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Effects of several temporomandibular disorders on the stress distributions of temporomandibular joint: a finite element analysis a
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a
Zhan Liu , Yingli Qian , Yuanli Zhang & Yubo Fan
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Provincial Key Laboratory of Biomechanical Engineering, Sichuan University, Chengdu, Sichuan, P.R. China b
Strength Design Department, AVIC 611 Institute, Chengdu, Sichuan, P.R. China
c
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Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, P.R. China Published online: 14 Jan 2015.
To cite this article: Zhan Liu, Yingli Qian, Yuanli Zhang & Yubo Fan (2015): Effects of several temporomandibular disorders on the stress distributions of temporomandibular joint: a finite element analysis, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2014.996876 To link to this article: http://dx.doi.org/10.1080/10255842.2014.996876
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Computer Methods in Biomechanics and Biomedical Engineering, 2015 http://dx.doi.org/10.1080/10255842.2014.996876
Effects of several temporomandibular disorders on the stress distributions of temporomandibular joint: a finite element analysis Zhan Liua1, Yingli Qianb1, Yuanli Zhanga and Yubo Fanc* a
Provincial Key Laboratory of Biomechanical Engineering, Sichuan University, Chengdu, Sichuan, P.R. China; bStrength Design Department, AVIC 611 Institute, Chengdu, Sichuan, P.R. China; cKey Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, P.R. China
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(Received 14 February 2014; accepted 7 December 2014) The aim of this study was to evaluate stress distributions in the temporomandibular joints (TMJs) with temporomandibular disorders (TMDs) for comparison with healthy TMJs. A model of mandible and normal TMJs was developed according to CT images. The interfaces between the discs and the articular cartilages were treated as contact elements. Nonlinear cable elements were used to simulate disc attachments. Based on this model, seven models of various TMDs were established. The maximum stresses of the discs with anterior, posterior, medial and lateral disc displacement (ADD, PDD, MDD and LDD) were 12.09, 9.33, 10.71 and 6.07 times magnitude of the identically normal disc, respectively. The maximum stresses of the posterior articular eminences in ADD, PDD, MDD, LDD, relaxation of posterior attachments and disc perforation models were 21, 59, 46, 21, 13 and 15 times greater than the normal model, respectively. TMDs could cause increased stresses in the discs and posterior articular eminences. Keywords: finite element analysis; temporomandibular disorder; temporomandibular joint; articular disc; stress distribution
1.
Introduction
Temporomandibular joints (TMJs), located between the condyle of mandible and the articular fossa– eminence, are the unique bilateral linked joints in the human body. Both TMJs are necessary for mastication, swallowing, speech and facial expressions. Temporomandibular disorder (TMD) is the most common TMJ disease. It is reported that the prevalence of TMD signs and symptoms in the population is higher than 20% (Ingawale and Goswami 2009; Manfredini et al. 2012). The major symptoms of TMD are joint pain, abnormal joint tone and movement disorders of the mandible. TMD could be caused by many factors, such as abnormal occlusion, joint trauma, bad habits (bruxism, clenching, unilateral chewing, etc.), loss of posterior teeth and psychological factors. Almost 70% of TMD patients have disc displacement (Ingawale and Goswami 2009), defined as abnormal position between the disc and facies articularis of the condyle and articular fossa. TMD may be caused by abnormal loads in the TMJ. On the other hand, TMD could also lead to the increased magnitude of stress and abnormal stress distributions in the TMJ (Alvarez Areizaa et al. 2013; Creuillot et al. 2013). Tanaka et al. evaluated the differences of stress distribution for models with and without anterior disc displacement during maximum occlusion (2000) and jaw opening
*Corresponding author. Email: [email protected] q 2015 Taylor & Francis
(Tanaka et al. 2004). They also analysed the regularity of stress distribution in the TMJ during prolonged clenching and found that the maximum stress was located in the central and lateral zones of the disc (Tanaka et al. 2008). Perez del Palomar and Doblare (2007) simulated anteriorly displaced discs with and without reduction during jaw opening. The results showed that anterior displacement of the disc could lead to the greater compressive stress in the posterior band of the disc. They also compared the displacements and stress distributions of an anteriorly displaced disc without reduction and a surgically repositioned one with those of a healthy disc during jaw opening (Perez del Palomar and Doblare 2006a). Roh et al. (2012) used MRI scans to study the relationships between anterior disc displacement, joint effusion and degenerative changes of the TMJ with TMD. The results showed that anterior disc displacement was significantly related to degenerative changes of the condyles and joint effusions in patients with TMD. Koolstra (2012) analysed the influence of friction on anterior disc displacement and suggested that an increase in friction may not be the cause of anterior disc displacement. These studies about TMD were focused on anterior disc displacement. Other types of TMD are also necessary to investigate, such as other directions of disc displacements (Okochi et al. 2008; Ikeda and Kawamura 2013), relaxation of discal attachment and disc perforation.
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Figure 1.
Z. Liu et al.
(A) The 3D model of the mandible and TMJs and (B) details of the TMJ.
