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.     

Development of a dynamic index finger and thumb model to study impairment

Modeling of the human hand provides insight for explaining deficits and planning treatment following injury. Creation of a dynamic model, however, is complicated by the actions of multi-articular tendons and their complex interactions with other soft tissues in the hand. This study explores the creation of a musculoskeletal model, including the thumb and index finger, to explore the effects of muscle activation deficits. The OpenSim model utilizes physiological axes of rotation at all joints, passive joint torques, and appropriate moment arms. The model was validated through comparison with kinematic and kinetic experimental data. Simulated fingertip forces resulting from modeled musculotendon loading largely fell within one standard deviation of experimental ranges for most index finger and thumb muscles, although agreement in the sagittal plane was generally better than for the coronal plane. Input of experimentally obtained electromyography data produced the expected simulated finger and thumb motion. Use of the model to predict the effects of activation deficits on pinch force production revealed that the intrinsic muscles, especially first dorsal interosseous (FDI) and adductor pollicis (ADP), had a substantial impact on the resulting fingertip force. Reducing FDI activation, such as might occur following stroke, altered fingertip force direction by up to 83° for production of a dorsal fingertip force; reducing ADP activation reduced force production in the thumb by up to 62%. This validated model can provide a means for evaluating clinical interventions.     

Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses

There are different opinions in the literature on whether the cost functions: the sum of muscle stresses squared and the sum of muscle stresses cubed, can reasonably predict muscle forces in humans. One potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization-based models. In this study, the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees-of-freedom (DOF) model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function. Analytical results revealed that, generally, the non-zero optimal force of each muscle depends in a very complex non-linear way on moments at all three joints and moment arms and physiological cross-sectional areas (PCSAs) of all muscles. Deviations of the model parameters (moment arms and PCSAs) from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria, but also the number of non-zero forces in the optimal solution and the combination of muscles with non-zero predicted forces. Muscle force magnitudes calculated by both criteria were similar. They could change several times as model parameters changed, whereas patterns of muscle forces were typically not as sensitive. It is concluded that different opinions in the literature about the behavior of optimization-based models can be potentially explained by differences in employed model parameters.     

Finger Muscle Attachments for an OpenSim Upper-Extremity Model

We determined muscle attachment points for the index, middle, ring and little fingers in an OpenSim upper-extremity model. Attachment points were selected to match both experimentally measured locations and mechanical function (moment arms). Although experimental measurements of finger muscle attachments have been made, models differ from specimens in many respects such as bone segment ratio, joint kinematics and coordinate system. Likewise, moment arms are not available for all intrinsic finger muscles. Therefore, it was necessary to scale and translate muscle attachments from one experimental or model environment to another while preserving mechanical function. We used a two-step process. First, we estimated muscle function by calculating moment arms for all intrinsic and extrinsic muscles using the partial velocity method. Second, optimization using Simulated Annealing and Hooke-Jeeves algorithms found muscle-tendon paths that minimized root mean square (RMS) differences between experimental and modeled moment arms. The partial velocity method resulted in variance accounted for (VAF) between measured and calculated moment arms of 75.5% on average (range from 48.5% to 99.5%) for intrinsic and extrinsic index finger muscles where measured data were available. RMS error between experimental and optimized values was within one standard deviation (S.D) of measured moment arm (mean RMS error = 1.5 mm < measured S.D = 2.5 mm). Validation of both steps of the technique allowed for estimation of muscle attachment points for muscles whose moment arms have not been measured. Differences between modeled and experimentally measured muscle attachments, averaged over all finger joints, were less than 4.9 mm (within 7.1% of the average length of the muscle-tendon paths). The resulting non-proprietary musculoskeletal model of the human fingers could be useful for many applications, including better understanding of complex multi-touch and gestural movements.     

Chimpanzee thumb muscle cross sections, moment arms and potential torques, and comparisons with humans.

