Medical Engineering & Physics 25 (2003) 107–113www.elsevier.com/locate/medengphy

Effects of condylar fibrocartilage on the biomechanical loading ofthe human temporomandibular joint in a three-dimensional,

nonlinear finite element model

Kai Hu a, Rong Qiguob, Jing Fangb, Jeremy J. Maoa,∗

a Tissue Engineering Laboratory, Departments of Orthodontics and Bioengineering, University of Illinois at Chicago, Chicago, IL 60612, USAb Department of Mechanical Engineering, Peking University, Beijing, People’s Republic of China 100871

Received 17 August 2001; received in revised form 10 June 2002; accepted 9 October 2002

Abstract

The present study was undertaken to test a hypothesis that the addition of articular fibrocartilage in the condyle of the temporoman-dibular joint reduces three-dimensional stress distribution in the condyle, the disc and articular eminence. A three-dimensional,nonlinear finite-element model was developed for analysis of joint loading before and after the addition of condylar fibrocartilageto the osseous mandibular condyle reconstructed from spiral computer topography data. In the model, each of the disc, condyleand articular eminence was arbitrarily divided into five regions: the anterior, posterior, medial, lateral and central. Von Misesstresses that in virtually all regions of the disc, condyle and articular eminence became lower after the addition of condylar fibrocart-ilage. Especially remarkable was the approximately four-fold reduction in von Mises stresses in the anterior, central and medialregions of the mandibular condyle. In comparison, only slight to moderate stress reductions occurred in the disc and articulareminence, suggesting that condylar fibrocartilage absorbs considerable stresses and likely dampens more loads than the disc andarticular eminence. The mandibular condyle demonstrated the largest total displacement in all directions after the addition of articularfibrocartilage, followed by the disc and articular eminence. We conclude that the addition of articular fibrocartilage primarily reducesloading of the mandibular condyle, rather than the disc and articular eminence. These findings lead to a hypothesis that the mandibu-lar condyle more likely functions as a shock absorber than the disc. 2002 IPEM. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Joint; Cartilage; Finite element; Force; Biomechanics

1. Introduction

The temporomandibular joint (TMJ), like many othersynovial articulations, is composed of two articulatingbones covered by cartilage and with an articular disc inbetween. Unlike many other synovial articulations, thearticulating surfaces of the TMJ consist of fibrous tissueand fibrocartilage in a number of vertebrate species thathave been studied [1–3]. Although finite element modelshave been increasingly used to determine stress distri-bution among various joint components, few modelshave incorporated articular fibrocartilage of the man-

∗ Corresponding author. Tel.:+1-312-996-2649; fax:+1-312-996-7854.

E-mail address: jmao2@uic.edu (J.J. Mao).

1350-4533/03/$30.00 2002 IPEM. Published by Elsevier Science Ltd. All rights reserved.doi:10.1016/S1350-4533(02)00191-1

dibular condyle [4]. This is surprising because condylarfibrocartilage is not only an integral component of theTMJ, but also adapts considerably to sustained mechan-ical loads in vivo [3,5–8]. In a finite element model ofthe mandibular condyle that has incorporated propertiesof femoral cartilage, compressive and tensile stresseswere applied to different regions of the condyle and discreconstructed from a dry human skull [9]. However,there has been no comparison of loading of various jointstructures with or without addition of articular fibrocart-ilage in the mandibular condyle.

While the great majority of finite element models ofthe TMJ have incorporated linear simulation, nonlinearsimulation is of interest for its potential to better mimicin vivo biological loading. Previous two-dimensionalnonlinear models of the human TMJ have identifieduneven distribution of stresses among various joint

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components [10,11]. Recently we constructed a three-dimensional nonlinear finite element model from in vivospiral computerized topography (CT) data [12].Additionally we have obtained region-specific propertiesof articular fibrocartilage of the rabbit mandibular con-dyle by nanoindentation with atomic force microscopy[13]. These experimental data on the biomechanicalproperties of articular fibrocartilage of the mandibularcondyle provide more realistic conditions for finiteelement modeling. In the present study, we incorporatedour previous experimental data on region-specificproperties of condylar fibrocartilage in the three-dimen-sional nonlinear finite element model to test the hypoth-esis that the addition of articular fibrocartilage in themandibular condyle reduces three-dimensional loadingnot only of the condyle, but also the disc and articulareminence.

