Stress distribution in the temporomandibular joint after mandibular protraction: A 3-dimensional finite element method study. Part 1

ORIGINAL ARTICLE

Stress distribution in the temporomandibularjoint after mandibular protraction: A3-dimensional finite element method study. Part 1

Anurag Gupta,a Virender S. Kohli,b Pushpa V. Hazarey,c Om P. Kharbanda,d and Amit Gunjale

New Delhi, Jabalpur, Maharashtra, and Mumbai, India

Introduction: This study was designed to evaluate patterns of stress generation in the temporomandibularjoint after mandibular protraction, by using a 3-dimensional finite element method. The results of the initialinvestigation are reported here in Part 1. The effects of varying the construction bite are reported in Part 2.Methods: A 3-dimensional computer-aided design model was developed from the magnetic resonanceimages of a growing boy (age, 12 years), by using I-DEAS NX (version 11.0, Siemens PLM Software, Plano,Tex). The model simulated mandibular protraction, with 5 mm of sagittal advancement and 4 mm of verticalopening. Stress distributions on the condylar neck, the glenoid fossa, and the articular disc in the anteropos-terior and mediolateral directions were assessed. Results: Tensile stresses were located on the posterosupe-rior aspects and compressive stresses on the anterior and anterosuperior aspects of the condylar head.Tensile stresses were found in the posterior region of the glenoid fossa near the attachment of the posteriorconnective tissues. Conclusions: These results suggest that, on mandibular protraction, the mandibularcondyle experiences tensile stresses in the posterosuperior aspect that might help explain condylar growthin this direction. Similarly, on the glenoid fossa, tensile stresses are created in the region of posterior connec-tive tissues; this might be correlated with the increased cellular activity in this region. Further study withvariable vertical heights of the construction bites is needed. (Am J Orthod Dentofacial Orthop2009;135:737-48)

Remodeling changes in the condylar head and theglenoid fossa have been reported after func-tional appliance treatment for correction of

Class II skeletal dysplasia with mandibular retrogna-thia.1-12 The posterior displacement of the condylarhead and the anterior relocation of the glenoid fossahave been recorded radiographically on serial cephalo-grams.13,14 Computed tomography scans have showna double contour on the bony outline of the condylarhead and the fossa articularis.15 Magnetic resonanceimaging (MRI) studies have shown that the posterosu-

a Research scientist, Department of Orthodontics, Center for Dental Education

and Research, All India Institute of Medical Sciences, New Delhi, India.b Professor and head, Department of Orthodontics, Hitkarni Dental College and

Hospital, Jabalpur, Madhya Pradesh, India.c Professor and head, Department of Orthodontics and Dentofacial Orthopedics,

Sharad Pawar Dental College and Hospital, Datta Meghe Institute of Medical

Sciences, Wardha, Maharashtra, India.d Professor and head, Department of Orthodontics, Center for Dental Education

and Research, All India Institute of Medical Sciences, New Delhi, India.e Senior mechanical engineer, Milestone Technologies, Mumbai, India.

The authors report no commercial, proprietary, or financial interest in the prod-

ucts or companies described in this article.

Reprint requests to: Anurag Gupta, Department of Orthodontics, Center for

Dental Education and Research, All India Institute of Medical Sciences, New

Delhi 110049, India; e-mail, [email protected].

Submitted, July 2007; revised and accepted, December 2007.

0889-5406/$36.00

Copyright � 2009 by the American Association of Orthodontists.

doi:10.1016/j.ajodo.2007.12.025

perior region of the condyle and the anterior border ofthe post-glenoid spine have distinct areas of active con-dylar remodeling through increased density signals.16

Single photon emission computerized tomographyscans of the temporomandibular joint (TMJ) by usingTc-99m MDP showed significant increases in the bonecount, indicating increased bone formation in the TMJafter mandibular anterior repositioning splint treat-ment.17 Animal histologic studies showed that cellularproliferation could be seen in the posterosuperior aspectof condylar cartilage.5-9,18 Rabie et al,19-21 in Sprague-Dawley rat studies, found statistically significantincreases in the level of expression of vaso-endothelialgrowth factor, SOX 9 gene, type II collagen, and rateof mesenchymal cell proliferation in the posterosuperioraspect of the condylar head and the posterior aspect ofthe glenoid fossa during forward mandibular position-ing compared with natural growth. These findings im-plied that mandibular advancement caused significantincreases in neovascularization and osteogenesis in themandibular condyle and the glenoid fossa.

