| Sign In to gain access to subscriptions and/or personal tools. |
Consequences of Viscoelastic Behavior in the Human Temporomandibular Joint Disc Department of Functional Anatomy, Academic Centre for Dentistry Amsterdam (ACTA), Meibergdreef 15, 1105 AZ Amsterdam, the Netherlands Correspondence: * corresponding author, j.h.koolstra{at}amc.uva.nl
The consequences of the viscoelastic behavior of the temporomandibular joint disc were analyzed in simulated jaw open-close cycles. It was hypothesized that viscoelasticity helps protect the underlying bone, while augmenting the smoothness of articular movements. Simulations were performed with a dynamic model of the masticatory system, incorporating the joints’ cartilaginous structures as Finite Element Models. A non-linear viscoelastic material model was applied for the disc. The apparent stiffness of the disc to principal stress was largest when the jaw was closed, whereas, with the Von Mises’ stress, it appeared largest when the jaw was open. The apparent stiffnesses appeared to be dependent on both the speed of the movements and the presence of a resistance between the teeth. It was concluded that the disc becomes stiffer when load concentrations can be expected. During continued cyclic motion, it softens, which favors smoothness of joint movement at the cost of damage prevention.
Key Words: temporomandibular joint • articular disc • Finite Element modeling • viscoelasticity
The cartilaginous articular disc in the human temporomandibular joint is assumed to act as a shock absorber and distributor of joint loads (Beek et al., 2001b; Tanaka and van Eijden, 2003). Due to its viscoelastic nature, it is able to dissipate mechanical energy during cyclic loading (Beek et al., 2001a; Donzelli et al., 2004). Furthermore, its apparent stiffness is proportional to the rate of loading. It is not known, however, how these properties are influenced during masticatory behavior, and how they influence function and maintenance of the joint. Since the human body is functionally optimized in many aspects, it can be assumed that they are mainly beneficial. Viscoelastic properties of the temporomandibular joint disc have been identified from experiments performed on isolated samples (Beek et al., 2001a; Tanaka et al., 2003a,b, 2004). The temporomandibular joint is irregularly shaped, and its movements are complex combinations of rotations and translations, which have been suggested to generate nonuniform patterns of stresses and strains in its cartilaginous structures during masticatory movements (Koolstra and van Eijden, 2005, 2006). Due to this complexity, extrapolation of shear, tension, and compression tests to habitual situations is not straightforward. For analysis of the influence of viscoelasticity on the mechanical behavior of the temporomandibular joint disc, it is necessary that one obtain information about its deformations and tensions during relevant masticatory tasks. While this is virtually impossible to achieve experimentally, the consequences of viscoelastic behavior of the temporomandibular joint disc were studied with a dynamic model of the human masticatory system. A non-linear viscoelastic material model was applied to the implemented Finite Element Models of the articular discs. Tensions and deformations occurring during loaded and unloaded jaw open-close cycles at different speeds were analyzed. The hypothesis tested was that the viscoelastic properties provide protection to the underlying bone, while assisting in the smoothness of articular movements.
The Model A biomechanical model of the human masticatory system (Fig. 1A  ) was constructed with the use of MADYMO 6.2 (TNO Automotive, the Netherlands), a simulation program that combines the capabilities of multi-body motion and Finite Element modeling. It contained the skull and the mandible, articulating at 2 six-degrees-of-freedom temporomandibular joints. Twelve pairs of Hill-type muscles were able to move the mandible with respect to the skull. Their attachments, maximum force, fiber length, and sarcomere length (for a complete overview, see Koolstra and van Eijden, 2005) had been obtained from eight human cadavers (van Eijden et al., 1995, 1996, 1997). The contractile characteristics had been shaped according to van Ruijven and Weijs (1990).
