Finite element analysis of biomechanical alterations in the temporomandibular joint induced by posterior tooth wear under the centric occlusion

Abstract

Background

Posterior tooth wear is a common clinical finding, yet the biomechanical impact after tooth wear on the temporomandibular joint (TMJ) remains unclear. This finite element analysis (FEA) study aimed to investigate stress alterations within the TMJ articular disc induced by varying patterns of posterior tooth wear under the centric occlusion.

Methods

A subject-specific three-dimensional finite element model of the skull, including the TMJs with articular discs, was developed from medical imaging. The models of varying patterns of posterior tooth wear were built to analyze the effects of the number of worn teeth, wear depth, and wear symmetry (symmetric vs. asymmetric) on disc stress. Simulations were performed under static centric occlusion.

Results

The high stress areas were located notably in the intermediate zones of disc. The results demonstrated that increasing the number and depth of worn teeth led to a progressive elevation in von Mises and minimum principal stresses within the articular disc. Crucially, in asymmetric wear scenarios, the disc on the more worn side sustained higher stress compared to the less worn side, with the stress disparity widening as asymmetry increased.

Conclusions

Progressive posterior tooth wear, particularly when asymmetric, significantly increases the biomechanical burden on the TMJ disc. This provides a plausible biomechanical explanation for the clinical observation of ipsilateral TMD symptoms in patients with unilateral tooth wear. The findings underscore the importance of occlusal management in patients with significant tooth wear to mitigate adverse TMJ loading.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12903-026-08757-x.

Introduction

Temporomandibular disorders (TMD) represent a complex cluster of musculoskeletal conditions affecting the masticatory system, with their etiology is multifactorial and incompletely understood. A substantial body of evidence identifies sleep bruxism as a significant risk factor for TMD development [1, 2]. The associated repetitive muscular hyperactivity may induce microtrauma to the temporomandibular joint (TMJ) and masticatory muscles [3]. Elevated electromyographic activity associated with bruxism has further been implicated as a potential contributor to myofascial pain in the temporomandibular region [4]. Nevertheless, the precise causal relationship between bruxism and TMD has persisted as a subject of longstanding controversy. While Huhtela et al. demonstrated that bruxism increases susceptibility to TMD symptoms [5], contradictory studies report no significant correlation between their clinical manifestations [6].

Concurrently, the role of dental occlusion in TMD pathogenesis remains contentious. Many clinicians posit that occlusion—as an integral component of the stomatognathic system’s functional equilibrium—must harmonize structurally and functionally with the temporomandibular joint. Malocclusions such as anterior/posterior crossbites and molar loss are frequently implicated in inducing occlusal dysfunction and subsequent TMD [7, 8]. Consequently, some scholars advocate occlusal abnormalities as potential primary etiological factors or predisposing elements in TMD development. In contrast, emerging research suggests minimal or negligible correlation between occlusal factors and TMD onset or progression [9].

Tooth wear describes non-physiological hard tissue loss resulting from abnormal tooth-to-tooth or tooth-to-object contacts. Although there was still lack of evidences that the tooth wear was related to bruxism, a potential risk to TMD, the structural and occlusal changes may have a possible impact on the TMJ. Previous studies reported exceeding 60% TMD patients with posterior tooth wear [10], and no significant association was found between TMD and incisal tooth wear [11]. However, research of the potential mechanism of tooth wear, especially posterior tooth, to the biomechanical status of TMJ remains scarce.

As a load-bearing joint, the TMJ’s physiology is associated with TMJ stresses. Finite element analysis (FEA) is frequently adopted to evaluate the biomechanical status in the TMJ, to avoid physiological invasion measurement of stresses. With the help of FEA, the force transmission of the human masticatory system can be precisely obtained [12]. Further, anterior disc displacement (ADD) alters the stress distribution within the TMJ and the occlusion [13], and severe ADD had visibly effects on the stress response of the TMJ [14]. Also, the occurrence of unilateral TMD was found to be harmful to the contralateral healthy TMJ [15]. Increased stress can also lead to an increase in the incidence of TMD [16]. Thus, to evaluate further relations to tooth wear, the FEA and stresses in the TMJ play a significant role in the occurrence of TMD. And recent researches about wear joint mechanics were studied to predict wear of hip or knee related treatments under walking conditions [17–19], and these results motivated further wear assessment of prosthesis design and optimization. However, total wear predictions were not available for the computational model for tooth wear.

