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Journal of Biomechanics 38 (2005) 2431–2439

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Combined finite-element and rigid-body analysis of humanjaw joint dynamics

J.H. Koolstra�, T.M.G.J. van Eijden

Department of Functional Anatomy, Academic Centre for Dentistry Amsterdam (ACTA), Universiteit van Amsterdam and Vrije Universiteit,

Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands

Accepted 7 October 2004

Abstract

The jaw joint plays a crucial role in human mastication. It acts as a guidance for jaw movements and as a fulcrum for force

generation. The joint is subjected to loading which causes tensions and deformations in its cartilaginous structures. These are

assumed to be a major determinant for development, maintenance and also degeneration of the joint. To analyze the distribution of

tensions and deformations in the cartilaginous structures of the jaw joint during jaw movement, a dynamical model of the human

masticatory system has been constructed. Its movements are controlled by muscle activation. The articular cartilage layers and

articular disc were included as finite-element (FE) models. As this combination of rigid-body and FE modeling had not been applied

to musculoskeletal systems yet, its benefits and limitations were assessed by simulating both unloaded and loaded jaw movements. It

was demonstrated that joint loads increase with muscle activation, irrespective of the external loads. With increasing joint load, the

size of the stressed area of the articular surfaces was enlarged, whereas the peak stresses were much less affected. The results suggest

that the articular disc enables distribution of local contact stresses over a much wider area of the very incongruent articular surfaces

by transforming compressive principal stress into shear stress.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Jaw joint; Finite-element modeling; Rigid-body modeling; Dynamics

1. Introduction

Biomechanical analysis of musculoskeletal systemdynamics has been performed widely by applyingrigid-body dynamics (for example, Koolstra and vanEijden, 1995, 1997, 1999; Anderson and Pandy, 1999;Peck et al., 2000; McLean et al., 2003). This method,which basically transforms forces into movements, isvery flexible and enables to investigate the influence ofmuscle activation on body movements. The distributionof forces in irregularly shaped joint structures, however,cannot be analyzed, and the deformations of articularcartilaginous layers cannot be taken into account(Pandy et al., 1997). Therefore, often simplified jointsare applied. For investigation of the mechanics of

e front matter r 2004 Elsevier Ltd. All rights reserved.

iomech.2004.10.014

ing author. Tel.: +3120 5665370; fax: +3120 6911856.

ess: j.h.koolstra@amc.uva.nl (J.H. Koolstra).

irregularly shaped deformable structures in joints, thefinite-element (FE) method is more applicable (Huiskesand Chao, 1983; Li et al., 1999; Beek et al., 2000, 2001b;Donzelli et al., 2004). This method enables the predic-tion of the internal forces and deformations. These aregenerated when a priori defined displacements areapplied that occur during joint movement. The rigid-body and FE method are supplementary. They cannotreplace each other and generally they have a differentarea of application.

The deformations in the cartilaginous structures injoints are caused by the mutual displacements of thearticulating body segments. These displacements are theresult of muscle forces, external forces, forces of inertiaand joint reaction forces. The latter forces are directlydependent on the mechanical behavior of the deform-able joint structures. They affect the displacementsof the articulating segments, which implies that the

ARTICLE IN PRESSJ.H. Koolstra, T.M.G.J. van Eijden / Journal of Biomechanics 38 (2005) 2431–24392432

deformations in articular cartilage are influenced bytheir own mechanical properties. This influence will belarger when the joint reaction force does not act in linewith the muscle forces and the moments of inertia of (atleast) one of the articulating segments are relativelysmall with respect to the corresponding joint torques.These circumstances are present in, for instance, thehuman masticatory system.

Recently, it has become possible to connect FEmethod routines to rigid-body models in commerciallyavailable simulation software. This enables the analysisof the dynamics of the bony structures in a musculoske-letal system simultaneously with the local distribution ofjoint forces. Moreover, it permits the evaluation of themutual influence of muscle activation patterns, rigid-body dynamics and the effects of deformations ofarticular cartilage. To our knowledge, this combinationhas not yet been applied to musculoskeletal systems.

The purpose of the present study was to test theapplicability of this new development for biomechanicalanalysis in a relatively complex musculoskeletal systemas the human masticatory system. In particular, it wasstudied whether it can enlighten the role of the articulardisc present in the temporomandibular joint during jawmovement, as this is still ill-understood.

