An exploration of the correlation between strain energy density in the temporomandibular joint and facial morphologic parameters

doi:10.21203/rs.3.rs-4950472/v1

Purpose: The purpose of this was to construct finite element (FE) models based on computed tomography (CT) data of individual patients during orthodontic treatment and to evaluate the relationship between strain energy density (SED) in the temporomandibular joint (TMJ) disc and the facial morphology of three skeletal patterns (Class 1–3) by cephalometric analysis.

Methods: Cephalometric analyses were performed on 53 patients. FE models based on the CT images of each patient were constructed, and the mean SED in the bilateral TMJ disc was calculated. The relationships between SED and the cephalometric parameters were evaluated.

Results: SED was significantly greater in Classes 1 and 2 than in Class 3 (p < 0.05). A positive correlation was observed between SED and the parameter of, convexity and ANB angle (p < 0.01), whereas a negative correlation was observed between SED and facial angle in Class 3(p < 0.05). A positive correlation was identified between SED and gonial angle in Class 1(p < 0.05). In all cases, correlations were observed between SED and facial angle (p < 0.05), convexity(p < 0.01), mandibular angle(p < 0.05), Y-axis(p < 0.05), SNB (p < 0.05), ANB angle(p < 0.01), and overjet(p < 0.05).

Conclusion: An increase in SED in the TMJ disc was observed when the mandible was rotated clockwise and positioned superior posteriorly. Furthermore, SED was affected by an overjet of dental parameters. Numerically, the present study suggests that SED generated in the TMJ disc was primarily affected by mandibular morphology. Considering that an increase in SED causes damage to the articular disc, three skeletal parameters (facial angle, convexity, and ANB) are useful in predicting TMJ dysfunction.

finite element analysis

temporomandibular joint dysfunction

X-ray computed tomography

strain energy density

cephalometric analysis

Previous studies have assessed the association between the radiographic depiction of osseous temporomandibular joint (TMJ) components and dentofacial morphology, and TMJ dysfunction (TMD) symptoms and malocclusion [1, 2]. In addition, the mechanical stress on the TMJ has been shown to vary with individual TMJ morphology [1, 3]. Park [4] reported the relationship between TMD and dentofacial deformity but failed to clarify it; however, it has been suggested that stress in the TMJ may constitute an important factor in solving this problem. Several studies have assessed the association between the state of the articular disc in the TMJ using magnetic resonance imaging and facial morphology using cephalometric radiography [1–3, 5–7]. In a recent systematic review, Shu et al. [8] reported that the relationship between TMD and facial morphology was unclear owing to insufficient data on possible pathogenic factors. The relationship between the mandible and the TMJ was evaluated using a rigid body spring network model of simplified mandibles and a biomechanical assessment of the TMJ [9]. However, because this method is a two-dimensional evaluation, it could not analyze three-dimensional (3-D) movements, such as jaw function. For this reason, a 3-D biomechanical analysis is required.

Mathematical methods such as finite element (FE) analysis have been used to evaluate the complex biomechanical behavior of the mandible [10, 11]. FE models of the TMJ have been developed to simulate condylar motion in response to changes in stress [12–14].

Currently, computed tomography (CT)-based FEM that uses newly developed software and incorporates information about the 3-D architecture and bone density distribution of the TMJ, allows precise assessment [14]. Shu et al. determined the stress distribution in the TMJ using a FE analysis [15].

However, the stress generated in soft tissues, such as the articular disc, is very low compared to that in the mandible; thus, it is difficult to examine the TMJ disc due to stress.

Some studies have evaluated the strain energy density (SED), which is the amount of scalar that has no direction around biomechanics [16–20]. SED is generally evaluated as an appropriate parameter for bone and cartilage remodeling simulations and is used as an evaluation parameter for these adaptations [16–21]. SED can be calculated using finite element analysis. Based on these reports, we considered that failure of the TMJ disc could be predicted based on an increase in SED.

Based on clinical statistics, most previous studies have reported a relationship between facial morphology and temporomandibular joint disorders [1–3, 5–8]. However, there is no numerical method for evaluating the effects of the maxillofacial morphology on articular discs.

