Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Biomechanical Analysis of the Forces Exerted during Different Occlusion Conditions following Bilateral Sagittal Split Osteotomy Treatment for Mandibular Deficiency

Biomechanical Analysis of the Forces Exerted during Different Occlusion Conditions following... Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4989013, 10 pages https://doi.org/10.1155/2019/4989013 Research Article Biomechanical Analysis of the Forces Exerted during Different Occlusion Conditions following Bilateral Sagittal Split Osteotomy Treatment for Mandibular Deficiency 1 1,2 3 1 Yuan-Han Chang , Man-Yee Chan , Jui-Ting Hsu , Han-Yu Hsiao , 4,5 and Kuo-Chih Su Department of Stomatology, Taichung Veterans General Hospital, Taichung, Taiwan School of Dentistry, College of Oral Medicine, Chung Shan Medical University, Taichung, Taiwan School of Dentistry, College of Medicine, China Medical University, Taichung, Taiwan Department of Biomedical Engineering, Hung Kuang University, Taichung, Taiwan Department of Medical Research, Taichung Veterans General Hospital, Taichung, Taiwan Correspondence should be addressed to Kuo-Chih Su; kcsu@vghtc.gov.tw Received 12 February 2019; Revised 25 April 2019; Accepted 6 May 2019; Published 2 June 2019 Guest Editor: Yuan-Chiao Lu Copyright © 2019 Yuan-Han Chang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The bilateral sagittal split osteotomy (BSSO) technique is commonly used to correct mandibular deficiency. If the patient is exposed to excessive external forces after the procedure, occlusal changes or nonunion may occur. However, previous studies only focused on single external forces on the mandible and did not conduct relevant research on the forces exerted by different occlusion conditions. The main purpose of this study was to use finite element analysis methods to determine the biomechanics of four common occlusion conditions after BSSO surgical treatment. This study constructed a finite element analysis computer model of a miniplate implanted in the lower jaw. The structure of the model consisted of the mandible, miniplate, and screws. In addition, external forces were applied to the superficial masseter, deep masseter, medial pterygoid, anterior temporalis, middle temporalis, and posterior temporalis muscles to simulate the incisal clench, intercuspal position (ICP), right unilateral molar clench (RMOL), and right group function occlusion conditions. Subsequently, this study observed the effects of these conditions on the miniplate, screws, and mandible, including the von Mises stress values. The results showed that all of the different occlusion conditions that this study evaluated placed high stress on the miniplate. In the ICP and RMOL occlusion conditions, the overall mandibular structure experienced very high stress. The screw on the proximal segment near the bone gap experienced high stress, as did the screw on the buccal side. According to the present analysis, although the data were not directly obtained from clinical practice, the finite element analysis could evaluate the trend of results under different external forces. The result of this study recommended that patients without intermaxillary fixation avoid the ICP and RMOL occlusion conditions. It can be used as a pilot study in the future for providing clinicians more information on the biomechanics of implantation. 1. Introduction prevalence of 1.1-21.5% [1]. To correct mandibular defi- ciency, mandibular advancement is often performed via intraoral vertical ramus osteotomy (IVRO) and bilateral sag- In oral surgery clinics, malocclusion and associated facial bone deformities are common and primarily affect the ittal split osteotomy (BSSO) [2]. In IVRO, a vertical incision is made in the ramus, which divides the mandible into two appearance and occlusion of patients. According to previous parts (anterior and posterior), thereby moving the mandible studies, mandibular deficiency is a common phenomenon, to achieve a reduction effect. The advantage of IVRO is that particularly in developing adolescents, with a worldwide 2 Applied Bionics and Biomechanics the operation is simple and fast. However, a disadvantage is to investigate the efficacy of different reconstruction methods that internal fixation of the mandible cannot be achieved for the treatment of mandibular defects [11]. Additionally, with artificial bone screws, and thus, bone healing must be other researchers have used finite element analysis to investi- gate various BSSO fixation methods and the effects of differ- assisted by intermaxillary fixation. Therefore, patients cannot ent materials (absorbable materials) on the strength and open their mouths for about 6 to 8 weeks after surgery [3]. As mechanics of fixation [12]. For instance, Erkmen et al. [13] for BSSO, the horizontal cutting line is located above the investigated the effects of using miniplates and different fixa- medial side of the ramus and above the lingua, while the tion methods for advancement surgery, while another study vertical cutting line is located at the distal side of the second evaluated whether locking miniplates have sufficient strength molar on the lateral side of the mandible. Next, the two to complete internal fixation of the mandible [14]. Although cutting lines are connected along the external oblique ridge. many previous studies have used finite element analysis to After cutting, the mandible is divided into two parts, a prox- investigate the biomechanical effects of BSSO fixation and imal segment and a distal segment, and fixed with miniplates. provide recommendations to clinicians, most of the simu- One advantage of BSSO over IVRO is that the bone has a lated models have been unilateral, the overall mandibular larger contact area and higher stability. In addition, both models are incomplete, and the applied external forces are mandibular advancement and setback can be achieved with simple, single external forces; hence, the simulated results BSSO surgery, as desired. Therefore, mandibular advance- likely do not reflect the actual conditions. Further, finite ele- ment with BSSO is the more common approach for treating ment analysis has been employed to investigate the effects of mandibular deficiency [4]. Clinically, intermaxillary fixation different external forces on implanted artificial total tempo- for several days to weeks after mandibular orthognathic romandibular joints, focusing on the incisal clench (INC), surgery can be performed. However, some physicians prefer intercuspal position (ICP), right unilateral molar clench to maintain an open airway for the patient after surgery (RMOL), left unilateral molar clench, right group function and thus decide against intermaxillary fixation [5]. Conse- (RGF), and left group function occlusion conditions [15]. quently, if the mandible without intermaxillary fixation expe- Therefore, the loading conditions and boundary conditions riences excessive external forces, then changes in occlusion or outlined in the present study will provide a reference for poor bone healing may occur. researchers in different occlusion conditions. Previously, researchers have used biomechanical methods As mentioned above, prior studies have demonstrated to evaluate the postoperative efficacy of BSSO. For instance, that BSSO surgery is commonly used to treat mandibular Hadi et al. [6] performed a general biomechanical analysis deficiency. However, because most previous in vitro studies of bicortical screws in the mandible. Although their study used a single external force, the effects of these forces on did not investigate the effects after BSSO surgery, their miniplates under different occlusion conditions cannot be research methods can be used as a reference framework for easily measured, and thus, they remain unclear. Hence, the performing biomechanical experiments following BSSO sur- main purpose of this study was to use finite element analysis gery. Additionally, Nieblerová et al. [7] and Olivera et al. [8] methods to simulate external forces from the mandibular used minipig and sheep mandibles to investigate the bio- muscles and investigate the effects of these forces on mini- mechanics of different BSSO reductions. However, the study plate implantation under four common occlusion conditions. samples were primarily animal based, and thus, the results The results of this study will provide clinicians with mecha- of the study may not accurately reflect the situation in the nical references for different occlusion forces in the overall human body. Oguz et al. [9] used a unilateral artificial mandibular structure and miniplate after miniplate implan- pseudobone mandibular model to investigate the biomechan- tation in BSSO surgeries, ultimately helping clinicians to ical effects of different plate reset patterns through biome- avoid surgical failure due to different occlusion conditions. chanical methods. Ribeiro-Junior et al. [10] used a similar approach to investigate the effects of different BSSO tech- niques, revealing that the locking miniplate approach had 2. Materials and Methods relatively better stability. Although locking miniplates have 2.1. Building a Simulation Geometry Model. This study was a good fixation effect, the prominent plate profile will not be accepted by patients. Therefore, facial bone fixation is still designed to investigate the effects of four different occlusion primarily based on miniplates. It should be noted that these conditions on the miniplate. To do this, this study con- structed a finite element analysis computer model of the man- studies mainly used in vitro biomechanics to investigate the effects of BSSO surgery, and as such, the external forces dible with the miniplate. The models used in this study included four components, namely, the cortical bone of the applied can only be simulated by a simple, single external mandible, cancellous bone, miniplate, and screws (Figure 1). force and the effects of muscles on actual chewing cannot be considered. Therefore, it is difficult for the results of in vitro The appearance of this study-constructed model was based on models of the mandible in previous studies [15], which studies to reflect the actual situation of different occlusion movements in human. were primarily composed of cortical bone and cancellous bone. The mandible model established in this study imports With advances in computer technology, finite element