This study examines the interrelationships between tooth wear and TMJ biomechanics in static central occlusion, addressing persistent controversies while synthesizing evidence regarding their synergistic roles in masticatory system dysfunction. Therefore, the hypothesis has arisen that tooth wear would increase the TMJ loads.

Materials & methods

The study protocol was approved by the Ethics Committee, and written informed consent was obtained from the participant. A subject without visible tooth wear and without TMD signs and symptoms and degenerative disease of TMD was recruited at Department of Stomatology, Affiliated Hospital of North Sichuan Medical College, and selected for this study (age: 22 years old; gender: male), according to the Research Diagnostic Criteria for Temporomandibular Disorders (RDC/TMD) [20]. The selected subject with normal dentition, without facial and TMJ asymmetry, and orthodontic or surgical history. This subject has a total of 31 teeth, with only the third molar in the lower right corner remaining unerupted.

The subject underwent a standardized cone-beam computed tomography (CBCT) scan (uCT 510, UIH, China) to acquire head views with a field of view of 230 mm. The resulting cross-sectional images had a resolution of 512 pixels with a pixel size of 0.44 mm. Each scan produced between 190 and 260 slices, each with a thickness of 1.0 mm. The CBCT data were subsequently converted into Digital Imaging and Communications in Medicine (DICOM) format.

The medical imaging was then imported to MIMICS software (Version: 21.0, Mimics Innovation Suite, Materialise, Leuven, Belgium), where three-dimensional (3D) models of the maxilla, mandible, and dentition were generated from grayscale values. The articular discs were modeled using magnet resonance imaging (MRI) in conjunction with anatomical reference points, registering, assembling, and yielding subject-specific model (Fig. 1). The registration method was derived from previous study [21], Briefly speaking, the mandible model established by CBCT and the condyle model with joint disc established by MRI were registered by matching the geometric similarity of the condyle. In this model, thicknesses of intermediate zones, anterior and posterior bands were 1.18, 1.71, and 2.13 mm for the left disc and 1.37, 1.98, and 2.06 mm for the right disc, respectively.

Fig. 1.

The scheme of the 3D model including worn dentition and TMJ

In our study, the wear at the occlusal surfaces were analyzed. The models were designated according to the following nomenclature convention. The intact dentition model without pathological wear served as the Control model. And only premolars and molars were designed to be worn teeth, as they were the teeth that are most frequently worn. Models simulating dental attrition followed a tripartite naming system (X–Y-Z), where: X denotes the side symmetry: A (asymmetric) or S (symmetric); Y denotes the number of worn teeth from 1 to 5, and wear begins with the thrid molar; Z specifies the wear depth: 1, 2, or 3.0 mm, which defined the total wear of upper and lower dentitions. In this study, all the teeth set as worn were involved in the simultaneous wear of the corresponding maxillary and mandibular opposing teeth.

Finite element simulations were carried out in ABAQUS (Version: 6.13, Dassault SIMULIA, RI, USA). Bone density and elastic modulus were assigned across the maxillary and mandibular structures according to established empirical correlations with grayscale intensity (Eqs. (1) and (2)) to represent the inherent heterogeneity of bone tissue [22–24]. A Poisson’s ratio of 0.3 was applied to both bony components [25, 26]. For the disc, a compressive Mooney–Rivlin hyperelastic constitutive model was implemented using material parameters C₁ = 9 × 10⁵ Pa and C₂ = 9 × 10² Pa [27–29], which has been widely employed in TMJ finite element studies [29–31]. The corresponding strain-energy function is provided as Eq. (3). Articular cartilage layers, 0.2 mm thick, were incorporated on the anterior and posterior condylar surfaces, assigned an elastic modulus of 17.12 and 16.9 MPa, and an elastic modulus of 23.94 MPa for articular eminence, respectively, according to a previous experimental study [32] (Table 1).

1

2

3

Table 1.