Based on these findings, it is hypothesized that facial morphology significantly influences the articular disc. Thus, the objective of this retrospective study was to construct FEMs based on the CT data of individual patients obtained during orthodontic treatment and to numerically evaluate the relationship, which, to date, has only been reported statistically, between SED in the articular disc and the facial morphology of three skeletal patterns (Class 1, 2 and Class 3) using x-ray lateral cephalometric analysis.

The study population comprised 16 men and 37 women who underwent orthodontic treatment before orthognathic surgery. Cephalometric X-ray images were taken one week before surgery, and cephalometric analysis was performed in all cases. The facial angle, occlusal plane angle, Y-axis, convexity, mandibular plane, gonial angle, SNA angle, SNB angle, ANB angle, overjet, and overbite were measured (Fig. 1a). In the ANB parameter of the cephalogram, a magnitude less than 1.6° was classified as Class 3 of the skeletal pattern, a magnitude from 1.6° to 6.0° was classified as Class 1, and a magnitude > 6.0° was classified as Class 2. The present study included 37 (Class 3), 12 (Class 1), and four (Class 2) cases. The age of the 57 patients ranged from 17 to 41 years (mean, 25.0 years). All patients had facial symmetry confirmed by anterior-posterior cephalometric analysis.

This study was performed in accordance with the principles outlined in the Declaration of Helsinki and was approved by the ethical committee of Nara Medical University (Permission Number: 3197). As the data is completely anonymized and cannot be used to identify you, Consent to Participate declarations are not applicable. This study conformed to Strengthening the Reporting of Observational Studies in Epidemiology guidelines.

Computed tomography

The patient underwent X-ray CT imaging one week before surgery. (In our department, we always take CT X-P before orthognathic surgery to perform a preoperative simulation for safety.) The same CT system (Somatom® Emotion 16; Siemens, Berlin, Germany) (130 kV, average of 150 mA, 0.7 s/rotation, helical pitch of 0.75) was used to assess the participants. Computed tomography (CT) data were obtained from a 1 mm-thick slice of the submental region to the supraorbital rim.

Condylar position in computed tomography images

The condylar position was measured using sagittal CT images according to the method proposed by Ueki et al. (Fig. 1b) [22]. Sagittal images were obtained at the intersection of the center of the condyle. To obtain consistent orientation of the sagittal images, the head of each patient was positioned in the Frankfurt plane perpendicular to the floor. The resulting data were converted into 3-D images using a 3-D computer program (AOC View®; Array Corporation, Tokyo, Japan).

The following measurements were taken from the sagittal images: (1) X, the distance between the lowest point of the articular eminence and the squamotympanic fissure, (2) Y, the length of a perpendicular line (line Y) drawn from line X to the highest point of the glenoid fossa, (3) y, the length of a perpendicular line (line y) drawn from line X to the highest point of the condyle, and (4) x, the distance between the lowest point of the articular eminence and the highest point of the condyle parallel to line X (Fig. 2). To examine the anteroposterior positional relationship of the condyle in the glenoid fossa, the anteroposterior ratio of the condylar position on the X-axis (x/X) was calculated. The large magnitude indicated that the condyle was located in the posterior region of the glenoid fossa. To determine the TMJ cavity width, Y-y (mm), the distance between the condylar head and glenoid fossa (Y-axis) was calculated.

Finite element analysis

CT-based FE models of 53 patients were constructed from the CT data (Figs. 2a–c). The 53 models were constructed using bone strength FE analysis software (Mechanical Finder®; Research Center of Computational Mechanics., Tokyo, Japan). The articular disc of the TMJ was created using 3-D computer graphics software (Metasequoia®; Tetraface, Tokyo, Japan) and positioned between the bilateral condylar head and the glenoid fossa (Fig. 2b). The space formed by the glenoid fossa and condylar head is defined as the articular disc, and the band from the anterior soft tissue of the articular disc to the anterior slope of the glenoid fossa and the articular tubercle is defined as the anterior connective tissue. The band formed from the posterior articular disc to the posterior surface of the mandibular fossa is defined as the posterior connective tissue. The anterior and posterior connective tissues of the articular disc were bonded to the maxillary and lateral temporal bones, respectively. The trabecular bone, cortical bone, and teeth were modeled using a 1–4-mm linear tetrahedral element. The FEMs comprised 529,560–1,163,606 tetrahedral elements, and 115,770–254,501 nodes.