The blueprint of the functional appliance is theconstruction bite, which helps in jumping the bite anddisplaces the mandible in the vertical and sagittal direc-tions. Graf,22 Witt,23 Woodside,24 and Noro et al25

showed that forces are generated in the stomatognathic

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mailto:[email protected]

738 Gupta et al American Journal of Orthodontics and Dentofacial Orthopedics

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Fig 1. MR scout images showing sagittal and coronal images of the patient’s skull. Dotted linesindicate areas selected for sections: A, sagittal plane; B, coronal plane.

Fig 2. FEM model of the human skull with a zoom-in view of the TMJ.

system by positioning the mandible forward, and thesecan cause skeletal changes in the mandibular condyleand the glenoid fossa. Zhou et al,26 in a 3-dimensional(3D) finite element method (FEM) study, found tensileforces on the posterosuperior aspect of the condylarhead and compressive forces on the anterior part ofthe condylar head. The reactions of the glenoid fossaand the articular disc were not reported.

The FEM is a fairly well-known research adjunct inorthodontics. It can be used to analyze the stress distribu-tion patterns in the tissues after application of force. It isa numeric analysis technique done on high-fidelity com-puters with powerful software, allows a reasonable ap-proximation of the biologic tissues through computeraided designing (CAD), and permits detailed analysesof various force applications on structures such as teeth,

bones, and joints. With the help of recent experiments onanimal and human cadavers, quantification of mechani-cal behavior of various tissues is possible. The propertieselucidated from these experiments are mostly homoge-nous and isotropic but can be relied on safely.27-35 Theessence of the FEM study of biologic tissue is its abilityto elucidate the qualitative nature and relative trends ofthe process rather than specific values. Therefore, theFEM is reasonable for elucidating the complex biome-chanical effects on TMJ structures.

We believe that evaluation of the biomechanical andstructural effects of functional protraction of the mandi-ble on the TMJ could lead to a better understanding ofthe exact effects of this popular and useful treatment mo-dality. It might also be useful to correlate with previouslyreported radiographic and histologic evidence of the

American Journal of Orthodontics and Dentofacial Orthopedics Gupta et al 739Volume 135, Number 6

growth mechanism elicited by functional appliances.Hence, stress distribution in the TMJ after mandibularprotraction by using 3D FEM was evaluated.

MATERIAL AND METHODS

The analytical model of the TMJ and the adjoiningbones was developed from the magnetic resonance(MR) images of a young patient, a boy aged 12 years,who had a skeletal Class II relationship with a retro-gnathic mandible and a favorable growth pattern(ANB angle, 8�; FMA, 24�; posterior: anterior facialheight ratio, 65%). Informed consent was obtainedfrom the patient’s parents to participate in the study.To obtain the positions of the condyle and the disc atthe physiologic rest position and at the planned con-struction bite, 2 wax bites were prepared. The patientsat upright in the dental chair with his head unsupported.The direct intraoral technique was used for determiningthe freeway space in the canine region. For recordingthe physiologic rest position, the patient practiced keep-ing his mandible in the physiologic rest position, withassistance from a mirror, and holding the mandible inthat position for some time. Soft wax was used to recordthis practiced position. The direct measurement of thefreeway space taken previously helped in verifying thewax record. The physiologic rest position recordedhere was assumed to be the zero baseline for comparisonof stresses later. The construction bite for the target po-sition was recorded at 5 mm of sagittal advancementand 4 mm of vertical opening.