This study investigates the morphological basis of differences between humans and chimpanzees in the kinematical and dynamical parameters of the musculature of the thumb. It is partly intended to test an hypothesis that human thumb muscles can exert significantly greater torques, due to larger muscle cross-sectional areas or to longer tendon moment arms or to both. We focus on the estimation of the potentials of thumb muscles to exert torques about joint axes in a sample of eight chimpanzee cadaver hands. The potential torque of a muscle is estimated by taking the product of a muscle's physiological cross-sectional area (an estimator of force) with its dynamical moment arm (derived from the slope of tendon excursion versus joint angular displacement, obtained during passive movements of cadaver thumb joints). Comparison of our results with similar data obtained for humans at the same Mayo Clinic laboratory shows significant differences between humans and chimpanzees in potential torque of most thumb muscles, those of humans generally exhibiting larger values. The primary reason for the larger torques in humans is that their average moment arms are significantly longer, permitting greater torque for a given muscle size. An additional finding is that chimpanzees and humans differ in the direction of secondary thumb metacarpal movements elicited by contraction of some muscles, as shown by differences in moment arm signs for a given movement in the same muscle. The differences appear to be related to differences in the musculo-skeletal structures of the trapeziometacarpal joint.     

Wrist tendon moment arms: Quantification by imaging and experimental techniques

Subject-specific musculoskeletal models require accurate values of muscle moment arms. The aim of this study was to compare moment arms of wrist tendons obtained from non-invasive magnetic resonance imaging (MRI) to those obtained from an in vitro experimental approach. MRI was performed on ten upper limb cadaveric specimens to obtain the centrelines for the flexor carpi radialis (FCR), flexor carpi ulnaris (FCU), extensor carpi radialis longus (ECRL), extensor carpi radialis brevis (ECRB), extensor carpi ulnaris (ECU), and abductor pollicis longus (APL) tendons. From these, the anatomical moment arms about each of the flexion-extension (FE) and radioulnar deviation (RUD) axes of the wrist were calculated. Specimens were mounted on a physiologic wrist simulator to obtain functional measurements of the moment arms using the tendon excursion method. No differences were observed between anatomical and functional values of the FE and RUD moment arms of FCR, ECRL and ECRB, and the RUD moment arm of ECU (p > .075). Scaling the anatomical moment arms relative to ECRB in FE and ECU in RUD reduced differences in the FE moment arm of FCU and the RUD moment arm of APL to less than 15% (p > .139). However, differences persisted in moment arms of FCU in RUD, and ECU and APL in FE (p < .008). This study shows that while measurements of moment arms of wrist tendons using imaging do not always conform to values obtained using in vitro experimental approaches, a stricter protocol could result in the acquisition of subject-specific moment arms to personalise musculoskeletal models.     

The evolution of hindlimb tendons and muscles on the line to crown-group birds

The anatomy and functions of muscle-tendon complexes and their bony attachments in birds and their outgroups show how the major pelvic limb muscle groups evolved. Fossils reveal that most changes evolved after the divergence of archosaurs in the Triassic, particularly in the dinosaurian precursors to birds. Three-dimensional limb control became concentrated at the hip joint; more distal joints and muscles were restricted to flexion or extension early in dinosaur evolution. Hip extensors expanded even though the primary femoral retractor M. caudofemoralis longus was reduced. Hip flexors and two-joint "hamstring" muscles were simplified to a few large heads. Knee extensors increased their sizes and moment arms early in bipedal dinosaurs, but the patella and cranial cnemial crest evolved later in birds. Lower limb muscles expanded as ossifications such as the hypotarsus increased their moment arms. The ossification of lower limb tendons, particularly in extensors, is a recent novelty of birds. Muscles and tendons that develop large forces, stresses, and moments to stabilize or move the limbs became increasingly prominent on the line to birds. Locomotion evolved in a stepwise pattern that only recently produced the derived limb control mechanisms of crown-group birds, such as the strongly flexed hip and knee joints.     

