Three-dimensional finite element analysis of the human temporomandibular joint disc

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Abstract

A three-dimensional finite element model of the articular disc of the human temporomandibular joint has been developed. The geometry of the articular cartilage and articular disc surfaces in the joint was measured using a magnetic tracking device. First, polynomial functions were fitted through the coordinates of these scattered measurements. Next, the polynomial description was transformed into a triangulated description to allow application of an automatic mesher. Finally, a finite element mesh of the articular disc was created by filling the geometry with tetrahedral elements. The articulating surfaces of the mandible and skull were modeled by quadrilateral patches. The finite element mesh and the patches were combined to create a three-dimensional model in which unrestricted sliding of the disc between the articulating surfaces was allowed. Simulation of statical joint loading at the closed jaw position predicted that the stress and strain distributions were located primarily in the intermediate zone of the articular disc with the highest values in the lateral part. Furthermore, it was predicted that considerable deformations occurred for relatively small joint loads and that relatively large variations in the direction of joint loading had little influence on the distribution of the deformations.

Introduction

The human mandible is connected to the skull by two temporomandibular joints. The articulating surfaces of these joints are highly incongruent, which provides the mandible with a large degree of movability with respect to the skull (Ostry and Flanagan, 1989; Koolstra and Van Eijden, 1999). Between the articulating surfaces a cartilaginous articular disc is situated, which is assumed to decrease the contact pressure by increasing the contact area between the incongruent joint surfaces, similar to the menisci in the knee joint (Scapino et al., 1996).

Experimental as well as analytic studies have demonstrated, that the human temporomandibular joint is loaded during masticatory function (Hatcher et al., 1986; Smith et al., 1986; Faulkner et al., 1987; Koolstra et al., 1988; Ferrario and Sforza, 1994; Throckmorton and Dechow, 1994). Development and degeneration of joint tissues and overloading caused by parafunctions like bruxism, are supposedly influenced by these loads (Moffet jr. et al., 1964; O'Ryan and Epker, 1984; Nickel et al., 1988; McCormack and Mansour, 1998; Newberry et al., 1998). However, detailed data about the distribution of the loads are still lacking, which means that the main causes of the processes mentioned cannot be fully understood.

Experimental studies regarding the distribution of the loads in the temporomandibular joint have been performed in animal models (e.g. Hylander, 1979; Brehnan et al., 1981; Hohl and Tucek, 1982; Boyd et al., 1990). The number of experimental studies is limited, because the joint is difficult to reach and the application of experimental devices, such as strain gauges, inside the joint will introduce damage to its tissues, which will influence their mechanical behavior.

Mathematical models of the human masticatory system including the temporomandibular joint have been demonstrated to be a powerful tool to predict the loads acting on this joint. Many studies, however, have oversimplified the geometry of the articulating surfaces and assumed them as being rigid (Koolstra et al., 1988; Ferrario and Sforza, 1994). Therefore, the tissue deformations and the distribution of loads inside the joint could not be analyzed.

The finite element (FE) method has been proven to be a suitable tool for approximating such mechanical quantities in structures with a complex geometry (Huiskes and Chao, 1983). Few FE analyses of the temporomandibular joint including a movable articular disc have been published (Chen and Xu, 1994; DeVocht et al., 1996; Chen et al., 1998). These analyses, however, were limited to the two-dimensional sagittal plane and thus unsuitable to investigate, for example, the influence of variations of the loading direction out of the sagittal plane or the development of peak stresses located medially or laterally.

The purpose of the present study was to develop a three-dimensional finite element model of the human temporomandibular joint in which unrestricted sliding of a deformable articular disc between the articulating surfaces was allowed. This model was used to investigate the three-dimensional load distribution in the articular disc during statical loading tasks. The results might contribute to a better understanding of the normal and abnormal functioning of the disc.

Section snippets

Geometry

The geometry of the model was obtained from the right temporomandibular joint of an embalmed male cadaver (age: 77 yr), showing no abnormalities, using a magnetic tracking device (Polhemus 3SPACE Digitizer). To avoid disturbing the geometry of the soft tissues by applying force with this device during the measurements, tight fitting plaster casts of the articular surfaces were made. To ensure that the separate measurements of the casts could be combined into one joint model afterwards, four

Reference simulation

When the joint was loaded in a direction according to the estimated joint reaction force, a displacement of 0.20 mm was simulated. This distance corresponded with almost half the thickness of the so-called intermediate zone of the articular disc (thickness: 0.46 mm). In this reference simulation, a force of 35.5 N was acting on the condyle. This force was calculated by summation of the nodal forces that were generated by the contact algorithm. In Fig. 5 the resulting stress distribution (Von

Discussion

The present model, as far as we know, is the first three-dimensional FE model of the temporomandibular joint disc. The disc was shaped according to its anatomical geometry which was sampled with high resolution. The transition zone between the fibrous attachment of the superior head of the lateral pterygoid muscle and the articular disc was also included in the present model. This probably explains why the disc of the present model and that reported by other researchers (e.g., Chen and Xu, 1994

Acknowledgements

This work was sponsored by the National Computing Facilities Foundation (NCF) for the use of supercomputing facilities, with financial support from Netherlands Organization for Scientific Research (NWO). This research was institutionally supported by the Interuniversity Research School of Dentistry, through the Academic Center for Dentistry, Amsterdam.

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