Table I. Physical properties of the condyle, the glenoidfossa, the articular disc, and their substructures

Elasticmodulus (E)

Poisson’sratio (v)

Condyle

Compact bone26-32,35,36 13700 MPa 0.3

Cancellous bone26-32,35,36 7930 MPa 0.3

Cartilage layer—0.5 mm28,31-32 0.79 MPa 0.49

Articular disc26

Anterior 10 MPa 0.4

Intermediate 10.73 MPa

Posterior 9.0 MPa

Glenoid fossa

Compact bone26-32,35,36 13700 MPa 0.3


Articular eminence

Compact bone26-32,35,36 13700 MPa 0.3


Connective tissue32,36 0.49 MPa 0.49

Joint capsule/ligament32,36 0.49 MPa 0.49

Muscles26 69.9 MPa 0.49

Teeth26 20290 MPa 0.3

The MR images were made so that soft tissues suchas articular disc, ligaments, and muscles could be cap-tured. The MRI machine used was a high intensity1.5-T magnet (Signa, Excite 11, General Electric, Chal-font St. Giles, United Kingdom) and a 3-in dual surfacecoil. The scanning procedure entailed positioning andstabilizing the head on the scanning table with the exter-nally marked Franfort horizontal plane (FHP) kept per-pendicular to the scanning table. The wax bite wasplaced in the patient’s mouth before MR imaging, andhe was asked to close his mandible in the wax bite.The wax bites helped to stabilize the mandible duringscanning, which was done at 3 positions: maximum in-tercuspation, physiologic rest position, and constructionbite position.

Fig 3. Locating the condylar head and the articular discon the MRI by using arbitrary reference lines (T1 and T2).T1 is the tangent to the superior-most point on theglenoid fossa. T2 is tangent to the post-glenoid spineand perpendicular to T1. A, Location of condylar head;B, location of articular disc.


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Table II. Displacement of the condylar head and the articular disc in the y- and z-axes

PositionSagittal position

of mandibleVertical position

of mandibleCondylar headz-axis (vertical)

Condylar heady-axis (horizontal)

Articular discz-axis (vertical)

Articular discy axis (horizontal)

Intercupsal position 6.36 mm 7.64 mm 6.36 mm 12.98 mm

PRP (baseline) 7.13 mm 8.15 mm 8.15 mm 13.75 mm

Target position 5 mm 4 mm 9.05 mm 9.42 mm 10.95 mm 15.47 mm

PRP, Physiologic rest position.

Fig 4. Marked points categorized into 6 regions on the condylar head: A and B, anteroposterior;C, mediolateral.

For complete 3D representation of the tissues, coro-nal and sagittal slices were obtained. A standard imag-ing sequence was used during scanning, with scout axialslices parallel to the FHP taken.32,36-38 Based on thesescout images, the sagittal plane of imaging was de-signed to be perpendicular to the long axis of the con-dyle (Fig 1). Ten contiguous sagittal slices 2 mm thickwere obtained. The coronal plane of imaging was deter-mined to be perpendicular to the median sagittal planeand the FHP. The 2 sets of parallel lines in the axial sliceindicated the positions of the imaged sagittal and coro-nal images. Fifteen contiguous coronal slices 2 mmthick were obtained. The coronal images were helpfulin making a precise TMJ model, especially the medialand lateral poles of the condyle. An optimized protondensity weighed fast spin echo sequence (repetitiontime 1500 ms/echo time 22.5 ms) was used for scan-ning. The fields of vision were 14 cm for sagittal imagesand 16 cm for coronal images. The scanned images wereprocured in CAD-compatible digital formats such asJPEG and DICOM file format.

For the construction of the 3D CAD model, a highlysophisticated workstation with a dedicated graphicRAM was used. We used Centricity DICOM MRIViewer, I-DEAS NX (version 11.0, General Electric)CAD software and ANSYS software (version 8.0, Can-onsburg, Pa). Because the bites were bilaterally sym-

metrical, only 1 side of the TMJ was used formodeling it and its associated structures. Only the func-tionally important structures for jaw movement such asthe TMJ proper, the ligaments, the muscles of mastica-tion, and the associated jaw bones were modeled. Thepurpose of simulating the various muscle attachmentsand ligaments in this CAD model was to simulate thestretch of the muscles generated during mandibular pro-traction. The CAD model was constructed by using im-ages at maximum intercuspation.