2. Materials and methods

2.1. The model

A three-dimensional biomechanical model of thehuman masticatory system (Fig. 1) was constructedusing MADYMO (TNO Automotive, the Netherlands),a simulation program which combines the capabilities ofmulti-body motion and FE modeling. It contained tworigid bodies, the skull and the mandible, which

Fig. 1. The model. (A) anterolateral view: red lines: muscle contractile elemen

posterior temporalis; Ms: superficial masseter; Mpa: anterior deep massete

lateral pterygoid; Pli: inferior lateral pterygoid; Dig: digastric; GH: geniohyo

lines: part of articular capsule; Dig, GH, and Mhp are connected to the hy

Cartilaginous structures of the jaw joint; blue: temporal cartilage layer; orang

of the jaw joint.

articulated at two six degree-of-freedom temporoman-dibular joints. Mutually impermeable dentures wereconnected to both of them. Twelve pairs of muscleportions were able to move the mandible with respect tothe skull (Koolstra and van Eijden, 1995, 1997, 1999).They were: superficial, deep anterior and deep posteriormasseter, anterior and posterior temporalis, medialpterygoid, superior and inferior lateral pterygoid,digastric, geniohyoid, and anterior and posterior mylo-hyoid. The muscle models were of the Hill-typeconsisting of a contractile element, a parallel elasticelement, and a series elastic element. The architecturalparameters (attachments, maximum force, fiber length,sarcomere length) had been obtained from eight humancadavers (van Eijden et al., 1995, 1996, 1997). Optimumlength of the contractile element was defined by[(optimum sarcomere length�fiber length)/sarcomerelength]. The series elastic element was modeled as aninextensible wire (muscle length–fiber length) (Table 1).The characteristics of the contractile and parallel elasticelements were shaped according to van Ruijven andWeijs (1990).

The two temporomandibular joints consisted of twodeformable articular cartilage layers of 0.5 mm (Hans-son et al., 1977) which were connected to the (rigid)temporal bone above and the mandibular condylebelow, respectively. Between the two cartilaginouslayers, a freely movable deformable cartilaginousarticular disc was situated. It was connected mediallyand laterally to the adjacent mandibular condyle withpairs of inextensible wires representing the lower part ofthe articular capsule. The geometry of the deformablejoint structures had been obtained from the righttemporomandibular joint of one cadaver (Beek et al.,2000, 2001b). The left side joint was constructed as amirror image of the right one. The volumes of thedeformable structures were divided into tetrahedral

t; black lines: muscle serial elastic element; Ta: anterior temporalis; Tp:

r; Mpp: posterior deep masseter; Pm: medial pterygoid; Pls: superior

id; MHa: anterior mylohyoid; MHp: posterior mylohyoid; thin black

oid bone (not shown), MHa to the mylohyoid raphe (black line). (B)

e: articular disc; red: condylar cartilage layer. (C) Sagittal cross-section

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Table 1

Model parameters

Moments of inertia Mass (kg) Ixx (kgm2) Iyy (kgm2) Izz (kgm2)

Lower jaw 0.44 0.00086 0.00029 0.00061

Muscles Muscle length (mm) Max. force (N) CEa optimum length (mm) SEa length (mm)

Superficial masseter 48.0 272.8 22.6 25.8

Deep anterior masseter 29.5 73.8 21.8 17.1

Deep posterior masseter 30.9 65.8 15.0 13.3

Anterior temporalis 57.4 308.0 30.7 24.2

Posterior temporalis 62.9 222.0 31.3 28.8

Medial pterygoid 43.3 240.0 14.1 27.6

Superior lateral pterygoid 29.1 38.0 21.5 9.4

Inferior lateral pterygoid 27.2 112.8 22.3 9.0

Anterior digastric 51.9 46.4 42.6 3.0

Geniohyoid 48.5 38.8 35.3 5.4

Anterior mylohyoid 21.8 63.6 24.0 0.0

Posterior mylohyoid 44.8 21.2 39.7 0.0

Number of finite elements Temporal cartilage Articular disc Condylar cartilage

Right joint 2190 2167 1853

Left joint 2320 2157 1960

aCE—contractile element, and SE—series elastic element.

