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.     

Trunk muscle activation and associated lumbar spine joint shear forces under different levels of external forward force applied to the trunk.

High anterior intervertebral shear loads could cause low back injuries and therefore the neuromuscular system may actively counteract these forces. This study investigated whether, under constant moment loading relative to L3L4, an increased externally applied forward force on the trunk results in a shift in muscle activation towards the use of muscles with more backward directed lines of action, thereby reducing the increase in total joint shear force. Twelve participants isometrically resisted forward forces, applied at several locations on the trunk, while moments were held constant relative to L3L4. Surface EMG and lumbar curvature were measured, and an EMG-driven muscle model was used to calculate compression and shear forces at all lumbar intervertebral joints. Larger externally applied forward forces resulted in a flattening of the lumbar lordosis and a slightly more backward directed muscle force. Furthermore, the overall muscle activation increased. At the T12L1 to L3L4 joint, resulting joint shear forces remained small (less than 200N) because the average muscle force pulled backward relative to those joints. However, at the L5S1 joint the average muscle force pulled the trunk forward so that the increase in muscle force with increasing externally applied forward force caused a further rise in shear force (by 102.1N, SD=104.0N), resulting in a joint shear force of 1080.1N (SD=150.4N) at 50Nm moment loading. It is concluded that the response of the neuromuscular system to shear force challenges tends to increase rather than reduce the shear loading at the lumbar joint that is subjected to the highest shear forces.     

Electromyography and mechanics of mastication in the albino rat.

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

Feedback control from the jaw joints during biting: An investigation of the reptile Sphenodon using multibody modelling

Sphenodon, a lizard-like reptile, is the only living representative of a group that was once widespread at the time of the dinosaurs. Unique jaw mechanics incorporate crushing and shearing motions to breakdown food, but during this process excessive loading could cause damage to the jaw joints and teeth. In mammals like ourselves, feedback from mechanoreceptors within the periodontal ligament surrounding the teeth is thought to modulate muscle activity and thereby minimise such damage. However, Sphenodon and many other tetrapods lack the periodontal ligament and must rely on alternative control mechanisms during biting. Here we assess whether mechanoreceptors in the jaw joints could provide feedback to control muscle activity levels during biting. We investigate the relationship between joint, bite, and muscle forces using a multibody computer model of the skull and neck of Sphenodon. When feedback from the jaw joints is included in the model, predictions agree well with experimental studies, where the activity of the balancing side muscles reduces to maintain equal and minimal joint forces. When necessary, higher, but asymmetric, joint forces associated with higher bite forces were achievable, but these are likely to occur infrequently during normal food processing. Under maximum bite forces associated with symmetric maximal muscle activation, peak balancing side joint forces were more than double those of the working side. These findings are consistent with the hypothesis that feedback similar to that used in the simulation is present in Sphenodon.     

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.     

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.     

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.     

Finger joint force minimization in pianists using optimization techniques

A numerical optimization procedure was used to determine finger positions that minimize and maximize finger tendon and joint force objective functions during piano play. A biomechanical finger model for sagittal plane motion, based on finger anatomy, was used to investigate finger tendon tensions and joint reaction forces for finger positions used in playing the piano. For commonly used piano key strike positions, flexor and intrinsic muscle tendon tensions ranged from 0.7 to 3.2 times the fingertip key strike force, while resultant inter-joint compressive forces ranged from 2 to 7 times the magnitude of the fingertip force. In general, use of a curved finger position, with a large metacarpophalangeal joint flexion angle and a small proximal interphalangeal joint flexion angle, reduces flexor tendon tension and resultant finger joint force.     

Comparative analysis of methods for determining bite force in the spiny dogfish Squalus acanthias

Many studies have identified relationships between the forces generated by the cranial musculature during feeding and cranial design. Particularly important to understanding the diversity of cranial form amongst vertebrates is knowledge of the generated magnitudes of bite force because of its use as a measure of ecological performance. In order to determine an accurate morphological proxy for bite force in elasmobranchs, theoretical force generation by the quadratomandibularis muscle of the spiny dogfish Squalus acanthias was modeled using a variety of morphological techniques, and lever-ratio analyses were used to determine resultant bite forces. These measures were compared to in vivo bite force measurements obtained with a pressure transducer during tetanic stimulation experiments of the quadratomandibularis. Although no differences were found between the theoretical and in vivo bite forces measured, modeling analyses indicate that the quadratomandibularis muscle should be divided into its constituent divisions and digital images of the cross-sections of these divisions should be used to estimate cross-sectional area when calculating theoretical force production. From all analyses the maximum bite force measured was 19.57 N. This relatively low magnitude of bite force is discussed with respect to the ecomorphology of the feeding mechanism of S. acanthias to demonstrate the interdependence of morphology, ecology, and behavior in organismal design.     