the CT images of the mandible to Mimics (Mimics Medical analysis has become a commonly used analytical method in the field of dental biomechanics because it can be used to 19.0, Materialise, Leuven, Belgium), selects the peripheral simulate the biomechanics of different structures, materials, contour of the mandibular cortical bone in Mimics using and force patterns. A prior study used finite element analysis circles, and retracts the whole model by 2 mm to establish Applied Bionics and Biomechanics 3 Fixation temporalis (PT) muscles (Figure 1). The magnitude and direction of the external forces are shown in Table 1. In addi- tion, fixation was applied at the incisor, canine, premolar, Anterior and molar tooth positions in the different occlusion condi- Fixation Posterior temporalis tions, as shown in Table 1. The sites of contact between the temporalis Middle miniplate and screws and between the miniplate and mandi- temporalis Medial ble were set to “no separation,” primarily to simulate the lack pterygold of separation between these surfaces, but also to allow for slight, frictionless sliding. Molar Deep 2.3. Material Properties of the Model. The research model was Incisor masseter composed of four parts, namely, the cortical bone, cancellous Canine bone, miniplate, and screws. The material properties used in Screw Premolar this study were obtained from previous studies [17]. Table 2 Superfical shows the material properties in this study simulation. All masseter materials were assumed to be homogeneous, isotropic, and linear elastic. Two independent parameters, i.e., Young’s Figure 1: Finite element analysis models and sites experiencing modulus (E) and Poisson’s ratio (ν), were used to character- muscular forces in the present study. ize the properties of the materials. The simulated miniplate material was composed primarily of titanium alloy. The the contour of the cancellous bone structure. This study bones were divided into the cortical bone and cancellous bone. Moreover, all of the finite element analysis computer employed three-dimensional computer-aided design soft- ware (SOLIDWORKS 2016; Dassault Systemes SOLID- models in this study used tetrahedral meshes (Figure 2(b)). The software used for mesh in this study was ANSYS Work- WORKS Corp., Waltham, MA, USA) for creating and bench 19.0. After the meshes passed the convergence test, all modifying the computer model. The peripheral contours of mandibular cortical and cancellous bones are imported to models reached the 5% stop criteria of the convergence test [18, 19]. The numbers of nodes and meshes were 144,969 SOLIDWORKS, and the complete solid model of mandibular cortical bone and cancellous bone is established using the loft and 74,878, respectively. Therefore, the finite element mesh model used herein to investigate the effects of different occlu- function of SOLIDWORKS software. The computer model of sion conditions on miniplate implantation was reasonable. the mandible was cut as described in previous studies [10], to simulate the treatment of mandibular deficiency by BSSO Following finite element analysis, this study utilized the von Mises stress values as an observational index. The von surgery. The distal segment was moved outward by 4 mm. In addition, the computer-aided design software SOLID- Mises stress distributions of the miniplate, eight screws, and mandibular screw positions on the left and right sides of WORKS was used to combine two miniplates and eight the mandible were observed to investigate the biomechanical screws (the sites and numbering of the eight different screws are shown in Figure 2(a)). After the three-dimensional com- effects of the four different occlusion conditions after BSSO treatment for mandibular deficiency. puter model was constructed, it was imported into the finite element analysis software (ANSYS Workbench 19.0; ANSYS Inc., Canonsburg, PA, USA) for analysis. 3. Results 2.2. Loading Conditions and Boundary Conditions. This After finite element analysis, this study obtained the overall study investigated four different occlusal conditions com- stress distributions on the mandible under the four different monly found in clinical practice, namely, INC, ICP, RMOL, occlusion conditions, as shown in Figure 3. This figure and RGF. Of these conditions, INC primarily simulated con- reveals that high stress occurred at the miniplate under all tact of the incisal edges, ICP simulated maximum intercuspa- four occlusion conditions. The mandibular stress was partic- tion of the posterior teeth, RMOL simulated contact of the ularly high in the ICP and RMOL conditions. right (unilateral) posterior teeth, and RGF simulated lateral Figure 4 shows the stress distributions on the left and movement of the right posterior dentition. In finite element right miniplates under the four occlusion conditions. High analysis, different boundary conditions and loading condi- stress primarily occurred in the region between the mini- tions must be provided based on these four different occlu- plates (the bone gap at the mandibular joint), especially at sion conditions. This study based the external force data the site of the screw in the proximal segment and at the cor- and application methods on those used in previous studies ner of the miniplate in the distal segment. Among the four [15, 16]. For the boundary conditions, the condyle was set conditions, the ICP and RMOL conditions in particular put as a fixed node and the displacement setting method was high stress on the miniplate. Table 3 shows the maximum used to fix the x-, y-, and z-axis displacements to 0, which von Mises stress values for the miniplates in the four different allows this point to rotate freely. For the loading conditions, occlusion conditions. external forces were applied to the superficial masseter Figure 5 shows the stress distributions on the eight screws (SM), deep masseter (DM), medial pterygoid (MP), anterior used for miniplate fixation (screw positions numbered as temporalis (AT), middle temporalis (MT), and posterior shown in Figure 2(a)). High stress was mainly observed at 4 Applied Bionics and Biomechanics 1 8 3 6 (a) (b) Figure 2: (a) Sites and numbers of the different screws after mandibular miniplate implantation. (b) Mesh of the computer model used in the present study. the junction of the miniplate and screws. Among the four proportional to Young’s modulus. In the present study, occlusion conditions, higher stress on the screws was Young’s modulus of the miniplate and cortical bone was observed under the ICP and RMOL conditions, especially 110,000 and 17,000 MPa, respectively, indicating that in the near the junction of the screws and miniplate. Table 4 shows overall structure, the miniplate experienced higher stress. the maximum von Mises stress values on the eight screws The results of this study show that the values for the mini- under the four different occlusion conditions. plate in the four groups are smaller than the yield strength Figure 6 shows the stress distributions on the mandible at of the titanium alloy (tensile strength of 1100 MPa [20]), the screw insertion positions (b1–b8 indicate the positions of and hence, the miniplate is not easily deformed under normal the different screws and the corresponding sites in the man- occlusion loading conditions. Further, of the four different dible). High stress on the mandible was produced primarily occlusion conditions, the INC and RGF conditions placed on the buccal side. The ICP and RMOL conditions appeared less stress on the mandible than did the other conditions. to place higher stress on the mandible than did the other con- The INC condition mainly simulated contact of the incisal ditions. Table 5 shows the maximum von Mises stress values edges, and because the muscles that produce this action apply on the mandible at the eight screw insertion sites in the four little force, the mandible only experienced some high stress at different occlusion conditions. the incisors. As the RGF condition simulated lateral move- ment of the right posterior dentition, the vertical force applied by the muscle to the mandible was also small (the 4. Discussion force observed on the tooth is about 100 N according to pre- To treat mandibular deficiencies, the BSSO surgical proce- vious literature [16]) and only the right posterior tooth area dure is often performed. However, this surgical treatment experienced relatively high stress. In addition, much higher requires destruction of the mandible border, because the stress is produced on mandible when ICP and RMOL condi- mandible border is the strongest part of the mandible and tion. The ICP condition simulated maximum intercuspation can resist bending forces. Therefore, it is essential that the fix- of the posterior teeth. According to the previous literature, ation strength of the miniplate in the mandible is sufficient. because of the small lever-arm relationship in the posterior Because of the limitations of previous in vitro experiments, tooth area (with the temporomandibular joint as the ful- crum), a high occlusion force occurs in the posterior tooth including the use of only single forces, conducting relevant research on the effects of different occlusion conditions has area (~700 N) [16], and thus, this study used a large external been difficult, and thus, no relevant references exist. To help force for the muscle boundary condition setting. Conse- resolve this, the present study used finite element analysis to quently, obvious high stress was observed in the posterior investigate the strength of the combination of the mandible tooth area of the mandible, along with high stress distribu- tions in the mandible; these results are similar to those and miniplate under four common occlusion conditions. The data in the study will provide clinicians with a reference reported in previous studies [16]. The RMOL condition sim- basis for the stress incurred on the screws, miniplate, and ulated contact of the right (unilateral) posterior teeth. This mandible under different occlusion conditions following action is an unbalanced occlusion condition. As such, in miniplate implantation. addition to the occlusal forces concentrated in the posterior tooth area, the external force applied by the muscles is also Herein, regarding the overall stress distributions of the mandible, this study noted that following miniplate fixation, large. Therefore, high stress occurred at the