Original Article
Stress distribution in the temporomandibular joint after mandibular protraction A three-dimensional finite element study Abhinav Shrivastavaa; Pushpa V. Hazareyb; Om P. Kharbandac; Anurag Guptad ABSTRACT Objective: To evaluate the stress patterns in temporomandibular joint (TMJ) during mandibular protraction at different horizontal advancements with constant vertical height in a construction bite using a three-dimensional finite element method. Materials and Methods: A three-dimensional computer-aided model was developed from the magnetic resonance imaging (MRI) of a growing boy (age 12 years) using MIMICS software (version 7.0, Materialise, Leuven, Belgium). Stresses with constant vertical opening of 5 mm changing the sagittal advancements from 0 mm to 5 mm and 7.5 mm were recorded. Differences in magnitude and pattern of stresses were compared. Results: The tensile stresses in the posterosuperior aspect of the condylar head and on the posterior aspect of the glenoid fossa migrated posteriorly with increased bite advancements. The location of tensile stresses changed in the condylar head and fossa on mandibular protraction of 5 mm to 7 mm. Conclusion: This study indicates that larger horizontal advancements of construction bites may not be favorable for tissues of TMJ. Clinical application necessitates study on an animal model. (Angle Orthod. 0000;00:1–10.) KEY WORDS: Mandibular protraction; 3D FEM study; Horizontal advancements; Stresses; Temporomandibular joint; Condyle; Fossa; Articular disc
INTRODUCTION
reactions of functional appliances. FEM is an in vitro, highly sophisticated, and noninvasive method. It explicates the qualitative nature and relative trends of compressive and tensile stresses of a complex biological structure like TMJ. Benefits of functional appliances on TMJ remodeling process have been universally acknowledged, while there is an assortment of opinions regarding construction bite used to protract the mandible.9–17 In a FEM study, increasing construction bite height generated more favorable stress patterns in TMJ. This could indicate a possible improved condylar response to functional appliance treatment.8 Inconsistent opinions have been recorded regarding the vertical component and horizontal advancement of the mandible. Andresen10 suggested protrusion of the mandible to neutro-occlusion and keeping the bite within the freeway space. Herren13 and Shaye et al.14 modified the activator appliance so that the mandible is advanced from a Class II position to 3–4 mm ahead of the Class I molar relation. Thus, the distal molar relationship is overcompensated. Schwarz15 advocated that optimal forward movement of the mandible
Functional appliances correct sagittal skeletal discrepancies in Class II malocclusion of growing individuals.1–8 Finite element method (FEM) studies on human temporomandibular joint (TMJ) are being increasingly carried out to elucidate the biomechanical a Senior Lecturer, Department of Orthodontics, Hitkarni Dental College, Jabalpur, India. b Professor and Head, Department of Orthodontics, Sharad Pawar Dental College, Wardha, India. c Professor and Head, Department of Orthodontics and Dentofacial Deformities, Centre for Dental Excellence and Research, All India Institute of Medical Sciences, New Delhi, India. d Head Consultant, Maximus Specialist Centre for Dental Research, New Delhi, India. Corresponding author: Dr Abhinav Shrivastava, Senior Lecturer, Department of Orthodontics, Hitkarni Dental College, Jabalpur, India (e-mail: [email protected])
Accepted: April 2014. Submitted: September 2013. Published Online: June 5, 2014 G 0000 by The EH Angle Education and Research Foundation, Inc. DOI: 10.2319/091913-690.1
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Figure 1. Total displacements of the condylar head (A) and disc (B). Locating the condylar head and the articular disc on the MRI by using arbitrary reference lines (T1 and T2). T1 is the tangent to the superior-most point on the glenoid fossa. T2 is tangent to the postglenoid spine and perpendicular to T1.
would be half of the individual’s maximum range. Woodside16 gave three theories of bite registration for the activator, based on the muscle and soft tissue actions in response to the engagement of the mandible in the activator. Changing the vertical opening
mandibular protrusion was kept constant at 3 mm distal to the most protrusive position the patient can achieve. Graber and Neumann15 advocated the limitation for protraction to 3 mm distal to the most protrusive position. Most authors favor a Class I molar relation or neutro-occlusion position with regard to the sagittal advancement of the mandible; none of the views has been examined using biomechanical studies.17 Hence, the present study was carried out with the objective of relating the changes in stress patterns in the TMJ applying construction bites of varying horizontal advancements keeping the vertical height constant. MATERIALS AND METHODS A 12-year-old boy, with skeletal Class II, retrognathic mandible, incisal overjet of 8 mm, and a favorable growth pattern considered suitable for functional appliance therapy was inducted in the present study. Approval by the institutional ethical review committee was obtained to conduct the study. Four wax construction bites were obtained at physiologic rest position, and at three other positions, Table 1.
Location of Condyle in Various Positions
Positions
Figure 2. Total displacements of the condylar head (A) and the disc (B) from maximum intercuspation through physiologic rest position, HA1 and HA2, up to HA3. Angle Orthodontist, Vol 00, No 0, 0000
Intercuspal position Postural rest position Position 1 Position 2 Position 3
Sagittal Vertical Vertical Horizontal Position of Position of Displacement Displacement Mandible, Mandible, of Condyle, of Condyle, mm mm mm mm _
_
7.86
8.36
_
_
0 5 7.5
5 5 5
8.62 10.14 10.64 11.15
8.87 9.12 10.90 11.40
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STRESS DISTRIBUTION IN THE TMJ Table 2. Location of Disc in Various Positions
Positions Intercuspal position Postural rest position Position 1 Position 2 Position 3
Table 3.