In this study, a three-dimensional finite element model of dentate mandible, disc and fossa –eminence complex was developed according to CT images. Based on this model, other seven models of typical TMDs were established: relaxation of discal attachment (relaxation of anterior and posterior attachments), disc displacement (anterior, posterior, medial and lateral disc displacements) and disc perforation. Contact elements were used to simulate the interaction between the discs and the cartilages in the TMJs of all the models. The mandibular ligaments and the attachments of discs were considered as nonlinear cable elements. The stress distributions between the TMJs with TMDs and the healthy joint were compared under centric occlusion.
2. Materials and methods 2.1 Finite element modelling The model of the dentulous mandible was developed by MIMICS 8.1 (Materialise, Leuven, Belgium) according to the CT images of a person with normal occlusion and without TMJ disease. Likewise, the bilateral articular fossa – eminence complexes were also constructed and the external surfaces were diced. Geometry of the cortical bones, the cancellous bones and the teeth was imported into ANSYS 8.0 (Swanson Analysis System Co., Houston, TX, USA), as shown in Figure 1(A). Fibrocartilage layers were simulated on the articular surfaces of the condyles and the articular fossa– eminence complexes. Based on the anatomical structure, the thickness of the cartilage layers varied from 0.2 mm at the crests of the condyles and the articular fossas to 0.5 mm at the anterior surfaces of the condyles and the temporal bones (Pullinger et al. 1990), as shown in Figure 1(B). According to the shapes of the articular surfaces and the anatomy of the disc (Hansson and Nordstrom 1977), the models of the two articular discs were constructed. The minimum thickness of the intermediate zone was about 1 mm, while the maximum
thicknesses of the anterior and posterior bands were 2 and 3 mm, respectively (Liu et al. 2007). This model was named as NOR. A finite element mesh with 10-node quadratic tetrahedral elements was built using ANSYS free meshing techniques because of the inherently irregular geometries. The FE model consisted of 186,772 tetrahedral elements and 285,210 nodes in total after convergence. The mechanical properties of the cortical bone, cancellous bone, cartilage and teeth were assumed to be homogeneous, isotropic and linearly elastic, and the articular disc to be nonlinearly elastic (Tanaka et al. 2001; Liu et al. 2007, 2008), as shown in Table 1.
2.2 Simulations of the TMJs The interfaces between the disc and the cartilages of the condyle and the temporal bone were simulated as contact elements based on a previous study (Liu et al. 2008), as shown in Figure 1(B). Thus, 5961 contact elements between the discs and the cartilage layers were obtained. The frictional coefficient of 0.001 was chosen according to related studies on asymptomatic TMJs (Tanaka et al. 2004; Liu et al. 2008). The temporomandibular ligaments, sphenomandibular ligaments and stylomandibular ligaments were considered in the models due to their close relationship to the functions of the TMJ, as shown in Figure 1(A). Ligaments scarcely Table 1. Material properties of the models. Tissue
Young’s modulus (GPa)
Poisson’s ratio
Cortical bone Cancellous bone Cartilage Articular disc
13,700 7930 0.79 44.1 (Stress # 1.5 MPa) 92.4 (Sress . 1.5 MPa) 18,600
0.3 0.3 0.49 0.4 0.4 0.31
Tooth
Computer Methods in Biomechanics and Biomedical Engineering
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bear compressive stress, so the nonlinear cable elements were used to simulate the ligaments. Stiffness values were assigned to the ligaments according to previous research (Liu et al. 2008, 2011). The discal attachments, including temporal anterior attachment, mandibular anterior attachment and bilaminar zones, were also modelled as nonlinear cable elements with referenced stiffness (Chen and Xu 1994; Liu et al. 2008, 2011). 2.3 Development of the TMD models Seven models of typical TMDs were established based on the model with normal TMJs: relaxation of anterior attachments or posterior attachments, anterior, posterior, medial and lateral disc displacements, and disc perforation. Only the TMJs in the models were modified. Meanwhile, the other parts of these models and the simulated method of all the TMJs were identical with the NOR model. Relaxations of anterior and posterior attachments were simulated by decreasing the stiffness of the cable elements, called as relaxation of anterior disc attachments (RAA) and relaxation of posterior disc attachments (RPA), respectively. According to the typical morphology of the displaced discs, the models of anterior, posterior, medial and lateral disc displacements were developed, called as ADD, PDD, MDD and LDD, respectively. Perforation of the bilaminar zones frequently occurs in the patients with the anterior disc displacement, the bilaminar zones were not modelled in the ADD model. Likewise, the temporal anterior attachment and mandibular anterior attachment were not modelled in the PDD model. Also, the inner layer of the temporomandibular ligament was not considered in the MDD model. Disc perforation typically occurs at the lateral intermediate zone, so this region was perforated in the model of disc perforation, called as DF. 2.4
Loading and boundary conditions
The force vectors of the bilateral masticatory muscles (superficial and deep masseter, anterior and posterior temporalis, medial pterygoid, superior and inferior lateral pterygoid) corresponding to centric occlusion were applied to the eight models. The magnitude of each muscle force was assigned according to its physiological cross section and the scaling factor (Koolstra et al. 1988). In addition, the origin and direction of each muscle force were defined from anatomical measurements (Faulkner et al. 1987). The models were fixed at the occlusal surface on the teeth and the external regions of the temporal bone (Tanaka et al. 2000, 2001; Liu et al. 2008). 3.