2. Materials and methods

2.1. Ingestion and transformation of TMJ numericalimage

Construction of the three-dimensional finite elementmodel was described in detail elsewhere [12]. Briefly,the right temporomandibular joint of a healthy adultfemale volunteer (age: 38.5 years) was used to build themodel. The subject had complete dentition and was freefrom any clinical disorders of the temporomandibularjoint. The subject’s mandible was scanned on the rightside from the chin to the condylar head using a PhilipsTomoscan SR 7000 CT scanner and Easy Vision CT/MRR2 workstation (Philips Medical, Amsterdam, TheNetherlands). A total of 36 serial CT scans in 1.5 mmincrements was obtained. An edge detection algorithmwas run with Adobe Photoshop 4.0 (Adobe, San Jose,CA) to distinguish cortical bone from cancellous boneand to detect the boundary of various components of themandible. After the boundary and reference coordinateswere exported in Auto-CAD format, the bitmap coordi-nates were changed to the real coordinates for export toDXF format by smooth shift and pro rata zoom. Thepresent study was approved by IRB.

The three-dimensional (3-D) image reconstruction andsolid modeling were conducted using ANSYS 5.3 finiteelement (FE) program (Swanson Analysis Systems,Houston, TX). The boundary coordinates were directlywritten to the ANASYS command by custom developedsoftware. The boundary lines were generated step by stepfor varying surfaces and solids using the solid modelingmethod in the ANSYS program. Upon reconstruction ofthe condyle and articular eminence, a disc was addedbetween them with a uniform thickness of 2 mm [14].Articular fibrocartilage with a uniform thickness of 0.2mm [15] was added to the bony surface of the mandibu-

lar condyle. Construction of the entire model with theaddition of the disc was completed by ANSYS 5.3 pre-processing program software. The structures of the con-dyle, disc and articular eminence were regarded as a con-tinuous integer. The solid model was freely meshed witha tetrahedron element. The common contact surfacesamong the condyle, disc and articular eminence weremeshed again, using the 3-D point-surface contactelement of ANSYS 5.3’s Contact Element Storeroomwhich enabled contact and glide between the upper andlower surfaces of the disc in three dimensions. The final3-D non-linear FE model consisted of 1967 nodes, 7618solid elements and 115 contact elements as shown inFig. 1.

Fig. 1. A: Three-dimensional, nonlinear finite element model of thehuman temporomandibular joint including the mandible, the articulardisc and articular eminence. Joint loading was simulated along thelong axis of the mandibular ramus. B: Schematic diagram showing thearticular eminence (AE) of the temporal bone, mandibular condyle (C)and the disc (indicated with an arrow).

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Table 1Three-dimensional muscle force vectors and physiological cross-section areas (PCS) of masticatory muscles during centric occlusiona,b

Muscles PCS (cm2) Muscle force vector (Left) Muscle force vector (Right)

Superficial masseter 5.7 43.7i � 88.4j � 186.4k �43.7i � 88.4j � 186.4kDeep masseter 2.3 46.7i � 30.5j � 64.5k �46.7i�30.5j � 64.5kMedial pterygoid 4.4 �60.1i � 46.1j � 97.9k 60.1i � 46.1j � 97.9kAnterior temporalis 4.3 23.2i � 6.9j � 154.0k �23.2i � 6.9j � 154.0kMiddle temporalis 2.6 20.5i�78.0j � 43.8k �20.5i�78.0j � 43.8kPosterior temporalis 2.0 14.5i�59.5j � 32.0k �14.5i � 59.5j � 32.0kSuper lateral pterygoid 0.8 �8.8i � 10.6j�2.4k 8.8i � 10.6j � 2.4kInferior lateral pterygoid 1.4 �13.3i � 11.3j � 1.3k 13.3i � 11.3j � 1.3k

a i,j and k represent x, y and z directions.b From Osborn and Baragar [16]; Korioth and Hannam [17]; Koolstra et al. [18].

