Estimation of the forces generated by the thigh muscles for transtibial amputee gait

The forces generated by the muscles with origin on the human femur play a major role in transtibial amputee gait, as they are the most effective of the means that the body can use for propulsion. By estimating the forces generated by the thigh muscles of transtibial amputees, and comparing them to the forces generated by the thigh muscles of normal subjects, it is possible to better estimate the energy output needed from prosthetic devices. The purpose of this paper is to obtain the forces generated by the thigh muscles of transtibial amputees and compare these with forces obtained from the same muscles in the case of normal subjects. Two transtibial amputees and four normal subjects similar in size to the amputees were investigated. Level ground walking was chosen as the movement to be studied, since it is a common activity that most amputees engage in. Inverse dynamics and a muscle recruitment algorithm (developed by AnyBody Technology^®) were used for generating the muscle activation patterns and for computing the muscle forces. The muscle forces were estimated as two sums: one for all posterior muscles and one for the anterior muscles, based on the position of the muscles of the thigh relative to the frontal plane of the human body. The results showed that a significantly higher force is generated by the posterior muscles of the amputees during walking, leading to a general increase of the metabolic cost necessary for one step.     

Role of trunk muscles in generating follower load in the lumbar spine of neutral standing posture

Recently, experimental results have demonstrated that the load carrying capacity of the human spine substantially increases under the follower load condition. Thus, it is essential to prove that a follower load can be generated in vivo by activating the appropriate muscles in order to demonstrate the possibility that the stability of the spinal column could be maintained through a follower load mechanism. The aim of this study was to analyze the coordination of the trunk muscles in order to understand the role of the muscles in generating the follower load. A three-dimensional finite element model of the lumbar spine was developed from T12 to S1 and 117 pairs of trunk muscles (58 pairs of superficial muscles and 59 pairs of deep muscles) were considered. The follower load concept was mathematically represented as an optimization problem. The muscle forces required to generate the follower load were predicted by solving the optimization problem. The corresponding displacements and rotations at all nodes were estimated along with the follower forces, shear forces, and joint moments acting on those nodes. In addition, the muscle forces and the corresponding responses were investigated when the activations of the deep muscles or the superficial muscles were restricted to 75% of the maximum activation, respectively. Significantly larger numbers of deep muscles were involved in the generation of the follower load than the number of superficial muscles, regardless of the restriction on muscle activation. The shear force and the resultant joint moment are more influenced by the change in muscle activation in the superficial muscles. A larger number of deep trunk muscles were activated in order to maintain the spinal posture in the lumbar spine. In addition, the deep muscles have a larger capability to reduce the shear force and the resultant joint moment with respect to the perturbation of the external load or muscle fatigue compared to the superficial muscles.     

Response of the trunk muscles to training assessed by magnetic resonance imaging and muscle strength.

A group of 12 sedentary medical students (1 man and 11 women aged 21-27 years) participated in a strength training programme for the trunk muscles lasting 18 weeks. The maximal isometric flexion and extension forces of the trunk muscles were measured before the training and at 18 weeks by dynamometer. The cross-sectional area of the back muscles, i.e. erector spinae, multifidus and psoas muscles, was measured from magnetic resonance images (spin echo sequence TR/TE 1500/80, slice thickness 10 mm) obtained at the L4-L5 disc level before the training, at 11 and 18 weeks. During training, no significant change in the body mass or body fat content was found. Muscle forces or muscle cross-sectional area were not related to body mass. There was a significant increase in both trunk muscle cross-sectional area (psoas muscle P < 0.001 and back muscles P < 0.01) and trunk muscle forces (flexion and extension forces P < 0.01) during the training but no direct association between the muscle cross-sectional area and strength of the flexors and extensors was detected before or after the training.     