Both temporomandibular joints contained deformable articular cartilage layers of 0.5 mm (Hansson et al., 1977), connected to the (rigid) temporal bone and the mandibular condyle, respectively. Between them, a deformable cartilaginous articular disc was situated (Figs. 1B, 1C  ). This was medially and laterally connected to the condylar neck with pairs of inextensible wires, representing the lower part of the articular capsule, and anteriorly to the attachment of the superior lateral pterygoid muscle to the condylar neck. The geometry of the deformable structures had been obtained from the right temporomandibular joint of one cadaver (Beek et al., 2000, 2001b). The left side joint was constructed as a mirror image. The deformable structures were divided into about 14,500, 12,500, and 12,200 tetrahedral finite elements, with edges of maximally 0.25 mm (HyperMesh 7.0, Altair Engineering GmbH, Böblingen, Germany) for the temporal cartilage, articular disc, and condylar cartilage, respectively. The mandibular condyle was guided free of friction along the articular surface of the temporal bone by the reaction forces from the contacts between the Finite Element models.
The material properties of the articular disc were approximated with a non-linear viscoelastic material model (Brands et al., 2004; Koolstra et al., 2007). This model was constructed as a four-mode Maxwell model, with second-order Mooney-Rivlin models as elastic elements. The parameters for this model were obtained by fitting the storage and loss moduli to the results obtained in dynamic shear tests with porcine TMJ discs (Tanaka et al., 2003a). They were: G0 = 0.65 MPa, G1 = 0.33 MPa, G2 = 0.30 MPa, G3 = 0.42 MPa, G4 = 0.90 MPa,
Simulations So that fast movements would be obtained, activation of each muscle group lasted 90 msec. For slower movements, 180-ms activation was applied. During the latter, the duration of the activation and deactivation ramps was doubled. We analyzed the influence of joint loading by repeating the simulations with a load of 40 N between the central incisors. The maximum jaw-closer activity, necessary to complete jaw closing with this resistance in about the same time as during the unloaded movements, was 20%. The results were analyzed and visualized with the use of HyperView 7.0 (Altair Engineering GmbH, Böblingen, Germany). We quantified the results by monitoring the instantaneous ratio between the average stress and strain in the elements of the middle one-third of the intermediate zone of the disc, as a measure for the instantaneous apparent stiffness. This region was selected because, on average, it is assumed to undergo the largest deformations during open-close movements (Koolstra and van Eijden, 2005, 2006). To account for both compressive and shear deformations, we analyzed the stress/strain ratio in the first principal direction, according to the Von Mises’ criterion.
Despite relatively coarse muscle recruitment patterns, the jaw movements had characteristics similar to those observed habitually (Koolstra and van Eijden, 2006). Except for their speed, the slow movements did not differ kinematically from the fast ones. The simulations of the faster and slower open-close cycles were completed in about 100 and 200 hrs, respectively, on a dual-CPU personal computer.
The distribution of stress occurring in the disc did not differ qualitatively between the faster and slower movements, nor between the loaded and unloaded ones (Fig. 2
An apparent stiffness of the central part of the articular disc in response to the different loading patterns was observed (Fig. 3 ). It is remarkable that the stiffness of the first principal stress was greatest when the jaw was completely closed (except for the starting position), and had its minimum when the jaw was open. In contrast, the stiffness according to the von Mises’ criterion had its maximum when the jaw was open and its minimum with the jaw closed. During the slow unloaded movements, the stiffnesses were reduced with respect to the fast ones during jaw opening and increased during jaw closing. The loaded movements differed from the unloaded ones for jaw-closing only, while during jaw opening the applied resistance was not effective. With respect to the unloaded movement, the stiffness was increased for the fast movements much more than for the slow ones. Therefore, the greatest stiffnesses were observed for the fast, loaded closing movements.
