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.     

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.     

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.     

Masticatory Muscle Anatomy and Feeding Efficiency of the American Beaver, <Emphasis Type="Italic">Castor canadensis</Emphasis> (Rodentia,Castoridae)

Beavers are well-known for their ability to fell large trees through gnawing. Yet, despite this impressive behavior, little information exists on their masticatory musculature or the biomechanics of their jaw movements. It was hypothesized that beavers would have a highly efficient arrangement of the masticatory apparatus, and that gnawing efficiency would be maintained at large gape. The head of an American beaver, Castor canadensis, was dissected to reveal the masticatory musculature. Muscle origins and insertions were noted, the muscles were weighed and fiber lengths measured. Physiological cross-sectional areas were determined, and along with the muscle vectors, were used to calculate the length of the muscle moment arms, the maximum incisor bite force, and the proportion of the bite force projected along the long axis of the lower incisor, at occlusion and 30° gape. Compared to other sciuromorph rodents, the American beaver was found to have large superficial masseter and temporalis muscles, but a relatively smaller anterior deep masseter. The incisor bite force calculated for the beaver (550–740 N) was much higher than would be predicted from body mass or incisor dimensions. This is not a result of the mechanical advantage of the muscles, which is lower than most other sciuromorphs, but is likely related to the very high percentage (>96 %) of bite force directed along the lower incisor long axis. The morphology of the skull, mandible and jaw-closing muscles enable the beaver to produce a very effective and efficient bite, which has permitted beavers to become highly successful ecosystem engineers.     

Estimates of forces exerted by the jaw muscles of some reptiles

Masses and muscle fibre lengths have been determined for the jaw muscles of Chrysemys (Chelonia). Varanus (Lacertilia) and Caiman (Crocodilia). Hence the force that each muscle can exert has been estimated. The position and direction of the line of action of each force have also been determined. The results are used to calculate the magnitude and direction of the bite forces that each reptile could exert, at particular positions in its mouth, and the magnitude and direction of the reactions at the jaw articulation.     

A biomechanical model for analysis of muscle force,power output and lower jaw motion in fishes

Fish skulls are complex kinetic systems with movable components that are powered by muscles. Cranial muscles for jaw closing pull the mandible around a point of rotation at the jaw joint using a third-order lever mechanism. The present study develops a lever model for the jaw of fishes that uses muscle design and the Hill equation for nonlinear length-tension properties of muscle to calculate dynamic power output. The model uses morphometric data on skeletal dimensions and muscle proportions in order to predict behavior and force transmission mediated by lever action. The computer model calculates a range of dynamic parameters of jaw function including muscle force, torque, effective mechanical advantage, jaw velocity, bite duration, bite force, work and power. A complete list of required morphometrics is presented and a software program (MandibLever 2.0) is available for implementing lever analysis. Results show that simulations yield kinematics and timing profiles similar to actual fish feeding events. Simulation of muscle properties shows that mandibles reach their peak velocity near the start of jaw closing, peak force at the end of jaw closing, and peak power output at about 25% of the closing cycle time. Adductor jaw muscles with different mechanical designs must have different contractile properties and/or different muscle activity patterns to coordinate jaw closing. The effective mechanical advantage calculated by the model is considerably lower than the mechanical advantage estimated from morphological lever ratios, suggesting that previous studies of morphological lever ratios have overestimated force and underestimated velocity transmission to the mandible. A biomechanical model of jaw closing can be used to interpret the mechanics of a wide range of jaw mechanisms and will enable studies of the functional results of developmental and evolutionary changes in skull morphology and physiology.     

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.     

Occlusal force and craniofacial biomechanics during growth in rhesus monkeys

The masticatory muscles in 132 anesthetized male and female rhesus monkeys ranging in age from juvenile to adult were unilaterally stimulated. Muscle forces and speeds were measured with a bite force transducer positioned at the incisors, premolars, and molars during twitch and tetanic contractions. Lateral cephalographs of all animals were used to estimate the orientation and mechanical advantage of the masticatory muscles. Results showed that maximal occlusal forces increased at a greater rate than body weight during growth. However, maximal occlusal forces increased isometrically relative to mandibular length. Mean forces at the incisors ranged from 70.3 newtons (n) in juveniles up to 139.9 n in adult males. Forces at the molars were 2-2.5 times greater than at the incisors. Time-to-peak tension decreased with increasing body size from 44.1 msec in juveniles to 37.4 msec in adult females to 31.0 msec in adult males. Regression analysis showed that adult males have faster muscles than adult females or juveniles even when corrected for body size. Temporalis and masseter orientation was found to change little throughout growth. The mechanical advantage of the masseter and temporalis muscles for producing occlusal forces on the distal molars improved between juveniles and adults, which is contrary to findings of Oyen et al. (Growth 43:174-187, 1979). Among adults, females had a greater mechanical advantage of the masseter muscles than males.     