Sagittal Vertical Vertical Horizontal Position of Position of Displacement Displacement Mandible, Mandible, of Disc, of Disc, mm mm mm mm _
_
7.60
12.42
_
_
0 5 7.5
5 5 5
9.38 10.64 11.40 12.71
13.68 14.44 15.71 16.42
Properties of Bone and Soft Tissues7 Elastic Modulus (E), MPa
Poisson’s Ratio (v)
13,700 7930 0.79
0.3 0.3 0.49
Condyle Compact bone Cancellous bone Cartilage layer Articular disc Anterior Intermediate Posterior
10 10.73 9.0
0.4
Glenoid fossa
which were HA1 at 0 mm horizontal activation, HA2 at 5 mm horizontal activation, and HA3 at 7.5 mm horizontal activation. A 5-mm vertical opening was kept constant for all three positions. The patient underwent five sequential magnetic resonance scans at maximum intercuspation position, while holding each of the four wax bites in his mouth. The scans were procured with a magnetic resonance imaging (MRI) machine, 1.5-T magnet (Signa, Excite 11, General Electric, Chalfont, St Giles, UK) and a 3-inch dual surface coil. The externally marked Frankfort horizontal plane was kept perpendicular to the scanning table. The positions of the condylar head and disc were noted, and their total translations during the entire study were mapped and plotted (Figures 1 and 2; Tables 1 and 2). The magnetic resonance images were obtained in DICOM and JPEG format, comprehensible in MIMICS and the Centricity DICOM MRI viewer. A threedimensional (3D) computer-aided design (CAD) model of the skull was constructed (Figure 3) on a highly sophisticated workstation using Centricity DICOM MRI viewer (General Electric) and MIMICS software
Compact bone Cancellous bone
13,700 7930
0.3 0.3
13,700 7930
0.3 0.3
0.49 0.49 69.9 20,290
0.49 0.49 0.49 0.3
Articular eminence Compact bone Cancellous bone Connective tissue Joint capsule/ligament Muscles Teeth
(version 7.10, Materialise, Leuven, Belgium). MIMICS software was preferred for its superiority to generate and modify surface 3D models from stacked medical through image segmentation done in the STL format. Nizam et al.18 found an error 0.08% 6 1.25% with MIMICS software for 3D CAD modeling of human tissue. It was effectively used by Cattaneo et al.19 for FEM studies related to orthodontic tooth movement. As the bites were bilaterally symmetrical, only the left side of the TMJ was modeled. The 3D CAD model, when fully constructed, was transferred to ANSYS software (version 13.0, ANSYS, Canonsburg, Pa), wherein it was discretized into finite elements, and a
Figure 3. Three-dimensional CAD model construction of temporomandibular joint and skull with muscle simulation. Angle Orthodontist, Vol 00, No 0, 0000
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SHRIVASTAVA, HAZAREY, KHARBANDA, GUPTA
Figure 4. Marked points categorized into six regions on the condylar head: (A,B) anteroposterior; (C) mediolateral.
3D finite element model was created. This finite element model consisted of 38,250 elements and 52,400 nodes. Young’s modulus and Poisson’s ratio of the TMJ tissues were incorporated in the model7 (Table 3).
Boundary conditions were applied and the finite element model was brought to the baseline position which is the physiologic rest position. physiologic rest position. The loading condition was defined by
Figure 5. Marked points categorized into six regions on the glenoid fossa: (A) anteroposterior; (B) mediolateral.
Figure 6. Marked points categorized into six regions on the articular disc for measurement of stresses: (A) anteroposterior; (B) mediolateral.
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STRESS DISTRIBUTION IN THE TMJ
RESULTS
Figure 7. Stress contour plots showing maximum and minimum principal stresses (MPa) on the condylar head at HA1, HA2, and HA3.
displacement-enforced deformation. That is, no force was applied to bring about the necessary deformation, but the mandible was physically brought forward to target positions. Then, the condylar head and disc positions for HA1, HA2, and HA3 were enforced one by one, and the stresses were generated on the model. The model was again brought to baseline position between the three simulations. A nonlinear stress analysis was carried out at three positions using ANSYS Workbench 13.0 software. The stresses were located on the condylar head and glenoid fossa (principal stresses [PS1, PS2]) and the articular disc (von Mises equivalent stresses). All stresses were measured in megapascal (MPa). The 15 equidistant points (anteroposterior and mediolateral) were used on the condylar head, the glenoid fossa, and the articular disc to record stresses (Figures 4 through 6).
A comparison of the mean stress lines in the anteroposterior direction in the condylar head showed that the pattern was different in HA1 from HA2 and HA3 (Figures 7 and 8; Table 4). In HA1, with highest tensile stress on superior aspect of the condylar head and thereafter values remained constant in posterosuperior and the posterior aspects of condylar head. Maximum compressive stresses (PS2) were in the anterior and anterosuperior aspect of the condylar head. Stress patterns were comparable in HA2 and HA3. The highest tensile stresses in HA2 were recorded in the posterosuperior aspect of the condylar head. While compressive stresses showed a steady pattern in HA2, they spiked down further in the superior part (point 8) of the condylar head before sharply changing into tensile character in position HA3. There was a steady increase in overall stress values in the condylar head as one moved from HA1 to HA2 and then to HA3. In the glenoid fossa (Figures 9 and 10; Table 5), mild tensile stresses were reported in the middle and the posterior aspect of the fossa at position HA1. The anterior part of the fossa experienced compressive forces. The highest value of compressive stress (PS2) was located at point 1 of the glenoid fossa. The tensile stresses (PS1) showed a steady pattern in the superior to posterior aspect. The stresses in HA3 were greater in magnitude than HA2 due to greater advancement. HA2 and HA3 positions presented tensile stresses (PS1) in the superior and posterior part of the fossa and compressive stresses in the anterior part. The highest tensile stress shifted more posterior from point 10 in HA2 to point 11 in HA3. The highest value of compressive stress (PS2) in HA3 was located more interiorly at point 4 than at HA2 (point 4). The trends in the mediolateral direction showed that in HA1, the condylar head experienced compressive stresses in both the medial and lateral aspect but mild
Figure 8. Mean principal stresses (MPa) on the condylar head in the anteroposterior direction at: (A) HA1, (B) HA2, and (C) HA3. Angle Orthodontist, Vol 00, No 0, 0000
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Table 4. Comparison of Condylar Head: Mean Principal Stresses (MPa) Sr. No
HA 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.0277565 0.0097055 20.389768 20.879789 20.462386 20.460025 20.288075 0.44925 0.60125 0.474375 0.3271935 0.2706325 0.3486435 0.3314925 0.33427
HA 2 Anteroposterior direction 0.020399 0.002817 20.07897 20.07898 20.08804 0.013316 20.22791 0.009788 1.895405 3.210915 4.266805 2.139825 1.329381 0.766985 0.5849
HA 3
HA 1
HA 2
HA 3
20.06471 20.13144 20.1312 20.15758 20.37897 20.42571 20.5045 20.75687 2.815665 4.38885 4.71625 4.74415 5.59705 3.31745 3.0501