posterior tooth the mandible experienced external forces when clenched, contact area and throughout the entire mandible. Addition- which placed high stress on the miniplate. This high stress ally, since the occlusion is unbalanced, high non-occlusal can primarily be explained by Hooke’s law. If the mandible stress occurred in the left side of the retromolar area, which may have been caused by the high stress that is produced and miniplate were displaced, the stress would be Applied Bionics and Biomechanics 5 Table 1: The loading conditions, size, and direction of the muscular forces produced by the different occlusion conditions and sites of tooth fixation in the present study. This table is reproduced from Huang et al. [15] and Korioth and Hannam [16]. Muscular force (N) Clenching tasks Side Direction Constraint SM DM MP AT MT PT Force 76.2 21.2 136.3 12.6 5.7 3.0 Fx -15.8 -11.6 66.3 -1.9 -1.3 -0.6 Right Fy -31.9 7.6 -50.9 -0.6 2.9 2.6 Fz 67.3 16.1 107.8 12.5 4.8 1.4 Incisal clench (INC) Constrained the incisor regions Force 76.2 21.2 136.3 12.6 5.7 3.0 Fx 15.8 11.6 -66.3 1.9 1.3 0.6 Left Fy -31.9 7.6 -50.9 -0.6 2.9 2.6 Fz 67.3 16.1 107.8 12.5 4.8 1.4 Force 190.4 81.6 132.8 154.8 91.8 71.1 Fx -39.4 -44.6 64.6 -23.1 -20.4 -14.8 Right Fy -79.8 29.2 -49.6 -6.8 45.9 60.8 Fz 168.3 61.9 105.1 153.0 76.8 33.7 Constrained the canine and Intercuspal position (ICP) premolar regions Force 190.4 81.6 132.8 154.8 91.8 71.1 Fx 39.4 44.6 -64.6 23.1 20.4 14.8 Left Fy -79.8 29.2 -49.6 -6.8 45.9 60.8 Fz 168.3 61.9 105.1 153.0 76.8 33.7 Force 137.1 58.8 146.8 115.3 63.1 44.6 Fx -28.4 -32.1 71.4 -17.2 -14.0 -9.3 Right Fy -57.4 21.0 -54.8 -5.1 31.5 38.1 Fz 121.2 44.5 116.1 114.0 52.8 21.1 Right unilateral molar clench (RMOL) Constrained the right molars Force 114.2 49.0 104.9 91.6 64.1 29.5 Fx 23.6 26.7 -51.0 13.7 14.2 6.1 Left Fy -47.9 17.5 -39.1 -4.0 32.0 25.2 Fz 101.0 37.1 83.0 90.5 53.6 14.0 Force 34.3 29.4 12.2 104.3 61.2 46.9 Fx -7.1 -16.0 6.0 -15.5 -13.6 9.8 Right Fy -14.4 10.5 -4.6 -4.6 30.6 40.1 Fz 30.3 22.3 9.7 103.0 51.2 22.2 Constrained the right canine, Right group function (RGF) premolars, and molars Force 51.4 21.2 132.8 11.1 5.7 4.5 Fx 10.6 11.6 -64.6 1.7 1.3 0.9 Left Fy -21.5 7.6 -49.6 -0.5 2.9 3.9 Fz 45.4 16.1 105.1 10.9 4.8 2.2 SM: superficial masseter; DM: deep masseter; MP: medial pterygoid; AT: anterior temporalis; MT: middle temporalis; PT: posterior temporalis. All raw data were obtained from Huang et al. [15] and Korioth and Hannam [16]. Table 2: Material properties used in the present study. years [5]. According to these study findings, after BSSO, patients should be advised to consume liquids and soft foods Young’s modulus (MPa) Poisson’s ratio and to avoid ICP and RMOL occlusion to reduce the force on Cancellous bone 1000 0.3 the mandible. Cortical bone 17000 0.3 In the current study, the stress distributions on the mini- Miniplate 110000 0.3 plate showed that high stress mainly occurred in the middle Screw 118000 0.3 part of the miniplate (the point of contact with the mandi- ble). As previously indicated by Chuong et al. [21], the pri- mary reason for this is that the miniplate area produces two by bending or torsion. After BSSO surgery, the teeth are usu- bending forces and two torsion forces (Figure 7). Since both sides of the miniplate are fixed using screws, the miniplate ally fixed in the ideal occlusion position (intermaxillary fixa- tion); however, to improve patient life quality of post is affected by torsion in the middle area, thereby producing operation and maintain an open airway, many clinicians higher stress. The miniplate is also subjected to an external have opted not to perform intermaxillary fixation in recent force. Because of the geometric shape of the miniplate, high 6 Applied Bionics and Biomechanics Unit: Mpa 20.000 17.501 15.003 12.504 Incisal clench (INC) Intercuspal position (ICP) 10.006 7.507 5.009 2.510 0.000 Right unilateral molar clench (RMOL) Right group function (RGF) Figure 3: Overall stress distributions in the mandibular region under the four different occlusion conditions. Unit: Mpa 120.000 105.270 90.545 Incisal clench (INC) 75.817 61.090 Intercuspal position (ICP) 46.362 31.635 Right unilateral molar clench (RMOL) 16.907 0.000 Right group function (RGF) Figure 4: Stress distributions on the right and left miniplates under the four different occlusion conditions. Table 3: Maximum von Mises stress values on the miniplates. stress is generated where the cross-sectional area changes. Peak von Mises stress values Peak von Mises stress However, the high stress that this study observed on the on the right-side miniplates values on the left-side (MPa) miniplates (MPa) miniplate in the present study was less than the yield strength of the titanium alloy, and hence, the miniplate was not INC 134.02 153.56 deformed under the four different occlusion conditions that ICP 443.75 491.00 this study evaluated. RMOL 302.60 372.80 When observing the stress distributions on the screws, RGF 157.10 138.58 this study found that the two screws near the middle of the Applied Bionics and Biomechanics 7 Intercuspal position (ICP) Incisal clench (INC) Unit: MPa 80.000 70.031 60.063 50.094 40.126 30.157 20.188 10.220 0.000 s1 s8 s1 s8 s2 s7 s2 s7 s6 s6 s3 s3 s4 s5 s5 s4 Right unilateral molar clench (RMOL) Right group function (RGF) Unit: MPa 80.000 70.031 60.063 50.094 40.126 30.157 20.188 10.220 0.000 s1 s1 s8 s8 s2 s7 s2 s7 s6 s6 s3 s3 s4 s5 s4 s5 Figure 5: Stress distributions on the eight screws under the four different occlusion conditions. Table 4: Maximum von Mises stress values on the eight screws. Peak von Peak von Peak von Peak von Peak von Peak von Peak von Peak von Mises stress Mises stress Mises stress Mises stress Mises stress Mises stress Mises stress Mises stress on the s1 on the s2 on the s3 on the s4 on the s5 on the s6 on the s7 on the s8 screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) INC 118.950 169.530 120.050 64.761 66.414 116.790 165.190 117.220 ICP 365.220 588.470 406.780 187.420 207.540 392.390 577.830 356.560 RMOL 280.500 356.330 275.180 168.350 177.800 428.110 544.040 230.680 RGF 97.732 222.130 167.530 53.090 67.689 153.370 199.390 67.678 miniplate experienced higher stress than did the other the buccal side. The principles underlying this high stress are related to Hooke’s law. During occlusion, when pulling screws, likely because the miniplate was being pulled to the screw that provided fixation of the mandible under the exter- by the miniplate produces displacement, the screw also nal bending and torsion forces. Thus, the two screws close to pulls on the mandible and the surface of the mandibular the middle of the miniplate experienced higher stress, espe- screw hole (buccal side) will be deformed. Therefore, cially the screw which is near the bone gap to the proximal according to Hooke’s law (the mandible has the same segment (number 2 or 7). These findings suggest that clini- Young’s modulus), high stress is produced near the buccal cians should pay careful attention to the high stress that side. The deformation of the screw hole loosens the screw may be placed on the screw during miniplate fixation. Fur- and miniplate, resulting in excessive movement between ther, to achieve overall postimplant stability, a thicker screw the bones, causing bone nonunion and potentially surgical should be used or the strength of the miniplate at that site failure, which may even require removal of the miniplate should be enhanced. and refixation. These study findings indicate that it may When observing the stress distributions in the mandible be advisable to use thicker screws for fixation to reduce at the screw insertion sites, this study noticed that the high the stress on the screw and the likelihood of mandible stress sites were similar to those on the screws, primarily near deformation (the hole for screw insertion), as this will help 8 Applied Bionics and Biomechanics Incisal clench (INC) Intercuspal position (ICP) Unit: MPa 15.000 13.134 11.268 9.402 7.536 5.670 3.804 1.938 0.000 b1 b8 b8 b1 b2 b7 b2 b7 b6 b3 b3 b6 b4 b5 b4 b5 Right unilateral molar clench (RMOL) Unit: MPa Right group function (RGF) 15.000 13.134 11.268 9.402 7.536 5.670 3.804 1.938 0.000 b1 b8 b8 b1 b2 b2 b7 b7 b6 b3 b6 b3 b4 b5 b5 b4 Figure 6: Stress distributions at the screw insertion sites in the mandible under the four different occlusion conditions. Table 5: Maximum von Mises stress values at the screw insertion sites. Peak von Peak von Peak von Peak von Peak von Peak von Peak von Peak von Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at b1 on the b2 on the b3 on the b4 on the b5 on the b6 on the b7 on the b8 on the mandible mandible mandible mandible mandible mandible mandible mandible (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) INC 20.324 39.124 29.273 15.191 26.173 25.474 39.034 20.462 ICP 66.423 126.500 102.480 43.784 52.865 86.761 125.960 66.597 RMOL 48.194 82.709 61.630 48.399 115.490 98.718 109.400 65.414 RGF 22.321 41.563 39.653 14.452 30.620 26.072 38.142 16.680 interest in the current study was the miniplate implantation to reduce surgical failure and increase the overall stability of the mandible. site and such simplification can reduce the computer simula- This study using finite element analysis to investigate the tion time. To perform the stress and strain analysis of the forces involved when implanting a miniplate to treat man- tooth root or periodontal ligament and alveolar bone, we dibular deficiency has some limitations related to the biome- must establish a complete tooth model. However, this study chanical analysis of the different occlusion conditions. First, mainly is aimed at investigating the efficacy of miniplate fix- all of the material properties in this study were assumed to ation on the mandible after BSSO surgery in 4 common be homogeneous, isotropic, and linearly elastic in order to occlusal conditions. This study was not aimed at investigat- simplify the simulation, and thus, the material properties ing the biomechanical behavior of the teeth or periodontal were set by referring to previous studies [15, 19]. Second, areas. Therefore, this study did not consider the establish- some of the models were simplified in the present study, that ment of a tooth model. This study only fixed the mandible is, this study only observed the effects in the mandible, not in in the occlusal planes of different tooth positions. The litera- the