A New Numerical Model to Analyze Stress Distribution of TMJ Disc from 2-D MRI Scans

From the anatomical and biomechanical points of view, temporomandibular jo int (TMJ) is sophisticated bicondylar articulatory complex with great demand on neuromuscular control with a frequency of motion indicated up to 2000 periods per day. This makes the TMJ one of the most frequently exerted joints of the human body and in conjunction with individual uniqueness of this joint places high demand on its design and reliability. Experimental studies concerning the distribution of the loads in the TMJ have been performed on an imal models. Numerical modeling provides more understanding of joint physiology and pathogenesis of the joint diseases. Magnetic resonance imaging (MRI) has replaced computed tomography (CT) and arthrography as the primary modality in the evaluation of the TMJ. At this study a new numerical method are used to build 3-D model of TMJ from 2-D MRI scans and applied some stress-strain analysis to validate this model for different normal and abnormal patients. These models are based on multi-ob ject reconstruction technique and tetrahedral elements building


Introduction
Temporo mandibular jo int (TMJ) is one of the profusely operational jo ints in the body; its disorders are also quite common. It is an estimate that 20 to 25% of the population suffers fro m a temporo mandibular d isorder (TM D), whereas only 3 to 4% of sufferers get suitable treatment. [1] Co mmonly TMDs are caused by malfunctioning of the following parts of the TMJ: art icular d isc, articu lar cartilage, muscles at the jo int, ligaments, teeth [18]. These may lead to TMDs like the pain dysfunction, Bru xism, arthrit is or internal irregularit ies [2][3][4][5]. The malfunctioning of the parts of the TMJ can be as follo ws: • Internal disarrangement of the articular disc causing it to slip out of its normal position in the joint capsule.
• Wearing out of the art icular disc due to continuous joint overloads, which might be due to clenching of teeth during sleep or teeth grinding, imp roper chewing pattern or excessive use of chewing gums.
• Wearing out of the joint cartilage may be caused due to arthritis, fatigue in the muscles of mastication, ligament tear or irregularities in teeth align ment. [6] The TMJ is anatomically structured to withstand loading d u ring mas tication d ue to its mech an is m o f s tress absorption and energy dissipation. The presence of the TMJ disc and articular cartilage is believed to prevent load concentrations. The cancellous bone of the mandibular condyle can resist compressive and tensile deformations during loading of the TMJ with min imu m amount of bone mass due to its plate-like trabecular structure. The loading in the TMJ could stimulate remodeling, involving increased synthesis of the extracellu lar matrix. [7][8][9][10][11][12] Experimental studies concerning the distribution of the loads in the TMJ have been performed on animal models. The number of such studies is limited, because it is difficu lt to implement experimental devices, such as strain gauges, into the joint and not to cause damage to its tissues without influencing their mechanical behavior. Mathematical models of the hu man masticatory system including the TMJ were found as a powerful tool to predict the loads acting on this joint. Ho wever, many studies have oversimplified the geometry of the TM d isc. Therefore, the tissue deformations and the distribution of loads inside the joint could not be analyzed properly. [7] The fin ite element (FE) method has been largely used in dental biomechanics to understand the stresses and the deformations in the normal mandibles to simu late the motions of the TMJ components to analyze the stress distribution in the two discs and ligaments of each side during nonsymmet rical movements of a healthy joint to analyze the differences in the stress distribution of the TMJ between subjects with and without internal derangement and so on. The FE method has been proven to be a useful tool for evaluating the mechanical quantities of TMJ. The biomechanical environ ment in the TMJ is a key to understand the origin and progression of temporo mandibula r d isorders, so the reasonable modeling is also useful for clin ical practice. [13][14][15][16][17][18].