Analysis of the musculoskeletal loading of the thumb during pipetting – A pilot study

Previous epidemiological studies indicate that the use of thumb-push mechanical pipettes is associated with musculoskeletal disorders (MSDs) in the hand. The goal of the current study was to analyze the loading in the muscle–tendon units in the thumb during pipetting. The hand is modeled as a multi-body linkage system and includes four fingers (index, long, ring, and little finger), a thumb, and a palm segment. Since the current study is focused on the thumb, the model includes only nine muscles attached to the thumb via tendons. The time-histories of joint angles and push force at the pipette plunger during pipetting were determined experimentally and used as model input; whereas forces in the muscle–tendon units in the thumb were calculated via an inverse dynamic approach combined with an optimization procedure. Results indicate that all nine muscles have force outputs during pipetting, and the maximal force was in the abductor pollicis brevis (APB). The ratio of the mean peak muscle force to the mean peak push force during the dispensing cycle was approximately 2.3, which is comparable to values observed in grasping tasks in the literature. The analysis method and results in the current study provide a mechanistic understanding of MSD risk factors associated with pipetting, and may be useful in guiding ergonomic designs for manual pipettes.     

Comparison of tendon tensions estimated from two biomechanical models of the thumb

Despite the paramount function of the thumb in daily life, thumb biomechanical models have been little developed and studied. Moreover, only two studies provided quantitative anthropometric data of tendon moment arms. To investigate thumb tendon tensions, biomechanicians and clinicians have to know the performances and the limits of these two data sets. The aim of this study was thus to compare the results of these two models and evaluate their performances in regard to prior electromyographic measurements (EMG).Thumb posture was recorded during the classical key pinch and pulp pinch grips. Various fingertip forces applied at the distal segment were simulated in a range including extension, adduction, flexion, abduction. Input data of thumb postures and fingertip forces were used to compute tendon tensions with both models. Tendon tensions obtained using these two models were then compared and correlated to EMG measurements provided in the literature.The results showed that both models predicted relevant muscle coordination for five of the nine muscles modelled. Opponent and abductor longus muscle coordinations were badly estimated by both models. Each model was sensible to kinematic errors but not in the same proportion. This study pointed out the advantages/limits of the two models to use them more appropriately for clinical and/or research purposes.     

Knee muscle moment arms from MRI and from tendon travel.

We tested magnetic resonance imaging (MRI) as a means to collect geometric data for moment arm estimation. A knee specimen in five successive flexion postures was scanned by MRI, while simultaneously tendon positions of loaded muscles were measured (long head of biceps femoris, lateral and medial gastrocnemius, gracilis, rectus femoris, sartorius, semimembranosus, semitendinosus, and tensor fasciae latae). Discrete rotation centres were derived from MRI pictures. Moment arms were estimated as the distances from these centres to the tendons. The ratio of tendon travel over the increment of joint angulation was the alternative, more reliable estimate of the moment arm. An important principal shortcoming of MRI is the impossibility of accounting for force distribution in taut tissue. As a consequence, for some muscles, considerable inaccuracies in moment arm estimation are found in a relatively small range of joint angulation (up to about 30% for the rectus femoris and semimembranosus). For the tensor fasciae latae, the moment arm cannot be estimated by MRI, while the estimate by tendon travel is unreliable owing to the deformability and attachments of the fascia lata.     

Studies on the tendinous compartments of the extensor muscles on the back of the human hand and their tendon sheaths. I