20.01175 20.00832 20.02641 20.06456 20.04416 0.22646 0.527815 0.410465 0.637885 0.273442 20.14799 20.07801 0.005521 20.00736 20.011
Mediolateral direction 0.299578 0.301735 0.29117 20.01821 20.0415 20.29518 0.632995 1.017895 0.82829 20.35947 20.07896 20.04866 20.02212 20.04709 20.04305
0.75468 0.61227 0.56767 0.5298 20.21 20.37284 0.1715 0.96877 1.5521 0.66055 20.27403 20.16889 20.07365 20.03426 20.07076
tensile stresses on the superior part. The results of HA2 and HA3 showed similarity. Very mild tensile stresses (PS1) were found at all points in the anterior, superior, and posterior aspect of fossa at position HA1. The highest value of tensile stresses was reported on point 13 on the medial aspect. HA2 and HA3 revealed that the highest tensile stresses were present in the medial direction of fossa. From HA2 to HA3, the highest tensile stress shifted from point 13 to point 10 in a more superior direction. Compressive stresses (PS2) were present in the lateral part of the fossa in positions HA2 and HA3. The change could be due to the angulation of the condylar head in the glenoid fossa. In the articular disc (Figures 11 and 12; Table 6) at HA1, the highest von Mises equivalent stresses were present in the middle aspect of the disc. This pattern was found to be different from those in HA2 and HA3. In the positions HA2 and HA3, the stresses were high
Figure 9. Stress contour plots showing maximum and minimum principal stresses (MPa) on the glenoid fossa at (A) HA1, (B) HA2, and (C) HA3. Angle Orthodontist, Vol 00, No 0, 0000
in the anterior and posterior aspects and less in the middle areas. In the mediolateral direction, the stresses were minimal in the middle part of the disc at HA1 position. In HA2 and HA3, the least amount of stresses was present in the medial direction, which increased in the superior aspect and reduced slightly in the posterior direction. The stresses increased with increased horizontal activations. DISCUSSION The amount of bite advancement required to be incorporated into functional appliances for the best treatment response and the biomechanics involved has remained a mystery for clinicians and researchers alike. The functional appliance controversy remains that favorable growth changes have been reported following phase 1 therapy, but they are generally not substantial and long-term stability appears to be poor.20 This FEM study reported biomechanical changes in human TMJ during varied degree of mandibular advancement yielding more information on the effects of the force applied during functional appliance treatment. The stresses recorded in the present study were of higher magnitude than the previous FEM studies.7,8 This could be attributed to the use of recent version of software with greater sophistication and advanced CAD modeling capabilities. The quality of pattern of stresses in the present study was similar to that in the studies by Gupta et al.7,8 who used IDEAS software and ANSYS 8.0 version, though this study used MIMICS software, which is believed to be more accurate for the CAD modeling procedure along with ANSYS 13.0 version for finite element analysis. Furthermore, the quantitative values of stress pattern of any FEM study are specific to the model and should not be compared with other studies. A
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STRESS DISTRIBUTION IN THE TMJ
Figure 10. Mean principal stresses (MPa) on the glenoid fossa in the anteroposterior direction at (A) HA1, (B) HA2, and (C) HA3.
possible limitation to the present study could be that only the left side of TMJ was modeled; thus, all results are based on the characteristics of a single subject. FEM studies in the past7,8 suggested that increasing construction bite heights was found to generate more favorable stress patterns in TMJ, which could be corelated with a possible improved condylar response to functional appliance treatment. There was availability of an experimental study by Noro et al.,21 wherein the similar hypothesis was investigated. However, for horizontal mandibular advancement, no experiments have been reported in the literature. Mean stress lines in the condylar head at HA1 showed that it experienced mild tensile stresses from the superior to posterior direction. The compressive stresses were located in the anterior and anterosuperior aspects. These results can be correlated with Tanaka et al.4 who conducted a similar FEM study of mouth opening. As the horizontal activation increased, the maximum tensile stresses increased posteriorly in both HA2 and HA3. There was a change in the pattern of stresses from HA1 and these two positions. While the tensile stresses peaked at point 11 in HA2, they were maximal at point 13 in HA3. The anterior and
anterosuperior part of the condylar head showed compressive stress only in both HA2 and HA3. The change in the pattern could be attributed to the difference in the type of movement of the condylar head during these displacements. HA1 primarily included lowering of the mandible in a vertical direction from the physiologic rest position, but in HA2 and HA3, both horizontal advancement and vertical descent were made. In comparison of the mean stress lines in HA2 and HA3, the condylar head showed that the maximum tensile stresses moved more posteriorly with the increase in the advancement of the construction bite. The magnitude of stresses also increased due to more viscoelastic stretch of the retrodiscal tissues.22 In all positions, the glenoid fossa experienced mean tensile stresses in the posterior parts, with maximum tensile stresses being located in the middle part in HA2 bite and in the posterior part in HA3. Histologic studies of Woodside et al.23 and Hinton and McNamara24 confirmed the appearance of new bone in this region in response to the stretch of retrodiscal tissues. The anterior and anterosuperior part of the fossa where articular eminence is located showed compressive stresses. This mechanism can be co-related
Table 5. Comparison of Glenoid Fossa: Mean Principal Stresses (MPa) Sr. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HA 1 20.5431 20.2843 20.2544 20.1687 20.4892 0.35806 0.37143 0.50905 0.4825 0.50065 0.2746 0.31455 0.25435 0.26695 0.22335
HA 2 Anteroposterior direction 20.087211 20.029665 20.024866 20.022822 20.032015 20.194066 0.770385 1.05825 1.246755 1.3705345 0.912915 0.6713 0.48168 0.45766 0.276925
HA 3 20.1589 20.2451 20.354 20.5147 20.0318 20.2483 1.60189 2.33574 3.14397 3.4541 3.8458 3.1193 1.86195 1.8246 1.3273
HA 1
HA 2
HA 3
0.14491 0.19509 0.21474 0.2161 0.2965 0.36345 0.42515 0.33435 0.37145 0.42385 0.47466 0.47085 0.56148 0.42636 0.31485
Mediolateral direction 20.8677 20.5623 20.3396 0.12068 0.20148 0.26379 0.23939 0.30376 0.86208 1.02003 1.1044 1.0588 1.1749 1.00331 0.12831
20.4507 20.1159 20.1396 0.75873 0.83918 0.79313 0.91081 1.4332 2.06395 2.15175 2.12905 1.87475 1.38855 0.5427 0.61145
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SHRIVASTAVA, HAZAREY, KHARBANDA, GUPTA Table 6. Comparison of Articular Disc: Von Mises Equivalent Stresses (MPa) Sr. No
Figure 11. Stress contour plots showing von Mises equivalent stresses (MPa) on the articular disc at HA1, HA2, and HA3.