entire skull, and no teeth were constructed. This study ture has several reports on this method [15, 22]. The model opted to use this simplified model because the main area of used in this study was mainly designed with reference to Applied Bionics and Biomechanics 9 study, in addition to providing a biomechanical basis for the forces generated on the miniplate, screws, and mandible fol- lowing BSSO surgery, will also improve the design of mini- plates and screws in the future to reduce the stress that is exerted on the screws and mandible. Moreover, patients are advised to avoid ICP and RMOL occlusion in order to reduce the incidence of miniplate implantation failure and to improve patients’ prognoses. Torsion Data Availability The data used to support the findings of this study are avail- able from the corresponding author upon request. Conflicts of Interest Bending The authors declare that there is no conflict of interest regarding the publication of this paper. Figure 7: The miniplate region produces two bending forces and two torsion forces. Authors’ Contributions The authors Yuan-Han Chang and Man-Yee Chan contrib- previous studies and simulated 4 occlusal modes, namely, uted equally to this work. INC, ICP, RMOL, and RGF. In this method, we fixed the tooth positions, utilized the external force on the mandible Acknowledgments (giving boundary conditions by simulating muscle contrac- tions) and applied restraint (using tooth position fixation as We would like to thank Taichung Veterans General Hospital load conditions). However, due to these simplifications, this (TCVGH-1077320C) in Taiwan for providing the funding study finding may not directly replicate reality; nevertheless, for this research. In addition, we also would like to thank clear trends can be identified for the topics of interest in the 3D Printing Research and Development Group, Tai- the study. chung Veterans General Hospital, for helping us to build Here, this study used finite element analysis and visual the BSSO simulation computer model of this study. observations to investigate the biomechanical forces exerted on the miniplate, screws, and mandible under different References occlusion conditions. The results showed that among the four evaluated occlusion conditions, the ICP and RMOL con- [1] S. T. Daokar, G. Agrawal, C. Chaudhari, and S. Yamyar, ditions in particular stressed and deformed the mandible and “Ortho-surgical management of severe skeletal class II Div 2 miniplate. Although the values identified in the present study malocclusion in adult,” Orthodontic Journal of Nepal, vol. 7, are likely different from those in actual clinical situations, no. 1, pp. 44–50, 2018. these study findings will provide a reference basis both for [2] I. Yoshioka, A. Khanal, K. Tominaga, A. Horie, N. Furuta, and the maxillofacial surgeons when performing the BSSO sur- J. Fukuda, “Vertical ramus versus sagittal split osteotomies: gery to treat mandibular deficiencies and for the patients dur- comparison of stability after mandibular setback,” Journal of Oral and Maxillofacial Surgery, vol. 66, no. 6, pp. 1138–1144, ing the recovery period. Patients should be advised to avoid specific occlusion movements to reduce the incidence of fail- [3] L. H. Guernsey and R. W. DeChamplain, “Sequelae and com- ure after surgical implantation and to improve their progno- plications of the intraoral sagittal osteotomy in the mandibular sis. This study data will also provide a biomechanical basis for rami,” Oral Surgery, Oral Medicine, Oral Pathology, vol. 32, the design and development of miniplates in the future. no. 2, pp. 176–192, 1971. [4] J. Hartlev, E. Godtfredsen, N. T. Andersen, and T. Jensen, 5. Conclusion “Comparative study of skeletal stability between postoperative skeletal intermaxillary fixation and no skeletal fixation after The effects of different occlusal conditions on the miniplate, bilateral sagittal split ramus osteotomy: an 18 months retro- screws, and mandible after BSSO surgery for treating man- spective study,” Journal of Oral and Maxillofacial Research, dibular deficiency were investigated through finite element vol. 5, no. 1, 2014. analysis. The results showed that the implanted miniplate [5] L. Krekmanov, J. Lilja, and M. Ringqvist, “Sagittal split osteot- exhibited high stress under various occlusion conditions. In omy of the mandible without postoperative intermaxillary fix- the ICP and RMOL occlusion conditions, the overall man- ation: a clinical and cephalometric study,” Scandinavian dibular structure experienced very high stress. According to Journal of Plastic and Reconstructive Surgery, vol. 23, no. 2, this study model, the screw near the bone gap in the proximal pp. 115–124, 2009. segment experienced high stress. High stress was also gener- [6] G. Hadi, B. G. Karine, C. Yves, and L. Pierre, “Stability of ated at the site near the buccal side. The results of the present osteosynthesis with bicortical screws placed in a triangular 10 Applied Bionics and Biomechanics analysis,” Journal of Mechanics in Medicine and Biology, shape in mandibular sagittal split 5 mm advancement osteot- omy: biomechanical tests,” British Journal of Oral and Maxil- vol. 16, no. 4, article 1650046, 2016. lofacial Surgery, vol. 48, no. 8, pp. 624–628, 2010. [19] K. C. Su, C. H. Chang, S. F. Chuang, and E. Y. K. Ng, “Biome- [7] J. Nieblerová, R. Foltán, T. Hanzelka et al., “Stability of the chanical evaluation of endodontic post-restored teeth—finite miniplate osteosynthesis used for sagittal split osteotomy for element analysis,” Journal of Mechanics in Medicine and Biol- closing an anterior open bite: an experimental study in mini- ogy, vol. 13, no. 1, article 1350012, 2013. pigs,” International Journal of Oral and Maxillofacial Surgery, [20] J. Enderle and J. Bronzino, Introduction to Biomedical Engi- vol. 41, no. 4, pp. 482–488, 2012. neering, Academic Press, Boston, MA, USA, 3rd Edition edi- [8] L. B. d. Olivera, E. Sant´Ana, A. J. Manzato, F. L. B. Guerra, tion, 2012. and G. W. Arnett, “Biomechanical in vitro evaluation of three [21] C. J. Chuong, B. Borotikar, C. Schwartz-Dabney, and D. P. stable internal fixation techniques used in sagittal osteotomy of Sinn, “Mechanical characteristics of the mandible after bilat- the mandibular ramus: a study in sheep mandibles,” Journal of eral sagittal split ramus osteotomy: comparing 2 different fixa- Applied Oral Science, vol. 20, no. 4, pp. 419–426, 2012. tion techniques,” Journal of Oral and Maxillofacial Surgery, [9] Y. Oguz, E. R. Watanabe, J. M. Reis, R. Spin-Neto, M. A. Gab- vol. 63, no. 1, pp. 68–76, 2005. rielli, and V. A. Pereira-Filho, “In vitro biomechanical com- [22] S. M. Park, J. W. Lee, and G. Noh, “Which plate results in bet- parison of six different fixation methods following 5-mm ter stability after segmental mandibular resection and fibula sagittal split advancement osteotomies,” International Journal free flap reconstruction? Biomechanical analysis,” Oral Sur- of Oral and Maxillofacial Surgery, vol. 44, no. 8, pp. 984–988, gery, Oral Medicine, Oral Pathology and Oral Radiology, vol. 126, no. 5, pp. 380–389, 2018. [10] P. D. Ribeiro-Junior, O. Magro-Filho, K. A. Shastri, and M. B. Papageorge, “In vitro biomechanical evaluation of the use of conventional and locking miniplate/screw systems for sagittal split ramus osteotomy,” Journal of Oral and Maxillofacial Sur- gery, vol. 68, no. 4, pp. 724–730, 2010. [11] T. Nagasao, J. Miyamoto, T. Tamaki, and H. Kawana, “A com- parison of stresses in implantation for grafted and plate-and- screw mandible reconstruction,” Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, vol. 109, no. 3, pp. 346–356, [12] F. Sarkarat, M. H. K. Motamedi, B. Bohluli, N. Moharamnejad, S. Ansari, and H. Shahabi-Sirjani, “Analysis of stress distribu- tion on fixation of bilateral sagittal split ramus osteotomy with resorbable plates and screws using the finite-element method,” Journal of Oral and Maxillofacial Surgery, vol. 70, no. 6, pp. 1434–1438, 2012. [13] E. Erkmen, B. Simsek, E. Yücel, and A. Kurt, “Comparison of different fixation methods following sagittal split ramus osteo- tomies using three-dimensional finite elements analysis. Part 1: advancement surgery-posterior loading,” International Journal of Oral and Maxillofacial Surgery, vol. 34, no. 5, pp. 551–558, 2005. [14] F. R. L. Sato, L. Asprino, P. Y. Noritomi, J. V. L. da Silva, and M. de Moraes, “Comparison of five different fixation tech- niques of sagittal split ramus osteotomy using three- dimensional finite elements analysis,” International Journal of Oral and Maxillofacial Surgery, vol. 41, no. 8, pp. 934–941, [15] H. L. Huang, K. C. Su, L. J. Fuh et al., “Biomechanical analysis of a temporomandibular joint condylar prosthesis during var- ious clenching tasks,” Journal of Cranio-Maxillofacial Surgery, vol. 43, no. 7, pp. 1194–1201, 2015. [16] T. W. Korioth and A. G. Hannam, “Mandibular forces during simulated tooth clenching,” Journal of Orofacial Pain, vol. 8, no. 2, pp. 178–189, 1994. [17] C. H. Lee, C. M. Shih, K. C. Huang, K. H. Chen, L. K. Hung, and K. C. Su, “Biomechanical analysis of implanted clavicle hook plates with different implant depths and materials in the acromioclavicular joint: a finite element analysis study,” Artificial Organs, vol. 40, no. 11, pp. 1062–1070, 2016. [18] K. M. Su, M. H. Yu, H. Y. Su, Y. C. Wang, and K. C. Su, “Inves- tigating biomechanics of different materials and angles of blades of forceps for operative delivery by finite element International Journal of Advances in Rotating Machinery Multimedia Journal of The Scientific Journal of Engineering World Journal Sensors Hindawi Hindawi Publishing Corporation Hindawi Hindawi Hindawi Hindawi www.hindawi.com Volume 2018 http://www www.hindawi.com .hindawi.com V Volume 2018 olume 2013 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 Submit your manuscripts at www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Hindawi Hindawi Hindawi Volume 2018 Volume 2018 Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com www.hindawi.com www.hindawi.com Volume 2018 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Hindawi Hindawi Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Bionics and Biomechanics Hindawi Publishing Corporation

Biomechanical Analysis of the Forces Exerted during Different Occlusion Conditions following Bilateral Sagittal Split Osteotomy Treatment for Mandibular Deficiency

Loading next page...