Results and discussion
In the model with normal TMJ (NOR), the posterior bands of the discs were located between the crests of the
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condyles and the articular fossas, consistent with the physiological position under centric occlusion. The maximum contact stresses were located between the anterior condyle and the lower surface of the intermediate zone of the disc and between the upper surface of the intermediate zone of the disc and the posterior articular eminence (i.e. anterior temporal bone), respectively. Also, the maximum contact stress and the contact area on the lower interface were greater than those on the upper interface, accordant with related studies (Beek et al. 2001; Liu et al. 2008). Therefore, the maximum stresses occurred at the intermediate zone of the disc, and the anterior of the condyle and temporal bone, in agreement with the physiological function and related biomechanical research (Oberg et al. 1971; Koolstra and van Eijden 2005; Perez del Palomar and Doblare 2006b; Liu et al. 2008). Anatomical studies found that the maximum pressure of disc was located at the intermediate zone during mandibular movements and injury to the condylar and temporal cartilages usually occurred in the anterior segment (Oberg et al. 1971). The tensile stress was dominant in the anterior band, accordant with the tensionbearing structure (Kang et al. 2006). However, the compressive stress was dominant in the posterior band, consistent with the pressure-bearing structure (Kang et al. 2006). The forces of the discal attachments were small and the maximum tensile force was located at the anterior attachments, in accordance with related studies (Chen et al. 1998; Liu et al. 2008). 3.1 Relaxation of discal attachment Abnormal positioning of the pathologic disc with respect to the condyle and articular fossa– eminence was caused by relaxation of disc attachments. The interaction between the lateral intermediate zone of the disc and the lateral side of the condyle and the articular fossa –eminence was evident in the model with RAA. Therefore, the maximum stresses of the pathologic disc were located at the lateral intermediate zone. The stress level in the pathologic disc was significantly greater than the identical disc in the NOR model, as shown in Figures 2 and 3. The maximum compressive stress of the pathologic disc was about 5 times greater than the identical disc in the NOR model, and the maximum tensile stress of the pathologic disc was about triple the magnitude of the NOR model, as shown in Figure 4. Thinning or perforation of the lateral intermediate zone of the disc with relaxed anterior attachment may result from long-term effects of occlusion and mandibular movement. According to the contact status, the maximum stresses of the condyle and the temporal bone were located at the lateral region. The stress levels of the lateral cartilages of the condyle and temporal bone in the RAA model were close to the anterior cartilages of the condyle and temporal bone in the NOR
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Figure 2. von Mises stress distributions of the right discs in NOR (A), RAA (B), RPA (C), DF (D), ADD (E), PDD (F), MDD (G) and LDD (H) models (the maximum stresses were listed, MPa). NOR represents normal disc. RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, MDD and LDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
model, as shown in Table 2. However, the maximum stresses of the condylar and temporal cartilages in the RAA model were almost half of the NOR model. In the model with relaxation of the bilaminar zones (posterior disc attachments), the maximum contact stress, located at the intermediate zone of the disc and posterior articular eminence, was much greater than that of the NOR model. On the contrary, the interaction between the disc and the condyle was weaker than that of the NOR model. The maximum stresses of the pathologic disc were located at the intermediate zone. The stress level in the pathologic disc was slightly greater than the identical disc in the NOR model, as shown in Figures 2 and 3. Based on the contact status, the maximum stresses of the condyle and the temporal bone were located at the anterior region. The stress levels of the condyle were much lower than the identical condyle in the NOR model (Table 2). On the other hand, the maximum compressive and shear stresses of the posterior articular eminence increased by 41.6 and 6.4 times those in the NOR model, respectively. Damage to the posterior articular eminence may be induced by the significantly high stress.
