J.H. Koolstra

A three-dimensional mathematical model of the human masticatory system predicting maximum possible bite forces

A three-dimensional mathematical model of the human masticatory system, containing 16 muscle forces and two joint reaction forces, is described. The model allows simulation of static bite forces and concomitant joint reaction forces for various bite point locations and mandibular positions. The system parameters for the model were obtained from a cadaver head. Maximum possible bite forces were computed using optimization techniques; the optimization criterion we used was the minimizing of the relative activity of the most active muscle. The model predicts that at each specific bite point, bite forces can be generated in a wide range of directions, and that the magnitude of the maximum bite force depends on its direction. The relationship between bite force direction and its maximum magnitude depends on bite point location and mandibular position. In general, the direction of the largest possible bite force does not coincide with the direction perpendicular to the occlusal plane.

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

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.

Dynamic Properties of the Human Temporomandibular Joint Disc

The cartilaginous intra-articular disc of the human temporomandibular joint shows clear anteroposterior variations in its morphology. However, anteroposterior variations in its tissue behavior have not been investigated thoroughly. To test the hypothesis that the mechanical properties of fresh human temporomandibular joint discs vary in anteroposterior direction, we performed dynamic indentation tests at three anteroposteriorly different locations. The disc showed strong viscoelastic behavior dependent on the amplitude and frequency of the indentation, the location, and time. The resistance against deformations and the shock absorbing capabilities were larger in the intermediate zone than in regions located more anteriorly and posteriorly. Because several studies have predicted that the intermediate zone is the predominantly loaded region of the disc, it can be concluded that the topological variations in its tissue behavior enable the disc to combine the functions of load distribution and shock absorption effectively.

Application and validation of a three-dimensional mathematical model of the human masticatory system in vivo

A previously described three-dimensional mathematical model of the human masticatory system, predicting maximum possible bite forces in all directions and the recruitment patterns of the masticatory muscles necessary to generate these forces, was validated in in vivo experiments. The morphological input parameters to the model for individual subjects were collected using MRI scanning of the jaw system. Experimental measurements included recording of maximum voluntary bite force (magnitude and direction) and surface EMG from the temporalis and masseter muscles. For bite forces with an angle of 0, 10 and 20 degrees relative to the normal to the occlusal plane the predicted maximum possible bite forces were between 0.9 and 1.2 times the measured ones and the average ratio of measured to predicted maximum bite force was close to unity. The average measured and predicted muscle recruitment patterns showed no striking differences. Nevertheless, some systematic differences, dependent on the bite force direction, were found between the predicted and the measured maximum possible bite forces. In a second series of simulations the influence of the direction of the joint reaction forces on these errors was studied. The results suggest that they were caused primarily by an improper determination of the joint force directions.

Biomechanical and biochemical characteristics of the mandibular condylar cartilage

The human masticatory system consists of a mandible which is able to move with respect to the skull at its bilateral temporomandibular joint (TMJ) through contractions of the masticatory muscles. Like other synovial joints, the TMJ is loaded mechanically during function. The articular surface of the mandibular condyle is covered with cartilage that is composed mainly of collagen fibers and proteoglycans. This construction results in a viscoelastic response to loading and enables the cartilage to play an important role as a stress absorber during function. To understand its mechanical functions properly, and to assess its limitations, detailed information about the viscoelastic behavior of the mandibular condylar cartilage is required. The purpose of this paper is to review the fundamental concepts of the biomechanical behavior of the mandibular condylar cartilage. This review consists of four parts. Part 1 is a brief introduction of the structure and function of the mandibular condylar cartilage. In Part 2, the biochemical composition of the mandibular condylar cartilage is summarized. Part 3 explores the biomechanical properties of the mandibular condylar cartilage. Finally, Part 4 relates this behavior to the breakdown mechanism of the mandibular condylar cartilage which is associated with the progression of osteoarthritis in the TMJ.

Accuracy of microCT in the quantitative determination of the degree and distribution of mineralization in developing bone

PURPOSE To evaluate the accuracy and applicability of a commercially available microCT system for comparative measurements of the degree and distribution of mineralization of developing bone. MATERIAL AND METHODS Homogeneous K2HPO4 solutions with different concentrations (range 0-800 mg/cm3) were used to assess the accuracy of a microCT system equipped with a polychromatic X-ray source. Both high (45 kV) and low (70 kV) tube peak voltages were explored. The resulting attenuation was compared with calculated theoretical attenuation values to estimate the accuracy. As an example of its applicability, the method was used to assess changes in the degree of mineralization of various regions of the mandible from two pigs of different developmental age. RESULTS On average, the estimated error of the measured linear attenuation was 10% or less. Accuracy was dependent on the average mineral concentration, the size of the sample, and the energy of the X-ray beam. The accuracy of the microCT system appeared sufficient to distinguish regional differences in the degree of mineralization within and between specimens of developing mandibular bone. Furthermore, the resolution of the system allowed identification of different degrees of mineralization within trabeculae. CONCLUSION Accuracy of microCT with polychromatic radiation can be considered adequate for assessment of the degree of mineralization of developing bone. Therefore, this method provides a three-dimensional means by which to simultaneously investigate the bone structure as well as the degree of mineralization during development in a non-destructive manner and with high resolution.

