Passive force characteristics of an architecturally complex muscle

In architecturally complex muscles with large attachment areas, it can be expected that during movement different muscle regions undergo different amounts of length excursions. As a consequence, the amount of passive force produced by the regions will differ. Therefore, we tested the hypothesis that during movement the vector of the passive force of such a muscle, which defines the magnitude, position and orientation of the resultant force of the various regions, has no fixed position, between the muscle's center of origin and insertion. As a model for an architecturally complex muscle we used the masseter muscle. It was expected that during jaw opening anterior muscle regions are more stretched than posterior regions, leading to an anterior shift of the passive force vector. A three-component force transducer was used to measure both the position and magnitude of passive force in the masseter muscle of 9 rabbits. Forces were recorded during repeated cycles of stepwise opening and closure of the jaw. The muscle exhibited a clear hysteresis: passive force measured during jaw opening was larger than that during jaw closing. With an increase of the jaw gape there was an approximately exponential increase of the magnitude of the passive muscle force, while simultaneously the passive force vector shifted anteriorly. Moment arm length of passive force increased by about 100%. This anterior shift contributed substantially to the increase of the passive muscle moment generated during jaw opening. It can be concluded that in architecturally complex muscles the increase of the passive resistance moment which is associated with muscle lengthening might not only be due to an increase of the magnitude of passive muscle force but also to an increase of the moment arm of this force.     

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.     

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.     

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.     

A functional analysis of carnassial biting

The jaw mechanism of carnivores is studied using an idealized model (Greaves, 1978). The model assumes: (i) muscle activity on both sides of the head, and (ii) that the jaw joints and the carnassial teeth are single points of contact between the skull and the lower jaw during carnassial biting. The model makes the following predictions: (i) in carnivores with carnassial teeth the resultant force of the jaw muscles will be positioned approximately 60% of the way from the jaw joint to the tooth—this arrangement delivers the maximum bite force possible together with a reasonably wide gape (remembering that bite force and gape cannot both be maximized); (ii) in an evolutionary sense, if greater bite force is required at the carnassial tooth, either the animal will get larger so as to deliver an absolutely larger bite force or the architecture of the muscles may change, becoming more pinnate, for example, but jaw geometry (i.e. the relative positions of the jaw joints, the carnassial tooth, and the muscle resultant force) will not change; (iii) if greater gape is required, the animal will get larger so as to have longer jaws and therefore an absolutely wider gape or change its muscle architecture allowing for greater stretch while the geometry remains unchanged; and (iv) in animals with a longer shearing region (e.g. the extinct hyaenodonts) the shearing region will be approximately 20% of jaw length and the muscle resultant force will be positioned approximately 60% of the way from the jaw joint to the most anterior shearing tooth.     

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.     

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.     

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.     

Dependence of alignment direction on magnitude of strain in esophageal smooth muscle cells

The response of cells in vitro to mechanical forces has been the subject of much research using devices to exert controlled mechanical stimulation on cultured cells or isolated tissue. In this study, esophageal smooth muscle cells were seeded on flexible polyurethane membranes to form a confluent cell layer. The cells were then subjected to uniform cyclic stretch of varying magnitudes at a frequency of approximately five cycles per minute in a custom made mechatronic bioreactor, providing similar strains experienced in the in vivo mechanical environment of the esophagus. The results show that the orientation response is dependent on the magnitude of cyclic stretch applied. Smooth muscle cells showed parallel alignment to the force direction at low cyclic strains (2%) compared to the hill‐valley morphology of static controls. At higher strains (5% and 10% magnitude), the cells exhibited a consistent alignment perpendicular to the strain. To our knowledge, this is the first time that the alignment direction's dependence on strain magnitude has been demonstrated. MTS analysis indicated that cell metabolism was reduced when mechanical strain was applied, and proliferation was inhibited by mechanical strain. Protein expression indicates a decrease in smooth muscle α‐actin, indicative of changes in cell phenotype, an increase in vimentin, which is associated with increased cell motility, and an increase in desmin, indicating differentiation in stimulated cells. Biotechnol. Bioeng. 2009;102: 1703–1711. © 2008 Wiley Periodicals, Inc.     

The generalized carnivore jaw

A model is presented of the jaw mechanism that relies on the geometrical similarities among mammalian carnivores with carnassial teeth. These similarities, together with estimates of the location of the resultant force of the jaw muscles, allow the model to predict that the mechanical advantage of the jaw lever system is the same in all carnivores with carnassials and, therefore, that the magnitude of the bite force is mainly determined by the absolute amount of jaw musculature.     