Loading and boundary conditions

All 53 models were placed under the same loading and boundary conditions. The contact (contact element with multi-point constraints) and sliding conditions between the occlusal surfaces of the upper and lower dentitions (frictional coefficient [salivary lubrication] of µ = 0.2) [23], between the disc and the condylar head and between the disc and the glenoid fossa (frictional coefficient of µ = 0.001) [15], were defined. The loading condition was based on the assumption of clenching and was defined as the force of the masticatory muscles (i.e., the masseter, temporal, external pterygoid, and medial pterygoid muscles). The proportion of muscle force magnitude and direction of the muscle forces were defined according to an approach used in previous studies [24] (Table. 1). For boundary conditions, the nodes on the upper side of the zygoma, zygomatic arch, lateral temporal bone, and orbital rim were constrained in all directions (Fig. 2c). Mandibular movement was not constrained in all direction and the mandible was connected to the temporal bone (glenoid fossa) by the anteroposterior connective tissue of the articular disc.

Material property

To determine bone heterogeneity, the mechanical properties of each element and Young’s modulus were calculated for each element based on Hounsfield unit values using the equations proposed by Keyak et al. [25]; Poisson’s ratio of the element in the bone was 0.4. Poisson’s ratio and Young’s modulus were 0.4 and 40 MPa for the articular disc; and0.48 and 8 MPa for the posterior and anterior bands. Regarding teeth, a shell element with a thickness of 1 mm was set as enamel in the element around the crown, and Poisson's ratio and Young's modulus were 0.3 and 5 × 10⁴ MPa for the enamel. The region except enamel was defined as dentin, with Poisson's ratio and Young's modulus of 0.3 and 1.07 × 10⁴ MPa [14].

Solution

The mean energy generated on the entire articular disc was calculated to evaluate SED of the bilateral articular discs. The analysis was performed using a static nonlinear analysis.

Statistical analysis

We compared the condylar positions by class and sex and compared the SED in the articular disk among the three classes. Furthermore, we compared the SED between groups with and without temporomandibular joint symptoms. For comparison between the two groups, the data were tested for normal distribution and homoscedasticity using the F test. Student’s t-test was used to evaluate normally distributed variables, and the Mann–Whitney U test was used to assess variables with an irregular distribution. For the comparison of the three groups, a post-hoc test was used after examination using a one-factor ANOVA.

Correlations among the CT image data, cephalometric data, and SED were identified using Pearson’s correlation coefficient or Spearman’s rank correlation coefficient. Pearson’s and Spearman’s rank correlation coefficients were calculated for data with normal and irregular distributions, respectively. Statistical significance was denoted by a p-value of < 0.05.

Furthermore, after determining the above correlation, we performed a regression analysis between cephalometric parameters with high correlation and SED and investigated whether the parameters of the cephalometric analysis are useful for predicting SED that occurs in the articular disc.

The number of cases with temporomandibular joint symptoms

TMD symptoms were identified in two of the 12 cases (16.7%) (Class Ⅰ), six of the 37 cases (16.2%) (Class Ⅲ), and two of the four cases (50%) (Class Ⅱ). The breakdown of the TMJ symptoms in each class is presented in Table 2.

Table 1

The muscle forces and directions applied to FE models
	Force	Direction
		Right side			Left side
		cos-x	cos-y	cos-z	cos-x	cos-y	cos-z
Masseter	272.0N	-0.212	-0.367	0.906	0.212	-0.367	0.906
Medial Pterygoid	132.8N	0.486	-0.373	0.791	-0.486	-0.373	0.791
Temporalis	316.0N	-0.222	0.500	0.837	0.222	0.500	0.837
External Pterygoid (upper)	18.1N	0.761	-0.645	0.074	-0.761	-0.645	0.074
External Pterygoid (lower)	16.9N	0.630	-0.757	-0.174	-0.630	-0.757	-0.174