2.2. Loading of TMJ articular components in the finiteelement model

Joint loading was simulated by incorporating 16 mus-cle force vectors of bilateral masticatory muscles,namely the superficial and deep masseters, the anterior,middle and posterior temporalis muscles, the medialpterygoid, and the superior and inferior lateral ptery-goids. Upon anatomic assignment of muscle attach-ments, physiological cross-sectional areas (PCS) and 3-D muscle force vectors were defined, as shown in Table1, from previous work [16–18]. The biomechanicalproperties of the cortical and cancellous bone [19,20],and the elastic properties of the articular disc of the man-dible [21], were defined as shown in Table 2. The surfacenodes of the mandible were assigned to the propertiesof the cortical bone, whereas internal nodes wereassigned to the properties of the cancellous bone. Theelastic moduli and Poisson’s ratios of different regions ofarticular fibrocartilage of the mandibular condyle werederived from our previous data, shown in Table 3, usingnanoindentation with atomic force microscopy [13]. Thearticular surfaces of the disc, mandibular condyle andarticular eminence were each arbitrarily divided into fiveregions: anterior, central, posterior, medial and lateral asshown in Fig. 2A. The joint reaction forces were evenlyallocated to both the left and right condyles and weredetermined during centric occlusion. The boundary con-ditions involved constraining all the degrees of freedom

Table 2Mechanical properties of various components of the TMJa

Material Elastic modulus (MPa) Poisson’s ratio

Cortical bone 1.37 × 104 0.3Cancellous bone 7.93 × 103 0.3Articular disc 4.41 × 10∗∗b 0.4

9.24 × 10∗∗∗b 0.4

a From Huiskes [19]; Carter and Hayes [20]; and Tanne et al. [21].b ∗∗ Stress � 1.50 MPa; ∗∗∗ Stress � 1.50 MPa.

Table 3Mechanical properties of different regions of condylar cartilagea

Regions Elastic modulus (MPa) Poisson’s ratio

Anterior 2.34 0.46Central 1.48 0.39Posterior 1.51 0.41Medial 1.11 0.38Lateral 0.95 0.31

a From Hu et al. [13].

for 43 nodes at the superior border of the temporal boneand 50 nodes at the occlusal surface to simulate jointloading and restrain rigid-body motion of the mandible.Stress analysis was performed by ANSYS 5.3 post-pro-cessing program. The von Mises stresses and maximumthree-dimensional displacements of all joint componentswere determined by calculating the averages of six nodesper region.

3. Results

Von Mises stresses of the disc, mandibular condyleand articular eminence changed after addition of condy-lar fibrocartilage (Fig. 2B, C and D) with Fig. 2A servingas a guide for dividing each of the disc, mandibular con-dyle and articular eminence into five regions. Especiallyremarkable was the approximately four-fold reduction invon Mises stresses in the anterior, central and medialregions of the mandibular condyle (Fig. 2B), in compari-son with slight to moderate stress reductions in the corre-sponding regions of the disc and articular eminence (Fig.2C and D, respectively). The posterior and lateralregions of the disc, mandibular condyle and articulareminence showed only slight reductions in von Misesstresses (Fig. 2B, C and D).