The apparent stiffnesses in the second cycle were less than in the first one (Fig. 3 ) during the later opening phase and during closing. In contrast, during the first part of jaw opening, the stiffnesses were greater. The differences between the first and second cycles were almost independent of the speed and loading characteristics (Fig. 4). During the second open-close cycle, the reduction was more than 10% about half-way during jaw opening. When the jaw was closed for the second time, the reduction in stiffness was about 5% compared with the first time. For the loaded jaw movements, the decrease in stiffness during the occlusive phase of the second cycle became larger.
Methodological Limitations The shear moduli of the applied multi-mode Maxwell model (Ferry, 1980) were related to relaxation times between 0.01 and 10 sec. The maximum frequency of cyclic jaw movements, about 2.7 Hz (Plesh et al., 1993), lies well within this range. Joint loading beyond the modeled range may be generated during impact loading—for instance, when the teeth meet unexpected resistance during closing. Such impact, however, will partially be damped by the periodontal ligament (Natali and Pavan, 2003) and by the trabeculi of the alveolar bone. In the present analysis, these influences were not taken into account. Therefore, the consequences of tooth impact, visualized by large fluctuations in apparent stiffness, could have been overestimated. The present model underestimated absorption of frequency components above 100 Hz. Although, in articular cartilage, the viscoelastic properties almost vanish beyond a frequency of 40 Hz, so that it behaves effectively as elastic (Park et al., 2004), this may not apply to the TMJ disc, since it contains far fewer proteoglycan molecules (Allen and Athanasiou, 2006). It is likely that the observed increase of its loss modulus with frequency (Tanaka et al., 2003a) will continue beyond 100 Hz. The relatively fast jaw-open/-close cycles were applied for the purposes of efficiency. The computation time was about 100 hrs. Slower movements required proportionally more time, with increasing probability of interruptions and crashes. Since the faster movements were qualitatively similar to the slower ones, they were considered adequate. The jaw movements were indirectly controlled by the time-course of muscle forces. The jaw was maximally open at about 45 msec and 25 msec after the jaw-openers had attained their maximum force for the fast and slow movements, respectively. This may have resulted in differences in the movement trajectory. These differences, however, did not cause qualitatively different joint-loading patterns.
Influence of Velocity and Loading Loading was applied to mimic food processing and, therefore, was present only during jaw-closing. Consequently, it affected predominantly the mechanical reaction of the disc in that period. The resistance between teeth caused an increase in joint loading, reflected by an increase in stiffness of the disc. For the fast movements, the increase was less gradual than for the slower ones. Possibly, the disc had a better opportunity to adapt its shape during the latter, causing the loads to be distributed more evenly.
Influence of Subsequent Cycles The reduction of the apparent stiffness of the disc in the second cycle relates to both principal and Von Mises’ stresses. This is most probably related to strain relaxation in response to prolonged loading. As a consequence, the disc will be able to improve the congruence between the articular surfaces and will perform jaw movements more smoothly. However, the disc will be more susceptible to unexpected large deformations—for instance, during impact loading.
Stiffness in Response to Principal and Von Mises’ Stresses In conclusion, the hypothesis that viscoelastic properties augment the possibilities for the joint to maintain its integrity is only partially confirmed. In general, the cartilage becomes stiffer in situations where the joint is susceptible to load concentrations, thereby protecting the subchondral bone. However, during continued cyclic behavior, the smoothness of joint movement seems to prevail over damage prevention.
The authors gratefully thank Dr. G.E.J. Langenbach for his constructive comments on the manuscript. This research was institutionally supported by the Interuniversity Research School of Dentistry, through the Academic Centre for Dentistry Amsterdam (ACTA).
 deceased since manuscript was submitted  Received for publication February 1, 2007. Revision received July 13, 2007. Accepted for publication July 31, 2007.
Journal of Dental Research, Vol. 86, No. 12,
1198-1202 (2007) This article has been cited by other articles:
|
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 |
|
|
 |
|
Sign In to gain access to subscriptions and/or personal tools.
TOP
ABSTRACT
INTRODUCTION
1 = 10 sec, 