During construction of the model, the scannedimages were imported to the CAD program, and thesurface contours were traced digitally. Since the MRimages were scanned according to a constant reference,the FHP, and the scale, it became easier to trace thesequential slices and orient them systematically tomaintain the surface continuity. While the sagittal slicesgave the y- and z-coordinates, the coronal slices, whenoriented and positioned with the reference and the scale,gave the corresponding x-coordinate. The tracings ofthe slices were piled up in an oriented fashion torepresent the 3D geometry of the joint and the relatedstructures. The construction of the CAD model wasdone according to the method of Tanaka et al.32 Thesevariables were arranged in data sets Ps and Pc forsagittal and coronal slices respectively, and the datawere entered in the program to produce a point cloud.


Three-dimensional reconstruction of the TMJ compo-nents was separately conducted with each data set ofthe coronal and the sagittal slices. The point cloudthus created was joined to give localized surfacepatches. Gradually, some adjoining surface patches be-came larger surface models. These surface models in thesagittal plane and coronal plane were defined based onthe 3D point data sets in the sagittal plane and coronalplane of the glenoid fossa and the condyle. After the sur-face modeling, volume was added to the model. Thesystem of coordinates in this study consisted of theFHP, and the coronal and midsagittal planes, whichare the x-y, x-z, and y-z planes, respectively.

The MR images were converted from a regularblack and grey pattern to black and white pattern by us-ing the Centricity DICOM viewer. This improved theborder definitions of the bones and the soft tissues,thus helping in their identification. The posterior con-nective tissue, capsule, and the oblique and horizontal

Fig 5. Marked points categorized into 6 regions on theglenoid fossa: A, anteroposterior; B, mediolateral.

bands of the temporomandibular ligament had to be de-signed by using references to anatomic structures fromanatomy textbooks.39,40 After construction of the im-portant bones, the muscles were modeled. They wereessentially 3D bands of natural shape and contours.The actual thickness, length, and width were measuredon the Centricity DICOM viewer and fed into the modelfor accurate reproduction. The dental segments in bothjaws were modeled as 1 unit, assuming that they aresplinted into a single unit with a protraction appliance.Although the orbital cavity, the nasal cavity, and the an-terior regions of the maxilla and the mandible (Points Aand B) were not included in the MRI images, they werearbitrarily constructed to make the model more esthetic.For final corrections in the model, the important but su-perficial cephalometric measurements of the mandibularplane angle and the gonial angle were added to accu-rately represent the patient’s characteristics.

Fig 6. Marked points categorized into 6 regions on thearticular disc for measurement of stresses: A, antero-posterior; B, mediolateral.


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After the 3D-CAD model was fully constructed, itwas transferred to the ANSYS software (Fig 2). Here,it was discretized into finite elements. The model con-

sisted of 28,453 elements and 44,993 nodes. Whereasthe inside structure comprising the cancellous bonehad tetrahedral elements, the peripheral cortical areaswith irregular contours were optimized with triangularprism elements. The cartilage layers over the condylarhead and the glenoid fossa were given a uniform thick-ness of 0.5 mm according to the measurements by Hans-son et al.41 The cortical bone was modeled as a uniform1-mm thick layer under the cartilage layer and coveringthe cancellous bone. The disc and the posterior connec-tive tissue were discretized into tetrahedral elements.The capsule was discretized into hexahedral elementsand triangular prisms. Element discretization was re-peatedly examined and modified according to the distor-tion check tool in the ANSYS program.

Next, contact conditions were defined between var-ious parts to formulate various surface joints. This wasdone in pairs. Depending on the type of surface joints,

Fig 7. Stress contour plots showing various stresses on the condylar head: A, maximum principalstresses; B, minimum principal stresses.

Fig 8. Stress contour plots showing various stresseson the glenoid fossa: A, maximum principal stresses;B, minimum principal stresses.