The maximum three-dimensional displacements ofvarious joint components were both remarkable andchanged considerably by the addition of condylar fibro-

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Fig. 2. A: Arbitrary division of the articular disc and mandibular condyle into five regions: anterior, central, posterior, medial and lateral. B, Cand D illustrate von Mises stresses in the mandibular condyle (B), the articular disc (C) and articular eminence (D) with or without the additionof condylar fibrocartilage (dark and open histograms, respectively). In contrast to the approximately four-fold reductions in von Mises stresses inthe anterior, central and medial regions of the mandibular condyle (B), only slight to moderate stress reductions are present in both the disc andarticular eminence (C and D, respectively).

cartilage. The disc, mandibular condyle and articulareminence all showed complex displacement patterns,moving upwards, posteriorly and medially (Table 4).The mandibular condyle demonstrated the largest dis-placement before addition of condylar fibrocartilage, incontrast to minimal displacements of the disc and articu-lar eminence. As shown in Table 4, the addition ofcondylar fibrocartilage resulted in increases in the three-dimensional displacements of the mandibular condyle inall directions, including the horizontal and lateral direc-tions (HLD), the horizontal anteroposterior direction(HAPD) and the perpendicular direction (PD) and their

Table 4Effects of addition of condylar fibrocartilage on the three-dimensional displacement (µm) of joint componentsa

HLD HAPD PD SUM

With FC Without FC With FC Without FC With FC Without FC With FC Without FC

Disc �9.214 �2.743 �10.270 �7.319 11.600 4.770 14.220 7.899Mandibular codyle �96.100 �165.400 �56.080 �113.300 63.520 80.880 111.500 182.700Articular eminence �0.023 �0.016 0.101 �0.090 0.035 0.028 0.104 0.090

a FC: fibrocartilage; HLD: horizontal lateral direction; HAPD: horizontal anterioposterior direction; PD: perpendicular direction; SUM: vectorsum of maximum displacement; Positive values indicate the anterior, lateral and upward displacements; Negative values indicate the posterior,medial and inferior displacements.

vector sum (SUM). In contrast, the three-dimensionaldisplacements of the disc and articular eminence werereduced in all directions, including HLD, HAPD, PD andSUM, albeit small magnitudes (Table 4).

4. Discussion

Our initial hypothesis that the addition of articularfibrocartilage in the mandibular condyle reduces three-dimensional loading not only of the condyle, but the discand articular eminence is also partially satisfied.

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Whereas von Mises stresses in the mandibular condylewere reduced considerably by approximately four-foldin the anterior, central and medial regions, little stressreductions were present in the disc and articular emi-nence. The anterior, central and medial regions of themandibular condyle are considered important functionalregions that sustain masticatory loading [22,23]. A lackof simultaneous increases in stress magnitude in the pos-terior and lateral regions of the disc, mandibular condyleand articular eminence indicates that stresses have beeneffectively transmitted to other skeletal components ofthe skull that are not measured in the present finiteelement model. For instance, the zygomatic arch canexperience the significantly higher bone strain inducedby loading the dentition than regions adjacent to the den-tition [24]. The present data showing considerablereductions in stress magnitude in the anterior, central andmedial regions of the mandibular condyle due to theaddition of articular fibrocartilage lead to a new hypoth-esis that the mandibular condyle more likely functionsas a shock absorber than the disc. The biological basisfor potentially a better shock absorbing role of the man-dibular condyle than the disc is that the disc in severalspecies consists of largely fibrous tissue [25,26], whereasthe condylar fibrocartilage is composed of mostly largeproteoglycans such as aggrecan and versican [3,8]. Ingeneral, large proteoglycans such as aggrecan and ver-sican are more suited for resisting compressive forces(shock absorbing) than the fibrous articular disc that isknown to be composed of mostly collagen fibers [25].Therefore, the function of the disc is likely to destabilizethe two articulating parts, the mandibular condyle andarticular eminence, and facilitates relative movement ofthe mandibular condyle against the temporal articulareminence. This is not to say, however, that the disc doesnot have a shock-absorbing role at all. The temporoman-dibular joint is characterized by its apparent ability toallow movement of the mandible against the temporalarticular eminence while it is highly loaded [23]. Takentogether, our hypothesis that articular fibrocartilage ofthe mandibular condyle is the principal shock absorberinstead of the disc warrants further investigation, prefer-ably with experimental approaches.

