Mandibular function in Galago crassicaudatus and Macaca fascicularis: an in vivo approach to stress analysis of the mandible.

Single-element and/or rosette strain gages were bonded to mandibular cortical bone in Galago crassicaudatus and Macaca fascicularis. Five galago and eleven macaque bone strain experiments were performed and analyzed. In vivo bone strain was recorded from the lateral surface of the mandibular corpus below the postcanine tooth row during transducer biting and during mastication and ingestion of food objects. In macaques and galagos, the mandibular corpus on the balancing side is primarily bent in the sagittal plane during mastication and is both twisted about its long axis and bent in the sagittal plane during transducer biting. On the working side, it is primarily twisted about its long axis and directly sheared perpendicular to its long axis, and portions of it are bent in the sagittal plane during mastication and molar transducer biting. In macaques, the mandibular corpus on each side is primarily bent in the sagittal plane and twisted during incisal transducer biting and ingestion of food objects, and it is transversely bent and slightly twisted during jaw opening. Since galagos usually refused to bite the transducer or food objects with their incisors, an adequate characterization of mandibular stress patterns during these behaviors was not possible. In galagos the mandibular corpus experiences very little transverse bending stress during jaw opening, perhaps in part due to its unfused mandibular symphysis. Marked differences in the patterns of mandibular bone strain were present between galagos and macaques during the masticatory power stroke and during transducer biting. Galagos consistently had much more strain on the working side of the mandibular corpus than on the balancing side. These experiments support the hypothesis that galagos, in contrast to macaques, employ a larger amount of working-side muscle force relative to the balancing-side muscle force during unilateral biting and mastication, and that the fused mandibular symphysis is an adaption to use a maximal amount of balancing-side muscle force during unilateral biting and mastication. These experiments also demonstrate the effects that rosette position, bite force magnitudes, and types of food eaten have on recorded mandibular strain patterns.     

Factors influencing the anterior component of occlusal force

We hypothesized that the anterior component of occlusal force (ACF) generated by mandibular molars was a function of molar inclination, height of the transverse condylar axis above the occlusal plane, steepness of the occlusal plane, gape, molar root dimensions, interproximal tooth contact force when not biting, and bite force. Our research aim was to identify those biomechanical factors which determine ACF. Mandibular second molars were axially loaded with a 90 N force (10 mm second molar gape) in 15 subjects, and the resulting ACF was measured at the mandibular first molar-second premolar contact using a recording technique based on interproximal frictional forces. Morphologic measurements were obtained from lateral cephalometric radiographs of each subject and included: Frankfort mandibular plane angle, occlusal plane angle, angles formed by the longitudinal axis of the second molar and the occlusal and mandibular planes, perpendicular distance from the top of the condyle to the occlusal plane, and second molar root width and root length. For ten subjects, ACF resulting from axial loads of 50, 100, 150, and 200 N was measured. For ten subjects, ACF resulting from an axial load of 50 N and second molar gapes of 10 mm, 14 mm, 18 mm, and 22 mm were measured. ACF increased with increasing gape and increased proportionally to increasing bite force. Correlation and stepwise regression analyses revealed that ACF varies with interproximal tooth contact force when not biting (contact ‘tightness’) and molar root width (model R² = 0.71, p < 0.01). The hypothesis that ACF is a function of bite force, gape, molar root width, and interproximal contact tightness has been supported, and the hypothesis that ACF is a function of molar inclination, occlusal plane steepness, condylar axis height, and root length was rejected.     

Experimental analysis of temporomandibular joint reaction force in macaques

Mandibular bone strain in the region immediately below the temporomandibular ligament was analyzed in adult and sub-adult Macaca fascicularis and Macaca mulatta. Following recovery from the general anesthetic, the monkeys were presented food objects, a wooden rod, or a specially designed bite-force transducer. Bone strain was recorded during incisal biting and mastication of food, and also during isometric biting of the rod and/or the transducer. The bone strain data suggest the following: The macaque TMJ is loaded by a compressive reaction force during the power stroke of mastication and incision of food, and during isometric molar and incisor biting. TMJ reaction forces are larger on the contralateral side during both mastication and isometric molar biting. Patterns of ipsilateral TMJ reaction force in macaques during isometric biting vary markedly in response to the position of the bite point. During biting along the premolars or first two molars a compressive reaction force acts about the ipsilateral TMJ; however, when the bite point is positioned along the M3, the ipsilateral TMJ has either very little compressive stress, no stress, or it is loaded in tension.     

