The purpose of this study is to develop three-dimensional (3D) finite element models of temporomandibular joints (TMJs) and to investigate stress distributions. To determine the causes of temporomandibular disorders (TMDs), the magnitude and location of the maximum stresses under physiological loading must be considered. Stress analysis TMD models were reconstructed from computed tomography (CT) data. Several studies have investigated finite element TMJ models, but few have used a bilateral mandible model that includes jaw closing and maximum opening. In this study, the authors defined an asymmetry index for the different stress values on each side joint; this index has not yet been investigated. According to clinical observation, one joint affects the other side joint during mastication. Three symptom-free volunteers and three symptomatic patients were selected as the control group (CG) and TMD group (TG), respectively. For the TG, data analysis indicated that the condyle was asymmetrical during jaw closing, while both the condyle and disc were slightly asymmetrical during jaw opening. The maximum stresses did not significantly differ between the CG and TG for either closing or opening of the jaw. The results of this study have a potential clinical benefit in terms of proving superior biomechanical behaviour.
Temporomandibular disorders (TMDs) are common in adults; one-third of adults are reported to have one or more symptoms, which include joint pain, headaches, and clicking or muscle tenderness. TMDs are defined by a cluster of conditions characterized by pain in the temporomandibular joint (TMJ) during jaw motion. The major symptoms causing the problem are disc degeneration or displacement ( Fig. 1 ), The TMJ is a geometrically complex and extremely mobile joint; its motion is described by large displacements, rotations, and deformations. The aetiology of TMDs remains unclear, but they have been connected to cases of joint trauma, advanced degenerative disease, tumours, developmental anomalies, and ankylosis of the joint following injury. Many therapies have been used for treatment, such as intra-aural (ear) devices, splints, night-time biofeedback, and complementary and alternative medicine (electro-acupuncture therapy).
Finite element analysis (FEA) is a useful tool that can be applied to quantify the stress distribution in the TMJ and surrounding tissues. It has been used to study the biomechanical behaviour of orthopaedic devices, including hip, knee, and spinal implants, under various loading conditions. Until recently, there have been no papers comparing a three-dimensional (3D) bilateral mandible model that includes jaw closing and maximum opening with computed tomography (CT) images to understand the stress fields for TMD cases, although other authors have performed finite element simulations for the TMJ.
To examine the biomechanical behaviour of TMDs, the magnitude and location of the maximum stresses under physiological loading must be considered. In this study, the authors defined an asymmetry index for different stress values on each side joint; this index had not been investigated before. The aim of this study was to demonstrate 3D finite element models reconstructed from in vivo CT data, quantify the maximum stress and asymmetrical index in the mandibular condyle, disc, and articular eminence, and compare the models for the TMD group (TG) and the control group (CG).
Materials and methods
A previously developed 3D finite element model of a human mandible, including the cancellous and cortical bones, was obtained from CT images (Brilliance CT, Philips Medical Systems, USA). TMD is a complex disease with many symptoms. Patients with disc displacement were assigned to the TG in this study. Three TMJs from adult patients were used to rebuild the models, and three symptom-free volunteers were selected as a control group. For geometry acquisition, a set of images were taken from CT slices through the TMJ and segmented for data extraction and to describe the surfaces of the condyle, disc, and articular eminence. An edge detection algorithm was run with the AVIZO 6.2 program to distinguish the cortical bone from cancellous bone and detect the various boundary components of the mandible.
The 3D image reconstruction bilateral models were constructed using the ANSYS Workbench 12.1 finite element program. On reconstruction of the condyle and articular eminence, a disc with a uniform thickness of 2 mm was added between them. A condyle cartilage layer with a uniform thickness of 0.1 mm was added to the bony surface of the mandibular condyle, and the friction coefficient inside the TMJ was assumed to be 0.01. The condyle, disc, and articular eminence structures were regarded as continuous integers. In order to obtain accurate results for the FEA, converging and reinforcing of the mesh are important major processes that let the model approach the real object. Through the convergence process, it can be assumed that the mesh is reliable. The average numbers of nodes and elements were approximately 33,000 and 24,000, respectively ( Fig. 2 ).
Material properties and muscle force
The surface mandible is defined by the properties of the cortical bone, whereas the internal nodes were assigned to the properties of the cancellous bone. The biomechanical properties of the cortical bone, cancellous bone, and the articular disc of the TMJ were defined as shown in Table 1 . To mimic the condyle better in vivo, the properties of the condyle cartilage layer were set as though it was a nonlinear material, because the elastic modulus of the condyle cartilage layer was similar to the hyaline of several other synovial joints, as shown in Table 2 .
|Elastic modulus (MPa)
|1.37 × 10 4
|7.93 × 10 3
|4.41 × 10 (stress range: less than 1.50 MPa)
|9.41 × 10 (stress range: more than 1.50 MPa)
|Elastic modulus (MPa)
The muscles of mastication have significant influence on the TMJ and transmit functional chewing forces to them. Of the four muscles of mastication, three are used for closing the mouth, and one is used for opening the mouth. This study considered the three muscles that are involved in mouth closure since these movements result in maximum physiological loading at the TMJ. The direction and magnitude of the muscle forces were adopted from previous studies; it was necessary to determine the cross-sectional area (CSA) and calculate the maximum muscle force via the following mathematical function. This method integrated the muscle CSA and is accurate and reliable. The maximum forces of each muscle are shown in Table 3 .
F i max = K × CSA
|Left side ( N )
|Right side ( N )
Eq. (1) estimates the maximum muscle forces possible based on the CSA, where K equals 37 N cm −2 .
The articular surfaces of the disc, mandibular condyle and articular eminence were divided into five regions: anterior, posterior, central, medal, and, lateral. The von Mises and shear stresses were determined for all joint components in these regions.
Stresses were higher for the TG than for the CG. For the TMJ model as a whole, the highest von Mises stress varied from 0.29 to 2.79 MPa for all models. Figure 3 shows the von Mises stress distribution of one model for the TG. The von Mises stress was reduced by approximately 20% in the condyle when the jaw was closed and by 45% in the disc when the jaw was opened; the stress distributions showed significant asymmetry, and most of the maximum stresses were in the lateral region for the TG.
For the mandibular condyle region, the von Mises stress varied from 1.77 to 2.79 MPa, and the average stress values were 2.48 and 2.00 MPa for the TG and CG, respectively ( Fig. 4 ). 75% of the highest stress was observed in the lateral region of the mandibular condyle for the TG, and major maximum stresses were all in the central or anterior regions ( Table 4 ). The condyle stresses were asymmetrical when the jaw was closed for the TG ( Fig. 5 ). The highest stresses varied from 0.43 to 0.91 MPa in the disc region when the jaw was closed, which is less than the failure stress, and the average stress value approached 0.70 MPa. The maximum von Mises stress did not differ much. On the other hand, the stress distributions were more uniform for the CG than for the TG. In the articular eminence, the highest von Mises stress varied from 1.21 to 1.48 MPa, and the average stress value was about 1.35 MPa. There were no significant differences in the maximum stress values between the two groups, and the TG showed slightly more asymmetry than the CG.