Accurate representation of articular fibrocartilage inthe mandibular condyle in finite element models is ofimportance for several reasons. First, although the elasticmodulus of articular fibrocartilage of the mandibularcondyle is in general similar to that of hyaline cartilageof several other synovial joints [27,28], the mandibularcondyle does appear to have specific regional variationin its biomechanical properties [13]. In addition, Pois-son’s ratios of various regions of the mandibular fibro-cartilage in the range of 0.31–0.46 (cf., Table 3, [13])differ from an assumed Poisson’s ratio of 0.49 derivedfrom femoral cartilage [9]. These seemingly subtle dif-ferences between mandibular fibrocartilage and proper-

ties of hyaline cartilage in finite element modeling,especially regional differences to an appreciable magni-tude, likely magnify and have an impact on the resultsof stress magnitude. Second, it is preferable to useproperties of the same tissue (e.g. rabbit fibrocartilagein Hu et al. [13]) for finite element modeling rather thandifferent tissues of the same species (e.g. articular carti-lage of the femoral condyle in humans) on the basis ofa correlation between the elastic modulus and the magni-tude of local mechanical loads in articular cartilage[27,29,30]. Third, nonlinear simulation of mandibularloading is likely to better mimic in vivo loading of themandibular condyle because the distribution of the elas-tic modulus of the condylar fibrocartilage is nonlinearand best fit with a third order polynomial equation [13].Nonlinear simulation is additionally called for by theobservation that the cortical and cancellous bone of themandibular condyle also has nonlinear distribution ofmechanical properties [31].

The considerable three-dimensional displacements ofthe mandibular condyle in comparison with minimal dis-placements of the disc and articular eminence are ofinterest for several reasons. First, displacement of themandibular condyle is large in comparison with dis-placements of the disc and articular eminence withoutsimulation of condylar fibrocartilage. Due to the fact thatthe same osseous properties were assigned to both thecondyle and articular eminence, the greater displacementof the condyle than the articular eminence likely resultsfrom differences in their different osseous structures. Itis also likely that the mandibular condyle is better suitedfor yielding to principal stresses parallel to its long axis(cf. Fig. 1), which in turn would be transverse to thelong axis of bone trabeculae of the articular eminence[32]. This further substantiates our aforementionedhypothesis that the mandibular condyle is better suitedas a shock absorber than the disc. Second, the increasingdisplacement of the mandibular condyle after additionof articular fibrocartilage likely reflects the yieldingproperties of the added fibrocartilage with a thicknessof 200 µm [15] because none of the absolute condylardisplacements in any direction in Table 4 exceeds 200µm.

The present data must be interpreted with severalcaveats. First, only loading axial to the long axis of themandibular condyle was simulated. For example, it islikely that the disc would demonstrate high resistance totensile loads and also large displacements axial to itslong axis. Second, the properties of both cortical andcancellous bone are derived from long bones for com-parison with other finite element models of the mandiblesuch as Tanaka et al. [9]. It is known that properties ofosseous structures of the mandibular condyle differ fromthose of long bones [31]. Third, if fibrocartilage had beenadded to the osseous articular eminence, it is likely thatconsiderable stresses would have been absorbed by the

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articular eminence. These caveats provide room foradditional investigations using the present or other finiteelement models.

5. Conclusions

The present data demonstrate that addition of condylarfibrocartilage primarily reduces loading of condyle,instead of the disc and articular eminence. Addition ofarticular fibrocartilage also facilitates stress transmissionto other structures. These findings lead to a hypothesisthat the mandibular condyle more likely functions as ashock absorber than the disc.

Acknowledgements

We are grateful to Drs. Jeffrey Osborn and RobertScapino for their critical review of early versions of themanuscript. Part of the present work was supported bya research grant from the National Natural Science Foun-dation (China) (NNSF 39900165). The effort to com-plete the present work was supported by a BiomedicalEngineering Research Grant from the Whitaker Foun-dation, USPHS Research Grants DE13088 andDE13964, both from the National Institute of Dental andCraniofacial Research, National Institutes of Health,Bethesda, MD 20892, USA.

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