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.     

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.     

Maximum isometric arm forces in the horizontal plane

In this paper, we measured the maximum isometric force at the hand in eight directions in the horizontal plane and at five positions in the workplace. These endpoint forces were the result of shoulder horizontal adduction/abduction and elbow flexion/extension torques. We found that the normalized maximum forces of all the six subjects deviated less than 15%, despite intra-subject differences in muscle strength of more than a factor of two. The maximum forces were found to systematically depend on the force direction and on the hand position in the workspace. The largest forces were found in a direction approximately along the line connecting shoulder joint and hand, and the smallest forces perpendicular to that line, thereby forming an elliptically shaped pattern. The elongation of the pattern was the largest for those hand positions having the more extended elbow joint. By using a lumped six-muscle model, with two mono-articular muscle pairs and one bi-articular pair, we were able to predict the observed force patterns. Here, we assumed that one of the muscles generates its maximum force and the others adjust their output to point the endpoint force in the required direction. We used a principal component analysis of the surface EMGs of simultaneously measured representatives of four of the six muscles. With the same model, we were then able to determine the principal directions of all the six muscle groups.     

The growth of the skull and jaw muscles and its functional consequences in the New Zealand rabbit (Oryctolagus cuniculus)

Between weaning and adulthood, the length and height of the facial skull of the New Zealand rabbit (Oryctolagus cuniculus) double, whereas much less growth occurs in the width of the face and in the neurocranium. There is a five-fold increase in mass of the masticatory muscles, caused mainly by growth in cross-sectional area. The share of the superficial masseter in the total mass increases at the cost of the jaw openers. There are changes in the direction of the working lines of a few muscles. A 3-dimensional mechanical model was used to predict bite forces at different mandibular positions. It shows that young rabbits are able to generate large bite forces at a wider range of mandibular positions than adults and that the forces are directed more vertically. In young and adult animals, the masticatory muscles differ from each other with respect to the degree of gape at which optimum sarcomere length is reached. Consequently, bite force can be maintained over a range of gapes, larger than predicted on basis of individual length-tension curves. Despite the considerable changes in skull shape and concurrent changes in the jaw muscles, the direction of the resultant force of the closing muscles and its mechanical advantage remain stable during growth. Observed phenomena suggest that during development the possibilities for generation of large bite forces are increased at the cost of a restriction of the range of jaw excursion.     

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.     

Sensitivity of temporomandibular joint force calculations to errors in muscle force measurements

A two-dimensional, five-muscle model was used to determine the degree of precision required for accurate calculation of temporomandibular joint force magnitude and direction. The sensitivity of the calculations to each variable were assessed by incrementing each variable through its presumed biological range and were expressed as rate of change in the joint force per unit change in each variable. Sensitivity of the calculations to variables depends upon both bite force direction and bite position. The bite force direction with maximum precision for joint force magnitude produced minimal precision for joint force direction. The accuracy needed for each muscle force varied greatly. The effect of error for each muscle parameter depended upon the magnitude, direction, and moment arm length of the muscle force relative to those of the resultant muscle force. If each of the five muscle forces was known to the nearest 1% of total muscle force magnitude, 1 degree of muscle force direction, and 1 mm of moment arm length, temporomandibular joint force magnitude could be calculated to the nearest 4 kg and joint force direction to the nearest 7 degrees. It is not known whether this precision for the muscle forces is possible.     

A new model for calculating muscle forces from electromyograms

A muscle model is described that uses electromyogram (EMG), muscle length and speed of contraction to predict muscle force. Physiological parameters are the Hill constants and the shape of the twitch response to a single stimulus. The model was incorporated in a jaw model of the rabbit and tested by predicting the bite force produced by the jaw muscles during mastication. The time course of the calculated force appeared to match the bite force, measured in vivo by a strain gauge, applied to the bone below the teeth. The variation in peak strain amplitude from cycle to cycle correlated with the variation predicted by the model. The peak amplitude of the integrated EMGs of individual jaw muscles showed an average correlation with peak strain of 0.41. Use of the sum of the available peak amplitudes, weighted according to their effect upon the bite force increased the correlation to 0.46; the model predicted bite forces showed a correlation of 0.57 with the strain. The increase in correlation was statistically significant. The muscle forces were calculated using a minimum number of easily obtainable constants.     

Predicted and observed shapes of human mandibular condyles.