Fig 9. Stress contour plots showing Von Mises equiva-lent stresses on the articular disc.


Table III. Various principal stresses (MPa) at the target position in the anteroposterior direction

Condylar head Glenoid fossa

Point Max Mid Min Mean Max Mid Min Mean

1 0.356 �0.197 �0.498 �0.113 �1.362 �1.599 �1.722 �1.561

2 0.245 �0.703 �0.796 �0.418 �1.993 �1.956 �2.343 �2.09733

3 �0.423 �1.186 �1.19 �0.933 �2.763 �2.715 �2.895 �2.791

4 �1.181 �1.464 �1.567 �1.404 �2.465 �2.947 �2.994 �2.802

5 �1.412 �0.943 �0.872 �1.07567 �2.149 �2.793 �2.885 �2.609

6 �1.423 �0.849 �0.716 �0.996 �1.782 �1.992 �2.502 �2.092

7 �0.359 �0.416 �0.538 �0.43767 1.239 �0.193 �0.469 0.192333

8 �0.432 �0.639 �0.732 �0.601 1.893 1.356 1.645 1.631333

9 0.134 �0.042 �0.221 �0.043 1.744 1.001 1.701 1.482

10 0.879 0.621 0.205 0.568333 2.285 1.653 1.943 1.960333

11 1.192 1.007 0.209 0.802667 2.294 2.029 2.197 2.173333

12 1.674 1.303 0.125 1.034 2.393 2.156 2.285 2.278

13 1.383 1.115 �0.132 0.788667 2.792 2.663 2.649 2.701333

14 1.333 1.11 �0.176 0.755667 2.799 2.735 2.699 2.744333

15 1.192 1.007 �0.169 0.676667 2.095 1.997 1.941 2.011

Max, Maximum; Mid, middle; Min, minimum.

various contact pairs (bonded, frictional, and so on)were generated manually. The ‘‘contact pair wizard’’tool was used to generate these pairs.

The physical properties—Young’s modulus andPoisson’s ratio—of the cortical and cancellous bones,articular disc, ligaments, and muscles were measuredas in previous studies (Table I).26-32,35,36

After creation of the 3D-FEM model, boundary con-ditions were defined. These conditions restrict un-wanted displacements of the model when subjected toforce. The model was restricted at the outer part of theskull at its most posterior superior edges. This way,even deformation and stress generation at the glenoidfossa could be shown. The simulation of the mandibularadvancement was done as in a construction bite. Themandible was advanced forward by 5 mm up to a ClassI molar relationship and opened vertically up to 4 mm.The loading condition was defined by the displacement

Fig 10. Principal stresses in the condylar head at thetarget position in the anteroposterior direction.

deformation by advancing the mandible forward. Themovement of the mandible (as one unit) was producedby feeding in the target positions of the condyle. Theconcomitant disc movement was also fed into the pro-gram. This gave a simple translatory motion for boththe mandible and the disc to the static target position.The target positions of the condyle and the disc weremeasured with the Centricity DICOM viewer. Thecenter of the condyle and the most anterior point onthe articular disc were identified and measured from 2reference lines (Fig 3, Table II). The CAD model wasfirst brought to the physiologic rest position, and this be-came the zero stress level condition for this model. Thestresses in the target position were considered relative tothis level.

Stress analysis was carried out at the target posi-tions by using the ANSYS software. Solutions were ob-tained at the following positions: mandibular condylarhead (principal stresses [s1, s2, s3]), glenoid fossa

Fig 11. Principal stresses on the glenoid fossa in theanteroposterior direction.


