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 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.     

Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models.     

Velocity-dependent cost function for the prediction of force sharing among synergistic muscles in a one degree of freedom model

Prediction of accurate and meaningful force sharing among synergistic muscles is a major problem in biomechanics research. Given a resultant joint moment, a unique set of muscle forces can be obtained from this mathematically redundant system using nonlinear optimization. The classical cost functions for optimization involve a normalization of the muscle forces to the absolute force capacity of the target muscles, usually by the cross-sectional area or the maximal isometric force. In a one degree of freedom model this leads to a functional relationship between moment arms and the predicted muscle forces, such that for constant moment arms, or constant ratios of moment arms, agonistic muscle forces increase or decrease in unison. Experimental studies have shown however that the relationship between muscle forces is highly task-dependent often causing forces to increase in one muscle while decreasing in a functional agonist, likely because of the contractile conditions and contractile properties of the involved muscles. We therefore, suggest a modified cost function that accounts for the instantaneous contraction velocity of the muscles and its effect on the instantaneous maximal force. With this novel objective function, a task-dependent prediction of muscle force distribution is obtained that allows, even in a one degree of freedom system, the prediction of force sharing loops, and simultaneously increasing and decreasing forces for agonist pairs of muscles.     

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.     

The sensitivity of endpoint forces produced by the extrinsic muscles of the thumb to posture

This study utilizes a biomechanical model of the thumb to estimate the force produced at the thumb-tip by each of the four extrinsic muscles. We used the principle of virtual work to relate joint torques produced by a given muscle force to the resulting endpoint force and compared the results to two separate cadaveric studies. When we calculated thumb-tip forces using the muscle forces and thumb postures described in the experimental studies, we observed large errors. When relatively small deviations from experimentally reported thumb joint angles were allowed, errors in force direction decreased substantially. For example, when thumb posture was constrained to fall within ±15° of reported joint angles, simulated force directions fell within experimental variability in the proximal–palmar plane for all four muscles. Increasing the solution space from ±1° to an unbounded space produced a sigmoidal decrease in error in force direction. Changes in thumb posture remained consistent with a lateral pinch posture, and were generally consistent with each muscle’s function. Altering thumb posture alters both the components of the Jacobian and muscle moment arms in a nonlinear fashion, yielding a nonlinear change in thumb-tip force relative to muscle force. These results explain experimental data that suggest endpoint force is a nonlinear function of muscle force for the thumb, support the continued use of methods that implement linear transformations between muscle force and thumb-tip force for a specific posture, and suggest the feasibility of accurate prediction of lateral pinch force in situations where joint angles can be measured accurately.     

Estimating the muscle forces generated in the human lower extremity when walking: a physiological solution

A model capable of estimating individual muscle activity during human lower extremity activity has been developed. This model was implemented and applied to normal gait. Both 3D cinematography and force platform records were collected to define the kinematics of the lower limb segments and the ground reaction forces. From these data the lengths, velocities, and moment arms of the muscles and the net muscle moments were calculated. These data were then used to estimate the output from a set of pattern generators which specified the neural input to and hence the force generated in each muscle. Results were obtained which demonstrate that it is feasible to construct a hierarchical physiological model which will estimate individual muscle forces. This statement must be tempered somewhat in that better anatomical and neurophysiological data must be made available and that this model, and all others attempting to estimate individual muscle forces, must be rigorously tested before being applied in a research, sports, or clinical setting.     

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.     

A method of calculating physiologically relevant joint reaction forces during forward dynamic simulations of movement from an existing knee model