The effect of changes in muscle function and bone growth on muscle migration

The elastic sleeve model of the periosteum of a long bone presents the periosteum as a structure which, because it is attached to the epiphyses rather than the diaphysis, expands interstitially and equally at all points as the bone grows at its ends. Structures attached to the periosteum are seen as essentially passive hitchhikers on the expanding periosteum. Two corollaries of this model are tested here. First, that changes in the magnitude or direction of the force that an attached structure exerts on the periosteum do not affect the migration of the structure. Second, that changes in the proportion of growth that occur at each end of the bone do not affect the migration of attached structures. Experiments performed on rabbits to test these corollaries include muscle paralysis, muscle transection, changes in the direction pull of a muscle, and epiphysiodesis. The results are in agreement with the hypotheses. This model should have applicability to functional and comparative anatomy, since it postulates that differences in positions of attachment of muscles and ligaments to bones reflect underlying genetic differences (phylogeny) rather than the effects of differences in behavior of the animal (ontogeny).     

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.     

Absolute strength of the muscles attached to the mandible

In the course of an anatomical investigation of the muscles, securing movements of the mandible, performed on 10 human corpses, the muscle fibre length, volume and weight of each muscle has been estimated. Owing to the formula suggested by P. F. Leshaft (1880)--q = v/e, the physiological diameter of the muscles has been determined. Since the muscle with the diameter equal to 1 cm2 develops an absolute forse of 10 kg, the absolute muscle force value of the anterior group of muscles has been obtained for the first time (venter anterior musculi digastri--4.8 kg, musculus mylohyoideus--10.7 kg and musculus geniohyoideus--6.3 kg). The data on the absolute force of the posterior group of muscles has been verified (musculus masseter--24.2 kg, musculus temporalis--28 kg, musculus pterygoideus medialis--15.6 kg and musculus pterygoideus lateralis--15.5 kg). Analysing the interaction of forces of the muscles participating in the mandible movements, direction and value of displacements of the mandibular fragments have been explained and confirmed on some clinical examples. The data on the absolute force of the muscles studied can be used for investigating the displacement mechanism of the mandibular fragments after its resection and when its integrity is broken.     

Functional links between canine height and jaw gape in catarrhines with special reference to early hominins

This study tests the hypothesis that decreased canine crown height in catarrhines is linked to (and arguably caused by) decreased jaw gape. Associations are characterized within and between variables such as upper and lower canine height beyond the occlusal plane (canine overlap), maximum jaw gape, and jaw length for 27 adult catarrhine species, including 539 living subjects and 316 museum specimens. The data demonstrate that most adult male catarrhines have relatively larger canine overlap dimensions and gapes than do conspecific females. For example, whereas male baboons open their jaws maximally more than 110% of jaw length, females open about 90%. Humans and hylobatids are the exceptions in that canine overlap is nearly the same in both the sexes and so is relative gape (ca. 65% for humans and 110% for hylobatids). A correlation analysis demonstrates that a large portion of relative gape (maximum gape/projected jaw length) is predicted by relative canine overlap (canine overlap/jaw length). Relative gape is mainly a function of jaw muscle position and/or jaw muscle‐fiber length. All things equal, more rostrally positioned jaw muscles and/or shorter muscle fibers decrease gape and increase bite force during the power stroke of mastication, and the net benefit is to increase the mechanical efficiency during chewing. Similarly, more caudally positioned muscles and/or longer muscle fibers increase the amount of gape and decrease bite force. Overall, the data support the hypothesis that canine reduction in early hominins is functionally linked to decreased gape and increased mechanical efficiency of the jaws. Am J Phys Anthropol, 2013. © 2012 Wiley Periodicals, Inc.     

