Mechanoreceptor distribution in stag beetle jaws corresponds to the material stress in fights

Male stag beetles (Lucanidae) use their extremely elongated jaws to pinch their rivals forcefully in male–male battles. The morphology of these jaws has to be a compromise between robustness (to withstand the bite forces), length and weight. Cyclommatus metallifer stag beetles circumvent this trade-off by reducing their bite force when biting with their slender jaw tips. Here we describe the functional mechanism behind the force modulation behaviour. Scanning Electron Microscopy and micro CT imaging show large numbers of small sensors in the jaw cuticle. We find a strong correlation between the distribution of these sensors and that of the material stress in the same jaw region during biting. The jaw sensors are mechanoreceptors with a small protrusion that barely protrudes above the undulating jaw surface. The sensors stimulate dendrites that extend from the neuronal cell body through the entire thickness of the jaw exoskeleton towards the sensors at the external surface. They form a sensory field that functions in a feedback mechanism to control the bite muscle force. This negative feedback mechanism enabled the stag beetles to evolve massive bite muscles without risking overloading their valuable jaws.     

The vector of jaw muscle force as determined by computer-generated three dimensional simulation: a test of Greaves' model

We present results from a detailed three-dimensional finite element analysis of the cranium and mandible of the Australian dingo (Canis lupus dingo) during a range of feeding activities and compare results with predictions based on two-dimensional methodology [Greaves, W.S., 2000. Location of the vector of jaw muscle force in mammals. Journal of Morphology 243, 293-299]. Greaves showed that the resultant muscle vector intersects the mandible line slightly posterior to the lower third molar (m3). Our work demonstrates that this is qualitatively correct, although the actual point is closer to the jaw joint. We show that it is theoretically possible for the biting side of the mandible to dislocate during unilateral biting; however, the bite point needs to be posterior to m3. Simulations show that reduced muscle activation on the non-biting side can considerably diminish the likelihood of dislocation with only a minor decrease in bite force during unilateral biting. By modulating muscle recruitment the animal may be able to maximise bite force whilst minimising the risk of dislocation.     

Jaws that snap: control of mandible movements in the ant Mystrium

Ants of the genus Mystrium employ a peculiar snap-jaw mechanism in which the closed mandibles cross over to deliver a stunning blow to an adversary within about 0.5 ms. The mandible snapping is preceded by antennation and antennal withdrawal. The strike is initiated by contact of the adversary with mechanosensory hairs at the side of the mandible, and is powered by large yet slow closer muscles whose energy is stored by a catapult mechanism. Recording of closer muscle activity indicates that the mandibles are not triggered by any fast muscle. Instead, we suppose that activity differences between the left and right mandible muscles imbalance a pivot at the mandible tip and release the strike. The likelihood for the strike to occur can be modulated by an alarm pheromone. The presence of specialized sensilla and of a complex muscle receptor organ shows that the mandibles are also adapted to functions other than snapping and suggests that the force of the mandible can be finely adjusted for other tasks.     

Trap‐jaws revisited: the mandible mechanism of the ant Acanthognathus

Abstract.Ants of the genus Acanthognathus stalk small insects and catch their prey by a strike with their long, thin mandibles. The mandibles close in less than 2.5 ms and this movement is controlled by a specialized closer muscle. In Acanthognathus , unlike other insects, the mandible closer muscle is subdivided into two distinct parts: as in a catapult, a large slow closer muscle contracts in advance and provides the power for the strike while the mandibles are locked open. When the prey touches specialized trigger hairs, a small fast closer muscle rapidly unlocks the mandibles and thus releases the strike. The fast movement is steadied by large specialized surfaces in the mandible joint and the sensory‐motor reflex is controlled by neurones with particularly large, and thus fast‐conducting, axons.     

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 control of mandible movements in the ant Odontomachus

Ants use their mandibles to manipulate many different objects including food, brood and nestmates. Different tasks require the modification of mandibular force and speed. Besides normal mandible movements the trap-jaw ant Odontomachus features a particularly fast mandible reflex during which both mandibles close synchronously within 3 ms. The mandibular muscles that govern mandible performance are controlled by four opener and eight closer motor neurons. During slow mandible movements different motor units can be activated successively, and fine tuning is assisted by co-activation of the antagonistic muscles. Fast and powerful movements are generated by the additional activation of two particular motor units which also contribute to the mandible strike. The trap-jaw reflex is triggered by a fast trigger muscle which is derived from the mandible closer. Intracellular recording reveals that trigger motor neurons can generate regular as well as particularly large postsynaptic potentials, which might be passively propagated over the short distance to the trigger muscle. The trigger motor neurons are dye-coupled and receive input from both sides of the body without delay, which ensures the synchronous release of both mandibles.     