radiographically with studies by Vargervik and Harvold25 and Paulsen26 who found that the glenoid fossa relocates anteroinferiorly by resorption along the posterior slope of the articular eminence and deposition along the anterior slope of the postglenoid spine. Similar results were reported by Gupta et al.7,8 as well as Zhou et al.2 and Voudouris and Kuftinec22 in their ‘‘Growth Relativity Hypothesis.’’ They also concluded that modification of the condylar head and the fossa can be clinically significant when the two structures are separated. It can be hypothesized from the above observations that horizontal activation beyond a certain limit may not be beneficial in increasing tensile stresses on the soft retrodiscal pad. Hence, this results in impaired treatment response and damage to the joint tissues. The stresses on the disc, as in mouth opening could be correlated to the study by del Pozo et al.5 who assessed the influence of friction on disc. In HA1 and HA2, where condylar movement was different, the stress pattern also showed a change. The middle part
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HA 1
HA 3
Anteroposterior direction 0.146 0.923 1.298 0.232 0.813 1.181 0.789 0.805 1.058 0.939 0.709 1.006 0.981 0.431 0.91 1.131 0.31 0.782 0.892 0.212 0.823 0.736 0.396 0.981 0.496 0.573 1.212 0.392 0.595 1.391 0.359 0.623 1.399 0.328 0.682 1.403 0.212 0.716 1.441 0.396 0.723 1.482 0.438 0.814 1.581
HA 1
HA 2
HA 3
Mediolateral direction 0.392 0.439 0.718 0.416 0.482 0.831 0.738 0.496 0.924 0.529 0.519 0.983 0.328 0.582 0.996 0.219 0.623 1.215 0.196 0.895 1.364 0.239 0.952 1.513 0.328 0.989 1.6 0.339 1.116 1.631 0.431 1.232 1.529 0.482 0.941 1.508 0.496 0.768 1.431 0.5 0.693 1.05 0.528 0.637 0.915
of the disc now experienced the minimal von Mises equivalent stresses, and higher stresses were seen in the anterior and posterior regions. Mediolaterally, the stresses were more on medial and lateral portions of the disc. The overall stress level in the disc increased with each sequential activation. As the bite was advanced from 5 mm to 7.5 mm in HA2 to HA3, the stresses increased considerably in the condylar head, glenoid fossa, and articular disc. The magnitude of stresses increased considerably in HA3 when compared to HA1 and HA2. A histologic study by Rabie et al.27 suggested that forward positioning of the mandible in a stepwise manner delivers a mechanical strain that solicits an increase in the number of replicating mesenchymal cells in the condyle which leads to more bone formation. Rabie et al.28 concluded that variation in the degree of advancements produces unequal levels of mechanical strain which trigger different levels of cellular responses in the form of mechanotransduction mediators (Ihh), regulator of cell maturity (PTHrP), amount of cartilage (type II collagen), and ultimately
Figure 12. Von Mises equivalent stresses (MPa) on the articular disc at HA1, HA2, and HA3. Angle Orthodontist, Vol 00, No 0, 0000
HA 2
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STRESS DISTRIBUTION IN THE TMJ
bone. Thus, pointing out the presence of a minimum threshold of strain that should be surpassed to solicit a response could lead to more growth of the condyle in the form of new bone formation. This threshold should be identified clinically as it could influence the tissue response to mandibular advancement. However, the findings of this preliminary study should be investigated further by in vivo experiments.
7.
8.
CONCLUSIONS N It can be concluded that the magnitude of stress increased with sagittal bite advancements. N In HA1, the anterior part of the condyle as well as the glenoid fossa experienced compressive stresses, and mild tensile stresses were experienced by the superior and posterior parts of the condyle. N In HA2, tensile stresses on the posterosuperior and medial aspect of the condyle were seen, and compressive stresses on the anterosuperior and lateral aspect. In the glenoid fossa, tensile stresses were evident on the posterior aspect with compressive stresses on the articular eminence. N With the increase in bite advancement, HA3, tensile stresses moved to a more posterior direction in both the condyle and glenoid fossa, thus reducing the favorable effects of functional appliance. N Also, the quantitative analysis of stress revealed that the stresses acquired a higher magnitude as bites were advanced. Thus, it can be postulated that with the maximal bite advancement, stresses might cross the physiological thresholds of tolerance as compared to smaller or incremental bite advancements.27,28 REFERENCES 1. Tanaka E, Tanne K, Sakuda M. A three-dimensional finite element model of mandible including the TMJ and its application to stress analysis in TMJ during clenching. Med Eng Phys. 1994;16:316–322. 2. Zhou X, Zhao Z, Zhao M. Analysis of the condyle in the state on the mandibular protraction by means of the threedimensional finite element method [in Chinese]. Zhonghua Kou Qiang Yi Xue Za Zhi. 1999;34:85–87. 3. Beek M, Koolstra JH, van Ruijven LJ, van Eijden TM. Threedimensional finite element analysis of the human temporomandibular joint disc. J Biomech. 2000;33:307–316. 4. Tanaka E, Rodrigo DP, Tanaka M, Kawaguchi A, Shibazaki T, Tanne K. Stress analysis in TMJ during jaw opening by use of three-dimensional finite element model based on magnetic resonance images. Int J Oral Maxillofac Surg. 2001;30:421–430. 5. del Pozo R, Tanaka E, Tanaka M, et al. Influence of friction at articular surfaces of temporomandibular joint on stresses in articular disk: a theoretical approach with the finite element method. Angle Orthod. 2003;73:319–327. 6. Ulusoya C, Darendeliler N. Effects of Class II activator and Class II activator high-pull headgear combination on the
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during stepwise advancement. Angle Orthod. 2003;73: 457–465. 28. Ha¨gg U, Rabie AB, Bendeus M, et al. Condylar growth and mandibular positioning with stepwise vs maximum advancement. Am J Orthod Dentofacial Orthop. 2008;134: 525–536.
