The study population included 19 women and 18 men aged between 21-49 years old and with a body mass index between 18.2-21.9 Kg.m-2. It should be noted that these patients had no other complications besides bruxism in the region of head, jaw and teeth. Normal samples included 18 women and 18 men aged between 26-52 years old and with a body mass index between 19.6-22.3 Kg.m-2. Using the images obtained from the CT scan of the jaw and teeth of samples and importing these images into Mimics software version 13.1 (Materialise, Leuven, Belgium), the point cloud of the maxilla, mandible and teeth of each sample were produced as separate parts (Fig 1, a). In Mimics, the bony parts of the maxilla, mandible and teeth in image file were kept. After modifying the areas containing soft tissue in all image slices and repeating these modifications layer by layer, the spaces between layers were finally modified and differentiated and the point clouds of the teeth and jaw bone were extracted as the software output. Subsequently, the point clouds were transferred to the CATIA software version 5R21 (Dassault Systemes, Waltham, Mass., USA), and a three-dimensional model of the maxilla, mandible and teeth were built (Fig 1, b).
Three-dimensional models of the maxilla, mandible and teeth of all 37 patients and 36 normal samples were assembled in conditions of no contact pressure respect to each other. Six months after insertion of the occlusal splint, the process of preparing CT scan images, creating the point cloud, and building the three-dimensional models of jaws and teeth were repeated for patients. At this stage, the 3D models of used splints of the same patients were constructed from their CT scan images and the 3D splint models were inserted between the upper and lower teeth of patients. It is worth noting that due to limitations, there was only possible to create the 3D model of jaw, teeth and splint of 10 women and 11 men after 6 months of using splint. Since the FEM solution is one of the most common methods for orthopedic simulation [24-26], the assembled models were transferred finally to ABAQUS software version 6.14 (Dassault Systemes) for FE analysis. Table 1 shows the material properties considered for jaw bones, teeth, and splints [19, 27]. One of the most important points in FE analysis is how different parts of the model interact with each other. In this study, these interactions and constraints were defined based on the actual anatomical function of these components in human body. The constraint considered for the contact between the inserted teeth on the upper and lower jaws with splint was a surface-to-surface constraint with a friction coefficient of 0.5 . The degree of freedom of the upper surface of maxilla was considered to be zero at all three directions of x, y and z, i.e., the surface was considered to be fixed. Other degrees of freedom were considered in accordance with the real performance of TMJ, so that the necessary degrees of freedom for opening and closing movements of jaw (rotational degree of freedom) as well as the translation and lateral displacement of jaws over each other (translational degree of freedom) were considered (Fig 2, a). According to previous study a first order Ogden hyperelastic model was used for defining the periodontal ligament with poisson's ratio of 0.45 and material parameter MPa . The average amount of force exerted by the medial pterigoid muscle and masseter muscle for both left and right muscles was assumed to be 50 N [19, 27]. It should be noted that, according to previous studies, the force of this muscles should be applied under a particular angle to the model, as shown in Fig 2, a. One of the most important issues in numerical computer simulations is to ensure the mesh independence of responses [29-33], The tetrahedral element was used for meshing the models (Fig 1, c). The results showed that the maximum difference between the stress values in the medium and fine meshes in all three groups of patients, normal samples and patients after 6 months of using the occlusal splint was less than 1.8%. Therefore, the convergence of responses from the grid and time step was ensured (Fig 2, b).
The mean value, standard deviation (SD) and coefficient of variation (CV) for maximum stress and maximum deformity were calculated in all three groups of patients, normal samples and patients after 6 months of using the occlusal splint using SPSS version 22 (IBM Corp., Armonk , New York, USA).