The biomechanical effects of bimaxillary osteotomies to the patients with mandibular retraction under incisal clenching

The purpose of this study is to investigate the biomechanical effect of bimaxillary osteotomies on patients with mandibular retraction. Mandibular retraction, as a typical maxillofacial deformity, and has great adverse effects on TMJ. Bimaxillary osteotomies are widely used to correct symptoms of mandibular retraction. It is necessary to understand the effect of surgery on temporomandibular disc (TMJ). Five patients with mandibular retraction and 10 asymptomatic subjects were involved in this study. Finite element models of preoperative, postoperative and control group were constructed based on the CT data. Nine sets of concentrated forces were used to simulate the muscle effect and contact method was used to simulate the interaction within the TMJs and dentitions. The results showed that bimaxillary osteotomies could effectively improve the maxillofacial morphology and alleviate the overload in TMJ. The facial asymmetry and right chewing side preference could cause imbalanced stress distributions in the TMJs and interfere the surgical treatment.


| INTRODUCTION
Maxillofacial deformities, including mandibular retraction, mandibular prognathism and facial asymmetry, are common facial diseases which cause great adverse effects on the appearance and life of the patients. 13][4] A pair of TMJs participate and control 2000 facial and oral activities, whose damage could lead to dysfunction, psychological problems, and even temporomandibular disorders (TMD). 5,6TMD is considered to be harmful to human's physical and mental health.However, even now some case reports and medical evidence showed the patients with mandibular retraction had TMD symptoms, 7,8 the association between mandibular retraction and TMD has not been fully studied. 9imaxillary osteotomies, a combination of bilateral sagittal split ramus osteotomy (BSSRO) and Lefort 1 osteotomy, were widely used to treat maxillofacial deformities.The satisfactory appearance and occlusal functions were restored after the osteotomies (Figure 1). 10,11However, the osteotomies were clinically designed and performed without the effects on the TMJs. 12,13Related literatures have pointed out that the TMJ structures became abnormal after bimaxillary surgery, and the TMD symptoms appeared or were aggravated. 11,14In contrast, some studies have also found that the TMD symptoms were improved or disappeared after the osteotomies. 15,16Due to the different types of maxillofacial deformities, TMJ would have different change after bimaxillary osteotomies. 4And unlike mandibular prognathism and facial asymmetry, the studies on mandibular retraction were relatively few.As a result, there was no definite conclusion about the influence of bimaxillary osteotomies on the TMJs with mandibular retraction. 9he TMD symptoms are closely related to the biomechanical environment of TMJ.Abnormal stress distributions or overload could cause the structural damage within TMJ, such as disc perforation and condylar rupture. 17,18And the biomechanical characteristics of the TMJs in the TMD patients was also different from those in the asymptomatic subjects. 19The appropriate stress distribution of TMJ could promote the postoperative recovery and alleviate the TMD symptoms. 20The biomechanical parameters are the signals to judge the health status of the TMJs.However, the biomechanical effects of bimaxillary osteotomies on the TMJs in mandibular retraction patients were still unclear. 21revious studies showed that different occlusal positions have distinct effects on the TMJs. 22Incisal clenching (INC), a common occlusal position, 23 is weak even lost for the patients with mandibular retraction due to the abnormal positions of the upper and lower anterior teeth.Therefore, it is necessary to investigate the TMJ biomechanics of the patients with mandibular retraction under INC.Since it was difficult to directly collect the vivo biomechanical data, finite element (FE) method was used to simulate the biomechanical environment within the TMJs before and after the F I G U R E 1 Preoperative and postoperative models of a patient and an asymptomatic subject, and the mesh, loading and boundary conditions of the FE mdel.AD, anterior digastric; AT, anterior temporalis; DM, deep masseter; ILP, inferior lateral pterygoid; MP, medial pterygoid; MT, middle temporalis; PT, posterior temporalis; SM, superficial masseter.
surgeries.The aim of this study was to investigate the biomechanical effects of bimaxillary osteotomies on the TMJs of the patients with mandibular retraction under INC.