The jaw open-close movements predicted by biomechanical modelling.

The aim of this study was to analyse unloaded jaw-opening and jaw-closing movements in humans. For this purpose a dynamical 6-degree-of-freedom mathematical model of the human masticatory system was developed. It incorporated morphology, muscle architecture and dynamical muscle properties. Various symmetrical jaw-opening and jaw-closing movements were simulated based upon different muscle activation schemes. It was found that the balance between swing and slide of the mandibular condyle at the onset of a jaw-opening movement was predominantly dependent on the level of activation of the digastric and inferior lateral pterygoid muscles. The level of activation of the temporalis muscle parts was of critical importance for the jaw-closing movements. The amount of jaw opening was limited by the passive forces of the jaw-closing muscles. In contrast, the influence of the passive forces of the jaw-opening muscles on the jaw-closing movement was neglectable. Throughout the movements the temporomandibular joints remained loaded. The average torques generated by the jaw-opening or jaw-closing muscles with respect to the centre of gravity of the lower jaw had similar orientations and can be considered to be responsible for joint stabilization. The average direction of their lines of action, however, was about opposite, and this can be considered as the major discriminant between a movement in opening or closing direction.

Biomechanical Analysis of Jaw-closing Movements

This study concerns the complex interaction between active muscle forces and passive guiding structures during jaw-closing movements. It is generally accepted that the ligaments of the joint play a major role in condylar guidance during these movements. While these ligaments permit a wide range of motions, it was assumed that they are not primarily involved in force transmission in the joints. Therefore, it was hypothesized that muscle forces and movement constraints caused by the articular surfaces imply a necessary and sufficient condition to generate ordinary jaw-closing movements. This hypothesis was tested by biomechanical analysis. A dynamic six-degrees-of-freedom mathematical model of the human masticatory system has been developed for qualitative analysis of the contributions of the different masticatory muscles to jaw-closing movement. In simulated symmetrical jaw-closing movements, it was found that the normally observed movement, which includes a swing-slide condylar movement along the articular eminence, can be generated by various separate pairs of masticatory muscles, among which the different parts of the masseter as well as the medial pterygoid muscle appeared to be the most suitable to complete this action. The results seem to be in contrast to the general opinion that a muscle with a forward-directed force component may not be suitable for generating jaw movements in which the condyle moves backward. The results can be explained, however, by biomechanical analysis which includes not only muscle and joint forces as used in standard textbooks of anatomy, but also the torques generated by these forces.

Three-dimensional Finite Element Analysis of the Cartilaginous Structures in the Human Temporomandibular Joint

While the movability of the human temporomandibular joint is great, the strains and stresses in the cartilaginous structures might largely depend on the position of the mandible with respect to the skull. This hypothesis was investigated by means of static three-dimensional finite element simulations involving different habitual condylar positions. Furthermore, the influence of several model parameters was examined by sensitivity analyses. The results indicated that the disc moved together with the condyle in the anterior direction without the presence of ligaments and the lateral pterygoid muscle. By adapting its shape to the changing geometry of the articular surfaces, the disc prevented small contact areas and thus local peak loading. In a jaw-closed configuration, the influence of 30° variations of the loading direction was negligible. The load distribution capability of the disc appeared to be proportional to its elasticity and was enhanced by the fibrocartilage layers on the articular surfaces.

Dynamics of the human masticatory muscles during a jaw open-close movement

The movements of the human jaw are controlled by the forces produced by the masticatory muscles. As the jaw moves, these muscles change in length and their force producing units, the sarcomeres, change in length simultaneously. The lengths and length changes of the sarcomeres are determinants for the forces they are able to produce. Hence, masticatory muscle force and jaw movement influence each other which makes it difficult to study their mutual relationship. In this paper, lengths and contraction velocities of the sarcomeres of the human jaw-opening and jaw-closing muscles are presented as well as the consequences for force production during jaw open-close movements simulated with a biomechanical model. Jaw-opening muscles acted almost synchronic in terms of sarcomere length, contraction velocity and force production. They were able to produce the largest isometric forces at relatively small jaw openings at the cost of reduced force production capabilities in wide open positions. In contrast, the jaw-closing muscles acted more differently. They were able to sustain active muscle force throughout a large range of the closing movement. Within this group the masseter and medial pterygoid contracted excentrically during a short time. The lateral pterygoid muscle portions behaved differently with respect to both groups. The jaw-opening muscles produced negligible passive forces during jaw closing. The passive forces of the jaw-closing muscles, however, contributed significantly to a limitation of the jaw-opening movement.