3.2 Disc displacements Contrary to normal TMJs, the interaction between the disc and the posterior articular eminence was much more intensive than that between the disc and the condyle in various disc displacements. Stress concentrations occurred at the intermediate zone of the anteriorly displaced disc. The maximum stresses of the disc were much greater than the identical disc in the NOR model (Figures 2 and 4). The maximum compressive stress of the disc was 14.6 times
that of the NOR model, which is similar to related publications (Arnett et al. 1996; Perez del Palomar and Doblare 2007), and greater than the other displaced disc. The maximum tensile stress of the disc, located at the
Figure 3. Average von Mises stresses of each band of the discs in all the eight models (A) and the NOR, RAA, RPA, ADD and DF models (B) in order to show the magnitudes clearly. NOR represents normal disc. RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, MDD and LDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
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Anterior Lateral Anterior
1.57 1.36 19.92
Anterior
32.59
Anterior Anterior Central Anterior
92.74 72.55 20.01 32.32
tensile stresses of the discs with posterior and lateral displacements, located at the intermediate zones, were 1.91 and 1.56 MPa, respectively (Figure 4). The magnitudes were greater than the tensile failure stress of the intermediate zones (1.53 MPa; Kang et al. 1998), so the significantly high tensile stresses could cause some pathological changes of the discs, such as perforation. The compressive stresses were greater than the tensile stresses of the anterior band in the two models, opposite from the tension-bearing structure (Kang et al. 2006). The maximum tensile stress of the anterior band of the posteriorly displaced disc was 1.47 MPa, close to its tensile failure stress (1.85 MPa; Kang et al. 1998). In the MDD model, stress concentrations occurred at each band of the disc. The stress levels of the anterior and posterior bands were significantly greater than those in the NOR model and other displaced discs (Figures 2 and 3). The maximum tensile stress of the anterior band of the disc was significantly greater than that of the intermediate zone and reached 2.23 MPa, exceeding the tensile failure stress (1.85 MPa; Kang et al. 1998). The tensile stresses of the posterior band were greater than the compressive stresses, inconsistent with the pressurebearing structure (Kang et al. 2006). The maximum tensile stress of the posterior band of the disc was 2.13 MPa, which is much higher than the tensile failure stress (1.35 MPa; Kang et al. 1998). Disc perforation and other pathological changes of the anterior and posterior bands could probably be induced by such significantly high tensile stresses. The average von Mises stresses of high stress regions of the condylar cartilages in the ADD and PDD models were approximately half as much as those in the NOR model, and the magnitudes were close to the NOR model in the MDD and LDD models, as shown in Table 2. However, the stresses of the posterior articular eminences with various disc displacements were much greater than those in the NOR model (Table 2). The average von Mises stresses of high stress regions of the posterior articular eminences in the PDD and MDD models were 59 and 46 times greater than the NOR model, respectively. Moreover, the maximum tensile stress of the posterior articular eminences occurred at the PDD model and reached 5.08 MPa, significantly exceeding the tensile failure stress (2.15 MPa). The significantly increased stresses in the posterior articular eminence could probably cause flattening and perforation of the cartilage, and possible bone resorption.
Anterior
23.47
3.3
Figure 4. The absolute value of maximum compressive and tensile stresses of the discs in the models. NOR represents normal disc. RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, MDD and LDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
intermediate zone, reached 1.43 MPa, close to the tensile failure stress obtained through experimental means (1.53 MPa; Kang et al. 1998). Thus, long-term occlusion could lead to thinning or perforation of the intermediate zone of the disc. In the models with posterior, medial and lateral disc displacements, the stress levels of all disc bands were greater than those of the discs in the NOR and ADD models (Figure 2). The stress distributions of the discs were similar in the PDD and LDD models. The maximum stresses of the anterior bands and intermediate zones of the discs were much greater than those of the posterior bands of the discs in the two models (Figure 3). The maximum Table 2. The high stress regions of the cartilages of the condyle and the temporal bone and the average von Mises stresses in these regions. Condylar cartilage High stress Models regions NOR RAA RPA ADD PDD MDD LDD
DF
Anterior Lateral Anterior Central Anterior Central Anterior Anterior Central Anterior Central Lateral Anterior Central
Temporal cartilage
Average von Average von Mises stress High stress Mises stress (kPa) regions (kPa) 9.42 11.49 0.89 0.75 4.39 3.06 4.52 8.16 8.02 5.06 4.84 10.81 3.26 2.12
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Note: RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, LDD and MDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
Disc perforation
Similar to disc displacements, the interaction between the disc and the articular fossa –eminence was much more intensive than that between the disc and the condyle in the DF model. The maximum contact stresses occurred
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between the anterior condyle and the lower surface of the intermediate zone of the disc and between the upper surface of the intermediate zone of the disc and the posterior articular eminence, respectively. Therefore, the stress concentration was located at the intermediate zone of the perforated disc (Figure 2). The stresses of all the bands of the perforated disc were greater than the identical disc in the NOR model (Figures 2 and 3). The compressive stresses in the anterior band of the perforated disc were much greater than the tensile stresses, inconsistent with the tension-bearing structure (Kang et al. 2006). On the contrary, the posterior band of the perforated disc undertook higher tensile stresses than compressive stresses, inconsistent with the pressure-bearing structure (Kang et al. 2006). The maximum stress of the three bands of the perforated disc may not lead to the continued perforation, accordant with Stratmann’s study (Stratmann et al. 1996). However, disc perforation could lead to increased stress and unreasonable stress distribution, possibly inducing other pathological changes to the perforated disc. The stress level of the condylar cartilage with perforated disc was lower than that in the NOR model, as shown in Table 2. On the other hand, disc perforation significantly increased the stress of the temporal cartilage, especially at the posterior articular eminence. The excessive stresses may cause some pathological changes, such as flattening and perforation of the cartilage. Obviously, treatment should be carried out prior to the perforation of the articular disc.
4. Conclusions In summary, the increased stresses and the abnormal stress distribution in the discs and articular cartilages could be induced by various TMDs, and could be the source of TMD development, such as thinning or perforation of the discs, flattening and perforation of the cartilage, and possible bone resorption. Therefore, an effective method to maintain and restore the normal structure and function of the TMJ should aim to treat the disorder as soon as initial symptoms are noticed, such as joint clicking.
Conflict of interest No potential conflict of interest was reported by the authors.
Funding This work was supported by the National Natural Science Foundation of China [grant number 11202143].
Note 1.
These authors contributed equally to this work.