The mechanical properties and mesh types in our models

Components	Material properties		Mesh type
	Elastic modulus	Poisson’s ratio
Maxilla and mandible	Linear elastic: Eqs. (1) and (2)	0.3	TMJ: C3D10M The rest: C3D4
Disc	Mooney–Rivlin hyperelastic: Eq. (3)		C3D10M
Cartilage	Linear elastic: anterior and posterior condylar cartilages: 17.12 and 16.9 MPa articular eminence cartilage: 23.94 MPa	0.4	S3

To balance numerical precision and computational cost, the temporomandibular joint regions were discretized with modified quadratic tetrahedral elements (C3D10M), while the rest of the model used four-node linear tetrahedral elements (C3D4) in 3-Matic software (Version: 12.0, Mimics Innovation Suite, Materialise, Leuven, Belgium) (Fig. 2a). The cartilages were composed of triangular shell element (S3) with a mesh edge length of 1.0 mm. In our model, the mesh intensity was increased at the dentition and TMJ region, which the mesh edge 1.0 mm. The model was comprised of approximately 200,000 elements and 90,000 nodes, proved through the mesh convergence analysis in our previous studies [33, 34]. The mesh quality, including aspect ratio, minimum face angle, and Jacobian, of all the models was checked. The analysis error of mesh was 0, and the analysis warning of mesh was under 5%.

Fig. 2.

The mesh, boundary conditions, and muscle forces of the model. a mesh and boundary conditions; b & c muscles forces

Interactions in the TMJ and teeth between contacting surfaces were simulated using a surface-to-surface contact algorithm with a hard contact pressure-overclosure relationship and a friction coefficient value of 0.001 [35], while the friction coefficient between upper and lower dentition was simultaneously set as 0.3 [36]. Four disc attachments—namely the anterior temporal attachment, anterior mandibular attachment, along with the superior and inferior bilaminar bands—were represented via nonlinear springs according to previous study [37].

Although dynamic process was important in assessment in oral functions, static centric occlusion was chosen and simulated for its meanings of oral normal functions restoration design, and biomechanical research [34]. Identical muscle forces and boundary conditions were assigned to the model. The nine major masticatory muscles were applied in our simulation included superficial masseter (SM), deep masseter (DM), medial pterygoid (MP), anterior temporalis (AT), middle temporalis (MT), anterior digastric (AD), posterior temporalis (PT), superior lateral pterygoid (SLP) inferior head of lateral pterygoid (ILP) muscle (Fig. 2b & c). Their magnitudes, efficiencies and orientations during centric occlusion were derived from published literature [8, 38, 39] (Supplementary materials). Firstly, 20% of all muscle forces were applied to the model, and after simulation convergence of 20% of all muscle forces, the rest magnitudes of muscle forces were added. The six degrees of freedom top surface of the maxilla was assigned a fixed boundary condition (Fig. 2a). Then, von Mises, maximum and minimum principal stresses were extracted and analyzed. The maximum and minimum principal stresses were chosen for their tensile and compressive natures of discs. The maximum stress values were calculated by averaging stress values of three nodes in the highest stress area.

Results

According to the finite element simulation results, a comparative analysis was performed regarding the number of worn teeth, the depth of wear, and the symmetry of wear on both sides.

Figure 3 illustrates the changes in the von Mises and minimum principal stress distributions within the bilateral articular discs as the number of worn teeth increases. The stress in both discs exhibited an increasing trend with a greater number of worn teeth. Areas of stress concentration became more pronounced, particularly in the posterior and intermediate zones of the discs. Figure 4 further quantifies the greatest von Mises stresses on the top and bottom surfaces of the discs (Fig. 4a and b), as well as the greatest minimum principal stresses on these surfaces (Fig. 4c and d), across the different models. The results demonstrated that both the maximum von Mises stress and the minimum principal stress on the disc surfaces increased with a higher number of worn teeth. As the number of worn teeth increased, the stress disparity between the bilateral discs progressively widened. However, no obvious changes in the maximum principal stresses on the discs were observed.

Fig. 3.