A mathematical model based on linear programming was used to study the directions of the joint forces used to maintain the human jaw in three-dimensional static equilibrium when producing bite forces of 100 N to a maximum of 1000 N down the long axis of a central incisor, first premolar, first molar and third molar. Seven different versions of the model were studied. The two simplest versions minimized the total muscle tension and the total joint load, respectively. Assuming that the joint force direction must be normal to some part of the articular surface of the condyle, neither version produced directions consistent with the observed shapes of human condyles. The other five versions minimized different combinations of muscle tensions and joint loads. Two of these versions produced joint force directions compatible with the shapes of condyles. Both minimized total muscle tension plus the (vertical) joint load on the back of the condyle. The results suggest that joint mechanoreceptors (probably non-directional) as well as muscle receptors contribute to the neuromuscular control of bite forces. Our results are consistent with some recent observations [Marshall and Tatton, Exp. Brain Res. 83, 137-150 (1990)] of the cat knee joint.     

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.     

Modeling the biomechanics of swine mastication – An inverse dynamics approach

A novel reconstructive alternative for patients with severe facial structural deformity is Le Fort-based, face-jaw-teeth transplantation (FJTT). To date, however, only ten surgeries have included underlying skeletal and jaw-teeth components, all yielding sub-optimal results and a need for a subsequent revision surgery, due to size mismatch and lack of precise planning. Numerous studies have proven swine to be appropriate candidates for translational studies including pre-operative planning of transplantation. An important aspect of planning FJTT is determining the optimal muscle attachment sites on the recipient?s jaw, which requires a clear understanding of mastication and bite mechanics in relation to the new donated upper and/or lower jaw. A segmented CT scan coupled with data taken from literature defined a biomechanical model of mandible and jaw muscles of a swine. The model was driven using tracked motion and external force data of one cycle of chewing published earlier, and predicted the muscle activation patterns as well as temporomandibular joint (TMJ) reaction forces and condylar motions. Two methods, polynomial and min/max optimization, were used for solving the muscle recruitment problem. Similar performances were observed between the two methods. On average, there was a mean absolute error (MAE) of <0.08 between the predicted and measured activation levels of all muscles, and an MAE of <7 N for TMJ reaction forces. Simulated activations qualitatively followed the same patterns as the reference data and there was very good agreement for simulated TMJ forces. The polynomial optimization produced a smoother output, suggesting that it is more suitable for studying such motions. Average MAE for condylar motion was 1.2 mm, which reduced to 0.37 mm when the input incisor motion was scaled to reflect the possible size mismatch between the current and original swine models. Results support the hypothesis that the model can be used for planning of facial transplantation.     

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

     

Relationship between the training of young recruits and values of bite forces

Analysis of masticatory function is the basis of clinical work in almost all fields of dentistry. Bite forces are the expression and measure of masticatory function. Physical training has an effect on the development of functional ability, motoric ability of the organism and the formation of desired physical proportions. The purpose of this study was to examine the association between physical fitness and bite force values. Because of strictly defined regulations in the army with regard to training and nutrition, Croatian Army recruits were ideal examinees for this examination. The examinees were 135 recruits. Bite forces were measured on three places (area of the central incisors, left and right in the area of the first molars) before and after three-months of training. Of all the examinees, 108 had increased their body weight, 12 had decreased it and 15 had not changed their body weight. The median of measured forces in the recruits prior to training was 291 N in the right (lateral quadrant), 285.5 N in the left lateral quadrant and 205 N in the anterior area. After training the median of measured forces in the right quadrant was 312 N, in the left 313 N and in the anterior area 216 N Greater bite forces after training on all measured places were statistically proved. Increased activity of masticatory muscles can have the same effect on the values of bite forces as bite training. There are few data on the correlation between physical muscles and values of bite forces. The results of those studies are doubtful. In this study, after three months of conditional training, the body mass of the recruits had increased and they expressed greater values of bite forces. However, correlation between body mass and bite forces cannot be proved with certainty.     