Comparison between in vivo and theoretical bite performance: Using multi-body modelling to predict muscle and bite forces in a reptile skull

In biomechanical investigations, geometrically accurate computer models of anatomical structures can be created readily using computed-tomography scan images. However, representation of soft tissue structures is more challenging, relying on approximations to predict the muscle loading conditions that are essential in detailed functional analyses. Here, using a sophisticated multi-body computer model of a reptile skull (the rhynchocephalian Sphenodon), we assess the accuracy of muscle force predictions by comparing predicted bite forces against in vivo data. The model predicts a bite force almost three times lower than that measured experimentally. Peak muscle force estimates are highly sensitive to fibre length, muscle stress, and pennation where the angle is large, and variation in these parameters can generate substantial differences in predicted bite forces. A review of theoretical bite predictions amongst lizards reveals that bite forces are consistently underestimated, possibly because of high levels of muscle pennation in these animals. To generate realistic bites during theoretical analyses in Sphenodon, lizards, and related groups we suggest that standard muscle force calculations should be multiplied by a factor of up to three. We show that bite forces increase and joint forces decrease as the bite point shifts posteriorly within the jaw, with the most posterior bite location generating a bite force almost double that of the most anterior bite. Unilateral and bilateral bites produced similar total bite forces; however, the pressure exerted by the teeth is double during unilateral biting as the tooth contact area is reduced by half.     

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.     

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.     

Free body analysis,beam mechanics,and finite element modeling of the mandible of Alligator mississippiensis

The mechanical behavior of mammalian mandibles is well‐studied, but a comprehensive biomechanical analysis (incorporating detailed muscle architecture, accurate material properties, and three‐dimensional mechanical behavior) of an extant archosaur mandible has never been carried out. This makes it unclear how closely models of extant and extinct archosaur mandibles reflect reality and prevents comparisons of structure–function relationships in mammalian and archosaur mandibles. We tested hypotheses regarding the mechanical behavior of the mandible of Alligator mississippiensis by analyzing reaction forces and bending, shear, and torsional stress regimes in six models of varying complexity. Models included free body analysis using basic lever arm mechanics, 2D and 3D beam models, and three high‐resolution finite element models of the Alligator mandible, incorporating, respectively, isotropic bone without sutures, anisotropic bone with sutures, and anisotropic bone with sutures and contact between the mandible and the pterygoid flange. Compared with the beam models, the Alligator finite element models exhibited less spatial variability in dorsoventral bending and sagittal shear stress, as well as lower peak values for these stresses, suggesting that Alligator mandibular morphology is in part designed to reduce these stresses during biting. However, the Alligator models exhibited greater variability in the distribution of mediolateral and torsional stresses than the beam models. Incorporating anisotropic bone material properties and sutures into the model reduced dorsoventral and torsional stresses within the mandible, but led to elevated mediolateral stresses. These mediolateral stresses were mitigated by the addition of a pterygoid‐mandibular contact, suggesting important contributions from, and trade‐offs between, material properties and external constraints in Alligator mandible design. Our results suggest that beam modeling does not accurately represent the mechanical behavior of the Alligator mandible, including important performance metrics such as magnitude and orientation of reaction forces, and mediolateral bending and torsional stress distributions. J.Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

Biomechanics of the masticatory apparatus of Pteropus giganteus (Megachiroptera)

Jaw mechanics in Pteropus were studied by means of a three-dimensional model. The model included several parameters of muscle architecture, combined with quantified movement and electromyographical data. Estimates of the nature of the applied forces that act upon the mandible during a chewing cycle, and subsequent estimates of reaction forces at the bite point and joints during the powerstroke, were thus obtained for different food consistencies. The resultant muscle force (relative to the palate) shifts from upward and slightly backward at large gapes to upward and markedly backward at the end of closing. The resultant simultaneously moves anteriorly. During the powerstroke it retains a constant position and orientation along the thickened anterior edge of the coronoid process. The early stages of opening are guided by the slope of the teeth and mandibular fossa; during the remaining part of opening the working line of the resultant crosses the skull behind the joint and thus acquires an opening moment. The bite force has downward and forward components, and a slight transverse component. For a given applied muscular force its magnitude is larger in more posteriorly positioned bite points. Both joints are loaded, the contralateral one more than the ipsilateral. Food consistency affects magnitude and orientation of the applied force, and hence, magnitude and orientation of the bite force and magnitude of the joint reaction forces. The magnitude of masseter activity relative to temporalis activity appears to be the key factor for the orientation of the bite force, and hence for the mechanical optimal position of the food. The adaptive value of the general topography of the masticatory muscles in Pteropus is discussed.     