J.H. Koolstra, T.M.G.J. van Eijden / Journal of Biomechanics 38 (2005) 2431–2439 2433

finite elements with edges of about 0.5 mm (HyperMesh6.0, Altair Engineering GmbH, Boblingen, Germany) asspecified in Table 1.

MADYMO does not apply a material model forcartilage. As both articular cartilage and the cartilage ofthe articular disc are subject to large deformations, theirmaterial properties were approximated according to theMooney–Rivlin material model (Chen et al., 1998). Todetermine the constants C1 and C2 that describe thebehavior of this rubber-like material model, weperformed simulations of indentation experiments onhuman temporomandibular joint discs (Beek et al.,2003) with this material. With C1 ¼ 9� 105 andC2 ¼ 9� 102 Pa the reaction forces upon indentationapproximated the experimental observations (Beek etal., 2001a) most closely. For the articular cartilage layerswe applied C1 ¼ 4.5� 105 and C2 ¼ 4.5� 102 Pa (videinfra).

2.2. Simulations

The jaw was closed at the start of all simulations.From this position, symmetrical jaw-open movementswere simulated. These were performed by a 10%, 50%or 100% activation of the digastric, geniohyoid,mylohyoid and lateral pterygoid muscles simulta-neously. Jaw-closing movements without food resistancewere simulated by a 1% or 10% simultaneous activationof the masseter, medial pterygoid and temporalismuscles after a maximum gape had been obtained in apreceding (100%) jaw-open movement. The influence offood resistance was investigated by adding a restraint,which generated a constant force during jaw closure. A

force of 50 N was applied symmetrically between thecentral incisors or 80 N unilaterally between the rightsecond molars of upper and lower jaw. Loaded jaw-closing movements were simulated by a bilateral 25%activation of all jaw-closing muscles, as this appeared tobe sufficient to overcome this restraint.

In all simulations, activation of each muscle wasindividually defined as a function of time. Thesefunctions included activation and deactivation rampsof 45 and 75 ms, respectively, to incorporate activationdynamics (Winters and Stark, 1987).

2.3. Analysis

The joint forces during the movements in response tothe applied muscle loads were characterized by theresultant reaction force generated by the contactingelements in the joint. The stress in the deformablestructures was characterized by the Von Mises stresscriterion and the maximum principal stress. Strain of acartilaginous structure was quantified by computing thenumber of elements that were strained by more than 1%and the mean maximum principal strain of theseelements. The results were analyzed and visualized usingHyperWorks 6.0 (Altair Engineering GmbH, Boblingen,Germany).

3. Results

The movements of the jaw predicted by the model as aconsequence of muscle activation were relatively fast,but similar to natural movements. The mandibular

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condyles moved forward as the jaw-opening musclesopened the jaw in about 50 ms. The articular disc movedtogether with the mandibular condyle along the articulareminence. After a 100%, 50% and 10% activation of thejaw-opening muscles, the maximum (inter-incisal) jawopening was 3.0, 2.6 and 1.8 cm and the joints wereloaded up to 85, 45 and 15 N, respectively (Fig. 2A).

Jaw closing took, dependent on muscle activation andmandibular load, between 60 and 125 ms. In the firststage, the mandibular condyle moved backwards overthe articular eminence. Thereafter it remained in themandibular fossa as the jaw closed further. If only themasseter, temporalis and medial pterygoid muscles wereactivated, the mandibular condyle moved backwardsout of the mandibular fossa as the jaw was almostclosed. This could be prevented by simultaneousactivation of the lateral pterygoid muscle. A 100%activation of this muscle was necessary to preventdislocation when the jaw-closing muscles had beenactivated to 10% or more.

During unloaded jaw closing, the load in each jointwas proportional to the muscle activation. It becameabout 10 or 90 N when the jaw closers were activated by1% or 10%, respectively (Fig. 2B and C). When the jawhad to close against a resistance at the dental elementsthe joints became more heavily loaded. The resultant

200

100

Join

t for

ce (

N)

0

200

100

0

200

100

00 5 10 15

Jaw gap

20 25

50 N, central incisor

unloaded, 1%

opening(A)

(B)

(D)

100%

50%

10%

Fig. 2. Joint forces as a function of jaw gape. (A) jaw-opening movement:

activation; continuous line: 100% jaw-opener activation. (B) Unloaded jaw-c

movement, 10% jaw-closer activation. (D) Jaw-closing movement with a 50

load; dotted line: contralateral joint, continuous line: ipsilateral joint; thin d

load in each joint increased to about 145N when a 50Nload was applied at the central incisors (Fig. 2D). Whena 80 N load was applied at the right molar region, itincreased to about 145 and 110 N for the contralateraland ipsilateral joint, respectively (Fig. 2E).