Stress distribution in the temporomandibular joint after mandibular protraction A three-dimensional finite element study Abhinav Shrivastavaa; Pushpa V. Hazareyb; Om P. Kharbandac; Anurag Guptad ABSTRACT Objective: To evaluate the stress patterns in temporomandibular joint (TMJ) during mandibular protraction at different horizontal advancements with constant vertical height in a construction bite using a three-dimensional finite element method. Materials and Methods: A three-dimensional computer-aided model was developed from the magnetic resonance imaging (MRI) of a growing boy (age 12 years) using MIMICS software (version 7.0, Materialise, Leuven, Belgium). Stresses with constant vertical opening of 5 mm changing the sagittal advancements from 0 mm to 5 mm and 7.5 mm were recorded. Differences in magnitude and pattern of stresses were compared. Results: The tensile stresses in the posterosuperior aspect of the condylar head and on the posterior aspect of the glenoid fossa migrated posteriorly with increased bite advancements. The location of tensile stresses changed in the condylar head and fossa on mandibular protraction of 5 mm to 7 mm. Conclusion: This study indicates that larger horizontal advancements of construction bites may not be favorable for tissues of TMJ. Clinical application necessitates study on an animal model. (Angle Orthod. 0000;00:1–10.) KEY WORDS: Mandibular protraction; 3D FEM study; Horizontal advancements; Stresses; Temporomandibular joint; Condyle; Fossa; Articular disc
INTRODUCTION
reactions of functional appliances. FEM is an in vitro, highly sophisticated, and noninvasive method. It explicates the qualitative nature and relative trends of compressive and tensile stresses of a complex biological structure like TMJ. Benefits of functional appliances on TMJ remodeling process have been universally acknowledged, while there is an assortment of opinions regarding construction bite used to protract the mandible.9–17 In a FEM study, increasing construction bite height generated more favorable stress patterns in TMJ. This could indicate a possible improved condylar response to functional appliance treatment.8 Inconsistent opinions have been recorded regarding the vertical component and horizontal advancement of the mandible. Andresen10 suggested protrusion of the mandible to neutro-occlusion and keeping the bite within the freeway space. Herren13 and Shaye et al.14 modified the activator appliance so that the mandible is advanced from a Class II position to 3–4 mm ahead of the Class I molar relation. Thus, the distal molar relationship is overcompensated. Schwarz15 advocated that optimal forward movement of the mandible
Functional appliances correct sagittal skeletal discrepancies in Class II malocclusion of growing individuals.1–8 Finite element method (FEM) studies on human temporomandibular joint (TMJ) are being increasingly carried out to elucidate the biomechanical a Senior Lecturer, Department of Orthodontics, Hitkarni Dental College, Jabalpur, India. b Professor and Head, Department of Orthodontics, Sharad Pawar Dental College, Wardha, India. c Professor and Head, Department of Orthodontics and Dentofacial Deformities, Centre for Dental Excellence and Research, All India Institute of Medical Sciences, New Delhi, India. d Head Consultant, Maximus Specialist Centre for Dental Research, New Delhi, India. Corresponding author: Dr Abhinav Shrivastava, Senior Lecturer, Department of Orthodontics, Hitkarni Dental College, Jabalpur, India (e-mail: [email protected])
Accepted: April 2014. Submitted: September 2013. Published Online: June 5, 2014 G 0000 by The EH Angle Education and Research Foundation, Inc. DOI: 10.2319/091913-690.1
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Figure 1. Total displacements of the condylar head (A) and disc (B). Locating the condylar head and the articular disc on the MRI by using arbitrary reference lines (T1 and T2). T1 is the tangent to the superior-most point on the glenoid fossa. T2 is tangent to the postglenoid spine and perpendicular to T1.
would be half of the individual’s maximum range. Woodside16 gave three theories of bite registration for the activator, based on the muscle and soft tissue actions in response to the engagement of the mandible in the activator. Changing the vertical opening
mandibular protrusion was kept constant at 3 mm distal to the most protrusive position the patient can achieve. Graber and Neumann15 advocated the limitation for protraction to 3 mm distal to the most protrusive position. Most authors favor a Class I molar relation or neutro-occlusion position with regard to the sagittal advancement of the mandible; none of the views has been examined using biomechanical studies.17 Hence, the present study was carried out with the objective of relating the changes in stress patterns in the TMJ applying construction bites of varying horizontal advancements keeping the vertical height constant. MATERIALS AND METHODS A 12-year-old boy, with skeletal Class II, retrognathic mandible, incisal overjet of 8 mm, and a favorable growth pattern considered suitable for functional appliance therapy was inducted in the present study. Approval by the institutional ethical review committee was obtained to conduct the study. Four wax construction bites were obtained at physiologic rest position, and at three other positions, Table 1.
Location of Condyle in Various Positions
Positions
Figure 2. Total displacements of the condylar head (A) and the disc (B) from maximum intercuspation through physiologic rest position, HA1 and HA2, up to HA3. Angle Orthodontist, Vol 00, No 0, 0000
Intercuspal position Postural rest position Position 1 Position 2 Position 3
Sagittal Vertical Vertical Horizontal Position of Position of Displacement Displacement Mandible, Mandible, of Condyle, of Condyle, mm mm mm mm _
_
7.86
8.36
_
_
0 5 7.5
5 5 5
8.62 10.14 10.64 11.15
8.87 9.12 10.90 11.40
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STRESS DISTRIBUTION IN THE TMJ Table 2. Location of Disc in Various Positions
Positions Intercuspal position Postural rest position Position 1 Position 2 Position 3
Table 3.
