543-13) of the American Society for Testing and Materials (ASTM). This contact was the pure penalty contact algorithm and the simulations were conducted under ideal osseeintegration conditions. Meshing is the most important process for enhancing the accuracy and convergence of an FE analysis. The cortical and cancellous bones were meshed using tetrahedral elements because of their irregular shapes, whereas hexahedral elements were selected for the membrane ligament and screw. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value (Unit)** \\ \hline Screw level & 10, 15, 20, and 25 (mm) \\ Diameter of screw & 3.5 and 4.5 (mm) \\ Material of screw & Titanium and stainless steel \\ Number of penetrated cortical bones & 3 and 4 \\ \hline \end{tabular}
\end{table} 
Table 1: Specifications of the finite element model. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Young’s Modulus (MPa)** & **Poisson’s Ratio** &
\begin{tabular}{c} **Tensile/Compressive Ultimate** \\ **Strength (MPa)** \\ \end{tabular} \\ \hline Cortical bone & 17.000 & 0.3 & 230 \\ Cancellous bone & 700 & 0.2 & 6 \\ Interosseous membrane & 260 & 0.49 & 45 \\ Screw (Titanium: T1-6 Al-4V) & 106.000 & 0.33 & 896 \\ Screw (Stainless steel: 316L) & 193.000 & 0.27 & 584 \\ \hline \end{tabular}
\end{table} 
Table 2: Properties of various materials. \begin{table}
\begin{tabular}{c c} \hline \hline
**Ligaments** & **Stiffness (N/cm)** \\ \hline Anterior latofibrular & 399.9 \\ Calcaneofibrular & 705.1 \\ Posterior latofibrular & 397.5 \\ Deep deltoid & 1288.2 \\ \hline \end{tabular}
\end{table} 
Table 3: Properties of ankle joint ligaments. As the ligaments were assumed to be formed by multiple lines with negligible area, they were modeled using spring elements. A total of 80,918 elements and 149,613 nodes were used for the FE models. The physical motion of the lower body of a walking person is generally divided into five motions: heel strike, foot flat, midstance, heel-off, and toe-off. In this study, we selected the midstance motion for the FE models. The loads on the tibia due to the midstance motion include a compressive force of 2352 N and a tangential force of 235 N [24].