Mandibular biomechanics and temporomandibular joint function in primates.

There is disagreement as to whether the mandibular condyles are stress-bearing or stress-free during mastication. In support of alternative models, analogies have been drawn with Class III levers, links, and couple systems. Physiological data are reviewed which indicate that maximum masticatory forces are generated when maxillary and mandibular teeth are in contact, and that this phase lasts for over 100 msec during many chewing strokes. During this period, the mandible can be modeled as a beam with multiple supports. Equations of simple beam theory suggest that large condylar reaction forces are present during mastication. With unilateral molar biting in man, the total condylar reaction force may be over 75% of the bite force. Analysis of a frontal projection demonstrates that up to 80% of the total condylar reaction force is borne by the contralateral (balancing side) condyle during unilateral molar biting. A comparison of human, chimpanzee (P. troglodytes), spider monkey (A. belzebuth), and macaque (Macaca sp.) morphology indicates that the frugivorous chimpanzee and spider monkey have a relatively lower condylar reaction force than the omnivorous macaque or man during molar biting. The percentage reaction force during incisal biting is lower in man than in the other primates, and lower in the frugivorous primates than in the macaque.     

In vivo bone strain in the mandible of Galago crassicaudatus.

Single element foil strain gages were bonded to mandibular cortical bone in eight specimens of Galago crassicaudatus. The gage was bonded below the Pm4 or M2 adjacent to the lower border of the mandible. The bonded strain gage was connected to form one arm of a Wheatstone bridge. Following recovery from the general anesthetic, the restrained Galago bit either a piece of wood, a food object, or a bite force transducer. During these biting episodes, mandibular bone strain deformed the strain gage and the resulting change in electrical resistance of the gage caused voltage changes across the Wheatstone bridge. These changes, directly proportional to the amount of bone strain along the gage site, were recovered by a strip chart recorder. Bone strain was measured on both the working and balancing sides of the jaws. Maximum values of bone strain and bite force were 435 microstrain (compression) and 8.2 kilograms respectively. During bending of the mandible, the correlation between bone strain (tension or compression) and bite force ranged from -0.893 (tension) to 0.997 (compression). The experiments reported here demonstrate that only a small percentage of the Galago bite force is due to balancing side muscle force during isometric unilateral molar biting. In addition, these experiments demonstrate that the Galago mandible is bent in a predictable manner during biting. The amount of apparent mandibular bone strain is dependent on (1) the magnitude of the bite force and (2) the position of the bite point.     

Balancing function of the masticatory muscles during incisal biting in two murid rodents,Apodemus speciosus and Clethrionomys rufocanus

The functional significance of masticatory muscle direction was estimated using a mechanical model in two murid rodents: the Japanese field mouse (Apodemus speciosus) and the gray red-backed vole (Clethrionomys rufocanus). Theoretical analyses of the data suggest that a balancing mechanism among the muscle forces occurs during incisal power stroke. The activation of the large deep masseter in both murids results in marked tensile separation of two hemimandibles at the flexible mandibular symphysis. Activation of the internal pterygoid decreases this large tensile force at the symphysis more efficiently than other muscles. The lines of action of the deep masseter and internal pterygoid are aligned to produce such a balancing function in both species studied here. The resultant force generated by the deep masseter on both sides is opposite in direction to the reaction force at the lower incisor tip. Therefore, the large deep masseter forms an effective mandibular support mechanism when the reaction forces during biting push the mandible downward. Because of the area of insertion and the line of action, the posterior temporalis appears to have an important role in stabilizing the position of the mandibular condyle in the glenoid fossa during incisal biting. J. Morphol. 236:49–56, 1998. © 1998 Wiley-Liss, Inc.     

The human mandible: Lever,link, or both?

Hylander ('78) recently published important new data on bite force in humans, and showed that the human mandible cannot function purely as a link during incisal biting. He concluded instead that the mandible acts as a lever. Reexamination of Hylander's data suggests that the mandible cannot function purely as a lever either, and in fact it probably functions simultaneously as both lever and link during incisal biting.     

Jaw-muscle activity in ferrets, Mustela putorius furo.