Magnetic resonance imaging (MRI) has replaced computed tomography (CT) and arthrography as the primary modality in the evaluation of the TMJ. Direct visualizat ion of the disk afforded by M RI is a d istinct advantage over arthrography. [19] Despite the superior resolution of CT and limited visualizat ion of cortical bone by MRI, most osseous pathology is accurately depicted. [20] Intra-articu lar abnormalit ies are readily visible on MRI images, providing further informat ion not available with other imaging modalities. [21] A small surface coil is placed over the TMJ; a bilateral examination can be performed with coupled coils. Images are obtained in the open-and closed-mouth positions to assess the position and reducibility (or recapture) o f the articular disk. Th is is facilitated by placing a specialized device in the patient's mouth to keep it open and by instructing the patient to bite down on it for the closed-mouth views. Fro m axial localizing images; sagittal and coronal planes are prescribed. Imaging is most commonly performed in these planes in order to document the position of the disk. Ob lique sagittal and coronal images can be oriented to the condyle, but are unnecessary to demonstrate internal derangements.
T1-weighted sagittal images are the cornerstone of the TMJ examination; the anatomy is clearly depicted, and the imaging p lane is optimal for assessing articular d isk position and for visualization of osseous and disc tissues, T2-weighted images are useful for detecting degenerative periart icular changes and the presence of a jo int effusion. [22] Fat saturation or inversion recovery renders these findings more conspicuous. Gradient-echo techniques have been imp lemented to obtain cine-loop mot ion studies. Three-dimensional volu me acquisitions allo w a volu me of tissue to be imaged rapidly and subsequently viewed in any plane. The use of intra-art icular and intravenous gadolinium may provide utility in certain clinical instances for instance, the inflamed synovium or an in flamed arthropathy will avidly enhance after the administration of intravenous gadoliniu m. [23][24][25] Hence the aim of this study was conducted to analyze the stress distribution patterns in the disc displacement, of the human TMJ fro m MRI with and without wearing of anterior repositioning splint and the ability of the splint to reduce disc displacement when the muscle loads are applied. A fin ite element technique was used to achieve this purpose. The goals of this technique are, first the develop ment of a new finite element model of a hu man TMJ fro m 2-D images and the surrounding bone, and second is to analy ze the stress/strain patterns developed in the TMJ when the physiological loads are applied and compare to human models of TMJ. The first goal is co mprised of t wo stages: the first stage develops a solid model fro m a M RI scan and the second stage creates a finite element mesh using this solid model and assigns suitable materials to this mesh. The second goal involves selecting relevant loads and boundary conditions. The final step is to obtain the stress/strain patterns within the TMJ by using a suitable force scenario and then compare those patterns with those obtained from human models. This finite element model of the TMJ will predict the stresses that help clinicians to understand how the TMJ behaves for a particular loading condition. So that in turn, they can develop a better clinical treat ment fo r the TMJ disorders.