The evolution of armament strength: evidence for a constraint on the biting performance of claws of durophagous decapods

Performance data for the claws of six sympatric species of Cancer crabs confirmed a puzzling pattern reported previously for two other decapod crustaceans (stone crabs, Menippe mercenaria, and lobsters, Homarus americanus): Although biting forces increased, maximum muscle stresses (force per unit area) declined with increasing claw size. The negative allometry of muscle stress and the stress at a given claw size were fairly consistent within and among Cancer species despite significant differences in adult body size and relative claw size, but were not consistent among decapod genera. Therefore, claw height can be used as a reliable predictor of maximum biting force for the genus Cancer, but must be used with caution as a predictor of maximum biting force in wider evolutionary and biogeographical comparisons of decapods. The decline in maximum muscle stress with increasing claw size in Cancer crabs contrasts with the pattern in several other claw traits. Significantly, three traits that affect maximal biting force increased intraspecifically with increasing claw size: relative claw size, mechanical advantage, and sarcomere length of the closer muscle. Closer apodeme area and angle of pinnation of the closer muscle fibers varied isometrically with claw size. The concordant behavior of these traits suggests selection for higher biting forces in larger crabs. The contrast between the size dependence of muscle stress (negative allometry) and the remaining claw traits (isometry or positive allometry) strongly suggests that an as yet unidentified constraint impairs muscle performance in larger claws. The negative allometry of muscle stress in two distantly related taxa (stone crabs and lobsters) further suggests this constraint may be widespread in decapod crustaceans. The implications of this performance constraint for the evolution of claw size and the "arms-race" between decapod predators and their hard-shelled prey is discussed.     

Leverage and muscle type in crab chelae (Crustacea: Brachyura)

The chelae of Cancer pagurus and Macropipus depurator were examined with respect to mechanical advantage. The closer muscles were investigated with respect to sarcomere length in the constituent fibres and to the force developed by the whole muscle during isometric contraction. Cancer chelae have a relatively high mechanical advantage, 0.329 ± 001. Cancer closer muscles contain a high proportion of fibres with long sarcomeres, mean lengths mostly falling between 12 and 15 μm, and develop a maximum stress of about 496 kN.m⁻² during contraction. These figures are typical for "slow" crustacean muscle. The chelae of M. depurator are dimorphic. In one, the strong chela, the mechanical advantage is 0.248 ± 0.066 while in the other, the fast chela, the mechanical advantage is 0.177 ± 0.006. M. depurator closer muscles contain fibres with mean sarcomere lengths mostly falling between 6 and 10 μm. The muscle develops a maximum stress of about 145 kN.m⁻² during contraction. These figures are typical of "intermediate" crustacean muscles. "Fast" muscle fibres with short sarcomeres (about 30 um) were found in the chelae of both Cancer and M. depurator but were much commoner in the latter. Thus in Cancer a high mechanical advantage is correlated with slow muscle while in M. depurator lower mechanical advantages are broadly correlated with faster muscle. Consistent correlation between mechanical advantage and muscle type in the dimorphic chelae of M. depurator , however, is lacking. No consistent regionation of fibres with similar properties was found in the muscles.     

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.     

Motor control of the mandible closer muscle in ants

Despite their simple design, ant mandible movements cover a wide range of forces, velocities and amplitudes. The mandible is controlled by the mandible closer muscle, which is composed of two functionally distinct subpopulations of muscle fiber types: fast fibers (short sarcomeres) and slow ones (long sarcomeres). The entire muscle is controlled by 10-12 motor neurons, 4-5 of which exclusively supply fast muscle fibers. Slow muscle fibers comprise a posterior and an antero-lateral group, each of which is controlled by 1-2 motor neurons. In addition, 3-4 motor neurons control all muscle fibers together. Simultaneous recordings of muscle activity and mandible movement reveal that fast movements require rapid contractions of fast muscle fibers. Slow and subtle movements result from the activation of slow muscle fibers. Forceful movements are generated by simultaneous co-activation of all muscle fiber types. Retrograde tracing shows that most dendritic arborizations of the different sets of motor neurons share the same neuropil in the subesophageal ganglion. In addition, fast motor neurons and neurons supplying the lateral group of slow closer muscle fibers each invade specific parts of the neuropil that is not shared by the other motor neuron groups. Some bilateral overlap between the dendrites of left and right motor neurons exists, particularly in fast motor neurons. The results explain how a single muscle is able to control the different movement parameters required for the proper function of ant mandibles.     

