T.M.G.J. van Eijden

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.

A mathematical model of the patellofemoral joint

A mathematical model of the patellofemoral joint taking into account movements and forces in the sagittal plane is described. The system parameters of the model are the locations of the attachments of the quadriceps muscle and the patellar ligament, the length of the patellar ligament, the dimensions of the patella and the geometry of the articulating surfaces. They were obtained from ten autopsy knees. The model enables calculation of the relative position of the patella, patellar ligament and quadriceps tendon, the location of the patellofemoral contact point and the magnitude of the patellofemoral compression force and the force in the patellar ligament as a function of the location of the tibial tuberosity at different flexion-extension angles of the knee. The model is validated by comparing model data with experimentally determined data.

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.

Masseter muscle thickness in growing individuals and its relation to facial morphology

It is widely accepted that an interaction exists between masticatory muscle function and craniofacial growth. In adults, correlations have been found between facial dimensions and jaw-muscle cross-sectional area, and between facial dimensions and masseter muscle thickness. Little is known about growth of the human masticatory muscles and its relation with facial dimensions at different ages. In 329 Greek individuals, aged 7-22 yr, masseter muscle thickness was measured by ultrasonography. Muscle thickness was related to age, stature and weight, and to facial dimensions, measured by means of anthropological calipers. Muscle thickness was statistically assessed by univariate analysis of variance, after the males and females had been divided into three age groups. Facial dimensions were assessed by multivariate analysis of variance, age being considered as a covariate. The relation between muscle thickness and facial dimensions was subjected to stepwise multiple regression analysis. Masseter muscle thickness increased with age in both sexes. No differences were found between the left- and right-hand side. For each age group (and corrected for stature and weight), males had significantly thicker masseters than females (p < 0.01). Variation in muscle size and facial dimensions mainly coincided with variation in age, stature and weight. Apart from these, muscle thickness showed a significantly negative relation with anterior facial height and mandibular length, and a significantly positive relation with intergonial width and bizygomatic facial width.

Electromyographic Heterogeneity in the Human Temporalis and Masseter Muscles during Static Biting, Open\ Close Excursions, and Chewing

The human temporalis and masseter muscles are not activated homogeneously during static bite force tasks. In this study, we studied the possible existence of regional differences in these muscles under dynamic conditions. Electromyographic (EMG) activity was recorded by means of bipolar fine-wire electrodes. Six electrodes were inserted into the temporalis muscle and three into the masseter muscle. Recordings were made during maximal-effort intercuspal and incisal static clenches, open\close excursions from both the intercuspal and incisal positions, and unilateral gum and licorice chewing on right and left sides. The EMG peak amplitudes and the peak occurrences were compared. During the static clenches and the open\close excursions, no differences could be demonstrated between the regions of the temporalis muscle. However, during the chewing tasks, the anterior and posterior regions behaved differently. Throughout almost all tasks, both superficial and deep parts could be distinguished in the masseter muscle. A further division of the deep masseter was task-dependent. In both the temporalis and masseter muscles, maximal activity (100%) was reached during intercuspal clenches. The average activity declined to 35% of the maximal activity in the temporalis muscle, to 47% in the deep, and to 86% in the superficial masseter during incisal clenches. During all chewing tasks, the EMG peak activity of the anterior temporalis and the superficial masseter muscles was higher in the working than in the balancing condition. The general finding was that different regions were preferentially activated, according to task. The detailed regional specialization previously observed during static bite force tasks could not be demonstrated in the present study.

The orientation of the distal part of the quadriceps femoris muscle as a function of the knee flexion-extension angle

Lateral view radiographs of ten autopsy knees were used to determine the orientation of the patellar ligament, patella and quadriceps tendon relative to tibia and femur at different flexion-extension angles (0-120 degrees) of the knee. The results show a linear relationship between the angle of flexion and the movement of the patellar ligament relative to the tibia and of the movement of the patella relative to tibia and femur. There is a non-linear relationship between angle of flexion and the movement of the quadriceps tendon relative to the patellar ligament, patella and femur. The angular changes between patella and patellar ligament are negligible. The complicated movements of the distal part of the quadriceps femoris muscle may significantly influence biomechanical parameters such as the forces acting at the patella and tibial tuberosity.

Coactivation of jaw muscles: Recruitment order and level as a function of bite force direction and magnitude

The aim of this study was to obtain insight into the coactivation behaviour of the jaw muscles under various a priori defined static loading conditions of the mandible. As the masticatory system is mechanically redundant, an infinite number of recruitment patterns is theoretically possible to produce a certain bite force. Using a three-component force transducer and a feedback method, subjects could be instructed to produce a bite force of specific direction and magnitude under simultaneous registration of the EMG activity of anterior and posterior temporal, masseter and digastric muscles on each side. Forces were measured at the second premolars. Vertical, anterior, posterior, lateral and medial force directions were examined; in each direction force levels between 50 N and maximal voluntary force were produced. The results show that for all muscles the bite force-EMG relationship obeys a straight-line fit for forces exceeding 50 N. The relationship varies with bite force direction, except in the case of the digastric muscles. Variation is small for the anterior temporal and large for the posterior temporal and masseter muscles. The relative activation of muscles for a particular force in a particular direction in unique, despite the redundancy.

Three-dimensional analyses of human bite-force magnitude and moment

The effect of the three-dimensional orientation of occlusal force on maximal bite-force magnitude was examined in seven human subjects at three different unilateral anteroposterior bite positions (canine, second premolar and second molar). At each position, bite-force magnitude was registered in 17 precisely defined directions using a three-component force transducer and a feedback method. In addition, to assess the efficiency of transfer of muscle to bite force, for bites produced in the sagittal plane, moment-arm length was determined and the produced bite-force moment calculated. The results showed that the largest possible bite force was not always produced in a direction perpendicular to the occlusal plane. Generally, maximal bite force in medial and posterior directions was larger than that in, respectively, corresponding lateral and anterior directions. In each direction the produced force was larger at the posterior bite point than at the anterior bite point. The combined moment produced by the jaw muscles was largest for vertical bites, smallest for posteriorly directed bites and intermediate for anteriorly directed bites. In the case of vertically and anteriorly directed bites the produced moment did not vary significantly with the bite position. Hence, for these bite positions the jaw closing moment of the muscles must have kept constant. In the case of posteriorly directed bites the produced moment decreased when bite position changed from the anterior to the posterior side of the dentition. This indicated that jaw muscle activity had declined.

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.