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Table IV. Various principal stresses (MPa) at the target position in the mediolateral direction

Condylar head Glenoid fossa

Point Max Mid Min Mean Max Mid Min Mean

1 �0.651 �0.798 �0.879 �0.776 �0.684 �0.596 �0.564 �0.61467

2 �0.752 �0.829 �0.921 �0.834 �0.827 �0.813 �0.789 �0.80967

3 �0.83 �0.859 �0.996 �0.895 �1.545 �1.4 �0.944 �1.29633

4 �1.21 �0.854 �0.995 �1.01967 �1.932 �1.894 �1.538 �1.788

5 �1.563 �0.997 �1.065 �1.20833 �2.149 �2.148 �2.214 �2.17033

6 �0.72 �0.723 �0.762 �0.735 �2.003 �1.894 �2.098 �1.99833

7 �1.203 �1.503 �1.989 �1.565 �1.774 �1.693 �1.993 �1.82

8 �1.432 �1.454 �1.732 �1.53933 �1.634 �1.623 �1.884 �1.71367

9 �1.293 �1.402 �1.655 �1.45 �1.194 �1.539 �1.758 �1.497

10 �1.121 �1.394 �1.534 �1.34967 �0.838 �1.425 �1.543 �1.26867

11 �1.112 �1.219 �1.392 �1.241 �0.759 �1.237 �1.246 �1.08067

12 �1.103 �1.094 �1.321 �1.17267 �0.677 �1.102 �1.202 �0.99367

13 �0.987 �1.049 �1.114 �1.05 �0.669 �0.852 �0.913 �0.81133

14 �0.893 �0.959 �0.998 �0.95 �0.696 �0.783 �0.874 �0.78433

15 �0.876 �0.894 �0.934 �0.90133 �0.787 �0.841 �0.923 �0.85033

Max, Maximum; Mid, middle; Min, minimum.

(principal stresses (s1, s2, s3]), and articular disc (VonMises equivalent stresses). The stresses were noted inthe above structures in both anterioposterior and medio-lateral directions at the 15 points selected on their sur-faces. Marked points were categorized into 6 regions onthe condylar head, the glenoid fossa, and the disc (Figs4-6).

RESULTS

The results of the FEM analysis showed the areas oftension and compression in the various parts of the TMJ.The values of maximum principal stresses (s1) are in-terpreted as the amount of tensile stresses generated in

Table V. Various equivalent Von Mises stresses (MPa) inthe articular disc at the target position in the anteropos-terior and mediolateral directions

Point Anteroposterior Mediolateral

1 0.427 0.402

2 0.401 0.425

3 0.334 0.438

4 0.274 0.825

5 0.207 0.619

6 0.179 0.576

7 0.136 0.543

8 0.128 0.599

9 0.129 0.549

10 0.169 0.497

11 0.262 0.457

12 0.321 0.434

13 0.393 0.427

14 0.432 0.421

15 0.473 0.412

the body. The values of minimum principal stresses(s3) normally have a negative sign and are interpretedas the amount of compressive stresses in the body; s2signifies middle principal stresses. Von Mises equiva-lent stresses (se) were picked up in the disc, and theseshowed the average stress levels in the disc (Figs 7-9).32

Analysis in the anteroposterior direction

The maximum principal stresses (s1) in the condylepeaked in the posterosuperior region (Table III, Fig 10).The highest tensile stresses were about 1.674 MPa atpoint 12 on the posterosuperior aspect of the condylarhead. Minimum principal stresses (s3) were locatedin the anterior and the anterosuperior regions of the con-dyle. The peak value of compressive loads of –1.567MPa was located in the anterosuperior region of the con-dyle and showed a gradual decrease toward the superiorregion of the condyle. The mean principal stress lineshowed the differential loading pattern of the condylein the anteroposterior direction, with compressiveforces concentrated in the anterior and anterosuperiorregions, and tensile stresses increasing from the poster-osuperior to the posterior direction.

Minimum principal stresses (s3) showed the great-est values in the glenoid fossa during the loading condi-tions (Table III, Fig 11). A maximum of –2.994 MPawas seen in the posterior slope of the articular eminencein the anterior region of the fossa. The loading pattern ofthe fossa in the anterior region was compressive witha negligible tensile component. Hence, even the valueof s1 was negative in the anterior and anterosuperior re-gions with peaking at –2.763 MPa. Maximum principal


stresses (s1) peaked in the posterior region of the fossaand measured 2.799 MPa at point 14. It was seen that,moving posteriorly, the tensile forces increased in theposterior regions of the fossa and remained so untilthe end of the post-glenoid spine.