Table 2

Breakdown of symptoms of temporomandibular disorders into classes
Class Ⅰ (n = 2/12 (Total cases in Class Ⅰ))	Class Ⅱ (n = 2/4 (Total cases in Class Ⅱ))	Class Ⅲ (n = 6/37 (Total cases in Class Ⅲ))
Unilateral Clicking(n = 1)	Disturbance on the opening mouth, unilateral clicking, and bilateral joint effusion (n = 1)	Unilateral Clicking(n = 3)
Disturbance on the opening mouth (n = 1)	Disturbance on the opening mouth (n = 1)	Unilateral joint effusion(n = 1)
		Disturbance of the protrusion(n = 1)
		Disturbance on the opening mouth (n = 1)
n: number of case

Cephalometric analysis

Cephalometric analyses of the participants in Classes Ⅰ, Ⅲ, and Ⅱ are presented in Table 3.

Table 3

Cephalometric analysis of all cases (Mean values ± standard deviation)
	Total cases (n = 53)	Class Ⅰ cases (n = 12)	Class Ⅲ cases (n = 37)	Class Ⅱ cases (n = 4)
Facial angle (°)	88.61 ± 5.81	86.64 ± 4.83	91.26 ± 3.88	78.64 ± 6.70
Occlusal plane (°)	9.75 ± 6.51	10.26 ± 5.56	7.92 ± 5.76	19.07 ± 8.05
Y-axis (°)	63.42 ± 5.46	65.02 ± 5.44	61.06 ± 4.09	71.32 ± 5.98
Convexity(°)	-2.21 ± 9.43	2.93 ± 2.26	-7.21 ± 5.76	19.31 ± 10.66
Mandibular plane (°)	34.67 ± 9.58	35.04 ± 10.42	30.97 ± 6.78	49.64 ± 6.44
Gonial angle (°)	135.09 ± 8.62	136.50 ± 11.06	133.46 ± 58.63	136.62 ± 6.80
SNA (°)	80.71 ± 4.40	81.28 ± 5.64	80.83 ± 4.30	80.52 ± 3.19
SNB (°)	81.63 ± 6.17	79.89 ± 5.66	84.13 ± 27.42	71.74 ± 6.52
ANB (°)	-0.84 ± 4.20	1.80 ± 0.23	-3.29 ± 2.59	8.78 ± 3.62
Overjet (mm)	-2.91 ± 4.76	0.31 ± 4.21	-5.55 ± 3.08	5.60 ± 2.59
Overbite (mm)	-0.31 ± 2.48	-0.74 ± 2.41	-0.16 ± 2.42	1.22 ± 2.00
n: number of case

Condylar positions identified on computed tomography

The mean magnitude of the bilateral x/X ratio was 0.57 for Class 3, 0.52 for Class Ⅰ and 0.45 for Class Ⅱ. A significant difference was observed between Classes Ⅲ and 2 (p < 0.01) (Fig. 3a). The results indicated that the condylar position in Class Ⅲ was in the posterior region compared with that in Class Ⅱ. The mean magnitude of the bilateral Y-y distance was 1.79 mm in Class Ⅲ, 1.70 mm in Class Ⅰ, and 4.11 mm in Class Ⅱ. A significant difference was observed between Class Ⅰ and 2 (p < 0.05), and between Class Ⅲ and Ⅱ (p < 0.01) (Fig. 3b).

In comparison between male and female participants, the mean magnitude of the bilateral x/X ratio was 0.58 for males and 0.57 for females. There were no significant differences between males and females (Fig. 3c). The mean magnitude of the bilateral Y-y distance was 2.14 mm in males and 1.74 mm in females. There was a significant difference between males and females (p < 0.05).

Finite element analysis

Distribution of strain energy density in the articular disc

Assuming a process from the start of occlusion to maximum voluntary clenching, the SED distribution was calculated by dividing the load value into four stages (25%, 50%, 75%, and 100% of the loading force). In most cases, the SED distribution on the upper side of the TMJ disc spread from the posterior to the anterior region as the loading force increased. In contrast, the SED on the lower side of the disc was concentrated in the anterior region of the lower side and spread to the posterior region with an increase in the loading force (Fig. 4). There were no particular differences in the SED distribution among the three classes.