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.     

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.     

Mediolateral reaction forces and forelimb anatomy in quadrupedal primates: implications for interpreting locomotor behavior in fossil primates

The forelimb joints of terrestrial primate quadrupeds appear better able to resist mediolateral (ML) shear forces than those of arboreal quadrupedal monkeys. These differences in forelimb morphology have been used extensively to infer locomotor behavior in extinct primate quadrupeds. However, the nature of ML substrate reaction forces (SRF) during arboreal and terrestrial quadrupedalism in primates is not known. This study documents ML-SRF magnitude and orientation and forelimb joint angles in six quadrupedal anthropoid species walking across a force platform attached to terrestrial (wooden runway) and arboreal supports (raised horizontal poles). On the ground all subjects applied a lateral force in more than 50% of the steps collected. On horizontal poles, in contrast, all subjects applied a medially directed force to the substrate in more than 75% of the steps collected. In addition, all subjects on arboreal supports combined a lower magnitude peak ML-SRF with a change in the timing of the ML-SRF peak force. As a result, during quadrupedalism on the poles the overall SRF resultant was relatively lower than it was on the runway. Most subjects in this study adduct their humerus while on the poles. The kinetic and kinematic variables combine to minimize the tendency to collapse or translate forelimbs joints in an ML plane in primarily arboreal quadrupedal primates compared to primarily terrestrial quadrupedal ones. These data allow for a more complete understanding of the anatomy of the forelimb in terrestrial vs. arboreal quadrupedal primates. A better understanding of the mechanical basis of morphological differences allows greater confidence in inferences concerning the locomotion of extinct primate quadrupeds.     

The human mandible: Lever or link?

The mammalian mandible, and in particular the human mandible, is generally thought to function as a lever during biting. This notion, however, has not gone unchallenged. Various workers have suggested that the mandible does not function as a lever, and they base this proposition on essentially two assertions: (1) the resultant of the forces produced by the masticatory muscles always passes through the bite point; (2) the condylar neck and/or the temporomandibular joint is unsuited to withstand reaction forces during biting. A review of the electromyographic data and of the properties of the tissues of the temporomandibular joint do not support the non-lever hypothesis of mandibular function. In addition, an analysis of the strength of the condylar neck demonstrates that this structure is strong enough to withstand the expected reaction force during lever action. Ordinarily the human mandible and the forces that act upon it are analyzed solely in the lateral projection. Moments are then usually analyzed about the mandibular condyle; however, some workers have advocated taking moments about other points, e.g., the instantaneous center of rotation. Obviously it makes no difference as to what point is chosen since the moments about any point during equilibrium conditions are equal to zero. It is also useful to analyze the forces acting on the mandible in the frontal projection, particularly during unilateral biting. The electromyographic data suggest that during powerful unilateral molar biting the resultant adductor muscle force is passing between the bite point and the balancing (non-biting side) condyle. Therefore, in order for this system to be in equilibrium there must be a reaction force acting on the balancing condyle. This suggests that reaction forces are larger on the balancing side than on the working side, and possibly explains why individuals with a painful temporomandibular joint usually prefer to bite on the side of the diseased joint.     

The maximum average bite force for a given jaw length

Major osteological landmarks were used to prepare idealized drawings of mammalian and reptilian lower jaws. Measurements from these drawings allowed the average output or bite force, along the entire jaw, to be calculated for many different anteroposterior positions of the input or muscle force. In the mammalian drawing, the maximum average bite force is exerted when the resultant force is located at about 30% of the way along the jaw from the joints. Because of geometric differences in the reptilian drawing, a resultant positioned at 20% of the way along the jaw exerts the maximum average bite force; a maximum force that is smaller than that in the mammalian case. The estimated location of the muscle resultant in actual cases corresponds to these calculated positions. Therefore, in real animals, the muscles are located in the position that produces the largest average force for any jaw length. The geometric changes necessary to transform the idealized reptilian drawing, with a smaller maximum average bite force, into that of the mammalian drawing, with a larger maximum force, are the same as those changes seen in the fossil record of the reptile/mammal transition. This finding suggests that the morphological changes that occurred in the jaws increased the average bite force in the primitive mammals.     

