## 2 Methodology
### Finite Element Analysis  
The customized TMJ Implant and intact natural mandible were both studied and analysed in ANSYS workbench R15 to study and analyse the biomechanical behaviour of the patient-specific TMJ prostheses implant for static loading scenario. Patient-specific total TMJ implant was designed using SOLIDWORKS 2018 designing software. The geometry of the model with dimensions are shown in Figure 3.  
The designed solid model is then converted into a mesh model to perform static simulation. ANSYS (Workbench R15) Software was utilized to mesh the assembly using the 4-noded tetrahedral linear element with six degrees of freedom. Bonded contacts have been used for the interfaces between TMJ Implant and jaw-mandible. The numbers of nodes and elements of the model were 153,610 and 87,932 for the combined mandible and natural TMJ in the mesh model while corresponding numbers of nodes and elements for designed patient-specific implant were 166,512 and 94,653, respectively. The convergence of the solutions for both cases was obtained at the element size of 0.5 mm. The masticatory muscles have a remarkable impact on the temporomandibular joint assembly. These muscles are mainly involved in the transferring of chewing forces to the TMJ. In this study, we have considered the three muscles that are involved in mouth closing, because these muscles are always involved in the biting and chewing process which in turn exerts pressure on the TMJ complex. All loading conditions were given as per standard muscle loading magnitude and direction by temporal, pterygoid and masseter muscle. The masticatory muscles load of 1 kN was transferred and distributed uniformly to the mandible into the corresponding enclosures of the masseter, medial pterygoid and temporal jaw muscles. In this simulation study, the intense situation of chewing was used in order to authenticate the reaction of the mandible jaw to the severe situations of implementation of chewing forces [18]. Finally, the simulation was conducted on the model by keeping boundary conditions from the literature as shown below in Table 2[19; 20]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Young’s Modulus MPa** & **Poisson’s Ratio** \\ \hline UHMWPE & 500 & 0.29 \\ Ti-6 Al-4V & \(1.1\times 10^{5}\) & 0.3 \\ Co-Cr alloy & \(2.2\times 10^{5}\) & 0.3 \\ Human Bone & \(14.7\times 10^{3}\) & 0.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Materials properties used in finite element analysis [6]. Figure 3: Solid works design of patient-specific TMJ implant with schematic of model in actual situation. The masseter muscles, medial pterygoid muscles and the temporalis muscles were subjected to a load of 500 N, 300 N and 200 N, respectively, which in turn represents the muscle reaction force during the mastication. Table 2 displays the directions of muscle forces in the three-dimensional axis of the coordinate system. The upper portion of the articular fossa was approximated as rigidly fixed. One more approximation of high stiffness springs placed symmetrically in INCISOR teeth [22] was taken in the present study with all boundary conditions and constraints as depicted in Figure 4.  
Moreover, the value of maximum stress, found at the inferior part of the collar of the condyle, is far behind the ultimate strength of the adult bone in the range of 130-190 MPa [20]. For customized total TMJ prostheses, the von-Mises stress contours for Ti alloy and Co-Cr alloy are shown in Figures 6 and 7, respectively. Figure 5: For intact mandible **(a)** The von-Mises stresses contours **(b)** deformations contours. Figure 6: _Cont._  
Figure 6: The von-Mises stress contours for (**a**) Total TM) prostheses with mandible (**b**) Condylar and fossa parts without screws (**c**) fossa and condylar screws in case of Ti-alloy model of customized TMJ prostheses.