 
/lp/hindawi-publishing-corporation/biomechanical-analysis-of-the-forces-exerted-during-different-8KrnpnHnZU
Publisher
Hindawi Publishing Corporation
Copyright
Copyright © 2019 Yuan-Han Chang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ISSN
1176-2322
eISSN
1754-2103
DOI
10.1155/2019/4989013
Publisher site
See Article on Publisher Site

Abstract

Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4989013, 10 pages https://doi.org/10.1155/2019/4989013 Research Article Biomechanical Analysis of the Forces Exerted during Different Occlusion Conditions following Bilateral Sagittal Split Osteotomy Treatment for Mandibular Deficiency 1 1,2 3 1 Yuan-Han Chang , Man-Yee Chan , Jui-Ting Hsu , Han-Yu Hsiao , 4,5 and Kuo-Chih Su Department of Stomatology, Taichung Veterans General Hospital, Taichung, Taiwan School of Dentistry, College of Oral Medicine, Chung Shan Medical University, Taichung, Taiwan School of Dentistry, College of Medicine, China Medical University, Taichung, Taiwan Department of Biomedical Engineering, Hung Kuang University, Taichung, Taiwan Department of Medical Research, Taichung Veterans General Hospital, Taichung, Taiwan Correspondence should be addressed to Kuo-Chih Su; kcsu@vghtc.gov.tw Received 12 February 2019; Revised 25 April 2019; Accepted 6 May 2019; Published 2 June 2019 Guest Editor: Yuan-Chiao Lu Copyright © 2019 Yuan-Han Chang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The bilateral sagittal split osteotomy (BSSO) technique is commonly used to correct mandibular deficiency. If the patient is exposed to excessive external forces after the procedure, occlusal changes or nonunion may occur. However, previous studies only focused on single external forces on the mandible and did not conduct relevant research on the forces exerted by different occlusion conditions. The main purpose of this study was to use finite element analysis methods to determine the biomechanics of four common occlusion conditions after BSSO surgical treatment. This study constructed a finite element analysis computer model of a miniplate implanted in the lower jaw. The structure of the model consisted of the mandible, miniplate, and screws. In addition, external forces were applied to the superficial masseter, deep masseter, medial pterygoid, anterior temporalis, middle temporalis, and posterior temporalis muscles to simulate the incisal clench, intercuspal position (ICP), right unilateral molar clench (RMOL), and right group function occlusion conditions. Subsequently, this study observed the effects of these conditions on the miniplate, screws, and mandible, including the von Mises stress values. The results showed that all of the different occlusion conditions that this study evaluated placed high stress on the miniplate. In the ICP and RMOL occlusion conditions, the overall mandibular structure experienced very high stress. The screw on the proximal segment near the bone gap experienced high stress, as did the screw on the buccal side. According to the present analysis, although the data were not directly obtained from clinical practice, the finite element analysis could evaluate the trend of results under different external forces. The result of this study recommended that patients without intermaxillary fixation avoid the ICP and RMOL occlusion conditions. It can be used as a pilot study in the future for providing clinicians more information on the biomechanics of implantation. 1. Introduction prevalence of 1.1-21.5% [1]. To correct mandibular defi- ciency, mandibular advancement is often performed via intraoral vertical ramus osteotomy (IVRO) and bilateral sag- In oral surgery clinics, malocclusion and associated facial bone deformities are common and primarily affect the ittal split osteotomy (BSSO) [2]. In IVRO, a vertical incision is made in the ramus, which divides the mandible into two appearance and occlusion of patients. According to previous parts (anterior and posterior), thereby moving the mandible studies, mandibular deficiency is a common phenomenon, to achieve a reduction effect. The advantage of IVRO is that particularly in developing adolescents, with a worldwide 2 Applied Bionics and Biomechanics the operation is simple and fast. However, a disadvantage is to investigate the efficacy of different reconstruction methods that internal fixation of the mandible cannot be achieved for the treatment of mandibular defects [11]. Additionally, with artificial bone screws, and thus, bone healing must be other researchers have used finite element analysis to investi- gate various BSSO fixation methods and the effects of differ- assisted by intermaxillary fixation. Therefore, patients cannot ent materials (absorbable materials) on the strength and open their mouths for about 6 to 8 weeks after surgery [3]. As mechanics of fixation [12]. For instance, Erkmen et al. [13] for BSSO, the horizontal cutting line is located above the investigated the effects of using miniplates and different fixa- medial side of the ramus and above the lingua, while the tion methods for advancement surgery, while another study vertical cutting line is located at the distal side of the second evaluated whether locking miniplates have sufficient strength molar on the lateral side of the mandible. Next, the two to complete internal fixation of the mandible [14]. Although cutting lines are connected along the external oblique ridge. many previous studies have used finite element analysis to After cutting, the mandible is divided into two parts, a prox- investigate the biomechanical effects of BSSO fixation and imal segment and a distal segment, and fixed with miniplates. provide recommendations to clinicians, most of the simu- One advantage of BSSO over IVRO is that the bone has a lated models have been unilateral, the overall mandibular larger contact area and higher stability. In addition, both models are incomplete, and the applied external forces are mandibular advancement and setback can be achieved with simple, single external forces; hence, the simulated results BSSO surgery, as desired. Therefore, mandibular advance- likely do not reflect the actual conditions. Further, finite ele- ment with BSSO is the more common approach for treating ment analysis has been employed to investigate the effects of mandibular deficiency [4]. Clinically, intermaxillary fixation different external forces on implanted artificial total tempo- for several days to weeks after mandibular orthognathic romandibular joints, focusing on the incisal clench (INC), surgery can be performed. However, some physicians prefer intercuspal position (ICP), right unilateral molar clench to maintain an open airway for the patient after surgery (RMOL), left unilateral molar clench, right group function and thus decide against intermaxillary fixation [5]. Conse- (RGF), and left group function occlusion conditions [15]. quently, if the mandible without intermaxillary fixation expe- Therefore, the loading conditions and boundary conditions riences excessive external forces, then changes in occlusion or outlined in the present study will provide a reference for poor bone healing may occur. researchers in different occlusion conditions. Previously, researchers have used biomechanical methods As mentioned above, prior studies have demonstrated to evaluate the postoperative efficacy of BSSO. For instance, that BSSO surgery is commonly used to treat mandibular Hadi et al. [6] performed a general biomechanical analysis deficiency. However, because most previous in vitro studies of bicortical screws in the mandible. Although their study used a single external force, the effects of these forces on did not investigate the effects after BSSO surgery, their miniplates under different occlusion conditions cannot be research methods can be used as a reference framework for easily measured, and thus, they remain unclear. Hence, the performing biomechanical experiments following BSSO sur- main purpose of this study was to use finite element analysis gery. Additionally, Nieblerová et al. [7] and Olivera et al. [8] methods to simulate external forces from the mandibular used minipig and sheep mandibles to investigate the bio- muscles and investigate the effects of these forces on mini- mechanics of different BSSO reductions. However, the study plate implantation under four common occlusion conditions. samples were primarily animal based, and thus, the results The results of this study will provide clinicians with mecha- of the study may not accurately reflect the situation in the nical references for different occlusion forces in the overall human body. Oguz et al. [9] used a unilateral artificial mandibular structure and miniplate after miniplate implan- pseudobone mandibular model to investigate the biomechan- tation in BSSO surgeries, ultimately helping clinicians to ical effects of different plate reset patterns through biome- avoid surgical failure due to different occlusion conditions. chanical methods. Ribeiro-Junior et al. [10] used a similar approach to investigate the effects of different BSSO tech- niques, revealing that the locking miniplate approach had 2. Materials and Methods relatively better stability. Although locking miniplates have 2.1. Building a Simulation Geometry Model. This study was a good fixation effect, the prominent plate profile will not be accepted by patients. Therefore, facial bone fixation is still designed to investigate the effects of four different occlusion primarily based on miniplates. It should be noted that these conditions on the miniplate. To do this, this study con- structed a finite element analysis computer model of the man- studies mainly used in vitro biomechanics to investigate the effects of BSSO surgery, and as such, the external forces dible with the miniplate. The models used in this study included four components, namely, the cortical bone of the applied can only be simulated by a simple, single external mandible, cancellous bone, miniplate, and screws (Figure 1). force and the effects of muscles on actual chewing cannot be considered. Therefore, it is difficult for the results of in vitro The appearance of this study-constructed model was based on models of the mandible in previous studies [15], which studies to reflect the actual situation of different occlusion movements in human. were primarily composed of cortical bone and cancellous bone. The mandible model established in this study