An improved multi-joint EMG-assisted optimization approach to estimate joint and muscle forces in a musculoskeletal model of the lumbar spine

Muscle force partitioning methods and musculoskeletal system simplifications are key modeling issues that can alter outcomes, and thus change conclusions and recommendations addressed to health and safety professionals. A critical modeling concern is the use of single-joint equilibrium to estimate muscle forces and joint loads in a multi-joint system, an unjustified simplification made by most lumbar spine biomechanical models. In the context of common occupational tasks, an EMG-assisted optimization method (EMGAO) is modified in this study to simultaneously account for the equilibrium at all lumbar joints (M-EMGAO). The results of this improved approach were compared to those of its conventional single-joint equivalent (S-EMGAO) counterpart, the latter method being applied to the same lumbar joints but one at a time. Despite identical geometrical configurations and passive contributions used in both models, computed outcomes clearly differed between single- and multi-joint methods, especially at larger trunk flexed postures and during asymmetric lifting. Moreover, muscle forces predicted by L5-S1 single-joint analyses do not maintain mechanical equilibrium at other spine joints crossed by the same muscles. Assuming that the central nervous system does not attempt to balance the external moments one joint at a time and that a given muscle cannot exert different forces at different joints, the proposed multi-joint method represents a substantial improvement over its single-joint counterpart. This improved approach, hence, resolves trunk muscle forces with biological integrity but without compromising mechanical equilibrium at the lumbar joints.     

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.     

Bite forces and their resultants during forceful intercuspal clenching in humans

We aimed to develop a method of gathering complete information on the system of bite forces acting on the dental arches during clenching with the teeth in maximum intercuspation. Further, we attempted to reduce this system into an equivalent wrench—a force–couple system comprising a single force and a single couple acting along a unique line of action. We investigated the normative distribution of the bite forces and the location and orientation of their resultant wrench in 30 young adults (18–23 yr) with natural dentitions. The number of detected occlusal contacts varied from 12 to 46 (mean: 26.1; SD: 8.4), and was significantly greater for the molars than the premolar and anterior teeth, as were the bite-force magnitudes at individual occlusal contacts (1.2–218.4 N); those resulted in the antero-posteriorly slanted bite-force distribution. The magnitude of the bite-force resultants varied from 246.9 to 2091.9 N, and the points at which the resultant wrench axes intersected the mandibular occlusal plane were located 21.3–37.6 mm posterior to the incisal point and less than 8.9 mm from the midline bilaterally. The bite-force resultant was slightly inclined anteriorly from the perpendicular direction to the mandibular occlusal plane. Our method of using pressure-sensitive films to obtain information on all parameters needed to mechanically define a force (such as magnitude, direction, and point of application) is novel. To our knowledge, this is the first study investigating the system of bite forces during forceful intercuspal clenching in six degrees-of-freedom.     

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.     

An integrated model of active glenohumeral stability

We present the first model of the glenohumeral joint implementing active muscle driven humeral positioning and stabilization without a priori constraints on glenohumeral kinematics. Previously established methods were used to predetermine the path, activation timing and resultant force contribution of 27 individual muscle segments at any given joint position. Artificial boundary conditions were applied in a three-dimensional finite element model of the joint and progressively released until the humeral head was completely free to rotate and translate within the fixed glenoid according to the compressive component of the predetermined resultant force. The shear component was then added such that no boundary conditions other than muscular force were applied. The framework was exploited to simulate elevation as a composite of instantaneous positions and theoretically demonstrate that joint stability can be achieved exclusively through muscular activity. Predicted muscle moment arms, muscle activation timing, humeral head translations, joint contact forces and stability ratio were comparable with existing experimental and in vivo data. This framework could be valuable for subject specific modeling and may be used to address clinical hypotheses related to shoulder joint stability that cannot be pursued using simplified modeling approaches.