Symphyseal fusion and jaw-adductor muscle force: an EMG study

The purpose of this study is to test various hypotheses about balancing-side jaw muscle recruitment patterns during mastication, with a major focus on testing the hypothesis that symphyseal fusion in anthropoids is due mainly to vertically- and/or transversely-directed jaw muscle forces. Furthermore, as the balancing-side deep masseter has been shown to play an important role in wishboning of the macaque mandibular symphysis, we test the hypothesis that primates possessing a highly mobile mandibular symphysis do not exhibit the balancing-side deep masseter firing pattern that causes wishboning of the anthropoid mandible. Finally, we also test the hypothesis that balancing-side muscle recruitment patterns are importantly related to allometric constraints associated with the evolution of increasing body size. Electromyographic (EMG) activity of the left and right superficial and deep masseters were recorded and analyzed in baboons, macaques, owl monkeys, and thick-tailed galagos. The masseter was chosen for analysis because in the frontal projection its superficial portion exerts force primarily in the vertical (dorsoventral) direction, whereas its deep portion has a relatively larger component of force in the transverse direction. The symphyseal fusion-muscle recruitment hypothesis predicts that unlike anthropoids, galagos develop bite force with relatively little contribution from their balancing-side jaw muscles. Thus, compared to galagos, anthropoids recruit a larger percentage of force from their balancing-side muscles. If true, this means that during forceful mastication, galagos should have working-side/balancing-side (W/B) EMG ratios that are relatively large, whereas anthropoids should have W/B ratios that are relatively small. The EMG data indicate that galagos do indeed have the largest average W/B ratios for both the superficial and deep masseters (2.2 and 4.4, respectively). Among the anthropoids, the average W/B ratios for the superficial and deep masseters are 1.9 and 1.0 for baboons, 1.4 and 1.0 for macaques, and both values are 1.4 for owl monkeys. Of these ratios, however, the only significant difference between thick-tailed galagos and anthropoids are those associated with the deep masseter. Furthermore, the analysis of masseter firing patterns indicates that whereas baboons, macaques and owl monkeys exhibit the deep masseter firing pattern associated with wishboning of the macaque mandibular symphysis, galagos do not exhibit this firing pattern. The allometric constraint-muscle recruitment hypothesis predicts that larger primates must recruit relatively larger amounts of balancing-side muscle force so as to develop equivalent amounts of bite force. Operationally this means that during forceful mastication, the W/B EMG ratios for the superficial and deep masseters should be negatively correlated with body size. Our analysis clearly refutes this hypothesis. As already noted, the average W/B ratios for both the superficial and deep masseter are largest in thick-tailed galagos, and not, as predicted by the allometric constraint hypothesis, in owl monkeys, an anthropoid whose body size is smaller than that of thick-tailed galagos. Our analysis also indicates that owl monkeys have W/B ratios that are small and more similar to those of the much larger-sized baboons and macaques. Thus, both the analysis of the W/B EMG ratios and the muscle firing pattern data support the hypothesis that symphyseal fusion and transversely-directed muscle force in anthropoids are functionally linked. This in turn supports the hypothesis that the evolution of symphyseal fusion in anthropoids is an adaptation to strengthen the symphysis so as to counter increased wishboning stress during forceful unilateral mastication. (ABSTRACT TRUNCATED)     

Pattern of anterior cruciate ligament force in normal walking

The goal of this study was to calculate and explain the pattern of anterior cruciate ligament (ACL) loading during normal level walking. Knee-ligament forces were obtained by a two-step procedure. First, a three-dimensional (3D) model of the whole body was used together with dynamic optimization theory to calculate body-segmental motions, ground reaction forces, and leg-muscle forces for one cycle of gait. Joint angles, ground reaction forces, and muscle forces obtained from the gait simulation were then input into a musculoskeletal model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated gait cycle. The model simulation predicted that the ACL bears load throughout stance. Peak force in the ACL (303 N) occurred at the beginning of single-leg stance (i.e., contralateral toe off). The pattern of ACL force was explained by the shear forces acting at the knee. The balance of muscle forces, ground reaction forces, and joint contact forces applied to the leg determined the magnitude and direction of the total shear force acting at the knee. The ACL was loaded whenever the total shear force pointed anteriorly. In early stance, the anterior shear force from the patellar tendon dominated the total shear force applied to the leg, and so maximum force was transmitted to the ACL at this time. ACL force was small in late stance because the anterior shear forces supplied by the patellar tendon, gastrocnemius, and tibiofemoral contact were nearly balanced by the posterior component of the ground reaction.     