In the commonly used SIMM software, which includes a complete musculoskeletal model of the lower limbs, the reaction forces at the knee are computed. These reaction forces represent the bone-on-bone contact forces and the soft tissue forces (e.g. ligaments) other than muscles acting at the joint. In the knee model integrated into this software, a patellotibial joint rather than a patellofemoral joint is defined, and a force acting along the direction of the patellar ligament is not included. Although this knee model results in valid kinematics and muscle moment arms, the reaction forces at the knee calculated do not represent physiologic knee joint reaction forces. Hence our objectives were to develop a method of calculating physiologic knee joint reaction forces using the knee model incorporated into the SIMM software and to demonstrate the differences in the forces returned by SIMM and the physiologic forces in an example. Our method converts the anatomically fictional patellotibial joint into a patellofemoral joint and computes the force in an inextensible patellar ligament. In our example, the rectus femoris was fully excited isometrically, with the knee and hip flexed to 90 degrees . The resulting SIMM tibiofemoral joint reaction force was primarily shear, because the quadriceps force was applied to the tibia via the fictional patellotibial joint. In contrast the physiologic tibiofemoral joint reaction force was primarily compression, because the quadriceps force was applied through the patellar ligament. This result illustrates that the physiologic knee joint reaction forces are profoundly different than the forces returned by SIMM. However physiologic knee joint reaction forces can be computed with postprocessing of SIMM results.     

Effects of rotator cuff tears on muscle moment arms: a computational study

Rotator cuff tears cause morphologic changes to cuff tendons and muscles, which can alter muscle architecture and moment arm. The effects of these alterations on shoulder mechanical performance in terms of muscle force and joint strength are not well understood. The purpose of this study was to develop a three-dimensional explicit finite element model for investigating morphological changes to rotator cuff tendons following cuff tear. The subsequent objectives were to validate the model by comparing model-predicted moment arms to empirical data, and to use the model to investigate the hypothesis that rotator cuff muscle moment arms are reduced when tendons are divided along the force-bearing direction of the tendon. The model was constructed by extracting tendon, cartilage, and bone geometry from the male Visible Human data set. Infraspinatus and teres minor muscle and tendon paths were identified relative to the humerus and scapula. Kinetic and kinematic boundary conditions in the model replicated experimental protocols, which rotated the humerus from 45 degrees internal to 45 degrees external rotation with constant loads on the tendons. External rotation moment arms were calculated for two conditions of the cuff tendons: intact normal and divided tendon. Predicted moment arms were within the 1-99% confidence intervals of experimental data for nearly all joint angles and tendon sub-regions. In agreement with the experimental findings, when compared to the intact condition, predicted moment arms were reduced for the divided tendon condition. The results of this study provide evidence that one potential mechanism for the reduction in strength observed with cuff tear is reduction of muscle moment arms. The model provides a platform for future studies addressing mechanisms responsible for reduced muscle force and joint strength including changes to muscle length-tension operating range due to altered muscle and tendon excursions, and the effects of cuff tear size and location on moment arms and muscle forces.     

A three-dimensional model of the rat hindlimb: musculoskeletal geometry and muscle moment arms

As a first step towards developing a dynamic model of the rat hindlimb, we measured muscle attachment and joint center coordinates relative to bony landmarks using stereophotogrammetry. Using these measurements, we analyzed muscle moment arms as functions of joint angle for most hindlimb muscles, and tested the hypothesis that postural change alone is sufficient to alter the function of selected muscles of the leg. We described muscle attachment sites as second-order curves. The length of the fit parabola and residual errors in the orthogonal directions give an estimate of muscle attachment sizes, which are consistent with observations made during dissection. We modeled each joint as a moving point dependent on joint angle; relative endpoint errors less than 7% indicate this method as accurate. Most muscles have moment arms with a large range across the physiological domain of joint angles, but their moment arms peak and vary little within the locomotion domain. The small variation in moment arms during locomotion potentially simplifies the neural control requirements during this phase. The moment arms of a number of muscles cross zero as angle varies within the quadrupedal locomotion domain, indicating they are intrinsically stabilizing. However, in the bipedal locomotion domain, the moment arms of these muscles do not cross zero and thus are no longer intrinsically stabilizing. We found that muscle function is largely determined by the change in moment arm with joint angle, particularly the transition from quadrupedal to bipedal posture, which may alter an intrinsically stabilizing arrangement or change the control burden.     

Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces

Estimating tibiofemoral joint contact forces is important for understanding the initiation and progression of knee osteoarthritis. However, tibiofemoral contact force predictions are influenced by many factors including muscle forces and anatomical representations of the knee joint. This study aimed to investigate the influence of subject-specific geometry and knee joint kinematics on the prediction of tibiofemoral contact forces using a calibrated EMG-driven neuromusculoskeletal model of the knee. One participant fitted with an instrumented total knee replacement walked at a self-selected speed while medial and lateral tibiofemoral contact forces, ground reaction forces, whole-body kinematics, and lower-limb muscle activity were simultaneously measured. The combination of generic and subject-specific knee joint geometry and kinematics resulted in four different OpenSim models used to estimate muscle–tendon lengths and moment arms. The subject-specific geometric model was created from CT scans and the subject-specific knee joint kinematics representing the translation of the tibia relative to the femur was obtained from fluoroscopy. The EMG-driven model was calibrated using one walking trial, but with three different cost functions that tracked the knee flexion/extension moments with and without constraint over the estimated joint contact forces. The calibrated models then predicted the medial and lateral tibiofemoral contact forces for five other different walking trials. The use of subject-specific models with minimization of the peak tibiofemoral contact forces improved the accuracy of medial contact forces by 47% and lateral contact forces by 7%, respectively compared with the use of generic musculoskeletal model.     

Muscle forces predicted using optimization methods are coordinate system dependent

Optimization methods are widely used to predict in vivo muscle forces in musculoskeletal joints. Moment equilibrium at the joint center (usually chosen as the origin of the joint coordinate system) has been used as a constraint condition for optimization procedures and the joint reaction moments were assumed zero. This study, through the use of a three-dimensional elbow model, investigated the effect of coordinate system origin (joint center) location on muscle forces predicted using a nonlinear static optimization method. The results demonstrated that moving the origin of the coordinate system medially and laterally along the flexion-extension axis caused dramatic variations in the predicted muscle forces. For example, moving the origin of the coordinate system from a position 5mm medial to 5mm lateral of the geometric elbow center caused the predicted biceps force to vary from 12% to 46% and the brachialis force to vary from 80% to 34% of the total muscle loading. The joint reaction force reduced by 24% with this medial to lateral variation of the coordinate system origin location. This data revealed that the muscle forces predicted using the optimization method are sensitive to the coordinate system origin location due to the zero joint reaction moment assumption in the moment constraint condition. For accurate prediction of muscle load distributions using optimization methods, it is necessary to determine the accurate coordinate system origin location where the condition of a zero joint reaction moment is satisfied.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.     

Fibre operating lengths of human lower limb muscles during walking

Muscles actuate movement by generating forces. The forces generated by muscles are highly dependent on their fibre lengths, yet it is difficult to measure the lengths over which muscle fibres operate during movement. We combined experimental measurements of joint angles and muscle activation patterns during walking with a musculoskeletal model that captures the relationships between muscle fibre lengths, joint angles and muscle activations for muscles of the lower limb. We used this musculoskeletal model to produce a simulation of muscle-tendon dynamics during walking and calculated fibre operating lengths (i.e. the length of muscle fibres relative to their optimal fibre length) for 17 lower limb muscles. Our results indicate that when musculotendon compliance is low, the muscle fibre operating length is determined predominantly by the joint angles and muscle moment arms. If musculotendon compliance is high, muscle fibre operating length is more dependent on activation level and force-length-velocity effects. We found that muscles operate on multiple limbs of the force-length curve (i.e. ascending, plateau and descending limbs) during the gait cycle, but are active within a smaller portion of their total operating range.     

Three-dimensional temporomandibular joint muscle attachment morphometry and its impacts on musculoskeletal modeling

In musculoskeletal models of the human temporomandibular joint (TMJ), muscles are typically represented by force vectors that connect approximate muscle origin and insertion centroids (centroid-to-centroid force vectors). This simplification assumes equivalent moment arms and muscle lengths for all fibers within a muscle even with complex geometry and may result in inaccurate estimations of muscle force and joint loading. The objectives of this study were to quantify the three-dimensional (3D) human TMJ muscle attachment morphometry and examine its impact on TMJ mechanics. 3D muscle attachment surfaces of temporalis, masseter, lateral pterygoid, and medial pterygoid muscles of human cadaveric heads were generated by co-registering measured attachment boundaries with underlying skull models created from cone-beam computerized tomography (CBCT) images. A bounding box technique was used to quantify 3D muscle attachment size, shape, location, and orientation. Musculoskeletal models of the mandible were then developed and validated to assess the impact of 3D muscle attachment morphometry on joint loading during jaw maximal open-close. The 3D morphometry revealed that muscle lengths and moment arms of temporalis and masseter muscles varied substantially among muscle fibers. The values calculated from the centroid-to-centroid model were significantly different from those calculated using the ‘Distributed model’, which considered crucial 3D muscle attachment morphometry. Consequently, joint loading was underestimated by more than 50% in the centroid-to-centroid model. Therefore, it is necessary to consider 3D muscle attachment morphometry, especially for muscles with broad attachments, in TMJ musculoskeletal models to precisely quantify the joint mechanical environment critical for understanding TMJ function and mechanobiology.     