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Effects of several temporomandibular disorders on the stress distributions of temporomandibular joint: a finite element analysis a
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a
Zhan Liu , Yingli Qian , Yuanli Zhang & Yubo Fan
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Provincial Key Laboratory of Biomechanical Engineering, Sichuan University, Chengdu, Sichuan, P.R. China b
Strength Design Department, AVIC 611 Institute, Chengdu, Sichuan, P.R. China
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Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, P.R. China Published online: 14 Jan 2015.
To cite this article: Zhan Liu, Yingli Qian, Yuanli Zhang & Yubo Fan (2015): Effects of several temporomandibular disorders on the stress distributions of temporomandibular joint: a finite element analysis, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2014.996876 To link to this article: http://dx.doi.org/10.1080/10255842.2014.996876
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Computer Methods in Biomechanics and Biomedical Engineering, 2015 http://dx.doi.org/10.1080/10255842.2014.996876
Effects of several temporomandibular disorders on the stress distributions of temporomandibular joint: a finite element analysis Zhan Liua1, Yingli Qianb1, Yuanli Zhanga and Yubo Fanc* a
Provincial Key Laboratory of Biomechanical Engineering, Sichuan University, Chengdu, Sichuan, P.R. China; bStrength Design Department, AVIC 611 Institute, Chengdu, Sichuan, P.R. China; cKey Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, P.R. China
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(Received 14 February 2014; accepted 7 December 2014) The aim of this study was to evaluate stress distributions in the temporomandibular joints (TMJs) with temporomandibular disorders (TMDs) for comparison with healthy TMJs. A model of mandible and normal TMJs was developed according to CT images. The interfaces between the discs and the articular cartilages were treated as contact elements. Nonlinear cable elements were used to simulate disc attachments. Based on this model, seven models of various TMDs were established. The maximum stresses of the discs with anterior, posterior, medial and lateral disc displacement (ADD, PDD, MDD and LDD) were 12.09, 9.33, 10.71 and 6.07 times magnitude of the identically normal disc, respectively. The maximum stresses of the posterior articular eminences in ADD, PDD, MDD, LDD, relaxation of posterior attachments and disc perforation models were 21, 59, 46, 21, 13 and 15 times greater than the normal model, respectively. TMDs could cause increased stresses in the discs and posterior articular eminences. Keywords: finite element analysis; temporomandibular disorder; temporomandibular joint; articular disc; stress distribution
1.
Introduction
Temporomandibular joints (TMJs), located between the condyle of mandible and the articular fossa– eminence, are the unique bilateral linked joints in the human body. Both TMJs are necessary for mastication, swallowing, speech and facial expressions. Temporomandibular disorder (TMD) is the most common TMJ disease. It is reported that the prevalence of TMD signs and symptoms in the population is higher than 20% (Ingawale and Goswami 2009; Manfredini et al. 2012). The major symptoms of TMD are joint pain, abnormal joint tone and movement disorders of the mandible. TMD could be caused by many factors, such as abnormal occlusion, joint trauma, bad habits (bruxism, clenching, unilateral chewing, etc.), loss of posterior teeth and psychological factors. Almost 70% of TMD patients have disc displacement (Ingawale and Goswami 2009), defined as abnormal position between the disc and facies articularis of the condyle and articular fossa. TMD may be caused by abnormal loads in the TMJ. On the other hand, TMD could also lead to the increased magnitude of stress and abnormal stress distributions in the TMJ (Alvarez Areizaa et al. 2013; Creuillot et al. 2013). Tanaka et al. evaluated the differences of stress distribution for models with and without anterior disc displacement during maximum occlusion (2000) and jaw opening
*Corresponding author. Email: [email protected] q 2015 Taylor & Francis
(Tanaka et al. 2004). They also analysed the regularity of stress distribution in the TMJ during prolonged clenching and found that the maximum stress was located in the central and lateral zones of the disc (Tanaka et al. 2008). Perez del Palomar and Doblare (2007) simulated anteriorly displaced discs with and without reduction during jaw opening. The results showed that anterior displacement of the disc could lead to the greater compressive stress in the posterior band of the disc. They also compared the displacements and stress distributions of an anteriorly displaced disc without reduction and a surgically repositioned one with those of a healthy disc during jaw opening (Perez del Palomar and Doblare 2006a). Roh et al. (2012) used MRI scans to study the relationships between anterior disc displacement, joint effusion and degenerative changes of the TMJ with TMD. The results showed that anterior disc displacement was significantly related to degenerative changes of the condyles and joint effusions in patients with TMD. Koolstra (2012) analysed the influence of friction on anterior disc displacement and suggested that an increase in friction may not be the cause of anterior disc displacement. These studies about TMD were focused on anterior disc displacement. Other types of TMD are also necessary to investigate, such as other directions of disc displacements (Okochi et al. 2008; Ikeda and Kawamura 2013), relaxation of discal attachment and disc perforation.
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Figure 1.
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(A) The 3D model of the mandible and TMJs and (B) details of the TMJ.