Comparison of the magnitude of strain energy density in Class Ⅲ, Class Ⅰ, and Class Ⅱ

The magnitudes of the SED were 0.131 MPa for Class Ⅰ, 0.144MPa for Class Ⅱ, and 0.067 MPa for Class Ⅲ. There were statistically significant differences between Classes Ⅰ and Ⅲ (P < 0.05), and between Classes Ⅱ and Ⅲ (P < 0.05). (Mann-Whitney U test) (Fig. 5a).

Comparison of the magnitude of strain energy density between with and without symptom

The magnitudes of the SED with and without symptoms were 0.178 and 0.078MPa, respectively. There were statistically significant differences between with and without symptoms (P < 0.05). (Mann-Whitney U test) (Fig. 5b).

The relationship between the cephalometric data and mean strain energy density in the entire articular disc

The relationship between cephalometric data and the mean strain energy density (SED) of the entire articular disc is shown in Table 4 and Figure. 6 (Scatter plot). Correlations in all three classes were found between the SED and five skeletal parameters (facial angle, convexity, mandibular plane angle, Y-axis, and ANB angle) and dental parameters (overjet). Convexity and ANB showed a positive correlation with r ≧ 0.4, and facial angle, mandibular plane angle, Y-axis, and overjet showed a weak correlation with 0.2 ≦ r < 0.4. From these results, the SED was of low magnitude in cases where the mandible was located anteriorly and inferiorly to the maxilla, and tended to increase in response to the clockwise rotation of the mandible to the right on the cephalogram in the right view.

Table. 4 The correlation coefficients between cephalometric data and the mean strain energy density in the whole articular disc

In Class Ⅲ, weak correlations were observed between SED and the two skeletal parameters (facial angle and convexity), and a moderate correlation was observed between SED and ANB. The trends of Class Ⅲ were similar to the trends of the other cases. The SED increased with the posterior position of the mandible relative to the maxilla. There was no correlation between the dental parameters.

In Class 1, only correlations between SED and the gonial angle were identified.

In Class Ⅱ, some parameters showed large correlation coefficients; however, no significant correlation was found for all parameters owing to the small sample size.

A regression analysis was performed using facial angle, convexity, mandibular plane angle, and ANB angle for all the cases (these parameters have a significant correlation and have high power ( ≧ 0.7)) as explanatory variables, and SED as the objective variable. All the parameters showed P < 0.01. The cephalometric parameters were shown to be useful in predicting the SED of articular discs. (Fig. 7)

Condylar position

No significant difference in the vertical condylar position (Y-y (Y-axis)) was observed between Classes Ⅰ and Ⅲ; however, there were significant differences between Classes Ⅱ and another class. In Class Ⅱ malocclusions, idiopathic condylar resorption occurs most often in teenage girls [26]. In addition, resorption of the mandibular condyle indicates Class Ⅱ malocclusion with and without open bite [27].

From these reports, we deduce that the cause of this is that the resorption of the condyle in Class Ⅱ cases was greater than that in other classes. However, we cannot draw conclusions from this result due to the small sample size of Class Ⅱ.

A significant difference was observed between Classes Ⅲ and Ⅱ in the horizontal position (x/X (X-axis)). The condylar position in the Class Ⅲ group was primarily in the posterior region of the glenoid fossa, whereas that in the Class Ⅱ group was in the anterior region. Paknahad et al. [28] established that the condyles in patients with ClassⅡskeletal patterns were in the anterior region of the glenoid fossa in comparison with those of Classes Ⅰ and Ⅲ skeletal patterns, and a significant difference in condylar position was not detected between Class Ⅰ and Class Ⅲ subjects. In the present study, the condylar position in Class Ⅱ was anterior compared with another class. This result is consistent with the findings of Paknahad et al. [28]. In this study, it was observed that the mandibular condyle was located in the posterior region of the glenoid fossa when the mandible was in the anterior position and in the anterior region of the glenoid fossa when the mandible was in the posterior position. Mandibular morphology may affect condylar position.