Sagittal Vertical Vertical Horizontal Position of Position of Displacement Displacement Mandible, Mandible, of Disc, of Disc, mm mm mm mm _
_
7.60
12.42
_
_
0 5 7.5
5 5 5
9.38 10.64 11.40 12.71
13.68 14.44 15.71 16.42
Properties of Bone and Soft Tissues7 Elastic Modulus (E), MPa
Poisson’s Ratio (v)
13,700 7930 0.79
0.3 0.3 0.49
Condyle Compact bone Cancellous bone Cartilage layer Articular disc Anterior Intermediate Posterior
10 10.73 9.0
0.4
Glenoid fossa
which were HA1 at 0 mm horizontal activation, HA2 at 5 mm horizontal activation, and HA3 at 7.5 mm horizontal activation. A 5-mm vertical opening was kept constant for all three positions. The patient underwent five sequential magnetic resonance scans at maximum intercuspation position, while holding each of the four wax bites in his mouth. The scans were procured with a magnetic resonance imaging (MRI) machine, 1.5-T magnet (Signa, Excite 11, General Electric, Chalfont, St Giles, UK) and a 3-inch dual surface coil. The externally marked Frankfort horizontal plane was kept perpendicular to the scanning table. The positions of the condylar head and disc were noted, and their total translations during the entire study were mapped and plotted (Figures 1 and 2; Tables 1 and 2). The magnetic resonance images were obtained in DICOM and JPEG format, comprehensible in MIMICS and the Centricity DICOM MRI viewer. A threedimensional (3D) computer-aided design (CAD) model of the skull was constructed (Figure 3) on a highly sophisticated workstation using Centricity DICOM MRI viewer (General Electric) and MIMICS software
Compact bone Cancellous bone
13,700 7930
0.3 0.3
13,700 7930
0.3 0.3
0.49 0.49 69.9 20,290
0.49 0.49 0.49 0.3
Articular eminence Compact bone Cancellous bone Connective tissue Joint capsule/ligament Muscles Teeth
(version 7.10, Materialise, Leuven, Belgium). MIMICS software was preferred for its superiority to generate and modify surface 3D models from stacked medical through image segmentation done in the STL format. Nizam et al.18 found an error 0.08% 6 1.25% with MIMICS software for 3D CAD modeling of human tissue. It was effectively used by Cattaneo et al.19 for FEM studies related to orthodontic tooth movement. As the bites were bilaterally symmetrical, only the left side of the TMJ was modeled. The 3D CAD model, when fully constructed, was transferred to ANSYS software (version 13.0, ANSYS, Canonsburg, Pa), wherein it was discretized into finite elements, and a
Figure 3. Three-dimensional CAD model construction of temporomandibular joint and skull with muscle simulation. Angle Orthodontist, Vol 00, No 0, 0000
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Figure 4. Marked points categorized into six regions on the condylar head: (A,B) anteroposterior; (C) mediolateral.
3D finite element model was created. This finite element model consisted of 38,250 elements and 52,400 nodes. Young’s modulus and Poisson’s ratio of the TMJ tissues were incorporated in the model7 (Table 3).
Boundary conditions were applied and the finite element model was brought to the baseline position which is the physiologic rest position. physiologic rest position. The loading condition was defined by
Figure 5. Marked points categorized into six regions on the glenoid fossa: (A) anteroposterior; (B) mediolateral.
Figure 6. Marked points categorized into six regions on the articular disc for measurement of stresses: (A) anteroposterior; (B) mediolateral.
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RESULTS
Figure 7. Stress contour plots showing maximum and minimum principal stresses (MPa) on the condylar head at HA1, HA2, and HA3.
displacement-enforced deformation. That is, no force was applied to bring about the necessary deformation, but the mandible was physically brought forward to target positions. Then, the condylar head and disc positions for HA1, HA2, and HA3 were enforced one by one, and the stresses were generated on the model. The model was again brought to baseline position between the three simulations. A nonlinear stress analysis was carried out at three positions using ANSYS Workbench 13.0 software. The stresses were located on the condylar head and glenoid fossa (principal stresses [PS1, PS2]) and the articular disc (von Mises equivalent stresses). All stresses were measured in megapascal (MPa). The 15 equidistant points (anteroposterior and mediolateral) were used on the condylar head, the glenoid fossa, and the articular disc to record stresses (Figures 4 through 6).
A comparison of the mean stress lines in the anteroposterior direction in the condylar head showed that the pattern was different in HA1 from HA2 and HA3 (Figures 7 and 8; Table 4). In HA1, with highest tensile stress on superior aspect of the condylar head and thereafter values remained constant in posterosuperior and the posterior aspects of condylar head. Maximum compressive stresses (PS2) were in the anterior and anterosuperior aspect of the condylar head. Stress patterns were comparable in HA2 and HA3. The highest tensile stresses in HA2 were recorded in the posterosuperior aspect of the condylar head. While compressive stresses showed a steady pattern in HA2, they spiked down further in the superior part (point 8) of the condylar head before sharply changing into tensile character in position HA3. There was a steady increase in overall stress values in the condylar head as one moved from HA1 to HA2 and then to HA3. In the glenoid fossa (Figures 9 and 10; Table 5), mild tensile stresses were reported in the middle and the posterior aspect of the fossa at position HA1. The anterior part of the fossa experienced compressive forces. The highest value of compressive stress (PS2) was located at point 1 of the glenoid fossa. The tensile stresses (PS1) showed a steady pattern in the superior to posterior aspect. The stresses in HA3 were greater in magnitude than HA2 due to greater advancement. HA2 and HA3 positions presented tensile stresses (PS1) in the superior and posterior part of the fossa and compressive stresses in the anterior part. The highest tensile stress shifted more posterior from point 10 in HA2 to point 11 in HA3. The highest value of compressive stress (PS2) in HA3 was located more interiorly at point 4 than at HA2 (point 4). The trends in the mediolateral direction showed that in HA1, the condylar head experienced compressive stresses in both the medial and lateral aspect but mild
Figure 8. Mean principal stresses (MPa) on the condylar head in the anteroposterior direction at: (A) HA1, (B) HA2, and (C) HA3. Angle Orthodontist, Vol 00, No 0, 0000
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Table 4. Comparison of Condylar Head: Mean Principal Stresses (MPa) Sr. No
HA 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.0277565 0.0097055 20.389768 20.879789 20.462386 20.460025 20.288075 0.44925 0.60125 0.474375 0.3271935 0.2706325 0.3486435 0.3314925 0.33427
HA 2 Anteroposterior direction 0.020399 0.002817 20.07897 20.07898 20.08804 0.013316 20.22791 0.009788 1.895405 3.210915 4.266805 2.139825 1.329381 0.766985 0.5849
HA 3
HA 1
HA 2
HA 3
20.06471 20.13144 20.1312 20.15758 20.37897 20.42571 20.5045 20.75687 2.815665 4.38885 4.71625 4.74415 5.59705 3.31745 3.0501