As the jaw was at its open position, the largest stresseswere generated around the thin intermediate zone of thedisc (Fig. 3, 1st rows). Medio-laterally, this area wasextended from the middle of the joint to its lateral side.When the jaw closed this area shifted in medialdirection. The largest stresses in the cartilage layerswere associated with the articular eminence. In thecondylar cartilage this area shifted with condylarrotation. In the temporal cartilage the mandibular fossaregion became also stressed as the jaw closed.

In the disc, the Von Mises stresses were much largerthan in the articular layers. In the latter the (compres-sive) principal stresses were larger. The area of largeprincipal stress was proportional to the amount ofmuscle activation. In contrast to the articular cartilagelayers where the maximum principal stress was almostexclusively compressive, the disc showed both tensileand compressive stresses. Furthermore, the disc areaswith large principal stress were not necessarily the sameas the areas with large Von Mises stress. At the end ofthe unilaterally loaded closing movement, the Von

contralateral

ipsilateral

e (degrees)

0 5 10 15 20 25

unloaded, 10%

80 N, right molar

(C)

(E)

dotted line: 10% jaw-opener activation; dashed line: 50% jaw-opener

losing movement, 1% jaw-closer activation. (C) Unloaded jaw-closing

N symmetrical load. (E) Jaw-closing movement with a 80N unilateral

ashed lines: jaw-opening movement (100% jaw-opener activity).

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Fig. 3. Stress in the jaw joint during jaw closing as a function of jaw gape. (A) unloaded jaw-closing movement, 10% jaw-closer activation. Columns

1–2: Von Mises stress; Columns 3–6: maximum principal stress; Columns 1, 5: articular disc, top view; Columns 2, 3: sagittal section, right view;

Column 4: temporal cartilage layer, top view; Column 6: condylar layer, top view. a: anterior; p: posterior; m: medial; l: lateral. Rows: 1—maximum

open, 2—201 open, 3—151 open, 4—101 open, 5—51 open, 6—closed. (B) Jaw-closing movement with a 50N symmetrical load. Rows and columns as

(A). (C) Jaw-closing movement with a 80N unilateral load. Rows as A. Columns 1–6: right joint as (A). Columns 7–12: left joint as Columns 1–6 in

reverse order. Legends: Stress in Pa.

J.H. Koolstra, T.M.G.J. van Eijden / Journal of Biomechanics 38 (2005) 2431–2439 2435

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0.2

0.15

0.1

0.05

0

0.2

0.15

0.1

0.05

0

0.2

0.15

Mea

n el

emen

t str

ain

Str

aine

d el

emen

ts

0.1

0.05

2500

2000

1500

1000

500

0

2500

2000

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1000

500

0

2500

2000

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00 5 10

Jaw gape (degrees)

15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25

0 5 10

Jaw gape (degrees)

15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25

unloaded, 1% unloaded, 10% 50 N, central incisor 80 N, right molar

unloaded, 1% unloaded, 10% 50 N, central incisor 80 N, right molar

temporal cartilage

disc

condylar cartilage

temporal cartilage

disc

condylar cartilage

(A)

(B)

Fig. 4. Strain in the jaw joint structures as a function of jaw gape. (A) mean strain in temporal cartilage layer (row 1), articular disc (row 2) and

condylar cartilage layer (row 3) during unloaded close with 1% jaw-closer activity (column 1), unloaded close with 10% jaw-closer activity (column

2), jaw-closing movement with 50N symmetrical load (column 3) and jaw-closing movement with 80N unilateral load (column 4). Continuous lines:

ipsilateral joint; Dotted lines: contralateral joint; Thin dashed lines: jaw-opening movement. Elements strained less than 1% were excluded. (B)

Number of elements that were strained by more than 1% as a representation of the strained area. Organization as in (A).