imports With advances in computer technology, finite element the CT images of the mandible to Mimics (Mimics Medical analysis has become a commonly used analytical method in the field of dental biomechanics because it can be used to 19.0, Materialise, Leuven, Belgium), selects the peripheral simulate the biomechanics of different structures, materials, contour of the mandibular cortical bone in Mimics using and force patterns. A prior study used finite element analysis circles, and retracts the whole model by 2 mm to establish Applied Bionics and Biomechanics 3 Fixation temporalis (PT) muscles (Figure 1). The magnitude and direction of the external forces are shown in Table 1. In addi- tion, fixation was applied at the incisor, canine, premolar, Anterior and molar tooth positions in the different occlusion condi- Fixation Posterior temporalis tions, as shown in Table 1. The sites of contact between the temporalis Middle miniplate and screws and between the miniplate and mandi- temporalis Medial ble were set to “no separation,” primarily to simulate the lack pterygold of separation between these surfaces, but also to allow for slight, frictionless sliding. Molar Deep 2.3. Material Properties of the Model. The research model was Incisor masseter composed of four parts, namely, the cortical bone, cancellous Canine bone, miniplate, and screws. The material properties used in Screw Premolar this study were obtained from previous studies [17]. Table 2 Superfical shows the material properties in this study simulation. All masseter materials were assumed to be homogeneous, isotropic, and linear elastic. Two independent parameters, i.e., Young’s Figure 1: Finite element analysis models and sites experiencing modulus (E) and Poisson’s ratio (ν), were used to character- muscular forces in the present study. ize the properties of the materials. The simulated miniplate material was composed primarily of titanium alloy. The the contour of the cancellous bone structure. This study bones were divided into the cortical bone and cancellous bone. Moreover, all of the finite element analysis computer employed three-dimensional computer-aided design soft- ware (SOLIDWORKS 2016; Dassault Systemes SOLID- models in this study used tetrahedral meshes (Figure 2(b)). The software used for mesh in this study was ANSYS Work- WORKS Corp., Waltham, MA, USA) for creating and bench 19.0. After the meshes passed the convergence test, all modifying the computer model. The peripheral contours of mandibular cortical and cancellous bones are imported to models reached the 5% stop criteria of the convergence test [18, 19]. The numbers of nodes and meshes were 144,969 SOLIDWORKS, and the complete solid model of mandibular cortical bone and cancellous bone is established using the loft and 74,878, respectively. Therefore, the finite element mesh model used herein to investigate the effects of different occlu- function of SOLIDWORKS software. The computer model of sion conditions on miniplate implantation was reasonable. the mandible was cut as described in previous studies [10], to simulate the treatment of mandibular deficiency by BSSO Following finite element analysis, this study utilized the von Mises stress values as an observational index. The von surgery. The distal segment was moved outward by 4 mm. In addition, the computer-aided design software SOLID- Mises stress distributions of the miniplate, eight screws, and mandibular screw positions on the left and right sides of WORKS was used to combine two miniplates and eight the mandible were observed to investigate the biomechanical screws (the sites and numbering of the eight different screws are shown in Figure 2(a)). After the three-dimensional com- effects of the four different occlusion conditions after BSSO treatment for mandibular deficiency. puter model was constructed, it was imported into the finite element analysis software (ANSYS Workbench 19.0; ANSYS Inc., Canonsburg, PA, USA) for analysis. 3. Results 2.2. Loading Conditions and Boundary Conditions. This After finite element analysis, this study obtained the overall study investigated four different occlusal conditions com- stress distributions on the mandible under the four different monly found in clinical practice, namely, INC, ICP, RMOL, occlusion conditions, as shown in Figure 3. This figure and RGF. Of these conditions, INC primarily simulated con- reveals that high stress occurred at the miniplate under all tact of the incisal edges, ICP simulated maximum intercuspa- four occlusion conditions. The mandibular stress was partic- tion of the posterior teeth, RMOL simulated contact of the ularly high in the ICP and RMOL conditions. right (unilateral) posterior teeth, and RGF simulated lateral Figure 4 shows the stress distributions on the left and movement of the right posterior dentition. In finite element right miniplates under the four occlusion conditions. High analysis, different boundary conditions and loading condi- stress primarily occurred in the region between the mini- tions must be provided based on these four different occlu- plates (the bone gap at the mandibular joint), especially at sion conditions. This study based the external force data the site of the screw in the proximal segment and at the cor- and application methods on those used in previous studies ner of the miniplate in the distal segment. Among the four [15, 16]. For the boundary conditions, the condyle was set conditions, the ICP and RMOL conditions in particular put as a fixed node and the displacement setting method was high stress on the miniplate. Table 3 shows the maximum used to fix the x-, y-, and z-axis displacements to 0, which von Mises stress values for the miniplates in the four different allows this point to rotate freely. For the loading conditions, occlusion conditions. external forces were applied to the superficial masseter Figure 5 shows the stress distributions on the eight screws (SM), deep masseter (DM), medial pterygoid (MP), anterior used for miniplate fixation (screw positions numbered as temporalis (AT), middle temporalis (MT), and posterior shown in Figure 2(a)). High stress was mainly observed at 4 Applied Bionics and Biomechanics 1 8 3 6 (a) (b) Figure 2: (a) Sites and numbers of the different screws after mandibular miniplate implantation. (b) Mesh of the computer model used in the present study. the junction of the miniplate and screws. Among the four proportional to Young’s modulus. In the present study, occlusion conditions, higher stress on the screws was Young’s modulus of the miniplate and cortical bone was observed under the ICP and RMOL conditions, especially 110,000 and 17,000 MPa, respectively, indicating that in the near the junction of the screws and miniplate. Table 4 shows overall structure, the miniplate experienced higher stress. the maximum von Mises stress values on the eight screws The results of this study show that the values for the mini- under the four different occlusion conditions. plate in the four groups are smaller than the yield strength Figure 6 shows the stress distributions on the mandible at of the titanium alloy (tensile strength of 1100 MPa [20]), the screw insertion positions (b1–b8 indicate the positions of and hence, the miniplate is not easily deformed under normal the different screws and the corresponding sites in the man- occlusion loading conditions. Further, of the four different dible). High stress on the mandible was produced primarily occlusion conditions, the INC and RGF conditions placed on the buccal side. The ICP and RMOL conditions appeared less stress on the mandible than did the other conditions. to place higher stress on the mandible than did the other con- The INC condition mainly simulated contact of the incisal ditions. Table 5 shows the maximum von Mises stress values edges, and because the muscles that produce this action apply on the mandible at the eight screw insertion sites in the four little force, the mandible only experienced some high stress at different occlusion conditions. the incisors. As the RGF condition simulated lateral move- ment of the right posterior dentition, the vertical force applied by the muscle to the mandible was also small (the 4. Discussion force observed on the tooth is about 100 N according to pre- To treat mandibular deficiencies, the BSSO surgical proce- vious literature [16]) and only the right posterior tooth area dure is often performed. However, this surgical treatment experienced relatively high stress. In addition, much higher requires destruction of the mandible border, because the stress is produced on mandible when ICP and RMOL condi- mandible border is the strongest part of the mandible and tion. The ICP condition simulated maximum intercuspation can resist bending forces. Therefore, it is essential that the fix- of the posterior teeth. According to the previous literature, ation strength of the miniplate in the mandible is sufficient. because of the small lever-arm relationship in the posterior Because of the limitations of previous in vitro experiments, tooth area (with the temporomandibular joint as the ful- crum), a high occlusion force occurs in the posterior tooth including the use of only single forces, conducting relevant research on the effects of different occlusion conditions has area (~700 N) [16], and thus, this study used a large external been difficult, and thus, no relevant references exist. To help force for the muscle boundary condition setting. Conse- resolve this, the present study used finite element analysis to quently, obvious high stress was observed in the posterior investigate the strength of the combination of the mandible tooth area of the mandible, along with high stress distribu- tions in the mandible; these results are similar to those and miniplate under four common occlusion conditions. The data in the study will provide clinicians with a reference reported in previous studies [16]. The RMOL condition sim- basis for the stress incurred on the screws, miniplate, and ulated contact of the right (unilateral) posterior teeth. This mandible under different occlusion conditions following action is an unbalanced occlusion condition. As such, in miniplate implantation. addition to the occlusal forces concentrated in the posterior tooth area, the external force applied by the muscles is also Herein, regarding the overall stress distributions of the mandible, this study