20.01175 20.00832 20.02641 20.06456 20.04416 0.22646 0.527815 0.410465 0.637885 0.273442 20.14799 20.07801 0.005521 20.00736 20.011
Mediolateral direction 0.299578 0.301735 0.29117 20.01821 20.0415 20.29518 0.632995 1.017895 0.82829 20.35947 20.07896 20.04866 20.02212 20.04709 20.04305
0.75468 0.61227 0.56767 0.5298 20.21 20.37284 0.1715 0.96877 1.5521 0.66055 20.27403 20.16889 20.07365 20.03426 20.07076
tensile stresses on the superior part. The results of HA2 and HA3 showed similarity. Very mild tensile stresses (PS1) were found at all points in the anterior, superior, and posterior aspect of fossa at position HA1. The highest value of tensile stresses was reported on point 13 on the medial aspect. HA2 and HA3 revealed that the highest tensile stresses were present in the medial direction of fossa. From HA2 to HA3, the highest tensile stress shifted from point 13 to point 10 in a more superior direction. Compressive stresses (PS2) were present in the lateral part of the fossa in positions HA2 and HA3. The change could be due to the angulation of the condylar head in the glenoid fossa. In the articular disc (Figures 11 and 12; Table 6) at HA1, the highest von Mises equivalent stresses were present in the middle aspect of the disc. This pattern was found to be different from those in HA2 and HA3. In the positions HA2 and HA3, the stresses were high
Figure 9. Stress contour plots showing maximum and minimum principal stresses (MPa) on the glenoid fossa at (A) HA1, (B) HA2, and (C) HA3. Angle Orthodontist, Vol 00, No 0, 0000
in the anterior and posterior aspects and less in the middle areas. In the mediolateral direction, the stresses were minimal in the middle part of the disc at HA1 position. In HA2 and HA3, the least amount of stresses was present in the medial direction, which increased in the superior aspect and reduced slightly in the posterior direction. The stresses increased with increased horizontal activations. DISCUSSION The amount of bite advancement required to be incorporated into functional appliances for the best treatment response and the biomechanics involved has remained a mystery for clinicians and researchers alike. The functional appliance controversy remains that favorable growth changes have been reported following phase 1 therapy, but they are generally not substantial and long-term stability appears to be poor.20 This FEM study reported biomechanical changes in human TMJ during varied degree of mandibular advancement yielding more information on the effects of the force applied during functional appliance treatment. The stresses recorded in the present study were of higher magnitude than the previous FEM studies.7,8 This could be attributed to the use of recent version of software with greater sophistication and advanced CAD modeling capabilities. The quality of pattern of stresses in the present study was similar to that in the studies by Gupta et al.7,8 who used IDEAS software and ANSYS 8.0 version, though this study used MIMICS software, which is believed to be more accurate for the CAD modeling procedure along with ANSYS 13.0 version for finite element analysis. Furthermore, the quantitative values of stress pattern of any FEM study are specific to the model and should not be compared with other studies. A
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STRESS DISTRIBUTION IN THE TMJ
Figure 10. Mean principal stresses (MPa) on the glenoid fossa in the anteroposterior direction at (A) HA1, (B) HA2, and (C) HA3.
possible limitation to the present study could be that only the left side of TMJ was modeled; thus, all results are based on the characteristics of a single subject. FEM studies in the past7,8 suggested that increasing construction bite heights was found to generate more favorable stress patterns in TMJ, which could be corelated with a possible improved condylar response to functional appliance treatment. There was availability of an experimental study by Noro et al.,21 wherein the similar hypothesis was investigated. However, for horizontal mandibular advancement, no experiments have been reported in the literature. Mean stress lines in the condylar head at HA1 showed that it experienced mild tensile stresses from the superior to posterior direction. The compressive stresses were located in the anterior and anterosuperior aspects. These results can be correlated with Tanaka et al.4 who conducted a similar FEM study of mouth opening. As the horizontal activation increased, the maximum tensile stresses increased posteriorly in both HA2 and HA3. There was a change in the pattern of stresses from HA1 and these two positions. While the tensile stresses peaked at point 11 in HA2, they were maximal at point 13 in HA3. The anterior and
anterosuperior part of the condylar head showed compressive stress only in both HA2 and HA3. The change in the pattern could be attributed to the difference in the type of movement of the condylar head during these displacements. HA1 primarily included lowering of the mandible in a vertical direction from the physiologic rest position, but in HA2 and HA3, both horizontal advancement and vertical descent were made. In comparison of the mean stress lines in HA2 and HA3, the condylar head showed that the maximum tensile stresses moved more posteriorly with the increase in the advancement of the construction bite. The magnitude of stresses also increased due to more viscoelastic stretch of the retrodiscal tissues.22 In all positions, the glenoid fossa experienced mean tensile stresses in the posterior parts, with maximum tensile stresses being located in the middle part in HA2 bite and in the posterior part in HA3. Histologic studies of Woodside et al.23 and Hinton and McNamara24 confirmed the appearance of new bone in this region in response to the stretch of retrodiscal tissues. The anterior and anterosuperior part of the fossa where articular eminence is located showed compressive stresses. This mechanism can be co-related
Table 5. Comparison of Glenoid Fossa: Mean Principal Stresses (MPa) Sr. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HA 1 20.5431 20.2843 20.2544 20.1687 20.4892 0.35806 0.37143 0.50905 0.4825 0.50065 0.2746 0.31455 0.25435 0.26695 0.22335
HA 2 Anteroposterior direction 20.087211 20.029665 20.024866 20.022822 20.032015 20.194066 0.770385 1.05825 1.246755 1.3705345 0.912915 0.6713 0.48168 0.45766 0.276925
HA 3 20.1589 20.2451 20.354 20.5147 20.0318 20.2483 1.60189 2.33574 3.14397 3.4541 3.8458 3.1193 1.86195 1.8246 1.3273
HA 1
HA 2
HA 3
0.14491 0.19509 0.21474 0.2161 0.2965 0.36345 0.42515 0.33435 0.37145 0.42385 0.47466 0.47085 0.56148 0.42636 0.31485
Mediolateral direction 20.8677 20.5623 20.3396 0.12068 0.20148 0.26379 0.23939 0.30376 0.86208 1.02003 1.1044 1.0588 1.1749 1.00331 0.12831
20.4507 20.1159 20.1396 0.75873 0.83918 0.79313 0.91081 1.4332 2.06395 2.15175 2.12905 1.87475 1.38855 0.5427 0.61145
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SHRIVASTAVA, HAZAREY, KHARBANDA, GUPTA Table 6. Comparison of Articular Disc: Von Mises Equivalent Stresses (MPa) Sr. No
Figure 11. Stress contour plots showing von Mises equivalent stresses (MPa) on the articular disc at HA1, HA2, and HA3.