Analysis in the mediolateral direction

Compressive stresses dominated the condyle headfrom the medial through the middle region to the lateralpoles (Table IV). Minimum principal stresses (s3)peaked in the middle region of the condylar head ata value of –1.732 MPa. The mean principal stress lineshowed that the highest compressive stresses were atthe top of the condyle, with submaximal peaks in the lat-eral region.

The mean principal stress line indicated that thestress pattern is essentially compressive in the glenoidfossa with the highest stresses in the lateral regions(Table IV). The medial and lateral poles showed lowercompressive loads.

In the articular disc in both anteroposterior and me-diolateral directions (Table V), Von Mises equivalentstresses (se) were concentrated in the anterior and pos-terior regions of the disc with greater stresses in the pos-terior region. Mediolaterally, the Von Mises equivalentstresses were concentrated in the lateral aspect of thedisc, with a peak value of 0.825 MPa.

DISCUSSION

The construction of a 3D-FEM model of the TMJ hasreached a high level of sophistication and accuracy. Ta-naka et al,28 DeVocht et al,29 Zhou et al,26 Beek et al,30

and Del Pozo et al36 did FEM studies on the TMJ. Thesehave contributed much information about the articularcartilage and the articular disc under compression statessuch as clenching, maximal biting, and conditions of in-ternal derangement and disc displacement.

This FEM of the TMJ was carried out to elucidatethe biomechanical reactions of this joint under the influ-ence of mandibular protraction with functional appli-ances. Simulation of the mandibular protraction todifferent positions was brought about by displacingthe mandible to the target position. I-DEAS NX CADsoftware was used to create the 3D computer model ofthe TMJ and the adjoining structures. This same soft-ware was used by Price et al42 and Tanaka et al32 to con-struct 3D models of the skull and the TMJ. Price et al42

found 0% to 8% error in the dimensions of the recon-structed condyle and disc models; this is consideredacceptable.

Elastic modulus of the articular disc has variationsin the values as investigated by various researchers.43-45

This is because that disc is most affected during normaland abnormal functions and also with age. In this study,we used the elastic modulus values of Zhou et al,26

because they also used an adolescent subject. Theygave different values to the anterior, intermediate, andposterior parts of the disc because of the different stiff-ness of the disc in each part. The elastic modulus valuesdid not vary much in this model, because at a young agethe disc as a whole is flexible.

Combined z-axis and y-axis displacements of thecondylar head and the disc were fed into the programfor simulation. The results gave a simple translatorymotion of the condyle and the disc to the target positionat which the stress distribution is measured. Since ourFEM study was a static analysis of the stress distributionat a particular mandibular position, it was sufficient tobring the condyle and the disc to that particular positionfor measuring the stresses. The path did not affect thestresses at the end position.

The maximum principal stresses (s1) in the condylein the anteroposterior direction were in the posterosupe-rior and posterior regions of the condyle. This meant thatthe maximum tensile stresses were generated in this re-gion. This result confirms the findings of Zhou et al,26

who also found the maximum tensile stresses in poster-osuperior region. They advanced the mandible 8 mm andopened it 4 mm, and their maximum value of s1 was 10kgf/cm2, or about 1 MPa. The appearance of the tensilestresses in our studies corroborated the results of Zhou etal,26 that when the condyle is distracted from its superiorcounterpart, it experiences a certain pull or tension in theposterosuperior direction. This can also be interpreted asa reduction in functional stresses in the condyle in thisregion.46 This is also the region where increased prolif-erative activity in the condylar cartilage has been re-ported. Histologic and radiographic evidence pointstoward remarkable changes in this posterosuperior re-gion after anterior mandibular advancement.1-9,20,21

This finding is supported by those of Kantomaaet al47 and Kantomaa and Perttiniemi,18 who concludedthat reduction in functional stresses in rats led to in-creased proliferation in the condylar cartilage postero-superiorly. Moss46 quoted the Heuter Volkmann law toexplain why the condylar cartilage responds to mandib-ular advancement. He stated that, when the mandible ispassively lowered in space, there is a tendency todistract its head away from its superior, functional articu-lating surfaces. As a response to this distraction, con-dylar cartilage proliferates. Voudouris and Kuftinec,48

in their ‘‘growth relativity hypothesis,’’ also concludedthat modification of the condyle and the fossa canbe clinically significant when the 2 structures areseparated.