Characterization of food physical properties by the mastication parameters measured by electromyography of the jaw-closing muscles and mandibular kinematics in young adults

The relationship between the physical properties of solid food and the masticatory parameters is clarified. Eight solid foods of varying physical properties were chosen. Electromyography of the jaw-closing muscles and mandibular kinematics in eleven young subjects were recorded. The masticatory parameters were derived from the recorded data for the entire mastication process, for the first bite, and in the early, middle, and late stages of mastication. After calculating values relative to the mean value for each subject, nine parameters representing each group were chosen through a cluster analysis. Three principal components were extracted, each of them related to the masticatory time and cycle, minimum jaw opening at the early stage of mastication, and masticatory force. The principal component scores for each food were different, except for one combination in which the physical properties under large and extra-large deformations were similar, despite different breaking properties or small deformation properties. The masticatory parameters did not correlate with the physical properties of food measured for small deformation.     

Predicted pattern of human muscle activity during clenching derived from a computer assisted model: symmetric vertical bite forces

A computer assisted three-dimensional model of the jaw, based on linear programming, is presented. The upper and lower attachments of the muscles of mastication have been measured on a single human skull and divided into thirteen independent units on each side--a total of 26 muscle elements. The direction (in three dimensions) and maximum forces that could be developed by each muscle element, the bite reaction and two joint reactions are included in the model. It is shown for symmetrical biting that a model which minimizes the sum of the muscle forces used to produce a given bite force activates muscles in a way which corresponds well with previous observations on human subjects. A model which minimizes the joint reactions behaves differently and is rejected. An analysis of the way the chosen model operates suggests that there are two types of jaw muscles, power muscles and control muscles. Power muscles (superficial masseter, medial pterygoid and some of temporalis) produce the bite force but tend to displace the condyle up or down the articular eminence. This displacement is prevented by control muscles (oblique temporalis and lateral pterygoid) which have very poor moment arms for generating usual bite forces, but are efficient for preventing condylar slide. The model incorporates the concept that muscles consist of elements which can contract independently. It predicts that those muscle elements with longer moment arms relative to the joint are the first to be activated and, as the bite force increases, a ripple of activity spreads into elements with shorter moment arms. In general, the model can be used to study the three-dimensional activity in any system of joints and muscles.     

Characterization of Food Physical Properties by the Mastication Parameters Measured by Electromyography of the Jaw-Closing Muscles and Mandibular Kinematics in Young Adults

The relationship between the physical properties of solid food and the masticatory parameters is clarified. Eight solid foods of varying physical properties were chosen. Electromyography of the jaw-closing muscles and mandibular kinematics in eleven young subjects were recorded. The masticatory parameters were derived from the recorded data for the entire mastication process, for the first bite, and in the early, middle, and late stages of mastication. After calculating values relative to the mean value for each subject, nine parameters representing each group were chosen through a cluster analysis. Three principal components were extracted, each of them related to the masticatory time and cycle, minimum jaw opening at the early stage of mastication, and masticatory force. The principal component scores for each food were different, except for one combination in which the physical properties under large and extra-large deformations were similar, despite different breaking properties or small deformation properties. The masticatory parameters did not correlate with the physical properties of food measured for small deformation.     

Craniomandibular System and Postural Balance after 3-Day Dry Immersion

The objective of the study was to determine the influence of simulated microgravity by exposure to dry immersion on the craniomandibular system. Twelve healthy male volunteers participated in a 3-day dry immersion study. Before and immediately after exposure we measured maximal bite force using piezoresistive sensors. The mechanical properties of the jaw and cervical muscles were evaluated before, during, and after dry immersion using MyotonPRO. Because recent studies reported the effects of jaw motor activity on the postural stability of humans, stabilometric measurements of center of pressure were performed before and after dry immersion in two mandibular positions: rest position without jaw clenching, and intercuspidal position during voluntary teeth clenching. Results revealed no significant changes of maximal bite force after dry immersion. All postural parameters were significantly altered by dry immersion. There were however no significant differences in stabilometric data according to mandibular position. Moreover the masseter tonicity increased immediately after the end of dry immersion period. Dry immersion could be used as a valid model for studying the effects of microgravity on human subjects. However, 3 days appear insufficient in duration to evaluate the effects of weightlessness on maximal bite force. Our research suggests a link between postural disturbance after dry immersion and masseter tonicity.     