In this study, a three-dimensional finite element model of dentate mandible, disc and fossa –eminence complex was developed according to CT images. Based on this model, other seven models of typical TMDs were established: relaxation of discal attachment (relaxation of anterior and posterior attachments), disc displacement (anterior, posterior, medial and lateral disc displacements) and disc perforation. Contact elements were used to simulate the interaction between the discs and the cartilages in the TMJs of all the models. The mandibular ligaments and the attachments of discs were considered as nonlinear cable elements. The stress distributions between the TMJs with TMDs and the healthy joint were compared under centric occlusion.
2. Materials and methods 2.1 Finite element modelling The model of the dentulous mandible was developed by MIMICS 8.1 (Materialise, Leuven, Belgium) according to the CT images of a person with normal occlusion and without TMJ disease. Likewise, the bilateral articular fossa – eminence complexes were also constructed and the external surfaces were diced. Geometry of the cortical bones, the cancellous bones and the teeth was imported into ANSYS 8.0 (Swanson Analysis System Co., Houston, TX, USA), as shown in Figure 1(A). Fibrocartilage layers were simulated on the articular surfaces of the condyles and the articular fossa– eminence complexes. Based on the anatomical structure, the thickness of the cartilage layers varied from 0.2 mm at the crests of the condyles and the articular fossas to 0.5 mm at the anterior surfaces of the condyles and the temporal bones (Pullinger et al. 1990), as shown in Figure 1(B). According to the shapes of the articular surfaces and the anatomy of the disc (Hansson and Nordstrom 1977), the models of the two articular discs were constructed. The minimum thickness of the intermediate zone was about 1 mm, while the maximum
thicknesses of the anterior and posterior bands were 2 and 3 mm, respectively (Liu et al. 2007). This model was named as NOR. A finite element mesh with 10-node quadratic tetrahedral elements was built using ANSYS free meshing techniques because of the inherently irregular geometries. The FE model consisted of 186,772 tetrahedral elements and 285,210 nodes in total after convergence. The mechanical properties of the cortical bone, cancellous bone, cartilage and teeth were assumed to be homogeneous, isotropic and linearly elastic, and the articular disc to be nonlinearly elastic (Tanaka et al. 2001; Liu et al. 2007, 2008), as shown in Table 1.
2.2 Simulations of the TMJs The interfaces between the disc and the cartilages of the condyle and the temporal bone were simulated as contact elements based on a previous study (Liu et al. 2008), as shown in Figure 1(B). Thus, 5961 contact elements between the discs and the cartilage layers were obtained. The frictional coefficient of 0.001 was chosen according to related studies on asymptomatic TMJs (Tanaka et al. 2004; Liu et al. 2008). The temporomandibular ligaments, sphenomandibular ligaments and stylomandibular ligaments were considered in the models due to their close relationship to the functions of the TMJ, as shown in Figure 1(A). Ligaments scarcely Table 1. Material properties of the models. Tissue
Young’s modulus (GPa)
Poisson’s ratio
Cortical bone Cancellous bone Cartilage Articular disc
13,700 7930 0.79 44.1 (Stress # 1.5 MPa) 92.4 (Sress . 1.5 MPa) 18,600
0.3 0.3 0.49 0.4 0.4 0.31
Tooth
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bear compressive stress, so the nonlinear cable elements were used to simulate the ligaments. Stiffness values were assigned to the ligaments according to previous research (Liu et al. 2008, 2011). The discal attachments, including temporal anterior attachment, mandibular anterior attachment and bilaminar zones, were also modelled as nonlinear cable elements with referenced stiffness (Chen and Xu 1994; Liu et al. 2008, 2011). 2.3 Development of the TMD models Seven models of typical TMDs were established based on the model with normal TMJs: relaxation of anterior attachments or posterior attachments, anterior, posterior, medial and lateral disc displacements, and disc perforation. Only the TMJs in the models were modified. Meanwhile, the other parts of these models and the simulated method of all the TMJs were identical with the NOR model. Relaxations of anterior and posterior attachments were simulated by decreasing the stiffness of the cable elements, called as relaxation of anterior disc attachments (RAA) and relaxation of posterior disc attachments (RPA), respectively. According to the typical morphology of the displaced discs, the models of anterior, posterior, medial and lateral disc displacements were developed, called as ADD, PDD, MDD and LDD, respectively. Perforation of the bilaminar zones frequently occurs in the patients with the anterior disc displacement, the bilaminar zones were not modelled in the ADD model. Likewise, the temporal anterior attachment and mandibular anterior attachment were not modelled in the PDD model. Also, the inner layer of the temporomandibular ligament was not considered in the MDD model. Disc perforation typically occurs at the lateral intermediate zone, so this region was perforated in the model of disc perforation, called as DF. 2.4
Loading and boundary conditions
The force vectors of the bilateral masticatory muscles (superficial and deep masseter, anterior and posterior temporalis, medial pterygoid, superior and inferior lateral pterygoid) corresponding to centric occlusion were applied to the eight models. The magnitude of each muscle force was assigned according to its physiological cross section and the scaling factor (Koolstra et al. 1988). In addition, the origin and direction of each muscle force were defined from anatomical measurements (Faulkner et al. 1987). The models were fixed at the occlusal surface on the teeth and the external regions of the temporal bone (Tanaka et al. 2000, 2001; Liu et al. 2008). 3.