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.     

Bone-Breaking Bite Force of Basilosaurus isis (Mammalia,Cetacea) from the Late Eocene of Egypt Estimated by Finite Element Analysis

Bite marks suggest that the late Eocence archaeocete whale Basilosaurus isis (Birket Qarun Formation, Egypt) fed upon juveniles of the contemporary basilosaurid Dorudon atrox. Finite element analysis (FEA) of a nearly complete adult cranium of B. isis enables estimates of its bite force and tests the animal’s capabilities for crushing bone. Two loadcases reflect different biting scenarios: 1) an intitial closing phase, with all adductors active and a full condylar reaction force; and 2) a shearing phase, with the posterior temporalis active and minimized condylar force. The latter is considered probable when the jaws were nearly closed because the preserved jaws do not articulate as the molariform teeth come into occulusion. Reaction forces with all muscles active indicate that B. isis maintained relatively greater bite force anteriorly than seen in large crocodilians, and exerted a maximum bite force of at least 16,400 N at its upper P³. Under the shearing scenario with minimized condylar forces, tooth reaction forces could exceed 20,000 N despite lower magnitudes of muscle force. These bite forces at the teeth are consistent with bone indentations on Dorudon crania, reatract-and-shear hypotheses of Basilosaurus bite function, and seizure of prey by anterior teeth as proposed for other archaeocetes. The whale’s bite forces match those estimated for pliosaurus when skull lengths are equalized, suggesting similar tradeoffs of bite function and hydrodynamics. Reaction forces in B. isis were lower than maxima estimated for large crocodylians and carnivorous dinosaurs. However, comparison of force estimates from FEA and regression data indicate that B. isis exerted the largest bite forces yet estimated for any mammal, and greater force than expected from its skull width. Cephalic feeding biomechanics of Basilosaurus isis are thus consistent with habitual predation.     

Incisal bite force direction in humans and the functional significance of mammalian mandibular translation

Incisal bite force direction was recorded and analyzed in ten human subjects using a specially designed force transducer. In all ten subjects the maxillary incisal bite force was vertically and anteriorly directed both during static biting and during biting associated with simultaneous mandibular translation and rotation. Since the resultant muscle force could not have been equal and opposite to the mandibular bite force, the mandibular condyles must have been loaded. These data demonstrate that the mandible acts as a lever during incisal biting and that there is no consistent relationship between incisal bite force direction and object size. In some individuals the bite force direction was more vertical during biting on a large transducer (30 mm high), while in other subjects it was more vertical during biting on a small transducer (10 mm high).     

Validation of a musculo-skeletal model of the mandible and its application to mandibular distraction osteogenesis

Mandibular distraction osteogenesis will lead to a change in muscle coordination and load transfer to the temporomandibular joints (TMJ). The objective of this work is to present and validate a rigid-body musculo-skeletal model of the mandible based on inverse dynamics for calculation of the muscle activations, muscle forces and TMJ reaction forces for different types of clenching tasks and dynamic tasks. This approach is validated on a symmetric mandible model and an application will be presented where the TMJ reaction forces during unilateral clenching are estimated for a virtual distraction patient with a shortened left ramus. The mandible model consists of 2 rigid segments and has 4 degrees-of-freedom. The model was equipped with 24 hill-type musculotendon actuators. During the validation experiment one subject was asked to do several tasks while measuring EMG activity, bite force and kinematics. The bite force and kinematics were used as input for the simulations of the same tasks after which the estimated muscle activities were compared with the measured muscle activities. This resulted in an average correlation coefficient of 0.580 and an average of the Mean Absolute Error of 0.109. The virtual distraction model showed a large difference in the TMJ reaction forces between left and right compared with the symmetric model for the same loading case. The present work is a step in the direction of building patient-specific mandible models, which can assess the mechanical effects on the TMJ before mandibular distraction osteogenesis surgery.     

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.