J.H. Koolstra, T.M.G.J. van Eijden / Journal of Biomechanics 38 (2005) 2431–24392436

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Mises stress was less and the maximum principal stresslarger than in the symmetrically loaded one (Fig. 3B andC, bottom row).

During all simulated movements, the mean principal(compressive and tensile) strain in the articular disc wasproportional to the joint load and almost all of thearticular disc was deformed with more than 1% (Fig. 4Aand B, 2nd row). The largest strains were observed in thedisc during loaded jaw-closing movements. Here themean disc strain increased gradually and reached 20%when the teeth bumped against each other. The meanstrain in the articular layer of the condyle varied muchless and in the mandibular fossa it was almost constant(Fig. 4A, 1st and 3rd row). In contrast, the size of thestrained area of the fossa layer changed with joint loadmore directly than that of the condyle (Fig. 4B, 1st and3rd row).

4. Discussion

Until recently, analysis of the interaction of muscle,joint and bone mechanics, all contributing to themechanical behavior of the same musculoskeletalsystem, has been laborious. With the availability ofsimulation software such as MADYMO, such analysiscan be performed with one integral model. The presentmodel, which is the first three-dimensional dynamicalmodel of the human masticatory system that includesnaturally shaped deformable structures in the joints,enables the performance of such analysis duringhabitual movements.

4.1. Muscle recruitment and joint force

In a jaw-opening movement, the jaw-opening muscleshave to overcome the increasing passive tensions of thejaw-closing muscles (Langenbach and Hannam, 1999;Koolstra and van Eijden, 2004). Therefore, the final jawgape is proportional to the activation of the jaw-openingmuscles. In contrast, the jaw-closing movement requiresvery little muscle activation, because the passive tensionsof the jaw-opening muscles are negligible. The amountof necessary muscle force is reflected in the joint forceand herewith in the amount of stress in the joint. Whenthe jaw is maximally open, both articulating surfacesshow their largest convexity in the sagittal plane. Thiscauses the occurring stresses to be concentrated morethan when the condyle is situated in the mandibularfossa or against the less-curved posterior surface of thearticular eminence.

The model did not contain the structures thatnormally are present behind the mandibular fossa, orthe capsule of the jaw joint. These may contribute toprevent dislocation of the joint in posterior directionwhich occurred, for instance, in simulations where the

temporalis muscle was activated beyond 25% while theteeth experienced a vertical (but not horizontal)resistance. This indicates that even during forcefulbiting, a subtle regulation of muscle force remainsnecessary. This is reflected by observations of largeinterindividual differences in masticatory muscle activityfor the same task. It is not possible to define one uniquepattern as generally applicable. Therefore, the appliedmuscle activation patterns were relatively simple.Proprioceptive modulation and timing of muscle activa-tion (Hof, 2003) were not incorporated as the recentmodel does not allow to include instantaneous inter-active muscle control (Koolstra and van Eijden, 2001).This can be considered as a considerable limitation.

4.2. Deformations and tensions

The model predicted that when the jaw joint is loaded,its articular disc deforms much more than the (softer)cartilaginous layers of the temporal bone and mandib-ular condyle. This is most likely caused by the fact thatthe articular cartilage layers are bonded to the bone onone side but the articular disc is not. The compressiveforces applied to the articular cartilage layers can betransmitted to the bone more directly and do notpropagate through the structure. In contrast, in thearticular disc they can propagate easily parallel to thearticular surfaces, thereby causing large deformationsaccompanied by large local tensions. This findingsuggests that the difference in mechanical propertiesbetween disc and cartilaginous layers is advantageousfor the joint. While the freely moving disc is moresusceptible to large deformations when it is compressedbetween the articular surfaces of temporal bone andcondyle, it needs to be stiffer than the articular cartilage.

In the articular disc the largest Von Mises stressesoccurred in the intermediate zone. In the adjacentcartilage layers the Von Mises stress was much less, buthere the principal (compressive) stress was larger than inthe disc. This indicates that the disc is primarily stressedwith shear (Von Mises stress is also indicated asoctahedral shear stress). This can be regarded as amechanism to spread the compressive stress of thecartilage layers over a larger area.