Results and discussion
In the model with normal TMJ (NOR), the posterior bands of the discs were located between the crests of the
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condyles and the articular fossas, consistent with the physiological position under centric occlusion. The maximum contact stresses were located between the anterior condyle and the lower surface of the intermediate zone of the disc and between the upper surface of the intermediate zone of the disc and the posterior articular eminence (i.e. anterior temporal bone), respectively. Also, the maximum contact stress and the contact area on the lower interface were greater than those on the upper interface, accordant with related studies (Beek et al. 2001; Liu et al. 2008). Therefore, the maximum stresses occurred at the intermediate zone of the disc, and the anterior of the condyle and temporal bone, in agreement with the physiological function and related biomechanical research (Oberg et al. 1971; Koolstra and van Eijden 2005; Perez del Palomar and Doblare 2006b; Liu et al. 2008). Anatomical studies found that the maximum pressure of disc was located at the intermediate zone during mandibular movements and injury to the condylar and temporal cartilages usually occurred in the anterior segment (Oberg et al. 1971). The tensile stress was dominant in the anterior band, accordant with the tensionbearing structure (Kang et al. 2006). However, the compressive stress was dominant in the posterior band, consistent with the pressure-bearing structure (Kang et al. 2006). The forces of the discal attachments were small and the maximum tensile force was located at the anterior attachments, in accordance with related studies (Chen et al. 1998; Liu et al. 2008). 3.1 Relaxation of discal attachment Abnormal positioning of the pathologic disc with respect to the condyle and articular fossa– eminence was caused by relaxation of disc attachments. The interaction between the lateral intermediate zone of the disc and the lateral side of the condyle and the articular fossa –eminence was evident in the model with RAA. Therefore, the maximum stresses of the pathologic disc were located at the lateral intermediate zone. The stress level in the pathologic disc was significantly greater than the identical disc in the NOR model, as shown in Figures 2 and 3. The maximum compressive stress of the pathologic disc was about 5 times greater than the identical disc in the NOR model, and the maximum tensile stress of the pathologic disc was about triple the magnitude of the NOR model, as shown in Figure 4. Thinning or perforation of the lateral intermediate zone of the disc with relaxed anterior attachment may result from long-term effects of occlusion and mandibular movement. According to the contact status, the maximum stresses of the condyle and the temporal bone were located at the lateral region. The stress levels of the lateral cartilages of the condyle and temporal bone in the RAA model were close to the anterior cartilages of the condyle and temporal bone in the NOR
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Figure 2. von Mises stress distributions of the right discs in NOR (A), RAA (B), RPA (C), DF (D), ADD (E), PDD (F), MDD (G) and LDD (H) models (the maximum stresses were listed, MPa). NOR represents normal disc. RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, MDD and LDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
model, as shown in Table 2. However, the maximum stresses of the condylar and temporal cartilages in the RAA model were almost half of the NOR model. In the model with relaxation of the bilaminar zones (posterior disc attachments), the maximum contact stress, located at the intermediate zone of the disc and posterior articular eminence, was much greater than that of the NOR model. On the contrary, the interaction between the disc and the condyle was weaker than that of the NOR model. The maximum stresses of the pathologic disc were located at the intermediate zone. The stress level in the pathologic disc was slightly greater than the identical disc in the NOR model, as shown in Figures 2 and 3. Based on the contact status, the maximum stresses of the condyle and the temporal bone were located at the anterior region. The stress levels of the condyle were much lower than the identical condyle in the NOR model (Table 2). On the other hand, the maximum compressive and shear stresses of the posterior articular eminence increased by 41.6 and 6.4 times those in the NOR model, respectively. Damage to the posterior articular eminence may be induced by the significantly high stress.
