2.2.1. FE Modeling and Mesh Generation

Subject-specific 3D anatomical reconstruction of patient's mandible and skull/articular eminence was performed using commercial software Mimics v14.12 (Materialise, Plymouth, MI, USA) from computed tomography (CT) scans of patient's TMJ. Upon importing the patients CT images in Mimics, anatomical model comprising of patient's mandible and fossa eminence was developed from the CT scan by performing a series of operations such as image processing, segmentation, mask formation for bone and teeth, region growing, and calculation of 3D equivalent similar to the 3D reconstruction method described elsewhere [18]. Using the design methodology discussed in previous sections, two patientspecific total TMJ prostheses systems—a 'simple implant' without notches, and another 'implant with notches'—were designed for total reconstruction of the patient's left TMJ (see Figures 24 and 25). For FE simulations, volume bound within surfaces of anatomical components (cortical bone, cancellous bone, and teeth) and prosthetic components (condyle, fossa, and screws) were meshed. Three-D volume mesh was generated for each of these components with ten-node quadratic tetrahedral elements of type C3D10 (see Figures 26 and 27). Mesh convergence was achieved using the technique discussed previously [18]. The finite element analyses were performed using a commercial FE package ABAQUS v6.10 (SIMULIA, Providence, RI, USA).

rotation of the prosthetic condylar head along the medio–lateral axis.

**Figure 25.** A patient-specific total TMJ prosthesis. (**A**,**B**) Show two views of the 'simple' total TMJ prosthesis along with left fossa bone and mandible after removal of left condyle. (**C**,**D**) Show two views of the total TMJ along with screws. **Figure 25.** A patient-specific total TMJ prosthesis. (**A**,**B**) Show two views of the 'simple' total TMJ prosthesis along with left fossa bone and mandible after removal of left condyle. (**C**,**D**) Show two views of the total TMJ along with screws.

**Figure 24.** A patient-specific total TMJ prosthesis with medial notches in fossa and condylar components. (**A**) Shows anterior–lateral view of the 'notched implants' with screw holes. Fossa prosthesis has two medial notches to be fit into host bone (**B**,**C**). The articular surface of fossa implant has medio–lateral openings, and is designed to allow optimal anterior and medial translation along with

## 2.2.1. FE Modeling and Mesh Generation 2.2.2. Model Constraints and Loads

Subject-specific 3D anatomical reconstruction of patient's mandible and skull/articular eminence was performed using commercial software Mimics v14.12 (Materialise, Plymouth, MI, USA) from computed tomography (CT) scans of patient's TMJ. Upon importing the patients CT images in Mimics, anatomical model comprising of patient's mandible and fossa eminence was developed from the CT scan by performing a series of op-As illustrated in Figure 28, the condylar head of the prosthetic TMJ was allowed to rotate along the medio–lateral axis, and translate in anterior-posterior direction. Similarly, for the TMJ on contralateral side, the natural condylar head was allowed to only rotate along the medio–lateral axis, and translate in anterior-posterior direction. The incisor teeth were fixed so that they could not translate in three directions, but could rotate. The entire fossa host bone was constrained in all directions.

erations such as image processing, segmentation, mask formation for bone and teeth, region growing, and calculation of 3D equivalent similar to the 3D reconstruction method described elsewhere [18]. Using the design methodology discussed in previous sections, two patient-specific total TMJ prostheses systems—a 'simple implant' without notches, and another 'implant with notches'—were designed for total reconstruction of the patient's left TMJ (see Figures 24 and 25). For FE simulations, volume bound within surfaces The interface between prosthetic condylar head and articulating surface of fossa prosthesis was modeled as sliding contact with a coefficient of friction of 0.3. The interface between the prostheses and bone in contact was modeled with contact elements having a coefficient of friction of 0.42 as reported in literature [26]. The screw-to-prosthesis and screw-to-bone interfacial conditions were assumed to be bonded. Since use of locking screws eliminates the possibility of movement between screw and prosthesis, the interface condition between screw heads and TMJ prostheses (condylar and fossa) was assumed to be perfect bonding. Two oblique bite forces, each 200 N for normal loading condition and 400 N for over–loading/worst-case scenario, were applied to the mandibular model in the angulus area as shown in Figure 28.

age ABAQUS v6.10 (SIMULIA, Providence, RI, USA).