Materials and Methods
This study included ten patients with symptoms of TMJ pain, jo int noises, limitation of jaw opening, tenderness located in the articular region. Their age ranged between 25-45 years. A ll the patients, selected, were partially edentulous with bilateral missing of posterior teeth. They underwent a complete history, clinical examination, and diagnostic MRI. The clin ical d iagnosis was based on the presence of clicking on auscultation, tenderness of the lateral or posterior aspect of the TMJ and local pain associated with mandibular movement directly to the TMJ. Prosthetic construction: For all the patients clear hard acrylic mandibular anterior repositioning splint was constructed. The splint was tried in the patient's mouth while closing in the forward position. All adjustments were performed with simu ltaneous contact in the stabilized fo rward position was obtained. The patients were instructed to wear the appliance continuously for two months. They were allo wed to discontinue only during brushing their teeth and during meal. The patients were seen at weekly intervals for necessary adjustment of the splint [26].

Magnetic Resonance Image
MRI was performed without insertion of disc repositioning appliance. The scanning was done for both right and left joint for confirming the presence of displaced disc .It was made with 1.5 Telsa M RI systems with TMJ surface coil 6.0cm in diameter (M RI, Philips Gyroscan). The scan parameter was adapted for every patient to fulfill the best spatial resolution for the image (TE 20, TR450, and FOV 130/1.7).The degree of d isc displacement was classified as follow: Less than half the disc d isplaced anteriorly to the anterior turbercle of g lenoid fossa (grade I), All the disc displaced (grade III), Less than full disc displacement (grade II). The scanning was done for both right and left jo int in closed -open mouth position. Then MRI and rescanning was performed after the two months of insertion of mandibular repositioning appliance with jaw in the splinted position and in opened positing for both right and left joint. The success of treatment method was assessed according to the criteria of disc capture, mentioned by Kurita et al [26]. Co mplete disc capture, part ial d isc capture, and no disc capture which is analy zed and confirmed by FE model.

Fi nite Element Study
Any finite element study needs five basic inputs to accomplish the analysis. [27] These are the geometry, mesh, material properties, loads and boundary conditions. The model used in this study based on the MR images from displaced disc and after capture by anterior repositioning mandibular splint to study the distribution of stresses in complete capture, part ial capture and in no capture.

Geo metry Creat ion
For the 2-D M RI that used, the image scanned to evaluate the contour of the TMJ disc and their contacts as shown at Figure 1 by segment the image to different zones and eliminate the undesired regions and then the all contours are assembled to calculate the 3-D model.
As the TMJ is comprised of the temporal bone, articu lar cartilage, articular disc, ligaments and the mandible arranged as shown in Figure 1, where: 1-Anterior band of articular disc, 2-Art icular disc, 3-Articu lar tubercle (eminence), 4-Glenoid fossa, 5-Inferior joint space, 6-Intermediate (central) thin zone, 7-Lateral pterygoid muscle raphe, 8-Lo wer head of lateral pterygoid muscle, 9-Mandibular condyle (head), 10-Mandibular condyle articulating surface, 11-Mandibular condyle marrow, 12-Posterior band of articular d isc, 13-Posterior disc attachment, 14-Superior joint space, 15-Upper head of lateral pterygoid muscle. In this study, assuming symmetry between the right and left TMJs only the left TMJ of a human was modeled. The current model includes the mandib le, the articular d isc, the surrounding part of the temporal bone and the ligaments. [28,29] The articular cart ilage was ignored in the current model. The geometry of the d isc was created manually fro m the surface models of the mandible and part of the temporal bone. The articulating surface of the mandibular condyle was extracted fro m its surface model as shown in Figure 2 (A), using Dico mesher (1). This surface formed the lower surface of the articulating disc. The articulating surface of the temporal bone shown in Figure 2 (B) was extracted similarly to the mandible. After extracting the surfaces for the lower and upper region, the next step was to combine the two surfaces in a single model as shown in Figure 2(C) and connect them. Both the extracted surfaces were imported into one file. The medial, lateral, anterior and posterior geomet ry was appro ximated [9] by manually generating elements to connect the two surfaces and form closed surface defining the disc, as shown in Figure 2 (D).
The articular d isc is not of uniform thickness, as was the case here. The disc thickness varied as we moved fro m anterior to posterior and lateral to medial directions. The disc was thinnest in the intermed iate zone where its thickness was 0.25 cm. It was thickest in the posterior region where its thickness was 0.63 cm. The thickness in the anterior part was 0.42 cm. To co mp lete the TMJ geometry, the final addit ion was the ligaments. In this study, the posterior ret rodiscal ligaments both superior and inferior [29,6] and the TMJ ligaments [15,16] were included, as shown in Figure 3.
The ligaments were added to the model after the solid meshes of the bones and the disc were generated and combined. The ligaments were introduced as linear springs. The node to node spring connections were used, as shown in Figure 4. Nodes for the insertion and origin of ligaments were picked according to Almora [31] and visual inspection of human TMJ models.