3.2 Disc displacements Contrary to normal TMJs, the interaction between the disc and the posterior articular eminence was much more intensive than that between the disc and the condyle in various disc displacements. Stress concentrations occurred at the intermediate zone of the anteriorly displaced disc. The maximum stresses of the disc were much greater than the identical disc in the NOR model (Figures 2 and 4). The maximum compressive stress of the disc was 14.6 times
that of the NOR model, which is similar to related publications (Arnett et al. 1996; Perez del Palomar and Doblare 2007), and greater than the other displaced disc. The maximum tensile stress of the disc, located at the
Figure 3. Average von Mises stresses of each band of the discs in all the eight models (A) and the NOR, RAA, RPA, ADD and DF models (B) in order to show the magnitudes clearly. NOR represents normal disc. RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, MDD and LDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
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Anterior Lateral Anterior
1.57 1.36 19.92
Anterior
32.59
Anterior Anterior Central Anterior
92.74 72.55 20.01 32.32
tensile stresses of the discs with posterior and lateral displacements, located at the intermediate zones, were 1.91 and 1.56 MPa, respectively (Figure 4). The magnitudes were greater than the tensile failure stress of the intermediate zones (1.53 MPa; Kang et al. 1998), so the significantly high tensile stresses could cause some pathological changes of the discs, such as perforation. The compressive stresses were greater than the tensile stresses of the anterior band in the two models, opposite from the tension-bearing structure (Kang et al. 2006). The maximum tensile stress of the anterior band of the posteriorly displaced disc was 1.47 MPa, close to its tensile failure stress (1.85 MPa; Kang et al. 1998). In the MDD model, stress concentrations occurred at each band of the disc. The stress levels of the anterior and posterior bands were significantly greater than those in the NOR model and other displaced discs (Figures 2 and 3). The maximum tensile stress of the anterior band of the disc was significantly greater than that of the intermediate zone and reached 2.23 MPa, exceeding the tensile failure stress (1.85 MPa; Kang et al. 1998). The tensile stresses of the posterior band were greater than the compressive stresses, inconsistent with the pressurebearing structure (Kang et al. 2006). The maximum tensile stress of the posterior band of the disc was 2.13 MPa, which is much higher than the tensile failure stress (1.35 MPa; Kang et al. 1998). Disc perforation and other pathological changes of the anterior and posterior bands could probably be induced by such significantly high tensile stresses. The average von Mises stresses of high stress regions of the condylar cartilages in the ADD and PDD models were approximately half as much as those in the NOR model, and the magnitudes were close to the NOR model in the MDD and LDD models, as shown in Table 2. However, the stresses of the posterior articular eminences with various disc displacements were much greater than those in the NOR model (Table 2). The average von Mises stresses of high stress regions of the posterior articular eminences in the PDD and MDD models were 59 and 46 times greater than the NOR model, respectively. Moreover, the maximum tensile stress of the posterior articular eminences occurred at the PDD model and reached 5.08 MPa, significantly exceeding the tensile failure stress (2.15 MPa). The significantly increased stresses in the posterior articular eminence could probably cause flattening and perforation of the cartilage, and possible bone resorption.
Anterior
23.47
3.3
Figure 4. The absolute value of maximum compressive and tensile stresses of the discs in the models. NOR represents normal disc. RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, MDD and LDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
intermediate zone, reached 1.43 MPa, close to the tensile failure stress obtained through experimental means (1.53 MPa; Kang et al. 1998). Thus, long-term occlusion could lead to thinning or perforation of the intermediate zone of the disc. In the models with posterior, medial and lateral disc displacements, the stress levels of all disc bands were greater than those of the discs in the NOR and ADD models (Figure 2). The stress distributions of the discs were similar in the PDD and LDD models. The maximum stresses of the anterior bands and intermediate zones of the discs were much greater than those of the posterior bands of the discs in the two models (Figure 3). The maximum Table 2. The high stress regions of the cartilages of the condyle and the temporal bone and the average von Mises stresses in these regions. Condylar cartilage High stress Models regions NOR RAA RPA ADD PDD MDD LDD
DF
Anterior Lateral Anterior Central Anterior Central Anterior Anterior Central Anterior Central Lateral Anterior Central
Temporal cartilage
Average von Average von Mises stress High stress Mises stress (kPa) regions (kPa) 9.42 11.49 0.89 0.75 4.39 3.06 4.52 8.16 8.02 5.06 4.84 10.81 3.26 2.12
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Note: RAA and RPA represent relaxation of anterior and posterior attachments, respectively. ADD, PDD, LDD and MDD represent anterior, posterior, medial and lateral disc displacements, respectively. DF represents disc perforation.
Disc perforation
Similar to disc displacements, the interaction between the disc and the articular fossa –eminence was much more intensive than that between the disc and the condyle in the DF model. The maximum contact stresses occurred
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between the anterior condyle and the lower surface of the intermediate zone of the disc and between the upper surface of the intermediate zone of the disc and the posterior articular eminence, respectively. Therefore, the stress concentration was located at the intermediate zone of the perforated disc (Figure 2). The stresses of all the bands of the perforated disc were greater than the identical disc in the NOR model (Figures 2 and 3). The compressive stresses in the anterior band of the perforated disc were much greater than the tensile stresses, inconsistent with the tension-bearing structure (Kang et al. 2006). On the contrary, the posterior band of the perforated disc undertook higher tensile stresses than compressive stresses, inconsistent with the pressure-bearing structure (Kang et al. 2006). The maximum stress of the three bands of the perforated disc may not lead to the continued perforation, accordant with Stratmann’s study (Stratmann et al. 1996). However, disc perforation could lead to increased stress and unreasonable stress distribution, possibly inducing other pathological changes to the perforated disc. The stress level of the condylar cartilage with perforated disc was lower than that in the NOR model, as shown in Table 2. On the other hand, disc perforation significantly increased the stress of the temporal cartilage, especially at the posterior articular eminence. The excessive stresses may cause some pathological changes, such as flattening and perforation of the cartilage. Obviously, treatment should be carried out prior to the perforation of the articular disc.
4. Conclusions In summary, the increased stresses and the abnormal stress distribution in the discs and articular cartilages could be induced by various TMDs, and could be the source of TMD development, such as thinning or perforation of the discs, flattening and perforation of the cartilage, and possible bone resorption. Therefore, an effective method to maintain and restore the normal structure and function of the TMJ should aim to treat the disorder as soon as initial symptoms are noticed, such as joint clicking.
Conflict of interest No potential conflict of interest was reported by the authors.
Funding This work was supported by the National Natural Science Foundation of China [grant number 11202143].
Note 1.
These authors contributed equally to this work.
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