noted that following miniplate fixation, large. Therefore, high stress occurred at the posterior tooth the mandible experienced external forces when clenched, contact area and throughout the entire mandible. Addition- which placed high stress on the miniplate. This high stress ally, since the occlusion is unbalanced, high non-occlusal can primarily be explained by Hooke’s law. If the mandible stress occurred in the left side of the retromolar area, which may have been caused by the high stress that is produced and miniplate were displaced, the stress would be Applied Bionics and Biomechanics 5 Table 1: The loading conditions, size, and direction of the muscular forces produced by the different occlusion conditions and sites of tooth fixation in the present study. This table is reproduced from Huang et al. [15] and Korioth and Hannam [16]. Muscular force (N) Clenching tasks Side Direction Constraint SM DM MP AT MT PT Force 76.2 21.2 136.3 12.6 5.7 3.0 Fx -15.8 -11.6 66.3 -1.9 -1.3 -0.6 Right Fy -31.9 7.6 -50.9 -0.6 2.9 2.6 Fz 67.3 16.1 107.8 12.5 4.8 1.4 Incisal clench (INC) Constrained the incisor regions Force 76.2 21.2 136.3 12.6 5.7 3.0 Fx 15.8 11.6 -66.3 1.9 1.3 0.6 Left Fy -31.9 7.6 -50.9 -0.6 2.9 2.6 Fz 67.3 16.1 107.8 12.5 4.8 1.4 Force 190.4 81.6 132.8 154.8 91.8 71.1 Fx -39.4 -44.6 64.6 -23.1 -20.4 -14.8 Right Fy -79.8 29.2 -49.6 -6.8 45.9 60.8 Fz 168.3 61.9 105.1 153.0 76.8 33.7 Constrained the canine and Intercuspal position (ICP) premolar regions Force 190.4 81.6 132.8 154.8 91.8 71.1 Fx 39.4 44.6 -64.6 23.1 20.4 14.8 Left Fy -79.8 29.2 -49.6 -6.8 45.9 60.8 Fz 168.3 61.9 105.1 153.0 76.8 33.7 Force 137.1 58.8 146.8 115.3 63.1 44.6 Fx -28.4 -32.1 71.4 -17.2 -14.0 -9.3 Right Fy -57.4 21.0 -54.8 -5.1 31.5 38.1 Fz 121.2 44.5 116.1 114.0 52.8 21.1 Right unilateral molar clench (RMOL) Constrained the right molars Force 114.2 49.0 104.9 91.6 64.1 29.5 Fx 23.6 26.7 -51.0 13.7 14.2 6.1 Left Fy -47.9 17.5 -39.1 -4.0 32.0 25.2 Fz 101.0 37.1 83.0 90.5 53.6 14.0 Force 34.3 29.4 12.2 104.3 61.2 46.9 Fx -7.1 -16.0 6.0 -15.5 -13.6 9.8 Right Fy -14.4 10.5 -4.6 -4.6 30.6 40.1 Fz 30.3 22.3 9.7 103.0 51.2 22.2 Constrained the right canine, Right group function (RGF) premolars, and molars Force 51.4 21.2 132.8 11.1 5.7 4.5 Fx 10.6 11.6 -64.6 1.7 1.3 0.9 Left Fy -21.5 7.6 -49.6 -0.5 2.9 3.9 Fz 45.4 16.1 105.1 10.9 4.8 2.2 SM: superficial masseter; DM: deep masseter; MP: medial pterygoid; AT: anterior temporalis; MT: middle temporalis; PT: posterior temporalis. All raw data were obtained from Huang et al. [15] and Korioth and Hannam [16]. Table 2: Material properties used in the present study. years [5]. According to these study findings, after BSSO, patients should be advised to consume liquids and soft foods Young’s modulus (MPa) Poisson’s ratio and to avoid ICP and RMOL occlusion to reduce the force on Cancellous bone 1000 0.3 the mandible. Cortical bone 17000 0.3 In the current study, the stress distributions on the mini- Miniplate 110000 0.3 plate showed that high stress mainly occurred in the middle Screw 118000 0.3 part of the miniplate (the point of contact with the mandi- ble). As previously indicated by Chuong et al. [21], the pri- mary reason for this is that the miniplate area produces two by bending or torsion. After BSSO surgery, the teeth are usu- bending forces and two torsion forces (Figure 7). Since both sides of the miniplate are fixed using screws, the miniplate ally fixed in the ideal occlusion position (intermaxillary fixa- tion); however, to improve patient life quality of post is affected by torsion in the middle area, thereby producing operation and maintain an open airway, many clinicians higher stress. The miniplate is also subjected to an external have opted not to perform intermaxillary fixation in recent force. Because of the geometric shape of the miniplate, high 6 Applied Bionics and Biomechanics Unit: Mpa 20.000 17.501 15.003 12.504 Incisal clench (INC) Intercuspal position (ICP) 10.006 7.507 5.009 2.510 0.000 Right unilateral molar clench (RMOL) Right group function (RGF) Figure 3: Overall stress distributions in the mandibular region under the four different occlusion conditions. Unit: Mpa 120.000 105.270 90.545 Incisal clench (INC) 75.817 61.090 Intercuspal position (ICP) 46.362 31.635 Right unilateral molar clench (RMOL) 16.907 0.000 Right group function (RGF) Figure 4: Stress distributions on the right and left miniplates under the four different occlusion conditions. Table 3: Maximum von Mises stress values on the miniplates. stress is generated where the cross-sectional area changes. Peak von Mises stress values Peak von Mises stress However, the high stress that this study observed on the on the right-side miniplates values on the left-side (MPa) miniplates (MPa) miniplate in the present study was less than the yield strength of the titanium alloy, and hence, the miniplate was not INC 134.02 153.56 deformed under the four different occlusion conditions that ICP 443.75 491.00 this study evaluated. RMOL 302.60 372.80 When observing the stress distributions on the screws, RGF 157.10 138.58 this study found that the two screws near the middle of the Applied Bionics and Biomechanics 7 Intercuspal position (ICP) Incisal clench (INC) Unit: MPa 80.000 70.031 60.063 50.094 40.126 30.157 20.188 10.220 0.000 s1 s8 s1 s8 s2 s7 s2 s7 s6 s6 s3 s3 s4 s5 s5 s4 Right unilateral molar clench (RMOL) Right group function (RGF) Unit: MPa 80.000 70.031 60.063 50.094 40.126 30.157 20.188 10.220 0.000 s1 s1 s8 s8 s2 s7 s2 s7 s6 s6 s3 s3 s4 s5 s4 s5 Figure 5: Stress distributions on the eight screws under the four different occlusion conditions. Table 4: Maximum von Mises stress values on the eight screws. Peak von Peak von Peak von Peak von Peak von Peak von Peak von Peak von Mises stress Mises stress Mises stress Mises stress Mises stress Mises stress Mises stress Mises stress on the s1 on the s2 on the s3 on the s4 on the s5 on the s6 on the s7 on the s8 screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) screw (MPa) INC 118.950 169.530 120.050 64.761 66.414 116.790 165.190 117.220 ICP 365.220 588.470 406.780 187.420 207.540 392.390 577.830 356.560 RMOL 280.500 356.330 275.180 168.350 177.800 428.110 544.040 230.680 RGF 97.732 222.130 167.530 53.090 67.689 153.370 199.390 67.678 miniplate experienced higher stress than did the other the buccal side. The principles underlying this high stress are related to Hooke’s law. During occlusion, when pulling screws, likely because the miniplate was being pulled to the screw that provided fixation of the mandible under the exter- by the miniplate produces displacement, the screw also nal bending and torsion forces. Thus, the two screws close to pulls on the mandible and the surface of the mandibular the middle of the miniplate experienced higher stress, espe- screw hole (buccal side) will be deformed. Therefore, cially the screw which is near the bone gap to the proximal according to Hooke’s law (the mandible has the same segment (number 2 or 7). These findings suggest that clini- Young’s modulus), high stress is produced near the buccal cians should pay careful attention to the high stress that side. The deformation of the screw hole loosens the screw may be placed on the screw during miniplate fixation. Fur- and miniplate, resulting in excessive movement between ther, to achieve overall postimplant stability, a thicker screw the bones, causing bone nonunion and potentially surgical should be used or the strength of the miniplate at that site failure, which may even require removal of the miniplate should be enhanced. and refixation. These study findings indicate that it may When observing the stress distributions in the mandible be advisable to use thicker screws for fixation to reduce at the screw insertion sites, this study noticed that the high the stress on the screw and the likelihood of mandible stress sites were similar to those on the screws, primarily near deformation (the hole for screw insertion), as this will help 8 Applied Bionics and Biomechanics Incisal clench (INC) Intercuspal position (ICP) Unit: MPa 15.000 13.134 11.268 9.402 7.536 5.670 3.804 1.938 0.000 b1 b8 b8 b1 b2 b7 b2 b7 b6 b3 b3 b6 b4 b5 b4 b5 Right unilateral molar clench (RMOL) Unit: MPa Right group function (RGF) 15.000 13.134 11.268 9.402 7.536 5.670 3.804 1.938 0.000 b1 b8 b8 b1 b2 b2 b7 b7 b6 b3 b6 b3 b4 b5 b5 b4 Figure 6: Stress distributions at the screw insertion sites in the mandible under the four different occlusion conditions. Table 5: Maximum von Mises stress values at the screw insertion sites. Peak von Peak von Peak von Peak von Peak von Peak von Peak von Peak von Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at Mises stress at b1 on the b2 on the b3 on the b4 on the b5 on the b6 on the b7 on the b8 on the mandible mandible mandible mandible mandible mandible mandible mandible (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) INC 20.324 39.124 29.273 15.191 26.173 25.474 39.034 20.462 ICP 66.423 126.500 102.480 43.784 52.865 86.761 125.960 66.597 RMOL 48.194 82.709 61.630 48.399 115.490 98.718 109.400 65.414 RGF 22.321 41.563 39.653 14.452 30.620 26.072 38.142 16.680 interest in the current study was the miniplate implantation to reduce surgical failure and increase the overall stability of the mandible. site and such simplification can reduce the computer simula- This study using finite element analysis to investigate the tion time. To perform the stress and strain analysis of the forces involved when implanting a miniplate to treat man- tooth root or periodontal ligament and alveolar bone, we dibular deficiency has some limitations related to the biome- must establish a complete tooth model. However, this study chanical analysis of the different occlusion conditions. First, mainly is aimed at investigating the efficacy of miniplate fix- all of the material properties in this study were assumed to ation on the mandible after BSSO surgery in 4 common be homogeneous, isotropic, and linearly elastic in order to occlusal conditions. This study was not aimed at investigat- simplify the simulation, and thus, the material properties ing the biomechanical behavior of the teeth or periodontal were set by referring to previous studies [15, 19]. Second, areas. Therefore, this study did not consider the establish- some of the models were simplified in the present study, that ment of a tooth model. This study only fixed the mandible