Mesh Process
As the surface models of the mandible, the temporal bone and articular disc were ready, the next step was to generate 3-D solid meshes of them and combine them into one model. For this purpose surface models of each of the three entities were imported as (STL: surface tessellation of bone components). Meshing divides an entity into a fin ite number of s mall elements. [29] In solid meshing the hollow solid is meshed internally to form a solid mesh. Solid meshing was done using the Patran tetrahedral meshing provided. Patran tetrahedral meshing preserved the triangles of the surface mesh wh ile the solid mesh was generated. [32] The solid mesh developed contained 4 nodes tetrahedral elements as shown in Table 1.
To generate the mandib le solid mesh, the mandible surface model was imported. Then this surface model was checked for presence of any cross elements and inside out elements. The overlapping elements are referred as cross elements and the elements a having surface normal directing in wards to the solid are referred to as inside out elements. [33] Then, using the sweep co mmand the nodes within a d istance of 0.001 cm fro m each other were combined as one node, to form the closed surface so that solid meshing can be done. Sweeping these nodes also helps to remove cross elements. After these checks on the surface model, the Pat ran tetrahedral meshing was invoked and a solid mesh of the mandib le was generated with 4 nodes tetrahedral elements.

Material Properties
The material properties of the articu lar d isc were considered to be linear elastic. In the enhanced model, a non-linear material model defined the articular disc as Mooney-Rivlin solid. The disc was considered to be homogenous and isotropic for both the early as well as the enhanced model. The mandib le and the temporal bone were considered to be linear elastic for both the early and enhanced models. [9, 14, 28, and 34] Linear material model the linear material propert ies are given in Tab le 2.
The material properties were assigned to the individual solid meshes of the articular disc, the mandib le and the temporal bone using material properties option, where E is the elastic modulus specified in MPa, and s for the Poisson's ratio and k for the spring stiffness. Source colu mn indicated the original source fro m where these values have been taken.

Loads and Boundary Conditions
There are t wo loading conditions used in the literature for TMJ finite element simu lations. The first uses condylar displacement and second uses muscle forces. Th is study uses muscle forces as point loads for loading the joint. The primary muscles of mastication are the masseter, the lateral and medial pterygoid and the temporalis [35][36][37][38]. The magnitudes of the muscle forces are obtained fro m Herring in wh ich she reports the maximu m possible muscle tension for each muscle [39]. Herring first calculated the cross sectional area of each muscle. The maximu m muscle force was taken as being directly proportional to the cross sectional area of the muscle.
Herring used the constant value of 40 N/cm2 to calculate the maximu m possible muscle tension for each one and the inclination of these muscle forces. The inclination is the angle between the lines of act ion of the muscle fo rces and the occlusal (bite) plane. The line of action for each muscle was obtained by tracing their respective points of insertion and origin. The angles were measured fro m the right lateral direction, in an anticlockwise sense by a protractor. [39,40] Herring reports that the accuracy of these measurements is within 5%. The details about the muscle forces are mentioned in Table 3. Position of the muscle forces are given as the x, y, z coordinates of the node referred as node id. The magnitude of force is given in Newtons. Inclinations are the angles made by the muscle force vectors with the occlusal plane. In the last column the x, y, z co mponents of muscles forces is specified.

Contact
As discussed earlier, there are two contact regions in the TMJ. The first contact region is between the TMJ disc and the surface of the temporal bone and the second region is between the TMJ disc and the mandibular condyle surface. [23] The contact definit ions used to define the nature of contact in these regions were touching contact model between the temporal bone and the articular disc [16] and glue contact between mandib le and articu lar d isc. These contact definitions were used with each of the material model. Table 4 lists all the TM J models examined under this study.