The von Mises and minimum principal stress distributions of disc with the increase of worn teeth. Notes: A = anterior; L = left; P = posterior; R = right

Fig. 4.

a & b The greatest von Mises stresses on the top (a) and bottom (b) surfaces of discs for the models with the number of worn teeth increased. c & d The greatest minimum principal stresses on the top (c) and bottom (d) surfaces of discs for the models with the number of worn teeth increased

Moreover, the comparison of wear depth showed that as the wear depth increased from 1.0 mm to 3.0 mm, the stress values in various regions of the articular disc also progressively increased (Fig. 5). Notably, in the model with 3.0 mm wear depth, the maximum von Mises stress on the top surface of the left disc increased by approximately 40% compared to the Control model (Fig. 6a). And the greatest minimum principal stress on the bottom surface of the right disc increased by 73% compared to the Control model (Fig. 6d). This further demonstrates that the depth of tooth wear has a substantial impact on the biomechanical state of the TMJ. However, there were no obvious changes in the maximum principal stresses on the discs.

Fig. 5.

The von Mises and minimum principal stress distributions of disc with the increase of wear depth. Notes: A = anterior; L = left; P = posterior; R = right

Fig. 6.

a & b The greatest von Mises stresses on the top (a) and bottom (b) surfaces of discs for the models with the increase of wear depth. c & d The greatest minimum principal stresses on the top (c) and bottom (d) surfaces of discs for the models with the increase of wear depth

Concerning the symmetry of wear, in asymmetric (A-series) models, the discal stresses increased more on the more worn side compared to that on the contralateral side. Stress concentration was more notable in the disc on the more worn side (Fig. 7). In Fig. 8, the greatest von Mises and minimum principal stress of discs on more worn side increased more. Fig. 9 illustrated the increase index (I) defined by following Eq. (4), which also displayed more worn teeth contributed more stresses on ipsilateral disc.

4

Fig. 7.

The von Mises and minimum principal stress distributions of discs for symmetric and asymmetric models. Notes: A = anterior; L = left; P = posterior; R = right

Fig. 8.

a & b The greatest von Mises stresses on the top (a) and bottom (b) surfaces of discs for the comparisons of symmetric and asymmetric models. c & d The greatest minimum principal stresses on the top (c) and bottom (d) surfaces of discs for the comparisons of symmetric and asymmetric models

Fig. 9.

a The increase index (I) of von Mises stresses on the top and bottom surfaces of discs for the comparisons of the S-5–2 model. b The increase index (I) of minimum principal stresses on the top and bottom surfaces of discs for the comparisons of the S-5–2 model. Notes: R-T = right disc-top surface; L–T = left disc-top surface; R-B = right disc-bottom surface; L-B = left disc-bottom surface

Discussion

Tooth wear is associated with the condition of TMJ and influences signs and symptoms of TMD [40]. However, the relationship between tooth wear and TMJ has not elucidated. By developing a subject-specific finite element model of the TMJ, this study systematically simulated stress variations in the articular disc under different tooth wear conditions, elucidating the potential biomechanical impact of progressive posterior tooth wear on the TMJ. The findings support the following conclusions.

The biomechanical interactions within the TMJ were simulated using frictional contact. To validate the predictive accuracy of the finite element (FE) models, their results were compared against physical 3D-printed experimental models replicating the same geometry, material properties, loads, and boundary conditions in our previous study [41]. The good agreement between the experimental and simulated results—with discrepancies of less than 5%—confirms the reliability of our current TMJ simulations. In our study, the methods were similar in our previous research but with different researching subjects.

The increase in the number of worn teeth led to elevated stress levels within the articular disc, potentially attributable to the reduction in occlusal vertical dimension. TMJ and dentitions were both contributed supporting the muscle forces. However, as the number of worn teeth increased, TMJ had to bear more loads as the dentition contact pair reduced. This observation aligns with the study by Zhang et al. on the effects of posterior tooth loss on TMJ stress [8, 38], suggesting that the loss of posterior occlusal support is a critical factor in the deterioration of the TMJ's biomechanical environment.

Increasing wear depth further exacerbated stress concentration within the disc. This indicates a progressive deterioration of the mechanical environment within the TMJ under centric occlusal loading as tooth wear advances. More possibility of TMD may be found in severer tooth wear patients [10]. The notable ~ 40% stress increase at the 3.0 mm depth highlights that severe tooth wear aggravates the biomechanical burden on the TMJ. This implies that for patients with severe tooth wear, clinical interventions such as occlusal rehabilitation or occlusal splint therapy should be considered promptly to restore the vertical dimension and mitigate joint loading [42, 43].