Bite force and occlusal stress production in hominin evolution

Maximum bite force affects craniofacial morphology and an organism's ability to break down foods with different material properties. Humans are generally believed to produce low bite forces and spend less time chewing compared with other apes because advances in mechanical and thermal food processing techniques alter food material properties in such a way as to reduce overall masticatory effort. However, when hominins began regularly consuming mechanically processed or cooked diets is not known. Here, we apply a model for estimating maximum bite forces and stresses at the second molar in modern human, nonhuman primate, and hominin skulls that incorporates skeletal data along with species‐specific estimates of jaw muscle architecture. The model, which reliably estimates bite forces, shows a significant relationship between second molar bite force and second molar area across species but does not confirm our hypothesis of isometry. Specimens in the genus Homo fall below the regression line describing the relationship between bite force and molar area for nonhuman anthropoids and australopiths. These results suggest that Homo species generate maximum bite forces below those predicted based on scaling among australopiths and nonhuman primates. Because this decline occurred before evidence for cooking, we hypothesize that selection for lower bite force production was likely made possible by an increased reliance on nonthermal food processing. However, given substantial variability among in vivo bite force magnitudes measured in humans, environmental effects, especially variations in food mechanical properties, may also be a factor. The results also suggest that australopiths had ape‐like bite force capabilities. Am J Phys Anthropol 151:544–557, 2013. © 2013 Wiley Periodicals, Inc.     

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90° in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.     

Total shoulder and relative muscle strength in the scapular plane.

Strength profiles of the shoulder joint are measured experimentally for two arm positions in "the scapular plane" in order to present quantitative data on the shoulder strength. Apart from yielding the actual force a subject can exert in various directions, these measurements also exhibit e.g. the strongest and weakest directions, in fact the relative strength in all directions. The inter-individual variation of the direction of maximal force was at most 14 degrees (sd). The experimental profiles are compared with the corresponding theoretical profiles, obtained by using a shoulder model. The calculations were made both with default muscle parameters and individually adapted parameters. The results show that the employed shoulder model, which is based on data from an elderly population, may be adapted to other populations and that the necessary changes in relative muscle strength are those expected on biomechanical grounds. Without model changes the difference between measured (in the mean) and predicted maximal force directions was at most 50 degrees. Muscle parameter adjustment reduced this difference to 23 degrees. The strength profiles clearly indicate in what direction a person can produce larger forces and which muscles that contribute.     

Activation of shoulder muscles in healthy men and women under isometric conditions

Purpose: Due to the low osseous lead of the shoulder joint a large portion of the shoulder muscles, in addition to executing movements, deals with stabilising tasks. This requires a permanent readjustment of the intermuscular co-ordination of all involved muscles. The aim of the study was to verify the existence of gender dependent differences in intramuscular co-ordination patterns of shoulder muscles.

Method: Fifteen healthy men and nine healthy women, who executed 24 isometric exercises in sagittal, frontal and horizontal planes with a loading of 50% of their individual isometric maximum force, were investigated. In every plane, four angular positions were chosen and both opposite force directions were measured, respectively. SEMG was taken from 13 muscles of the shoulder and the upper arm. Due to inter-individual differences SEMG amplitudes were normalised. Results: Gender specific differences of functional intermuscular co-ordination patterns could be proven systematically. Women showed less activation of muscles acting in the main force direction. In addition, those muscles less necessary for the actual force production were more activated in women than in men.

Conclusions: Functionally comparable shoulder function showed a gender dependency in terms of functional intermuscular co-ordination.     

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.     

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.     

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.     

Effect of bite force and diet composition on craniofacial diversification of Southern South American human populations

Ecological factors can be important to shape the patterns of morphological variation among human populations. Particularly, diet plays a fundamental role in craniofacial variation due to both the effect of the nutritional status—mostly dependent on the type and amount of nutrients consumed—on skeletal growth and the localized effects of masticatory forces. We examine these two dimensions of diet and evaluate their influence on morphological diversification of human populations from southern South America during the late Holocene. Cranial morphology was measured as 3D coordinates defining the face, base and vault. Size, form, and shape variables were obtained for 474 adult individuals coming from 12 samples. Diet composition was inferred from carious lesions and δ¹³C data, whereas bite forces were estimated using traits of main jaw muscles. The spatial structure of the morphological and ecological variables was measured using correlograms. The influence of diet composition and bite force on morphometric variation was estimated by a spatial regression model. Cranial variation and diet composition display a geographical structure, while no geographical pattern was observed in bite forces. Cranial variation in size and form is significantly associated with diet composition, suggesting a strong effect of systemic factors on cranial growth. Conversely, bite forces do not contribute significantly to the pattern of morphological variation among the samples analyzed. Overall, these results show that an association between diet composition and hardness cannot be assumed, and highlight the complex relationship between morphological diversification and diet in human populations. Am J Phys Anthropol 155:114–127, 2014. © 2014 Wiley Periodicals, Inc.