Dry versus wet and gross: Comparisons between the dry skull method and gross dissection in estimations of jaw muscle cross-sectional area and bite forces in sea otters

Bite force is a measure of feeding performance used to elucidate links between animal morphology, ecology, and fitness. Obtaining live individuals for in vivo bite-force measurements or freshly deceased specimens for bite force modeling is challenging for many species. Thomason's dry skull method for mammals relies solely on osteological specimens and, therefore, presents an advantageous approach that enables researchers to estimate and compare bite forces across extant and even extinct species. However, how accurately the dry skull method estimates physiological cross-sectional area (PCSA) of the jaw adductor muscles and theoretical bite force has rarely been tested. Here, we use an ontogenetic series of southern sea otters (Enhydra lutris nereis) to test the hypothesis that skeletomuscular traits estimated from the dry skull method accurately predicts test traits derived from dissection-based biomechanical modeling. Although variables from these two methods exhibited strong positive relationships across ontogeny, we found that the dry skull method overestimates PCSA of the masseter and underestimates PCSA of the temporalis. Jaw adductor in-levers for both jaw muscles and overall bite force are overestimated. Surprisingly, we reveal that sexual dimorphism in craniomandibular shape affects temporalis PCSA estimations; the dry skull method predicted female temporalis PCSA well but underestimates male temporalis PCSA across ontogeny. These results highlight the importance of accounting for sexual dimorphism and other intraspecific variation when using the dry skull method. Together, we found the dry skull method provides an underestimation of bite force over ontogeny and that the underlying anatomical components driving bite force may be misrepresented.     

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.     

The functional significance of morphological variation of the human mandible and masticatory muscles

A review is given of what is known about the functional significance of variation of the morphology of the human mandible and jaw muscles. First, the mandible is a lever transferring muscular forces to the teeth. The angle between corpus and ramus and the width of the ramus are particularly relevant in this respect as they determine the mechanical advantage of the lever system and the capacity for sagittal (open-close) movement. The stability of the mandible in asymmetric bites is especially affected by the ratio between the intermolar and intercondylar distances. The repertoire of bite forces that can be generated at any tooth and the loading pattern of the temporomandibular joint are strongly dependent on the relative size of the masseter, temporalis and medial pterygoid muscles. Second, executing its function as a lever, the mandible is subjected to shearing, bending and torsional forces. The bony parts harbouring the teeth, joints and muscle attachments serve to counter these forces; additional strength is needed in three areas i.e. in the symphysis, the condylar neck and in the transition area between corpus and ramus. In human populations there are clear-cut patterns of correlation between some facial skeletal traits, jaw joint morphology and strength and line of action of the jaw muscles. As a result, facial morphologies can be distinguished with marked differences in mechanical performance of their masticatory apparatus. It is suggested that they emerge as a result of diverging environmental influences during postnatal growth.     

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.     

Gape and bite force in the rodents Onychomys leucogaster and Peromyscus maniculatus: Does jaw‐muscle anatomy predict performance?

Compared with the deer mouse, Peromyscus maniculatus, the grasshopper mouse, Onychomys leucogaster, exhibits modifications in its jaw‐muscle architecture that promote wide gapes and large bite forces at wide gapes to prey upon large vertebrate prey. In this study, we determine whether jaw‐muscle anatomy predicts gape and biting performance in O. leucogaster, and we also assess the influence of gape on bite force in the two species. Although O. leucogaster has an absolutely longer jaw, which facilitates larger gapes, maximum passive gape is similar in both species, averaging ～12.5 mm. Thus, when scaled to jaw length, O. leucogaster has a smaller maximum passive gape. These results suggest that predatory behaviors of O. leucogaster may not require remarkably large gapes. On the other hand, both absolute and relative bite forces exerted by O. leucogaster are significantly larger than those of P. maniculatus. The largest bite forces in both species occur at 5.0 mm of gape at the incisors, or 40% of maximum gape. Although bite force in both species decreases at larger gapes, O. leucogaster does maintain a larger percentage of maximum bite force at gapes larger than 40% of maximum passive gape. Therefore, although structural modifications in the masticatory apparatus of O. leucogaster may constrain gape, they may help to maintain bite force at large gapes. These results suggest that increases in gape differentially influence the length‐tension properties of the jaw muscles in the two species. Finally, these results highlight the importance of considering the effect of muscle stretch on force production in comparative studies of bite force. As a first approximation, it appears that gapes of 40–50% of maximum gape in rodents optimizes bite force production at the incisors. J. Morphol., 2009. © 2009 Wiley‐Liss, Inc.     