In 47 dissected right and left hands of adults of both sexes, kept in a moist condition, significant practical-clinical investigations of the transitional zone between forearm and hand were undertaken. In particular it was sought to determine the characteristic sizes of the extensor retinaculum, the osteofibrous tunnels, the insertion tendons of the hand and finger extensor muscles, and their tendon sheaths. Together with the palmar carpal ligament, the 2 to 3 cm wide extensor retinaculum annularly surrounds the whole circumference of the carpus. It extends obliquely from radial-proximal to ulnar-distal and conducts the extensor tendons over the carpal articulations. According to recent studies, it is divided into a superficial and a deep fibrous layer. From the undermost surface, vertical and oblique septa run to the plane of the forearm and carpal bones. They separate the fibrous portion of the 6 tendinous compartments of the dorsum manus. In 8.5% of cases, an accessory and completely independent tunnel of the extensor pollicis brevis muscle exists in the material investigated, and in 2.2% of cases, there is an additional tunnel for the extensor carpi radialis muscle. Hence, one occasionally finds 8 separate osteofibrous gliding compartments for the extensor muscles in the dorsal hand region. The longest tunnel belongs, as a rule, to the extensor digiti minimi muscle, whilst the widest pertains to the extensor digitorum muscle. Within the tunnel and also proximal and distal to it, the extensor tendons are surrounded by synovial sheaths. Because of its wide encroachment on the dorsum of the hand, the insertion tendon of the extensor digiti minimi muscle possesses the longest tendon sheath, measuring 68.8 mm. The next longest sheath, that of the extensor pollicis longus muscle, which measures 56.2 mm, begins further proximal to the gap of the radiocarpal articulation. In 12.8% of cases, there are divided sheaths of the abductor pollicis longus and of the extensor pollicis brevis muscle. The tendon sheath of both extensor carpi radiales muscles is frequently divided into 2 compartments which, in 2/3 of cases, communicate. The compartment of the extensor carpi radialis brevis muscle, in 91.5% of cases, shares a window-like opening with the roof of the synovial vagina of the extensor pollicis longus muscle. The tendon sheath of the long extensor muscles of the fingers originates 5 mm proximal to the forearm border of the extensor retinaculum and has a communal recess. The IVth tendon sheath opens distally and splays out in a glove-like manner to some distal recesses.(ABSTRACT TRUNCATED AT 400 WORDS)     

Estimation of the effective static moment arms of the tendons in the index finger extensor mechanism

A novel technique to estimate the contribution of finger extensor tendons to joint moment generation was proposed. Effective static moment arms (ESMAs), which represent the net effects of the tendon force on joint moments in static finger postures, were estimated for the 4 degrees of freedom (DOFs) in the index finger. Specifically, the ESMAs for the five tendons contributing to the finger extensor apparatus were estimated by directly correlating the applied tendon force to the measured resultant joint moments in cadaveric hand specimens. Repeated measures analysis of variance revealed that the finger posture, specifically interphalangeal joint angles, had significant effects on the measured ESMA values in 7 out of 20 conditions (four DOFs for each of the five muscles). Extensor digitorum communis and extensor indicis proprius tendons were found to have greater MCP ESMA values when IP joints are flexed, whereas abduction ESMAs of all muscles except extensor digitorum profundus were mainly affected by MCP flexion. The ESMAs were generally smaller than the moment arms estimated in previous studies that employed kinematic measurement techniques. Tendon force distribution within the extensor hood and dissipation into adjacent structures are believed to contribute to the joint moment reductions, which result in smaller ESMA values.     

Moment arms of the human digital flexors

For the extrinsic hand flexors (flexor digitorum profundus, FDP; flexor digitorum superficialis, FDS; flexor pollicis longus, FPL), moment arm corresponds to the tendon's distance from the center of the metacarpalphalangeal (MP), proximal interphalangeal (PIP), or distal interphalangeal (DIP) joint. The clinical value of establishing accurate moment arms has been highlighted for biomechanical modeling, the development of robotic hands, designing rehabilitation protocols, and repairing flexor tendon pulleys (Brand et al., 1975; An et al., 1983; Thompson and Giurintano, 1989; Deshpande et al., 2010; Wu et al., 2010). In this study, we define the moment arms for all of the extrinsic flexor tendons of the hand across all digital joints for all digits in cadaveric hands.     

Reconstruction of shoulder function using a reflected long head biceps: a moment arm study

A tendon transfer technique is proposed for the reconstruction of the paralyzed shoulders secondary to brachial plexus injury. This innovative technique does not require bone-to-bone or tendon to-bone fixation, and attempts to overcome other clinical limitations such as those due to insufficient length of donor muscle. The approach is referred to as the reflected long head biceps (RLHB) technique. The long head of biceps tendons is utilized as a bridging tendon graft. Two surgical alternatives, namely the through-deltoid (TD) pathway and the sub-deltoid (SD) pathway, were studied. The moment arms of the transferred tendons were assessed and reported. The TD technique yielded a larger moment than the SD technique. In the plane 30 degrees anterior to the scapular plane, the average moment arms were 3.8cm TD and 3.0cm SD at zero elevation. Such differences tended to further widen with increasing elevation. At 80 degrees elevation, the moment arms became 3.2cm TD and 1.2cm SD. The results supported the clinical feasibility of this RLHB tendon transfer approach.     