Results and Discussion
Stresses are loaded to the 3-D meshed model as shown at Figure 4 to show the d ifference between normal and displacement disc.
Condylar and temporal cart ilage layer along with the TMJ disc play an important role in stress distribution. The presence of TMJ disc and cartilage is believed to prevent load concentration. The cancellous bone of the mandibular condyle can resist compressive and tensile deformation during loading of the TMJ with min imu m amount of bone mass due to its plate-like trabecular structure. [8,11,12] The loss of posterior teeth with subsequent abnormal loading of the TMJ leads to histomorphological, pathological and pathophysiological changes in the articular cartilage, the articular d isc, synovium and bony articular component. The behavior shows the inability of the neuromuscular system to achieve a reduction of the muscular activ ity in the edentulous side. [41,42] MRI assessment used in this study because it's very fast, very sensitive, accurate imaging modality, curative single screening method to assess the success of the prosthetic treatment of TMD [ 9,15,43]. Although CT can be used but they are applicable only for assessment of density and mineralizat ion degree of the bone and cartilage, so translation of this parameter to a load bearing capacity cannot be performed adequately without biomechanical models and measurement.
In this study, the anterior displaced disc were captured by anterior mandibular repositioning splint to show a clinical and MRI successful treatment, then a FEA was used to analyze the stress distribution in the disc because of high incidence of false negative results judged by clinical examination. FEA has been successfully used in this field because it enables us to estimate stresses in the TMJ without invasive approach and also examine not only the pathological status of the joint but also the 3-D relationship among them. [26,43] In normal TMJ fin ite element analysis showed a normal distribution of stresses in all the region of the disc .This may be attributed to the disc that well adapting to the histological features and plays an important role in the cushion of intra-art icular stress during its conduction .The disc has been shown to exhib ite v iscoelastic properties through its function as a stress absorber and stress distributor which prevent excessive stress concentration in the cartilage and bone components of the joint and also prevent damage fro m abnormal p rolonged stress . [35,42,43] The distribution of stress in the grade II displaced disc in our study showed non-uniform stress distribution which may be due to an abnormal relat ionship between the articular d isc and condyle. As the disc is forced out of the correct position there is often bone to bone contact which creates surface roughness, additional wear and tear on the joint, and often causes the TMD to worsen. Disc displacement induces change of stress distribution in the disc between articular surfaces, resulting in the secondary tissue damage and change in mechanical propert ies of the disc(loss of stress absorber function ) The d isc displacement in the closed mouth position, usually anteriorly, due to weakness of the discal ligaments . [1,18,28] Von mises stress distribution after using acrylic anterior mandibular repositioning splint in grade II disc displacement showed a uniform distribution of stresses as confirmed by the MRI may be contributed to the forward repositioning of the mandib le, keep ing a normal disc, condyle, glenoid fossa relationship, and avoiding the click resulting fro m the ju mp ing of the condyle below the posterior margin of the anteriorly displaced disk, causing the click. Also, acrylic splint has also the advantageous action of assisting the unloading of the joint and enhance adaptation of retrodiscal tissues [44]. Furthermo re, the acrylic splint reduced the microtrau ma to joint and condylar displacement, thus reducing the inflammat ion and cytokines release. Grade II displacement had the liability to change to grade I which captured by the splint. The Von mises distribution of grade III disc displacement showed a high stress distributed all over the disc which indicates that it's the worst type of displacement and with the least improvement by this method of treat ment. So another treatment modality should be used.

Conclusions
In conclusion, MRI is an objective method for examination of d isc displacement before and after treat ment with no radiation hazard to the patient, where the anterior mandibular repositioning prosthetic splint was absolutely necessary to improve the variation of abnormal disc -condyle relat ionship caused by partial loss of teeth as documented by the MRI image processing with fin ite element analysis, which are used as numerical method to evaluate the stresses for normal and abnormal disc.
Understanding of the biomechanical environment of the TMJ is essential for successful treatment and this are provided by mixing between image processing technique with FE methods, finally Grade III disc displacement is a sign of bad omen in the way of anatomical repositioning of the disc affecting different modalit ies.