Electromyographical (EMG) activity was recorded bilaterally from the masseter and temporalis muscles of alert ferrets (Mustela putorius furo) during mastication and crushing. Electromyographic activity was also recorded during biting while a bite-force transducer placed between the carnassial teeth registered forces ranging from 1.5 to 48.8 N. Linear regression analysis demonstrates that temporalis and masseter EMG activity are linearly related to bite force. Electromyographic activity from the balancing-side muscles is nearly equal to EMG activity of the working-side muscles during bone crushing with the carnassial teeth. It is hypothesized that a high percentage of balancing-side muscle activity in ferrets can be recruited during carnassial biting because the postglenoid process prevents ventral displacement of the working-side mandibular condyle.     

Altered control of submaximal bite force during bruxism in humans

The control of bite force during varying submaximal loads was examined in patients suffering from bruxism compared to healthy humans not showing these symptoms. The subjects raised a bar (preload) with their incisor teeth and held it between their upper and lower incisors using the minimal bite force required to keep the bar in a horizontal position. Further loading was added during the preload phase. A sham load was also used. Depending on the session, the teeth were loaded by the experimenter or the subject and in one session the subject did not see the load (no visual feedback). The bite force was measured continuously using a calibrated force transducer. In all the subjects, the bite force increased with increasing load. Following the addition of the load, the level of the tonic bite force was reached rapidly with no marked overshoot. The patients with bruxism used significantly higher bite forces to hold the submaximal loads compared to the control subjects. In the control subjects, the holding forces for each submaximal load were identical in the men and the women and were independent of subject maximal bite force. Sham loading evoked no marked responses in biting force. Whether the subject or the experimenter added the load or whether the subject had visual feedback or not were not significant factors in determining the level of bite force. The results indicated that the patients with bruxism used excessively large biting forces for each given submaximal load. This study showed no evidence that the inappropriate control of bite force by patients with bruxism was due to an abnormality in the higher cortical circuits that regulates the function of trigeminal motoneurons in the brainstem. This was shown by a lack of abnormality in coordination of voluntary hand movement with biting force, a lack of abnormal anticipation response to a sham load and a lack of any effect of visual feedback. The results were in line with the hypothesis that afferent input from oral (periodontal or masticatory muscle) tissues does not provide an appropriate control of motor command in bruxism.     

Bite forces and their resultants during forceful intercuspal clenching in humans

We aimed to develop a method of gathering complete information on the system of bite forces acting on the dental arches during clenching with the teeth in maximum intercuspation. Further, we attempted to reduce this system into an equivalent wrench—a force–couple system comprising a single force and a single couple acting along a unique line of action. We investigated the normative distribution of the bite forces and the location and orientation of their resultant wrench in 30 young adults (18–23 yr) with natural dentitions. The number of detected occlusal contacts varied from 12 to 46 (mean: 26.1; SD: 8.4), and was significantly greater for the molars than the premolar and anterior teeth, as were the bite-force magnitudes at individual occlusal contacts (1.2–218.4 N); those resulted in the antero-posteriorly slanted bite-force distribution. The magnitude of the bite-force resultants varied from 246.9 to 2091.9 N, and the points at which the resultant wrench axes intersected the mandibular occlusal plane were located 21.3–37.6 mm posterior to the incisal point and less than 8.9 mm from the midline bilaterally. The bite-force resultant was slightly inclined anteriorly from the perpendicular direction to the mandibular occlusal plane. Our method of using pressure-sensitive films to obtain information on all parameters needed to mechanically define a force (such as magnitude, direction, and point of application) is novel. To our knowledge, this is the first study investigating the system of bite forces during forceful intercuspal clenching in six degrees-of-freedom.     

Influence of bite force on jaw muscle activity ratios in subject-controlled unilateral isometric biting

Ratios of muscle activities in unilateral isometric biting are assumed to provide information on strategies of muscle activation independently from bite force. If valid, this assumption would facilitate experiments as it would justify subject-control instead of transducer-based force control in biting studies. As force independence of ratios is controversial, we tested whether activity ratios are associated with bite force and whether this could affect findings based on subject-controlled force. In 52 subjects, bite force and bilateral masseter and temporalis electromyograms were recorded during unilateral biting on a transducer with varying force levels and with uniform subject-controlled force. Working/balancing and temporalis/masseter ratios of activity peaks were related to bite force peaks. Activity ratios were significantly but weakly correlated with the bite force. The subject-controlled force varied within ±25% around the prescribed force in 95% of all bites. This scatter could cause a variation of group mean activity ratios of at most ±6% because of the weak correlation between bite force and ratios. As this small variation is negligible in most cases, subject-control of bite force can be considered an appropriate method to obtain group means of relative muscle activation in particular when force control with transducers is not feasible.     