radiographically with studies by Vargervik and Harvold25 and Paulsen26 who found that the glenoid fossa relocates anteroinferiorly by resorption along the posterior slope of the articular eminence and deposition along the anterior slope of the postglenoid spine. Similar results were reported by Gupta et al.7,8 as well as Zhou et al.2 and Voudouris and Kuftinec22 in their ‘‘Growth Relativity Hypothesis.’’ They also concluded that modification of the condylar head and the fossa can be clinically significant when the two structures are separated. It can be hypothesized from the above observations that horizontal activation beyond a certain limit may not be beneficial in increasing tensile stresses on the soft retrodiscal pad. Hence, this results in impaired treatment response and damage to the joint tissues. The stresses on the disc, as in mouth opening could be correlated to the study by del Pozo et al.5 who assessed the influence of friction on disc. In HA1 and HA2, where condylar movement was different, the stress pattern also showed a change. The middle part
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HA 1
HA 3
Anteroposterior direction 0.146 0.923 1.298 0.232 0.813 1.181 0.789 0.805 1.058 0.939 0.709 1.006 0.981 0.431 0.91 1.131 0.31 0.782 0.892 0.212 0.823 0.736 0.396 0.981 0.496 0.573 1.212 0.392 0.595 1.391 0.359 0.623 1.399 0.328 0.682 1.403 0.212 0.716 1.441 0.396 0.723 1.482 0.438 0.814 1.581
HA 1
HA 2
HA 3
Mediolateral direction 0.392 0.439 0.718 0.416 0.482 0.831 0.738 0.496 0.924 0.529 0.519 0.983 0.328 0.582 0.996 0.219 0.623 1.215 0.196 0.895 1.364 0.239 0.952 1.513 0.328 0.989 1.6 0.339 1.116 1.631 0.431 1.232 1.529 0.482 0.941 1.508 0.496 0.768 1.431 0.5 0.693 1.05 0.528 0.637 0.915
of the disc now experienced the minimal von Mises equivalent stresses, and higher stresses were seen in the anterior and posterior regions. Mediolaterally, the stresses were more on medial and lateral portions of the disc. The overall stress level in the disc increased with each sequential activation. As the bite was advanced from 5 mm to 7.5 mm in HA2 to HA3, the stresses increased considerably in the condylar head, glenoid fossa, and articular disc. The magnitude of stresses increased considerably in HA3 when compared to HA1 and HA2. A histologic study by Rabie et al.27 suggested that forward positioning of the mandible in a stepwise manner delivers a mechanical strain that solicits an increase in the number of replicating mesenchymal cells in the condyle which leads to more bone formation. Rabie et al.28 concluded that variation in the degree of advancements produces unequal levels of mechanical strain which trigger different levels of cellular responses in the form of mechanotransduction mediators (Ihh), regulator of cell maturity (PTHrP), amount of cartilage (type II collagen), and ultimately
Figure 12. Von Mises equivalent stresses (MPa) on the articular disc at HA1, HA2, and HA3. Angle Orthodontist, Vol 00, No 0, 0000
HA 2
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STRESS DISTRIBUTION IN THE TMJ
bone. Thus, pointing out the presence of a minimum threshold of strain that should be surpassed to solicit a response could lead to more growth of the condyle in the form of new bone formation. This threshold should be identified clinically as it could influence the tissue response to mandibular advancement. However, the findings of this preliminary study should be investigated further by in vivo experiments.
7.
8.
CONCLUSIONS N It can be concluded that the magnitude of stress increased with sagittal bite advancements. N In HA1, the anterior part of the condyle as well as the glenoid fossa experienced compressive stresses, and mild tensile stresses were experienced by the superior and posterior parts of the condyle. N In HA2, tensile stresses on the posterosuperior and medial aspect of the condyle were seen, and compressive stresses on the anterosuperior and lateral aspect. In the glenoid fossa, tensile stresses were evident on the posterior aspect with compressive stresses on the articular eminence. N With the increase in bite advancement, HA3, tensile stresses moved to a more posterior direction in both the condyle and glenoid fossa, thus reducing the favorable effects of functional appliance. N Also, the quantitative analysis of stress revealed that the stresses acquired a higher magnitude as bites were advanced. Thus, it can be postulated that with the maximal bite advancement, stresses might cross the physiological thresholds of tolerance as compared to smaller or incremental bite advancements.27,28 REFERENCES 1. Tanaka E, Tanne K, Sakuda M. A three-dimensional finite element model of mandible including the TMJ and its application to stress analysis in TMJ during clenching. Med Eng Phys. 1994;16:316–322. 2. Zhou X, Zhao Z, Zhao M. Analysis of the condyle in the state on the mandibular protraction by means of the threedimensional finite element method [in Chinese]. Zhonghua Kou Qiang Yi Xue Za Zhi. 1999;34:85–87. 3. Beek M, Koolstra JH, van Ruijven LJ, van Eijden TM. Threedimensional finite element analysis of the human temporomandibular joint disc. J Biomech. 2000;33:307–316. 4. Tanaka E, Rodrigo DP, Tanaka M, Kawaguchi A, Shibazaki T, Tanne K. Stress analysis in TMJ during jaw opening by use of three-dimensional finite element model based on magnetic resonance images. Int J Oral Maxillofac Surg. 2001;30:421–430. 5. del Pozo R, Tanaka E, Tanaka M, et al. Influence of friction at articular surfaces of temporomandibular joint on stresses in articular disk: a theoretical approach with the finite element method. Angle Orthod. 2003;73:319–327. 6. Ulusoya C, Darendeliler N. Effects of Class II activator and Class II activator high-pull headgear combination on the
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10 26. Paulsen HU. Morphological changes of TMJ condyles of 100 patients treated with Herbst appliance in period of puberty to adulthood: a long-term radiographic study. Eur J Orthod. 1997;19:657–668. 27. Rabie AB, Tsai MJ, Ha¨gg U, Du X, Chou BW. The correlation of replicating cells and osteogenesis in the condyle
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during stepwise advancement. Angle Orthod. 2003;73: 457–465. 28. Ha¨gg U, Rabie AB, Bendeus M, et al. Condylar growth and mandibular positioning with stepwise vs maximum advancement. Am J Orthod Dentofacial Orthop. 2008;134: 525–536.