The medio-lateral shift of the largest discal stresseswith jaw movement was similar to the observations ofBeek et al. (2001b). However, generalization of thisfinding should be performed with care as the same jointgeometry was applied. It is suggested that the mandib-ular condyles bend inwards during contraction of thejaw closers (van Eijden, 2000). Such bending, which wasnot included in the present model, most probablyinfluences the medio-lateral position of the largeststresses.

During a unilaterally loaded closing movement, thecontralateral joint is more heavily loaded than the

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ipsilateral one. Despite this difference, the average strainin the contralateral temporal cartilage is not larger thanin the ipsilateral one, but the strained area is larger. Thisillustrates the articular disc’s capacity to prevent over-loading of articular surfaces by a load distributionwhich becomes more effective when the amount ofapplied load increases. This effect is more dominant forthe temporal cartilage than for the condyle. Theconcavity of the mandibular fossa is less than theconvexity of the mandibular condyle. Furthermore, thebone of the mandibular condyle is suitable to distributeloads internally (Giesen and van Eijden, 2000).Although this may also be the case for the articulareminence, the roof of the mandibular fossa is hardlyable to withstand large forces because it is very thin.Apparently, the articular disc is also able to compensatefor these differences.

4.3. Consequences of model inaccuracies

Cartilage exhibits complex material behavior. Thearticular disc has been demonstrated to possess bothviscoelastic and hyperelastic properties and undergoeslarge deformations (Beek et al., 2001a). Unfortunately,MADYMO does not incorporate a material model thatcan model these properties accurately. Therefore, thehyperelastic Mooney–Rivlin material model has beenapplied as it behaves most reliably under largedeformations. Its hyperelasticity, however, is mainlydirected to stretch. Compressive hyperelasticity, asexhibited by cartilage, remains underrated. As thematerial constants were optimized for a 30% compres-sion, this implies that compressive strains smaller than30% may be underestimated while larger ones areoverestimated.

The material behavior of the articular cartilage layersin the temporomandibular joint is not known. Althoughthey have been obtained from condylar cartilage ofrabbits by nanoindentation (Hu et al., 2001), these arenot reflecting the behavior under large deformations(Hasler et al., 1999). Therefore, we have also applied aMooney–Rivlin material model for these structures. Therelevant constants were chosen to be half of those of thearticular disc, as articular cartilage is considered softerthan that of the disc (Chen et al., 1998; Beek et al.,2001b). This introduces a quantitative uncertainty in thepredicted stresses and strains. However, it has beendemonstrated that the location where these stresses andstrains occur is less dependent on the applied materialconstants (Beek et al., 2001b).

The FE models of the deformable cartilaginousstructures contained elements with edges of about0.5 mm length. This is of the same order of magnitudeas the thickness of the cartilage layers and theintermediate zone part of the articular disc. Conse-quently, the resulting meshes were relatively coarse. This

may reduce the quantitative accuracy of the predictedstresses and strains. As such, accuracy is dominantlyaffected by the applied material models, and a lawfulmesh architecture could be maintained despite therelatively large deformations, this was consideredacceptable.

4.4. Benefits and limitations

To our knowledge, the present model for the first timeenables the analysis of instantaneous deformations andtensions in the joints of a musculoskeletal system wherethe movements are not defined a priori, but controlledby muscle tensions. Furthermore, the reaction forces inthe joints, generated by the deformed cartilaginousstructures, are also a determinant for the resultingmovement. Presently, it enabled the simulation of tasksthat incorporated muscle forces up to about 25% oftheir capacity causing local deformations in the joints ofmore than 20%. Compared to the majority of modelsthat incorporated FE modeling, this is a considerableextension of force generation and deformation capacity.

The limitations of the present method include theinability to control muscle activation in feedback to theposition and velocity of the moving jaw. Furthermore,the applicability (especially in a quantitative sense) islimited by the absence of a more realistic material modelfor articular and discal cartilage. Inclusion of compres-sive hyperelasticity, for instance, could extend the rangeof applicable muscle forces because the materials wouldbecome stiffer and less susceptible to deformations asloading increases.

Acknowledgments

The authors gratefully thank Dr. G.E.J. Langenbachfor his constructive comments on the manuscript. Thisresearch was institutionally supported by the Interuni-versity Research School of Dentistry, through theAcademic Centre for Dentistry Amsterdam (ACTA).

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