The human mandible: Lever or link?

The mammalian mandible, and in particular the human mandible, is generally thought to function as a lever during biting. This notion, however, has not gone unchallenged. Various workers have suggested that the mandible does not function as a lever, and they base this proposition on essentially two assertions: (1) the resultant of the forces produced by the masticatory muscles always passes through the bite point; (2) the condylar neck and/or the temporomandibular joint is unsuited to withstand reaction forces during biting. A review of the electromyographic data and of the properties of the tissues of the temporomandibular joint do not support the non-lever hypothesis of mandibular function. In addition, an analysis of the strength of the condylar neck demonstrates that this structure is strong enough to withstand the expected reaction force during lever action. Ordinarily the human mandible and the forces that act upon it are analyzed solely in the lateral projection. Moments are then usually analyzed about the mandibular condyle; however, some workers have advocated taking moments about other points, e.g., the instantaneous center of rotation. Obviously it makes no difference as to what point is chosen since the moments about any point during equilibrium conditions are equal to zero. It is also useful to analyze the forces acting on the mandible in the frontal projection, particularly during unilateral biting. The electromyographic data suggest that during powerful unilateral molar biting the resultant adductor muscle force is passing between the bite point and the balancing (non-biting side) condyle. Therefore, in order for this system to be in equilibrium there must be a reaction force acting on the balancing condyle. This suggests that reaction forces are larger on the balancing side than on the working side, and possibly explains why individuals with a painful temporomandibular joint usually prefer to bite on the side of the diseased joint.     

The functional significance of primate mandibular form.

A stress analysis of the primate mandible suggests that vertically deep jaws in the molar region are usually an adaptation to counter increased sagittal bending stress about the balancing-side mandibular corpus during unilateral mastication. This increased bending stress about the balancing side is caused by an increase in the amount of balancing-side muscle force. Furthermore, this increased muscle force will also cause an increase in dorso-ventral shear stress along the mandibular symphysis. Since increased symphyseal stress can be countered by symphyseal fusion and as increased bending stress can be countered by a deeper jaw, deep jaws and symphyseal fusion are often part of the same functional pattern. In some primates (e.g., Cercocebus albigena), deep jaws are an adaptation to counter bending in the sagittal plane during powerful incisor biting, rather than during unilateral mastication. The stress analysis of the primate mandible also suggests that jaws which are transversely thick in the molar region are an adaptation to counter increased torsion about the long axis of the working-side mandibular corpus during unilateral mastication. Increased torsion of the mandibular corpus can be caused by an increase in masticatory muscle force, an increase in the transverse component of the postcanine bite force and/or an increase in premolar use during mastication. Patterns of masticatory muscle force were estimated for galagos and macaques, demonstrating that the ratio of working-side muscle force to balancing-side muscle force is approximately 1.5:1 in macaques and 3.5:1 in galagos during unilateral isometric molar biting. These data support the hypothesis that mandibular symphyseal fusion is an adaptative response to maximize unilateral molar bite force by utilizing a greater percentage of balancing-side muscle force.     

Incisal orientation and biting efficiency

Broad-edged 'spatulate' upper and lower incisors are distinctive of catarrhines and platyrrhines who use them in various ways to peel fruits, remove bark, and strip leaves from branches. The incisors of modern humans not only control the bite size of foods during ingestion, but often grip items in a number of non-food related tasks. Such uses have long been implicated for Neandertals as well. Despite the evolutionary importance of incision and the fact that the incisors feature prominently in clinical dentistry (via orthodontic practices designed both to correct incisal misalignments and adjust their orientation), little is known about what affects their functional efficiency. Few mechanical analyses of incisal action have been published and none that seem to take note of the mechanisms of both fracture and friction at the tooth-food interface. Here, we modeled the incisal tip as a wedge, finding that the efficiency of biting foods that fracture elastically is strongly dependent on both the apex angle of the incisor and the coefficient of friction. Based on apex angle measurements from a small sample of human central incisors, the overall efficiency of upper central incisors is predicted to be greatest when the angle between the apex bisector and the direction of applied force is zero. However, this is complicated greatly by friction, particularly for the lower incisors. The analysis probably applies not only to the use of incisors by humans, but also to some extent to frugivorous primates. This model should clarify the mechanics behind incision and can provide a basic foundation upon which more advanced models can be built on in the future.     