Electromyography and mechanics of mastication in the albino rat.

The masticatory apparatus in the albino rat was studied by means of electromyography and subsequent estimation of muscular forces. The activity patterns of the trigeminal and suprahyoid musculature and the mandibular movements were recorded simultaneously during feeding. The relative forces of the individual muscles in the different stages of chewing cycles and biting were estimated on the basis of their physiological cross sections and their activity levels, as measured from integrated electromyograms. Workinglines and moment arms of these muscles were determined for different jaw positions. In the anteriorly directed masticatory grinding stroke the resultants of the muscle forces at each side are identical; they direct anteriorly, dorsally and slightly lingually and pass along the lateral side of the second molar. Almost the entire muscular resultant force is transmitted to the molars while the temporo-mandibular joint remains unloaded. A small transverse force, produced by the tense symphyseal cruciate ligaments balances the couple of muscle resultant and molar reaction force in the transverse plane. After each grinding stroke the mandible is repositioned for the next stroke by the overlapping actions of three muscle groups: the pterygoids and suprahyoids produce depression and forward shift, the suprahyoids and temporal backward shift and elevation of the mandible while the subsequent co-operation of the temporal and masseter causes final closure of the mouth and starting of the forward grinding movement. All muscles act in a bilaterally symmetrical fashion. The pterygoids contract more strongly, the masseter more weakly during biting than during chewing. The wide gape shifts the resultant of the muscle forces more vertically and moreposteriorly. The joint then becomes strongly loaded because the reaction forces are applied far anteriorly on the incisors. The charateristic angle between the almost horizontal biting force and the surface of the food pellet indicates that the lower incisors produce a chisel-like action. Tooth structure reflects chewing and biting forces. The transverse molar lamellae lie about parallel to the chewing forces whereas perpendicular loading of the occlusal surfaces is achieved by their inclination in the transverse plane. The incisors are loaded approximately parallel to their longitudinal axis, placement that avoids bending forces during biting. It is suggested that a predominantly protrusive musculature favors the effective force transmission to the lower incisors, required for gnawing. By grinding food across transversely oriented molar ridges the protrusive components of the muscles would be utilized best. From the relative weights of the masticatory muscles in their topographical relations with joints, molars and incisors it may be concluded that the masticatory apparatus is a construction adapted to optimal transmission of force from muscles to teeth.     

Morphology of the Jaw-Closing Musculature in the Common Wombat (Vombatus ursinus) Using Digital Dissection and Magnetic Resonance Imaging

Wombats are unique among marsupials in having one pair of upper incisors, and hypsodont molars for processing tough, abrasive vegetation. Of the three extant species, the most abundant, the common wombat (Vombatus ursinus), has had the least attention in terms of masticatory muscle morphology, and has never been thoroughly described. Using MRI and digital dissection to compliment traditional gross dissections, the major jaw adductor muscles, the masseter, temporalis and pterygoids, were described. The masseter and medial pterygoid muscles are greatly enlarged compared to other marsupials. This, in combination with the distinctive form and function of the dentition, most likely facilitates processing a tough, abrasive diet. The broad, flat skull and large masticatory muscles are well suited to generate a very high bite force. MRI scans allow more detail of the muscle morphology to be observed and the technique of digital dissections greatly enhances the knowledge obtained from gross dissections.     

The retro-articular process, streptostyly and the caecilian jaw closing system

Caecilians have two functionally separate sets of jaw closing muscles. The jaw adductor muscles are parallel fibered muscles positioned close to the jaw joint and their lever mechanics suggests they are well suited to rapidly closing the jaws. A second set of muscles, the hypaxial interhyoideus posterior (IHP), levers the jaws closed by pulling on the retroarticular process (RA) of the lower jaw. Models of the lower jaw point out that the angle and length of the RA has a profound effect on the closure force exerted by the IHP. The caecilian skull is streptostylic – the quadrate-squamosal apparatus (QSA) moves relative to the rest of the skull, a condition that seems at odds with a well-ossified cranium. Modeling the contribution of this streptostylic suspension of the lower jaw shows that rotational freedom of the QSA amplifies the force of the IHP by redirecting force applied along the low axis of the lower jaw. Measurements from several species and life stages of preserved caecilians reveal a large variation in predicted bite force (as a multiple of IHP force) with age and phylogeny.