Finite element analysis

Distribution of strain energy density in the articular disc

The SED distribution in individual patients was calculated. SED distribution in the upper side of the TMJ disc spread from the intermitted posterior region to the anterior region as the loading force increased; by contrast, that in the lower side spread from the anterior to the posterior region with the increase in loading force. However, the SED concentration in the anterior region of the lower side was not as high as that in the posterior region of the upper side. This concentration was consistent with the loaded area reported by Nickel et al. [29] and Teng et al. [30]. It is likely that SED was generated in the articular disc by the inclination of the condylar process, mandibular ramus, and contraction of the masticatory muscle.

Comparison of strain energy density among three classes

The difference between Class Ⅲ and the other classes was statistically significant. From these results and the description of the relationship between cephalometric data and SED, if the mandible relative to the maxilla is anteriorly positioned, such as in Class Ⅲ, compared to Classes Ⅰ and Ⅱ, we consider that the reduction in SED should be demonstrated.

Comparison of strain energy density between with and without symptoms

The SED in symptomatic cases was significantly higher than that in asymptomatic cases. Liu et al. [31] reported that the stress on an articular disc with TMD was more than six times higher than that without TMD. We cannot clarify this conclusion because of the small sample size; however, if the mandibular morphology shows an abnormality, the incidence of symptoms is high, especially in Class Ⅱ. From these numerical calculations, it was concluded that the mandibular morphology greatly influenced TMD. This indicates that TMD symptoms may be biomechanically predictable.

The relationship between cephalometric data and mean strain energy density in the entire articular disc

Following an evaluation of the relationship between cephalometric analysis parameters and SED, SED increased when evaluating all the patients, as well as when evaluating only Class Ⅲ patients, when the mandible was positioned backward and rotated clockwise. We assumed that the tendency of the relationship in all cases was similar to that in Class Ⅲ, because the number of cases in Class Ⅲ accounted for approximately 70% of all cases.

Three skeletal cephalometric parameters (facial angle, convexity, and ANB angle) were correlated in both the entirety of the cases of the study and Class Ⅲ cases. Li et al. [31] reported that the stress generated in the TMJ was reduced by improving the ANB angle. Based on the results reported in Figure.7, the recommendation is that these parameters (especially ANB) are useful for monitoring the effects of SED on TMJ discs.

Although there were no significant differences, two skeletal parameters (convexity and ANB) and one dental parameter (overjet) were correlated (r = 1) in Class Ⅱ cases. This result indicated that the backward position induced an increase in the SED. However, owing to the extremely small sample size (n = 4) of Class Ⅱ cases, it may not be possible to draw any conclusions. Nevertheless, our finding was that changes in SED in Class Ⅲ cases could be predicted using FE analysis.

In Class Ⅰ cases, a correlation was demonstrated between SED and gonial angle. There was no correlation between SED and other skeletal parameters, except for the gonial angle.

Temporomandibular joint symptoms develop as the gonial angle increases [32, 33], and our present results for Class Ⅰ are consistent with these reports. A weak correlation with the overjet of the dental parameters in all cases is shown. Paknahad et al. [34] and Ahn et al. [6] reported that backward positioning and clockwise rotation of the mandible increased overjet with the progression of TMD. These reports suggest that changes in skeletal parameters may influence the overjet.

In a recent systematic review, Shu et al. [8] reported that patients with TMD possessed remarkable features, including a retruded and clockwise-rotated shorter mandible and smaller ramus height. Thus, related craniofacial features should be considered because they potentially indicate the presence of TMD.

SED has been used in biomechanical studies to describe a scalar quantity that has no direction [29]. SED is generally used as an appropriate assessment parameter in bone and cartilage remodeling simulations and adaptations [16–20]. Based on the assumption that an increase in SED is involved in the development of TMD, the results of the present study are consistent with those reported by Paknahad [34] and Ahn [6]. In particular, the present study was conducted to numerically prove the conclusion in the systematic review performed by Shu et al. [8]

Limitations

This study has some inherent limitations. The TMJ disc is a hollow tissue; in addition, it is characterized by viscoelasticity and anisotropy. The TMJ is comprised of a joint disc, upper and lower joint cavities, connective tissue, and synovial fluid. To obtain a high equivalence of the structure of the entire mandible and temporomandibular joint, a large number of elements are required. However, the computational power of our personal computer was limited. Therefore, the temporomandibular joint intervertebral disc was simplified. Furthermore, it was necessary to adapt the original muscle directions and forces for each patient in the FE model. However, the data on muscle directions were adapted from Korioth’s data [23] for all cases because it was impossible to measure each patient’s original muscle directions and forces at our institution.