Fast and Powerful: Biomechanics and Bite Forces of the Mandibles in the American Cockroach Periplaneta americana

Knowing the functionality and capabilities of masticatory apparatuses is essential for the ecological classification of jawed organisms. Nevertheless insects, especially with their outstanding high species number providing an overwhelming morphological diversity, are notoriously underexplored with respect to maximum bite forces and their dependency on the mandible opening angles. Aiming for a general understanding of insect biting, we examined the generalist feeding cockroach Periplaneta americana, characterized by its primitive chewing mouth parts. We measured active isometric bite forces and passive forces caused by joint resistance over the entire mandibular range with a custom-built 2D force transducer. The opening angle of the mandibles was quantified by using a video system. With respect to the effective mechanical advantage of the mandibles and the cross-section areas, we calculated the forces exerted by the mandible closer muscles and the corresponding muscle stress values. Comparisons with the scarce data available revealed close similarities of the cockroaches’ mandible closer stress values (58 N/cm2) to that of smaller specialist carnivorous ground beetles, but strikingly higher values than in larger stag beetles. In contrast to available datasets our results imply the activity of faster and slower muscle fibres, with the latter becoming active only when the animals chew on tough material which requires repetitive, hard biting. Under such circumstances the coactivity of fast and slow fibres provides a force boost which is not available during short-term activities, since long latencies prevent a specific effective employment of the slow fibres in this case.     

The effects of biting and pulling on the forces generated during feeding in the Komodo dragon (Varanus komodoensis)

In addition to biting, it has been speculated that the forces resulting from pulling on food items may also contribute to feeding success in carnivorous vertebrates. We present an in vivo analysis of both bite and pulling forces in Varanus komodoensis, the Komodo dragon, to determine how they contribute to feeding behavior. Observations of cranial modeling and behavior suggest that V. komodoensis feeds using bite force supplemented by pulling in the caudal/ventrocaudal direction. We tested these observations using force gauges/transducers to measure biting and pulling forces. Maximum bite force correlates with both body mass and total body length, likely due to increased muscle mass. Individuals showed consistent behaviors when biting, including the typical medial-caudal head rotation. Pull force correlates best with total body length, longer limbs and larger postcranial motions. None of these forces correlated well with head dimensions. When pulling, V. komodoensis use neck and limb movements that are associated with increased caudal and ventral oriented force. Measured bite force in Varanus komodoensis is similar to several previous estimations based on 3D models, but is low for its body mass relative to other vertebrates. Pull force, especially in the ventrocaudal direction, would allow individuals to hunt and deflesh with high success without the need of strong jaw adductors. In future studies, pull forces need to be considered for a complete understanding of vertebrate carnivore feeding dynamics.     

Mandibular corpus strain in primates: Further evidence for a functional link between symphyseal fusion and jaw-adductor muscle force