Asymmetric wear resulted in a pronounced disparity in disc stress between the more and less worn sides, with significantly higher stress on the more worn side. Thus, as for the patients with asymmetric tooth wear, the dental wear severer side would contribute more stresses on ipsilateral joints which would increase the possibility of the occurrence of TMD. These findings also suggested that patients with unilateral wear often reported TMD symptoms on the same side. It corroborates the findings of Yang et al. [15] regarding the biomechanical interplay between affected and healthy joints in unilateral TMD, underscoring the clinical importance of evaluating and managing occlusal symmetry.

According to the simulation results, patients with posterior tooth wear should pay more attention to their TMJ. In this study, 3 mm tooth wear only reached to the Grade 2 in Smith and Knight tooth wear index [44], however, it showed a notable increase of stress in the TMJ. And the TMD patients with more tooth wear were correspondingly increased [10]. Thus, once tooth wear occurred, the conditions in the TMJ should be considered.

Indeed, there were some limitations of this study. Only one subject was including in our study. Therefore, the presented results lack statistics and might differ from other subjects with different faces and occlusion. In addition, this study simulated a static centric occlusion, which cannot fully capture the complex mechanics of dynamic mastication. Some simplifications of mechanical properties were made for the efficiency of models, but the established model demonstrates good biomechanical credibility and provides a reliable tool for further investigation. Although different material properties may produce different magnitudes of TMJ stresses, the tendency of tooth wear might be similar. Besides, the wear process was not considered in our study, while we only considered the impact of the occlusion after tooth wear on the TMJ. And the long-term influence of wear to the change of TMJ was not considered. Future research incorporating dynamic loading conditions and multiple functional scenarios would offer a more comprehensive understanding of the relationship between wear and TMD. Moreover, more tooth wear was not considered because the models could no longer establish a stable occlusal relationship, making it difficult to converge. However, based on the existing data, more wear at the occlusal surfaces on teeth would deteriorate the stress on the TMJ.

Conclusions

Posterior tooth wear significantly alters the stress distribution within the TMJ and increases the biomechanical burden on the articular disc under the centric occlusion. This mechanism may speculate the higher susceptibility to TMD among patients with significant tooth wear. Clinically, for patients presenting with substantial tooth wear, a comprehensive management strategy encompassing occlusal reconstruction and TMJ protection should be implemented to improve long-term outcomes.

Abbreviations

TMD

Temporomandibular disorders

TMJ

Temporomandibular joint

FEA

Finite element analysis

ADD

Anterior disc displacement

RDC/TMD

The Research Diagnostic Criteria for Temporomandibular Disorders

CBCT

Cone-beam computed tomography

DICOM

Digital Imaging and Communications in Medicine

3D

Three-dimensional

MRI

Magnet resonance imaging

SM

Superficial masseter

DM

Deep masseter

MP

Medial pterygoid

AT

Anterior temporalis

MT

Middle temporalis

AD

Anterior digastric

PT

Posterior temporalis

SLP

Superior lateral pterygoid

ILP

Inferior head of lateral pterygoid

Authors’ contributions

J.S conceptualized the study. J.S. and S.Z. curated the data and provided resources, software, and visualization. J.S. and S.Z. performed formal analysis and investigation and developed the methodology. J.S. and L.L. administered the project and supervised the research. J.S. validated the findings. J.S. and L.L. wrote the original draft and reviewed and edited the manuscript.

Funding

This work was supported by the North Sichuan Medical College Scientific Research and Development Projects (CBY25-QDA32 & CBY25-QDA35), Clinical Medical College/Affiliated Hospital of North Sichuan Medical College's 2025 Annual Research Development Plan Project (2025CX003).

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Written informed consent form was obtained from the participant before recruitment in the study. This study was conducted in accordance with the Declaration of Helsinki. The protocol of this study was approved by North Sichuan Medical College Institutional Review Board (2024ER121-1).

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.