In the current study, Class Ⅰ and Ⅱ had smaller sample sizes compared to Class Ⅲ. In particular, there were very few samples in Class Ⅱ. However, a sufficient sample size for Class Ⅱ could not be obtained at the authors’ facility. It was possible to obtain sufficient samples for Class Ⅲ, in keeping with the racial characteristics of Japan. Therefore, in the future, the sample size for Class Ⅱ should be increased and all classes including Class Ⅱ cases should be compared.

SED is not always involved in the development of TMD. The present study did not evaluate all TMD conditions; TMD was evaluated in terms of muscular, joint, and psychological considerations [35]. However, several studies have evaluated the effects of SED on articular cartilage [16–21]; thus, it was hypothesized in the present study that SED impacts TMJ disc.

FE models were constructed for 53 individual patients, SED generated in the articular disc was calculated, and the relationship between SED in the TMJ disc and cephalometric parameters was determined. SED in Class Ⅲ was significantly lower than that in Class Ⅰ. Based on this result and the correlation, the SED in the TMJ disc increased when the mandible was rotated clockwise and existed in the posterosuperior position in all cases. The findings suggest that the SED generated in the TMJ disc was primarily influenced by mandibular morphology and that the four cephalometric parameters (facial angle, convexity, mandibular plane angle, and ANB angle) were useful in predicting TMJ dysfunction.

Ethical statement

This study was performed in accordance with the principles outlined in the Declaration of Helsinki and was approved by the ethical committee of Nara Medical University (Permission Number: 3197). As the data is completely anonymized and cannot be used to identify you, Consent to Participate declarations are not applicable. This study conformed to Strengthening the Reporting of Observational Studies in Epidemiology guidelines.

Contributions

Kazuhiro Murakami (Author 1) contributed to the conception, design, data acquisition, and interpretation; performed the statistical analysis; and drafted and critically revised the manuscript.

Masayoshi Kawakami (Author 2) contributed to the conception and design and critically revised the manuscript.

Kazuhiko Yamamoto (Author 3) contributed to the conception and drafted and critically revised the manuscript.

Horita Satoshi (Author 4) contributed to the conception and drafted and critically revised the manuscript.

All the authors gave their final approval and agreed to be accountable for all aspects of the work.

Acknowledgments

Contributions

Kazuhiro Murakami (Author 1) contributed to the conception, design, data acquisition, and interpretation; performed the statistical analysis; and drafted and critically revised the manuscript.

Masayoshi Kawakami (Author 2) contributed to the conception and design and critically revised the manuscript.

Kazuhiko Yamamoto (Author 3) contributed to the conception and drafted and critically revised the manuscript.

Horita Satoshi (Author 4) contributed to the conception and drafted and critically revised the manuscript.

All the authors gave their final approval and agreed to be accountable for all aspects of the work.

Funding

This research received no funding.

Conflict of interest

The authors declare no potential conflicts of interest concerning the authorship and/or publication of this article.

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No competing interests reported.

An exploration of the correlation between strain energy density in the temporomandibular joint and facial morphologic parameters

Status:

Version 1

Abstract

Figures

Introduction

Materials and methods

Computed tomography

Condylar position in computed tomography images

Finite element analysis

Loading and boundary conditions

Material property

Solution

Statistical analysis

Results

The number of cases with temporomandibular joint symptoms

Cephalometric analysis

Condylar positions identified on computed tomography

Finite element analysis

Distribution of strain energy density in the articular disc

Comparison of the magnitude of strain energy density between with and without symptom

Discussion

Condylar position

Finite element analysis

Distribution of strain energy density in the articular disc

Comparison of strain energy density among three classes

Comparison of strain energy density between with and without symptoms

The relationship between cephalometric data and mean strain energy density in the entire articular disc

Limitations

Conclusion

Declarations

References

Additional Declarations

Status:

Version 1