Previous work indicates that compared to adult thick-tailed galagos, adult long-tailed macaques have much more bone strain on the balancing-side mandibular corpus during unilateral isometric molar biting (Hylander [1979a] J. Morphol. 159:253–296). Recently we have confirmed in these same two species the presence of similar differences in bone-strain patterns during forceful mastication. Moreover, we have also recorded mandibular bone strain patterns in adult owl monkeys, which are slightly smaller than the galago subjects. The owl monkey data indicate the presence of a strain pattern very similar to that recorded for macaques, and quite unlike that recorded for galagos. We interpret these bone-strain pattern differences to be importantly related to differences in balancing-side jaw-adductor muscle force recruitment patterns. That is, compared to galagos, macaques and owl monkeys recruit relatively more balancing-side jaw-adductor muscle force during forceful mastication. Unlike an earlier study (Hylander [1979b] J. Morphol. 160:223–240), we are unable to estimate the actual amount of working-side muscle force relative to balancing-side muscle force (i.e., the W/ B muscle force ratio) in these species because we have no reliable estimate of magnitude, direction, and precise location of the bite force during mastication. A comparison of the mastication data with the earlier data recorded during isometric molar biting, however, supports the hypothesis that the two anthropoids have a small W/ B jaw-adductor muscle force ratio in comparison to thick-tailed galagos. These data also support the hypothesis that increased recruitment of balancing-side jaw-adductor muscle force in anthropoids is functionally linked to the evolution of symphyseal fusion or strengthening. Moreover, these data refute the hypothesis that the recruitment pattern differences between macaques and thick-tailed galagos are due to allometric factors. Finally, although the evolution of symphyseal fusion in primates may be linked to increased stress associated with increased balancing-side muscle force, it is currently unclear as to whether the increased force is predominately vertically directed, transversely directed, or is a near equal combination of these two force components (cf. Ravosa and Hylander [1994] In Fleagle and Kay [eds.]: Anthropoid Origins. New York: Plenum, pp. 447–468). Am J Phys Anthropol 107:257-271, 1998. © 1998 Wiley-Liss, Inc.     

Efficiency as a predictor of human jaw design in the sagittal plane

The effects of changing the direction of the bite force and of the mandibular joint reaction have been studied with a mathematical model assisted by a computer using the technique of linear programming. We conclude the following: In the sagittal plane the long axes of lower molars are each tilted in the direction that most efficiently converts muscle force into work at the bite point rather than in the direction that would maximize static bite force. These genetically determined angles are referred to as the most 'work efficient' angles. Collectively they lead to the appearance of the curve of Spee associated with the postcanines. Given the most work efficient angle of the first molar, the model indicates for bite forces generated in this direction the joint reaction is least when tilted forward from the vertical at between 20 degrees and 30 degrees. The joint reaction is normal to the articular surface of the condyle which is itself tilted forward 20-30 degrees from the occlusal plane. We conclude the condyle and articular eminence are remodelled to the angle that minimizes the joint reaction. The direction of the bite force may be controlled via neuronal circuitry connecting mechanoreceptors of the periodontal ligament with motor nerves supplying the jaw-closing muscles. The height of the occlusal plane in the molar region has little effect on jaw efficiency.     

Comparative functional analysis of skull morphology of tree-gouging primates

Many primates habitually feed on tree exudates such as gums and saps. Among these exudate feeders, Cebuella pygmaea, Callithrix spp., Phaner furcifer, and most likely Euoticus elegantulus elicit exudate flow by biting into trees with their anterior dentition. We define this behavior as gouging. Beyond the recent publication by Dumont ([1997] Am J Phys Anthropol 102:187-202), there have been few attempts to address whether any aspect of skull form in gouging primates relates to this specialized feeding behavior. However, many researchers have proposed that tree gouging results in larger bite force, larger internal skull loads, and larger jaw gapes in comparison to other chewing and biting behaviors. If true, then we might expect primate gougers to exhibit skull modifications that provide increased abilities to produce bite forces at the incisors, withstand loads in the skull, and/or generate large gapes for gouging.We develop 13 morphological predictions based on the expectation that gouging involves relatively large jaw forces and/or jaw gapes. We compare skull shapes for P. furcifer to five cheirogaleid taxa, E. elegantulus to six galagid species, and C. jacchus to two tamarin species, so as to assess whether gouging primates exhibit these predicted morphological shapes. Our results show little morphological evidence for increased force-production or load-resistance abilities in the skulls of these gouging primates. Conversely, these gougers tend to have skull shapes that are advantageous for creating large gapes. For example, all three gouging species have significantly lower condylar heights relative to the toothrow at a given mandibular length in comparison with closely related, nongouging taxa. Lowering the height of the condyle relative to the mandibular toothrow should reduce the stretching of the masseters and medial pterygoids during jaw opening, as well as position the mandibular incisors more anteriorly at wide jaw gapes. In other words, the lower incisors will follow a more vertical trajectory during both jaw opening and closing.We predict, based on these findings, that tree-gouging primates do not generate unusually large forces, but that they do use relatively large gapes during gouging. Of course, in vivo data on jaw forces and jaw gapes are required to reliably assess skull functions during gouging.     

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.