Effect of Postnatal Myostatin Inhibition on Bite Mechanics in Mice

As a negative regulator of muscle size, myostatin (Mstn) impacts the force-production capabilities of skeletal muscles. In the masticatory system, measures of temporalis-stimulated bite forces in constitutive myostatin KOs suggest an absolute, but not relative, increase in jaw-muscle force. Here, we assess the phenotypic and physiologic impact of postnatal myostatin inhibition on bite mechanics using an inducible conditional KO mouse in which myostatin is inhibited with doxycycline (DOX). Given the increased control over the timing of gene inactivation in this model, it may be more clinically-relevant for developing interventions for age-associated changes in the musculoskeletal system. DOX was administered for 12 weeks starting at age 4 months, during which time food intake was monitored. Sex, age and strain-matched controls were given the same food without DOX. Bite forces were recorded just prior to euthanasia after which muscle and skeletal data were collected. Food intake did not differ between control or DOX animals within each sex. DOX males were significantly larger and had significantly larger masseters than controls, but DOX and control females did not differ. Although there was a tendency towards higher absolute bite forces in DOX animals, this was not significant, and bite forces normalized to masseter mass did not differ. Mechanical advantage for incisor biting increased in the DOX group due to longer masseter moment arms, likely due to a more anteriorly-placed masseter insertion. Despite only a moderate increase in bite force in DOX males and none in DOX females, the increase in masseter mass in males indicates a potentially positive impact on jaw muscles. Our data suggest a sexual dimorphism in the role of mstn, and as such investigations into the sex-specific outcomes is warranted.     

Relationships between the size and spatial morphology of human masseter and medial pterygoid muscles, the craniofacial skeleton, and jaw biomechanics

The relationship between human craniofacial morphology and the biomechanical efficiency of bite force generation in widely varying muscular and skeletal types is unknown. To address this problem, we selected 22 subjects with different facial morphologies and used magnetic resonance imaging, cephalometric radiography, and data from dental casts to reconstruct their craniofacial tissues in three dimensions. Conventional cephalometric analyses were carried out, and the cross-sectional sizes of the masseter and medial pterygoid muscles were measured from reconstituted sections. The potential abilities of the muscles to generate bite forces at the molar teeth and mandibular condyles were calculated according to static equilibrium theory using muscle, first molar, and condylar moment arms. On average, the masseter muscle was about 66% larger in cross section than the medial pterygoid and was inclined more anteriorly relative to the functional occlusal plane. There was a significant positive correlation (P less than 0.01) between the cross-sectional areas of the masseter and medial pterygoid muscles (r = 0.75) and between the bizygomatic arch width and masseter cross-sectional area (r = 0.56) and medial pterygoid cross-sectional area (r = 0.69). The masseter muscle was always a more efficient producer of vertically oriented bite force than the medial pterygoid. Putative bite force from the medial pterygoid muscle alone correlated positively with mandibular length and inversely with upper face height. When muscle and tooth moment arms were considered together, a system efficient at producing force on the first molar was statistically associated with a face having a large intergonial width, small intercondylar width, narrow dental arch, forward maxilla, and forward mandible. There was no significant correlation between muscle cross-sectional areas and their respective putative bite forces. This suggests that there is no simple relationship between the tension-generating capacity of the muscles and their mechanical efficiency as described by their spatial arrangement. The study shows that in a modern human population so many combinations of biomechanically relevant variables are possible that subjects cannot easily be placed into ideal or nonideal categories for producing molar force. Our findings also confirm the impression that similar bite-force efficiencies can be found in subjects with disparate facial features.