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Compressive stresses in the anterior region up to thesuperior-most region of the condyle signify that a resorp-tive area is created in this region. With deposition poste-riorly and resorption superiorly, the condylar headgrows behind to attain functional contact with the gle-noid fossa. This pattern might also cause opening ofthe Stutzmann angle or redirect condylar growth morehorizontally.49 The radiographic study of Williams andMelsen14 and the laminagraphic study of Birkbaeket al50 also confirm the same; they found that condylargrowth direction changed from 120� in the control groupto 132� in the experimental group. This was also foundto result in anterior rotation of the mandible that is favor-able for basal sagittal correction.

Our most conspicuous finding was that maximumtensile stresses appeared in the posterior region of theglenoid fossa with a maximum value of 2.999 MPa.The tensile stresses dominated from the middle region(roof of the fossa) up to its whole posterior region.This region corresponded to the attachment of the pos-terior connective tissues from the posterior aspect of thedisc to the anterior surface of the post-glenoid spine.Thus, it is natural to conclude that the stretch from theposterior connective tissues created a high tensile-valuearea in this region of the fossa. Tensile stresses in the up-per parts of the post-glenoid spine could be due to lossof articulation with the condyle. Histologic studies ofWoodside et al10,12 and Hinton and McNamara11 con-firmed the appearance of new bone in this region inresponse to the stretch of retrodiscal tissues. Wies-lander,13 Paulson et al,15 and Ruf and Pancherz16 con-firmed these findings radiographically as new boneformation with the double contours in these locationsin the fossa articularis.

The articular eminence was uniformly loaded withcompressive stresses. Resorption in this region can beexplained by the intramembranous nature of the fossa,which naturally responds to compressive forces by re-sorption. Hinton and McNamara11 showed that, afterprotraction of the mandible, an extremely thin layer ofcartilage on the eminence was found, although a highdensity of hypertrophic cells was seen on the crest ofthe eminence. This mechanism was also shown radio-graphically by Wieslander,13 Vargervik and Harvold,51

and Paulson,52 who found that the glenoid fossa relocatesanterioinferiorly; this is possible by resorption along theposterior slope of the articular eminence and depositionalong the anterior slope of the post-glenoid spine.

The loading pattern of the disc corresponded faith-fully with those of the condylar head and the glenoidfossa in both anteroposterior and mediolateral direc-tions. A coherent pattern of stresses in the condyle,disc, and fossa supported the widely held notion that

the disc functions as a stabilizer and modulator ofstresses generated in the joint with mandibular move-ments. This implied that the model constructed in thisstudy was anatomically and functionally accurate.

CONCLUSIONS

A pattern of stresses is created in the TMJ when themandible is protracted with a functional appliance.Whether this pattern remains the same during all treat-ment and whether all biologic tissues respond in a simi-lar predictable manner over time are not known. Thelimitation of an FEM study is that it can record onlyinstantaneous stress patterns.

In this study, we elucidated the stress patterns cre-ated in the TMJ by simulated mandibular protractionof a functional appliance. Our findings suggest thatthe remodeling response of the condylar cartilage andthe glenoid fossa to mechanical forces might be corre-lated with the location of tensile and compressive stresspatterns.

This stress pattern might change with changes in thedimensions of the construction bite. The effects of vary-ing the heights of the construction bite on the stress pat-tern in the TMJ will be investigated in the part 2 of thisarticle.

The authors acknowledge the contributions of DrRajesh Kuril, Dr Narendra Sharma, and Dr ChanjotSingh during the course of the study; and Dr Anil Nafriafor editing and proofing of the article.

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Documents

Stress distribution in the temporomandibular joint after mandibular protraction: A 3-dimensional finite element method study. Part 1