Neural control exploits changing mechanical advantage and context dependence to generate different feeding responses in <Emphasis Type="Italic">Aplysia</Emphasis>

How does neural control reflect changes in mechanical advantage and muscle function? In the Aplysia feeding system a protractor muscle's mechanical advantage decreases as it moves the structure that grasps food (the radula/odontophore) in an anterior direction. In contrast, as the radula/odontophore is moved forward, the jaw musculature's mechanical advantage shifts so that it may act to assist forward movement of the radula/odontophore instead of pushing it posteriorly. To test whether the jaw musculature's context-dependent function can compensate for the falling mechanical advantage of the protractor muscle, we created a kinetic model of Aplysia's feeding apparatus. During biting, the model predicts that the reduction of the force in the protractor muscle I2 will prevent it from overcoming passive forces that resist the large anterior radula/odontophore displacements observed during biting. To produce protractions of the magnitude observed during biting behaviors, the nervous system could increase I2's contractile strength by neuromodulating I2, or it could recruit the I1/I3 jaw muscle complex. Driving the kinetic model with in vivo EMG and ENG predicts that, during biting, early activation of the context-dependent jaw muscle I1/I3 may assist in moving the radula/odontophore anteriorly during the final phase of protraction. In contrast, during swallowing, later activation of I1/I3 causes it to act purely as a retractor. Shifting the timing of onset of I1/I3 activation allows the nervous system to use a mechanical equilibrium point that allows I1/I3 to act as a protractor rather than an equilibrium point that allows I1/I3 to act as a retractor. This use of equilibrium points may be similar to that proposed for vertebrate control of movement.     

Morphogenesis of parrot jaw muscles: understanding the development of an evolutionary novelty

Parrots have developed novel head structures in their evolutionary history. The appearance of two new muscles for strong jaw adduction is especially fascinating in developmental and evolutionary contexts. However, jaw muscle development of parrots has not been described, despite its uniqueness. This report first presents the normal developmental stages of the cockatiel (Nymphicus hollandicus), comparable to that of the chick. Next, the peculiar skeletal myogenesis in the first visceral arch of parrots is described, mainly focusing on the development of two new jaw muscles. One of the parrot-specific muscles, M. ethmomandibularis, was initially detected at Nymphicus Stage 28 (N28) as the rostral budding of M. pterygoideus. After N32, the muscle significantly elongates rostrodorsally toward the interorbital septum, following a course lateral to the palatine bone. Another parrot-specific muscle, M. pseudomasseter, was first recognized at N36. The muscle branches off from the posteromedial M. adductor mandibulae externus and grows in a dorsolateral direction, almost covering the lateral surface of the jugal bar. The upper tip of the muscle is accompanied by condensed mesenchyme, which seems to be derived from cephalic neural crest cells.     

Longitudinal and transverse deformation of human Achilles tendon induced by isometric plantar flexion at different intensities

The present study determined in vivo deformation of the entire Achilles tendon in the longitudinal and transverse directions during isometric plantar flexions. Twelve young women and men performed isometric plantar flexions at 0% (rest), 30%, and 60% of the maximal voluntary contraction (MVC) while a series of oblique longitudinal and cross-sectional magnetic resonance (MR) images of the Achilles tendon were taken. At the distal end of the soleus muscle belly, the Achilles tendon was divided into the aponeurotic (ATapo) and the tendinous (ATten) components. The length of each component was measured in the MR images. The widths of the Achilles tendon were determined at 10 regions along ATapo and at four regions along ATten. Longitudinal and transverse strains were calculated as changes in relative length and width compared with those at rest. The ATapo deformed in both longitudinal and transverse directions at 30%MVC and 60%MVC. There was no difference between the strains of the ATapo at 30%MVC and 60%MVC either in the longitudinal (1.1 and 1.6%) or transverse (5.0～11.4 and 5.0～13.9%) direction. The ATten was elongated longitudinally (3.3%) to a greater amount than ATapo, while narrowing transversely in the most distal region (-4.6%). The current results show that the magnitude and the direction of contraction-induced deformation of Achilles tendon are different for the proximal and distal components. This may be related to the different functions of Achilles tendon, i.e., force transmission or elastic energy storage during muscle contractions.     

Quantitative calculations of temporomandibular joint reaction forces--I. The importance of the magnitude of the jaw muscle forces

The effect of measurement errors on quantitative calculation of temporomandibular joint reaction force was investigated in a two-dimensional, two-muscle model. A computer program using the model incremented the magnitude of the bite force and muscle forces and the lengths of their moment arms, and calculated the joint reaction force at each increment. Computation of the joint reaction force is most sensitive to the relative lengths of the bite force and muscle forces moment arms. Absolute values for each muscle force are not required and errors in the magnitudes of the muscle forces have only a minor effect on calculation of the total joint reaction force.