| MATERIALS AND METHODS
This study was approved by the Institutional Review Board (IRB) from the Affiliated Hospital of Stomatology, Chongqing Medical University.Each participant signed the informed consent form.Five female mandibular retraction patients (35 ± 14 years old) were selected in this study, assigned as the preoperative group.All the subjects received the bimaxillary osteotomies in the Affiliated Stomatological Hospital of Chongqing Medical University (CQHS-IRB-2014-01), assigned as the postoperative group.In addition, 10 volunteers without any TMD symptoms were selected as the control group.All the subjects received maxillofacial cone-beam computed tomography (CBCT) scanning (KaVo 3D eXam, Germany), and the five patients underwent a second CBCT scanning after the surgeries.The CT data were converted to Digital Imaging and Communications in Medicine (DICOM) format and imported into MIMICS (Materialise, Leuven, Belgium).According to the gray values of bone, the models of maxilla and mandible were established.The models of articular discs were constructed in MIMICS based on the CT images and anatomical structure.
The interaction between the articular disc and the maxilla/mandible were defined as contact with the frictional coefficient of .001. 24,25The models of maxilla and mandible were mainly composed of linear four node elements.The articular discs and adjacent contact region were meshed with modified quadric 10 node tetrahedron element to improve the precision.According to previous studies, 24,26,27 the discal attachments were simulated as connectors.9][30][31] The articular discs were modeled with linear elastic material properties with Young's modulus and Poisson's ratio of 44.1 MPa and .4,respectively. 32,33ine groups of muscle forces, including superficial masseter, deep masseter, medial pterygoid, anterior temporalis, middle temporalis, posterior temporalis, inferior lateral pterygoid; superior lateral pterygoid anterior digastric, which correspond to INC were applied to analyze the impacts of the bimaxillary osteotomies on the TMJs.5][36] The attachments of each muscle force in the models were determined by the usually anatomical positions. 37The directions of the muscles were finally defined as the three component forces in the x, y, z direction of cartesian coordinate systemin ABAQUS.The magnitude of each muscle force was obtained through the cross sectional area of the muscle and the scale factor, 34 shown in the following formula.
where XMI is the cross-sectional area of the muscle M, K is a general conversion constant for the skeletal muscle with the value of 1.4, and EMGMI is the ratio or scaled value of the muscle contraction relative to its maximum possible activity.The product [XMI Â K] is referred to the weighting factor given to the muscle M, and the value EMGMI as its scaling factor. 34The values of the parameters, along with the final muscle forces under INC are shown in Table 1.Skull was fixed in all degrees of freedom as shown in Figure 1. 37he maximum and minimum principal stresses and contact stress in the preoperative, postoperative and control groups were analyzed to evaluate the effects of the bimaxillary osteotomies on the TMJs.The normality of the data was strictly checked by Shapiro-Wilk (S-W) test.S-W test is a significance hypothesis test that compares a sample distribution to a normal distribution in a statistically significant way to determine if the data shows a deviation or conformity from normality.Nonparametric analysis was used for the abnormal distribution data.Paired sample t-test was used to compare the parameters between the left and right TMJs in each group.The stresses between the control group and the preoperative and postoperative groups were compared using analysis of variance.The significance of the analysis was achieved as p < .05.
3D printing models were used to validate the finite element models of TMJ. 37Five asymptomatic subjects were recruited to reconstructed 3D models of mandible, disc, and maxilla according to CBCT image data.Polylactic acid (PLA) was chosen for 3D printing models from bottom to top, and the mechanical properties of PLA were defined by tensile tests.Five pressures corresponding to the central occlusion were applied to the 3D printing models.The 10 strain gage rosettes were distributed on the mandible to.Contact was used in the finite element models with the same geometry, material properties, load and boundary conditions as 3D printing models to simulate the interaction of the disc-condyle, disc-temporal bone and upper-lower dentition. 37