**Figure 26.** Three-D finite element mesh of the host bone components prepared for total prosthetic replacement of the left TMJ. (**A**) Shows FE surface mesh of left fossa, and (**B**) shows a lateral crosssection of the 3D volume mesh of left fossa bone with screw holes. Similarly, (**C**,**D**) show surface mesh and anterior cross-section of volume mesh, respectively, of the mandible with screw holes and removal of damaged left condyle. **Figure 26.** Three-D finite element mesh of the host bone components prepared for total prosthetic replacement of the left TMJ. (**A**) Shows FE surface mesh of left fossa, and (**B**) shows a lateral crosssection of the 3D volume mesh of left fossa bone with screw holes. Similarly, (**C**,**D**) show surface mesh and anterior cross-section of volume mesh, respectively, of the mandible with screw holes and removal of damaged left condyle. *Materials* **2022**, *15*, x FOR PEER REVIEW 24 of 34

of anatomical components (cortical bone, cancellous bone, and teeth) and prosthetic components (condyle, fossa, and screws) were meshed. Three-D volume mesh was generated for each of these components with ten-node quadratic tetrahedral elements of type C3D10 (see Figures 26 and 27). Mesh convergence was achieved using the technique discussed previously [18]. The finite element analyses were performed using a commercial FE pack-

**Figure 27.** Three-D finite element mesh of the components of patient-specific total TMJ prostheses. (**A**–**C**) Show FE mesh of the condylar/ramal component of the 'simple' TMJ implant (without notches). (**D**,**E**) Show FE mesh of the fossa component, and (**F**) demonstrates FE mesh of a screw for device fixation. 2.2.2. Model Constraints and Loads **Figure 27.** Three-D finite element mesh of the components of patient-specific total TMJ prostheses. (**A**–**C**) Show FE mesh of the condylar/ramal component of the 'simple' TMJ implant (without notches). (**D**,**E**) Show FE mesh of the fossa component, and (**F**) demonstrates FE mesh of a screw for device fixation.

As illustrated in Figure 28, the condylar head of the prosthetic TMJ was allowed to rotate along the medio–lateral axis, and translate in anterior-posterior direction. Similarly,

teeth were fixed so that they could not translate in three directions, but could rotate. The

entire fossa host bone was constrained in all directions.

device fixation.

2.2.2. Model Constraints and Loads

entire fossa host bone was constrained in all directions.

**Figure 27.** Three-D finite element mesh of the components of patient-specific total TMJ prostheses. (**A**–**C**) Show FE mesh of the condylar/ramal component of the 'simple' TMJ implant (without notches). (**D**,**E**) Show FE mesh of the fossa component, and (**F**) demonstrates FE mesh of a screw for

As illustrated in Figure 28, the condylar head of the prosthetic TMJ was allowed to rotate along the medio–lateral axis, and translate in anterior-posterior direction. Similarly, for the TMJ on contralateral side, the natural condylar head was allowed to only rotate along the medio–lateral axis, and translate in anterior-posterior direction. The incisor teeth were fixed so that they could not translate in three directions, but could rotate. The

**Figure 28.** Assembly of all parts of the FE model (including anatomic and prosthetic components), and schematic representation of model constraints and load application for FE simulation of total TMJ prostheses and anatomical components. Green arrows depict the location and direction of bite forces applied in the angulus region on both sides of the mandibular mesh. The asterisks indicate constrained nodes at condyle, fossa, and incisor teeth. Left prosthetic condylar head and right natural condylar head were constrained such that they could only rotate along the medio–lateral axis and translate in anterior-posterior direction. The nodes at incisor teeth were so constrained such that they could only rotate. The entire fossa host bone was constrained in all directions. The interface between prosthetic condylar head and articulating surface of prosthetic fossa was modeled as sliding contact. The prosthesis-to-bone, screw-to-prosthesis, and screw-to-bone interfaces were assumed to be bonded. The interfacial and boundary conditions were kept similar for normal and over–load configurations; and only magnitude of applied forces was changed across the two loading configurations.