Application of spherical and cylindrical wrapping algorithms in a musculoskeletal model of the upper limb

In the modelling of the upper limb, many muscles cannot be represented as a straight line from origin to insertion due to the complex morphology causing them to wrap around passive structures. The majority of bony contours that form these obstructions can be described adequately as simple geometric shapes such as spheres and cylinders.A novel technique for the parameterisation of muscle paths as they wrap around such shapes has been developed for use in an upper limb model. The new method involves the definition of moving co-ordinate systems in which the path of a wrapped muscle does not move, allowing simplified specification. In addition, an analytical calculation of the wrapping path around a cylinder is presented over previous approximate methods.Muscle moment arms were pre-calculated from vector considerations and within SIMM by tendon excursion. Close agreement between the two suggests that the proposed implementations accurately follow the theoretical relationship and can be used with confidence in musculoskeletal models.     

Dimensions and moment arms of the hind- and forelimb muscles of common chimpanzees (Pan troglodytes).

This paper supplies quantitative data on the hind- and forelimb musculature of common chimpanzees (Pan troglodytes) and calculates maximum joint moments of force as a contribution to a better understanding of the differences between chimpanzee and human locomotion. We dissected three chimpanzees, and recorded muscle mass, fascicle length, and physiological cross-sectional area (PCSA). We also obtained flexion/extension moment arms of the major muscles about the limb joints. We find that in the hindlimb, chimpanzees possess longer fascicles in most muscles but smaller PCSAs than are predicted for humans of equal body mass, suggesting that the adaptive emphasis in chimpanzees is on joint mobility at the expense of tension production. In common chimpanzee bipedalism, both hips and knees are significantly more flexed than in humans, necessitating muscles capable of exerting larger moments at the joints for the same ground force. However, we find that when subject to the same stresses, chimpanzee hindlimb muscles provide far smaller moments at the joints than humans, particularly the quadriceps and plantar flexors. In contrast, all forelimb muscle masses, fascicle lengths, and PCSAs are smaller in humans than in chimpanzees, reflecting the use of the forelimbs in chimpanzee, but not human, locomotion. When subject to the same stresses, chimpanzee forelimb muscles provide larger moments at the joints than humans, presumably because of the demands on the forelimbs during locomotion. These differences in muscle architecture and function help to explain why chimpanzees are restricted in their ability to walk, and particularly to run bipedally.     

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.     

Analysis of human mandibular mechanics based on screw theory and in vivo data

In this paper the mechanics of human mandibular function is described in terms of the associated screws. The two distinct, yet related features of jaw mechanics, involving the motion itself as well as the forces, are both functions of the anatomical constraints, namely the contact areas that exist within the temporomandibular joint, and the forces of the muscles and tendons that allow motion to occur. The relationships that exist between these two aspects of jaw-motion are identified in this paper showing that muscle forces can be uniquely represented in terms of the action screw. This new approach to analyzing the mechanics of jaw-motion also incorporates the previously studied motion screw or helical axis. A consistent dynamic model is formulated where the action screw is used to represent the action of the closing muscle forces while the moment arms of the muscle forces are determined about the motion screw representing mandibular kinematics. The action screw formulation is verified using in vivo motion data and MR image information for a single asymptomatic subject. The results confirm the feasibility of the method and its application in dental research. A general increase in the mechanical advantage of most muscles, in the distance between action and motion screws as well as in the expended energy towards the end of the jaw-closing phase was observed. Asymmetries in the distribution of muscle force magnitudes appeared to influence the resultant force and moment of the action screw but had little effect on its spatial location. The method presented is intended to facilitate understanding of mandibular function and dysfunction.     

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

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.