| RESULTS
Under the 5 magnitudes of the forces, the differences of the simulated and experimental results for each sample were less than 5% (maximum 4.92%) And the magnitudes of all the strains increased with the increase of the force.
Before the bimaxillary osteotomies, the horizontal distance between the mandibular and maxillary anterior teeth of the patients was 3.5-9 mm, while that in the asymptomatic group was usually no more than 3 mm.The contact and principal stresses in the preoperative, postoperative, and control groups had no significant difference on the left and right sides.Therefore, the magnitudes of the stresses of the TMJ components in the three groups were defined as the averages of the both sides.The mean values of the principal stresses of articular disc, condyle, and temporal bone in the preoperative group were significantly greater than those in the control group.The regions with high maximum and minimum principal stresses were usually distributed in the anterior band and intermediate zone of the articular discs.And the regions with high stresses on condyle and temporal bone were mainly distributed in anterior inclines and condylar necks.The magnitude of peak maximum and minimum principal stresses of the articular disc reached 26.92 and À36 MPa, respectively (Figure 2).The contact stress distributions of the TMJ components were similar to those of the principal stresses.And the mean values of the contact stress on the TMJ components were much greater than those of the control group.
After the surgeries, the horizontal distance between the mandibular and maxillary anterior teeth of the patients decreased to .62-5.39 mm.The magnitudes of principal and contact stresses of the articular disc in the postoperative group were significantly lower than those in the preoperative group, but still significantly greater than those of the control group.The distributions of high stresses on the postoperative TMJ components were similar to those of preoperative group.And the magnitude of peak maximum and minimum principal stresses of the articular disc were 4.44 and À11.37 MPa, respectively.The postoperative magnitudes of the principal stresses and the contact stresses in the condyle and temporal bone also decreased, and had no significant difference with those in the control group (Figure 2).
The mean values of the preoperative contact stresses on the right articular disc, condyle and temporal bone were greater than those on the left side.Besides the region of temporal bone, the contact stresses in the most of the right TMJ components were still higher than those on the left side after the bimaxillary osteotomies, and the magnitudes were close to the control group (Figure 3).Mandibular retraction, a common maxillofacial deformity, has adverse effects on occlusal functions, especially under INC. 4,5It is believed that bimaxillary osteotomies could recover the maxillofacial morphologies and improve match- degree of the maxilla and mandible. 38However, the effects of the surgeries on the TMJs are still unclear.The biomechanical environment of TMJ, directly related to TMD, plays an important role in maintaining the morphology and functions. 39Previous study has showed bimaxillary osteotomies could change the distribution of the TMJ damage, and lead to TMD. 15 However, some contrary views also proved that orthognathic surgery have positive effects on the TMJs. 16Therefore, there is no definite conclusion about the effects of bimaxillary osteotomies on the TMJs.Since it is difficult to directly collect data from human body, finite element method was used to simulate the biomechanical impact of bimaxillary osteotomies on the TMJs in the patients with mandibular retraction in this study.Complete maxillofacial models, including maxilla, mandible and articular discs were established, and the interaction within the TMJs was defined as contact in this study.Five 3D printed human maxillofacial models were used to verify the rationality and accuracy of the FE model.Nine sets of strain gage rosette with the degrees of 0, 45, 90 were fixed on the mandible and the equivalent vertical pressure was used to simulate the clenching under anterior occlusal position.And the finite element analyses were exactly the same with the experiments, including model structure, loading and boundary conditions, material properties.There was no significant difference between the experimental and simulation results, and the maximum strain difference was within 5%. 25,37,38,40Validation experiments showed that it is reasonable and accurate to use the maxillofacial models and contact algorithm to simulate the biomechanical environment of TMJs.
Before the bimaxillary osteotomies, the horizontal distances between the mandibular and maxillary anterior teeth of the patients were significantly greater than those in the control group.The patients with excessive mandibular retraction were prone to occlusal dysfunction, especially the loss of INC ability.The magnitudes of the maximum and minimum principal stresses in the articular disc of preoperative group were significantly greater than those in the control group (Figure 2), consistent with previous studies. 22And in this study, the peak magnitudes of the principal stresses in anterior band and intermediate zone were much greater than the failure stress of the articular disc measured in cadavers. 41Excessive stresses of the disc could lead to degenerative changes, such as perforation and rupture. 42,43xcessive stresses of the condyle and temporal bone could also inhibit bone growth, and the condyle and temporal bone were overloaded in the preoperative group.These results showed that the stress distributions of the TMJs in the patients with mandibular retraction were abnormal, which could cause the damage of the TMJ structures and TMD.And the abnormal biomechanical environment was ascribed to the mandibular deformity and occlusal dysfunction.Thus, it is necessary to correct the mandibular retraction and restore the biomechanical environment of TMJ.
The horizontal distances between the mandibular and maxillary anterior teeth of the five patients decreased from 36% to 92% in the postoperative group, similar to those in the control group.Bimaxillary osteotomies could effectively improve mandibular retraction and restore the occlusal functions, consistent with previous studies. 23The maximum and minimum principal stresses of the condyle and temporal bone in the postoperative group decreased and were not significantly different from those in the control group.Previous studies proved that the variations of the contact stress in the TMJs were similar to those of the principal stresses, consistent with the results in this study.After the surgeries, the stress levels of the temporal bone were much lower than those of the articular disc and condyle, in accord with the control group and the anatomical characteristics of TMJ (Figure 2).These results indicated that bimaxillary osteotomies could reduce the stress level of the TMJs in the patients with mandibular retraction and improve the abnormal biomechanical environment.The improvement of the biomechanical environment within the TMJs was due to the recovery of the mandibular morphology and the INC in the patients after bimaxillary osteotomies.
However, the principal stresses of the articular disc decreased to some extent, but still significantly greater than those in the control group and the failure stresses.The high stresses of the discs were closely related to TMD.Therefore, bimaxillary osteotomies could not completely restore the biomechanical environment of the TMJs to exclude the risk of TMD.Thus, the individual TMD symptom was also an important indicator to evaluate the effect of the bimaxillary osteotomies on the TMJs.In addition, the mean value of the contact stress on the right TMJ components of the preoperative and postoperative groups were significantly higher than those of left side (Figure 3).The previous studies suggested that the right chewing side was preferred by the larger percentage of population. 39Long-time chewing side preference could impair the function and movement of mastication on the working side. 44And these results were conformed to the overload of right TMJ in this study.Moreover, long-time right chewing preference would cause facial asymmetry and defects of esthetics, even leading to asymmetry of human bodies. 45Therefore, it is suggested to correct unilateral chewing side preference for the patients with mandibular retraction.
Two patients with right deviation were assigned as Case1 and Case 2. Bilateral TMJs of Case1 had TMD symptoms.The magnitudes of the stresses of the right TMJs of Case 1 and Case 2 were significantly greater than those of the left TMJs.For other patients without facial asymmetry, such as Case 3, the stress distributions of the left and right TMJ were relatively balanced (Figure 4).The results indicated that mandibular retraction with facial asymmetry could significantly aggravate the stress level of the deviated TMJ, resulting in loading imbalance of the bilateral TMJs.Long-term imbalanced stress distributions could cause damage to unilateral TMJ, leading to TMD.After treatment, the bilateral TMJs of Case 1 and Case 2 still presented obvious asymmetry.And the results of case 2 had no obvious regularity before and after the surgery (Figure 4).This indicated that bimaxillary osteotomies could not eliminate the facial asymmetry to disturb the therapeutic effect.Although the TMD symptoms of Case 1 disappeared after the surgery, long-term stress imbalance would also lead to TMJ injury and TMD recurrence.Therefore, it is necessary to add medical measures for facial asymmetry during treating mandibular retraction.
This study had some limitations.First, only five patients were involved in this study.7][48] Second, the same muscle forces were loaded in all the models.In the future, some methods could be used to investigate the specificity of the muscles in each sample, such as electromyography.Third, only INC condition of mandibular retraction patients were investigated in this study and various clenching condition could cause different impact on TMJ. 42,43Thus, various clenching condition be considered in the further work.This research ignored the influence of bone remodeling to material properties, while the material properties would be viscosity during the remodeling period. 41,49So, it would be better to collect the CT image of patients after remodeling period.
F I G U R E 4 The absolute value of the minimum principal stress of the left and right articular discs in 3 subjects before and after the bimaxillary osteotomies (MPa).Pre indicated the preoperative group.Post indicated the postoperative group.