is, this study only observed the effects in the mandible, not in in the occlusal planes of different tooth positions. The litera- the entire skull, and no teeth were constructed. This study ture has several reports on this method [15, 22]. The model opted to use this simplified model because the main area of used in this study was mainly designed with reference to Applied Bionics and Biomechanics 9 study, in addition to providing a biomechanical basis for the forces generated on the miniplate, screws, and mandible fol- lowing BSSO surgery, will also improve the design of mini- plates and screws in the future to reduce the stress that is exerted on the screws and mandible. Moreover, patients are advised to avoid ICP and RMOL occlusion in order to reduce the incidence of miniplate implantation failure and to improve patients’ prognoses. Torsion Data Availability The data used to support the findings of this study are avail- able from the corresponding author upon request. Conflicts of Interest Bending The authors declare that there is no conflict of interest regarding the publication of this paper. Figure 7: The miniplate region produces two bending forces and two torsion forces. Authors’ Contributions The authors Yuan-Han Chang and Man-Yee Chan contrib- previous studies and simulated 4 occlusal modes, namely, uted equally to this work. INC, ICP, RMOL, and RGF. In this method, we fixed the tooth positions, utilized the external force on the mandible Acknowledgments (giving boundary conditions by simulating muscle contrac- tions) and applied restraint (using tooth position fixation as We would like to thank Taichung Veterans General Hospital load conditions). However, due to these simplifications, this (TCVGH-1077320C) in Taiwan for providing the funding study finding may not directly replicate reality; nevertheless, for this research. In addition, we also would like to thank clear trends can be identified for the topics of interest in the 3D Printing Research and Development Group, Tai- the study. chung Veterans General Hospital, for helping us to build Here, this study used finite element analysis and visual the BSSO simulation computer model of this study. observations to investigate the biomechanical forces exerted on the miniplate, screws, and mandible under different References occlusion conditions. The results showed that among the four evaluated occlusion conditions, the ICP and RMOL con- [1] S. T. Daokar, G. Agrawal, C. Chaudhari, and S. Yamyar, ditions in particular stressed and deformed the mandible and “Ortho-surgical management of severe skeletal class II Div 2 miniplate. Although the values identified in the present study malocclusion in adult,” Orthodontic Journal of Nepal, vol. 7, are likely different from those in actual clinical situations, no. 1, pp. 44–50, 2018. these study findings will provide a reference basis both for [2] I. Yoshioka, A. Khanal, K. Tominaga, A. Horie, N. Furuta, and the maxillofacial surgeons when performing the BSSO sur- J. Fukuda, “Vertical ramus versus sagittal split osteotomies: gery to treat mandibular deficiencies and for the patients dur- comparison of stability after mandibular setback,” Journal of Oral and Maxillofacial Surgery, vol. 66, no. 6, pp. 1138–1144, ing the recovery period. Patients should be advised to avoid specific occlusion movements to reduce the incidence of fail- [3] L. H. Guernsey and R. W. DeChamplain, “Sequelae and com- ure after surgical implantation and to improve their progno- plications of the intraoral sagittal osteotomy in the mandibular sis. This study data will also provide a biomechanical basis for rami,” Oral Surgery, Oral Medicine, Oral Pathology, vol. 32, the design and development of miniplates in the future. no. 2, pp. 176–192, 1971. [4] J. Hartlev, E. Godtfredsen, N. T. Andersen, and T. Jensen, 5. Conclusion “Comparative study of skeletal stability between postoperative skeletal intermaxillary fixation and no skeletal fixation after The effects of different occlusal conditions on the miniplate, bilateral sagittal split ramus osteotomy: an 18 months retro- screws, and mandible after BSSO surgery for treating man- spective study,” Journal of Oral and Maxillofacial Research, dibular deficiency were investigated through finite element vol. 5, no. 1, 2014. analysis. The results showed that the implanted miniplate [5] L. Krekmanov, J. Lilja, and M. Ringqvist, “Sagittal split osteot- exhibited high stress under various occlusion conditions. In omy of the mandible without postoperative intermaxillary fix- the ICP and RMOL occlusion conditions, the overall man- ation: a clinical and cephalometric study,” Scandinavian dibular structure experienced very high stress. According to Journal of Plastic and Reconstructive Surgery, vol. 23, no. 2, this study model, the screw near the bone gap in the proximal pp. 115–124, 2009. segment experienced high stress. High stress was also gener- [6] G. Hadi, B. G. Karine, C. Yves, and L. Pierre, “Stability of ated at the site near the buccal side. The results of the present osteosynthesis with bicortical screws placed in a triangular 10 Applied Bionics and Biomechanics analysis,” Journal of Mechanics in Medicine and Biology, shape in mandibular sagittal split 5 mm advancement osteot- omy: biomechanical tests,” British Journal of Oral and Maxil- vol. 16, no. 4, article 1650046, 2016. lofacial Surgery, vol. 48, no. 8, pp. 624–628, 2010. [19] K. C. Su, C. H. Chang, S. F. Chuang, and E. Y. K. Ng, “Biome- [7] J. Nieblerová, R. Foltán, T. Hanzelka et al., “Stability of the chanical evaluation of endodontic post-restored teeth—finite miniplate osteosynthesis used for sagittal split osteotomy for element analysis,” Journal of Mechanics in Medicine and Biol- closing an anterior open bite: an experimental study in mini- ogy, vol. 13, no. 1, article 1350012, 2013. pigs,” International Journal of Oral and Maxillofacial Surgery, [20] J. Enderle and J. Bronzino, Introduction to Biomedical Engi- vol. 41, no. 4, pp. 482–488, 2012. neering, Academic Press, Boston, MA, USA, 3rd Edition edi- [8] L. B. d. Olivera, E. Sant´Ana, A. J. Manzato, F. L. B. Guerra, tion, 2012. and G. W. Arnett, “Biomechanical in vitro evaluation of three [21] C. J. Chuong, B. Borotikar, C. Schwartz-Dabney, and D. P. stable internal fixation techniques used in sagittal osteotomy of Sinn, “Mechanical characteristics of the mandible after bilat- the mandibular ramus: a study in sheep mandibles,” Journal of eral sagittal split ramus osteotomy: comparing 2 different fixa- Applied Oral Science, vol. 20, no. 4, pp. 419–426, 2012. tion techniques,” Journal of Oral and Maxillofacial Surgery, [9] Y. Oguz, E. R. Watanabe, J. M. Reis, R. Spin-Neto, M. A. Gab- vol. 63, no. 1, pp. 68–76, 2005. rielli, and V. A. Pereira-Filho, “In vitro biomechanical com- [22] S. M. Park, J. W. Lee, and G. Noh, “Which plate results in bet- parison of six different fixation methods following 5-mm ter stability after segmental mandibular resection and fibula sagittal split advancement osteotomies,” International Journal free flap reconstruction? Biomechanical analysis,” Oral Sur- of Oral and Maxillofacial Surgery, vol. 44, no. 8, pp. 984–988, gery, Oral Medicine, Oral Pathology and Oral Radiology, vol. 126, no. 5, pp. 380–389, 2018. [10] P. D. Ribeiro-Junior, O. Magro-Filho, K. A. Shastri, and M. B. Papageorge, “In vitro biomechanical evaluation of the use of conventional and locking miniplate/screw systems for sagittal split ramus osteotomy,” Journal of Oral and Maxillofacial Sur- gery, vol. 68, no. 4, pp. 724–730, 2010. [11] T. Nagasao, J. Miyamoto, T. Tamaki, and H. Kawana, “A com- parison of stresses in implantation for grafted and plate-and- screw mandible reconstruction,” Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, vol. 109, no. 3, pp. 346–356, [12] F. Sarkarat, M. H. K. Motamedi, B. Bohluli, N. Moharamnejad, S. Ansari, and H. Shahabi-Sirjani, “Analysis of stress distribu- tion on fixation of bilateral sagittal split ramus osteotomy with resorbable plates and screws using the finite-element method,” Journal of Oral and Maxillofacial Surgery, vol. 70, no. 6, pp. 1434–1438, 2012. [13] E. Erkmen, B. Simsek, E. Yücel, and A. Kurt, “Comparison of different fixation methods following sagittal split ramus osteo- tomies using three-dimensional finite elements analysis. Part 1: advancement surgery-posterior loading,” International Journal of Oral and Maxillofacial Surgery, vol. 34, no. 5, pp. 551–558, 2005. [14] F. R. L. Sato, L. Asprino, P. Y. Noritomi, J. V. L. da Silva, and M. de Moraes, “Comparison of five different fixation tech- niques of sagittal split ramus osteotomy using three- dimensional finite elements analysis,” International Journal of Oral and Maxillofacial Surgery, vol. 41, no. 8, pp. 934–941, [15] H. L. Huang, K. C. Su, L. J. Fuh et al., “Biomechanical analysis of a temporomandibular joint condylar prosthesis during var- ious clenching tasks,” Journal of Cranio-Maxillofacial Surgery, vol. 43, no. 7, pp. 1194–1201, 2015. [16] T. W. Korioth and A. G. Hannam, “Mandibular forces during simulated tooth clenching,” Journal of Orofacial Pain, vol. 8, no. 2, pp. 178–189, 1994. [17] C. H. Lee, C. M. Shih, K. C. Huang, K. H. Chen, L. K. Hung, and K. C. Su, “Biomechanical analysis of implanted clavicle hook plates with different implant depths and materials in the acromioclavicular joint: a finite element analysis study,” Artificial Organs, vol. 40, no. 11, pp. 1062–1070, 2016. [18] K. M. Su, M. H. Yu, H. Y. Su, Y. C. Wang, and K. C. Su, “Inves- tigating biomechanics of different materials and angles of blades of forceps for operative delivery by finite element International Journal of Advances in Rotating Machinery Multimedia Journal of The Scientific Journal of Engineering World Journal Sensors Hindawi Hindawi Publishing Corporation Hindawi Hindawi Hindawi Hindawi www.hindawi.com Volume 2018 http://www www.hindawi.com .hindawi.com V Volume 2018 olume 2013 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 Submit your manuscripts at www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Hindawi Hindawi Hindawi Volume 2018 Volume 2018 Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com www.hindawi.com www.hindawi.com Volume 2018 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Hindawi Hindawi Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018

Journal

Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Jun 2, 2019

References