# Identification of Surgical Plan for Syndesmotic Fixation Procedure Based on Finite Element Method
## 1 Introduction  
Ankle fractures are among the most commonly occurring fractures, and in some cases, the distal tibiofibrular joint, which is a strong syndesmosis, may be injured [1]. Such a syndesmosis injury is generally due to the mechanisms of pronation-external rotation, pronation-abduction, and supination external rotation [2, 3]. If this injury is not properly treated and if the syndesmosis is fixed unstably or in a non-anatomical position, the ankle joint cannot function normally and patients may suffer from serious chronic pain and instability, thus causing post-traumatic arthritis [4]. Despite the recent development in the field of biomechanics, such as bioabsorbable screws and tightrope systems, the metal screw fixation technique is still the dominant treatment method [5]. However, this method has some shortcomings in appropriately selecting the following parameters: the point of screw insertion, the diameter and material of the screw, and the number of cortical bone penetrations [4]. In this method, an incision is made on the outside of the ankle and the position of the syndesmosis is corrected. Metal screws are then inserted to fix it. Generally, 1-2 screws are inserted from the fibula to the tibia and placed at a distance in the range of 20-30 mm above the tibia plafond [6]. However, many cadaveric studies, whichform the basis of syndesmosis surgeries, have statistical errors and depend on a simple experimental setting. Hence, it is essential to review the location where the syndesmotic screw is fixed in existing approaches [6]. Certain types of materials and materials with specific diameters are used for syndesmotic screws, which are widely employed in clinical practice. The screws are inserted at an appropriate level, and the number of cortical bones that require penetration is selected on the basis of the surgical method used. Titanium or stainless steel is used as the material for the screw, the diameter of which is either 3.5 or 4.5 mm, respectively. The screw is inserted at a distance ranging from 20 to 30 mm above the tibia plafond, and 3 or 4 cortical bones are penetrated for the surgery [7]. However, studies have shown that patients suffer from post-surgical complications, such as bone breakage near the screws and screw loosening or breakage [1,8]. To prevent these complications, we need to conduct an experimental measurement wherein the internal stress distributions of the distal tibiofibrular joint and screw are checked when the load applied to the syndesmosis exceeds a certain limit, and subsequently, measure the displacement of the syndesmosis in a quantitative manner. Thus, it is necessary to compare the insertion location and the dimensions of the screw from a biomechanical perspective. Many existing studies have determined the most favorable point for syndesmotic screw insertion by conducting cadaveric experiments and finite element (FE) analyses. The experiments and analyses have been conducted considering only 1 or 2 parameters among the following: the diameter, number, and level of the screw, and motion of the ankle joint. As a result of these studies, the displacement and angle of the bone, syndesmosis clear space, and maximum stress of the bone have been determined with insufficient evidence [4, 9, 10, 11, 12]. Unfortunately, as cadaveric experiments are restricted by limitation on the number of available specimens, not all the parameters have been analyzed in the experimental plan. Therefore, the results obtained using FE analyses considering only one or two parameters are inaccurate in comparison to studies wherein multiple parameters are considered, as a disease can have various causes. Hence, in this study, we used an FE analysis and considered the following four parameters: level, diameter, material of the syndesmotic screw and number of penetrated cortical bones. We obtained relevant results from the analysis and determined a more accurate and favorable position for screw insertion.