| CONCLUSION
Mandibular retraction would cause abnormal stresses of the TMJs, adverse to maintain the healthy physiological functions.Bimaxillary osteotomies could effectively improve the maxillofacial morphology and the biomechanical environment of the TMJs.The facial asymmetry could cause imbalanced stress distributions the TMJs and interfere the surgical treatment.

F I G U R E 2
The peak maximum, minimum principal, contact stresses and the stress distributions of the discs in the patients with mandibular retraction (MPa).# indicated statistically significant difference between the preoperative and control groups from ANOVA ( p < .05).* indicated statistically significant difference between the preoperative and postoperative groups from ANOVA (p < .05).T indicated statistically significant difference between the postoperative and control groups from ANOVA (p < .05).L indicated left, R indicated right, A indicated anterior, P indicated posterior, T indicated top, B indicated bottom.CPRESS indicated the contact stress, S max indicated the maximum principal stress, ÀS min indicated the absolute value of the minimum principal stress.

F I G U R E 3
The contact stresses of left and right TMJ components in preoperative and postoperative groups.TB indicated the temporal bone.Pre indicated the preoperative group, Post indicated the postoperative group.
The magnitudes, weighting factor and scaling factor of the muscle forces under INC.In front view of each model, XY plane was paralleled to the horizontal plane.The X axis was directed to the right.The Y axis faced backward in the positive direction.The Z axis was perpendicular to the XY plane with the positive direction upward.