Integrated approach for in vivo evaluation of respiratory muscles mechanics

The respiratory muscles constitute the respiratory pump, which determines the efficacy of ventilation. Any functional disorder in their performance may cause insufficient ventilation. This study was designed to quantitatively explore the relative contribution of major groups of respiratory muscles to global lung ventilation throughout a range of maneuvers in healthy subjects. A computerized experimental system was developed for simultaneous noninvasive measurement of inspired/expired airflow, mouth pressure and up to 8 channels of EMG surface signals from major respiratory muscles which are located near the skin (e.g., sternomastoid, external intercostal, rectus abdominis and external oblique) during various respiratory maneuvers. Lung volumes values were calculated by integration of airflow data. Hill's muscle model was utilized to calculate the forces generated by the muscles from the acquired EMG data. Analysis of EMG measurements and respiratory muscles forces revealed the following characteristics: (a) muscle activity increased with increased breathing effort, (b) inspiratory muscles contributed to inspiration even at relatively low flow rates, while expiratory muscles are recruited at higher flow rates, (c) the forces generated by the muscle depended on the muscle properties as well as on their EMG performance and (d) the pattern of the muscle's force curves varied between subjects, but were generally consistent for the same subject regardless of breathing effort.     

Investigation of the Differential Contributions of Superficial and Deep Muscles on Cervical Spinal Loads with Changing Head Postures

Cervical spinal loads are predominately influenced by activities of cervical muscles. However, the coordination between deep and superficial muscles and their influence on the spinal loads is not well understood. This study aims to document the changes of cervical spinal loads and the differential contributions of superficial and deep muscles with varying head postures. Electromyography (EMG) of cervical muscles from seventeen healthy adults were measured during maximal isometric exertions for lateral flexion (at 10°, 20° and terminal position) as well as flexion/extension (at 10°, 20°, 30°, and terminal position) neck postures. An EMG-assisted optimization approach was used to estimate the muscle forces and subsequent spinal loads. The results showed that compressive and anterior-posterior shear loads increased significantly with neck flexion. In particular, deep muscle forces increased significantly with increasing flexion. It was also determined that in all different static head postures, the deep muscle forces were greater than those of the superficial muscle forces, however, such pattern was reversed during peak efforts where greater superficial muscle forces were identified with increasing angle of inclination. In summary, the identification of significantly increased spinal loads associated with increased deep muscle activation during flexion postures, implies higher risks in predisposing the neck to occupationally related disorders. The results also explicitly supported that deep muscles play a greater role in maintaining stable head postures where superficial muscles are responsible for peak exertions and reinforcing the spinal stability at terminal head postures. This study provided quantitative data of normal cervical spinal loads and revealed motor control strategies in coordinating the superficial and deep muscles during physical tasks.     

A model for determination of muscle forces in a given movement of man

A model of a muscular-skeletal system of a man for determination of muscle forces knowing kinematics of the body is elaborated. Forces exerted by the muscles of the lower extremities in normal walking are presented (planar model of a leg, 8 muscles). The forces found were compared with corresponding EMG-activity of muscles.     

Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking

A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.     

Biomechanical Analysis of the Human Finger Extensor Mechanism during Isometric Pressing

This study investigated the effects of the finger extensor mechanism on the bone-to-bone contact forces at the interphalangeal and metacarpal joints and also on the forces in the intrinsic and extrinsic muscles during finger pressing. This was done with finger postures ranging from very flexed to fully extended. The role of the finger extensor mechanism was investigated by using two alternative finger models, one which omitted the extensor mechanism and another which included it. A six-camera three-dimensional motion analysis system was used to capture the finger posture during maximum voluntary isometric pressing. The fingertip loads were recorded simultaneously using a force plate system. Two three-dimensional biomechanical finger models, a minimal model without extensor mechanism and a full model with extensor mechanism (tendon network), were used to calculate the joint bone-to-bone contact forces and the extrinsic and intrinsic muscle forces. If the full model is assumed to be realistic, then the results suggest some useful biomechanical advantages provided by the tendon network of the extensor mechanism. It was found that the forces in the intrinsic muscles (interosseus group and lumbrical) are significantly reduced by 22% to 61% due to the action of the extensor mechanism, with the greatest reductions in more flexed postures. The bone-to-bone contact force at the MCP joint is reduced by 10% to 41%. This suggests that the extensor mechanism may help to reduce the risk of injury at the finger joints and also to moderate the forces in intrinsic muscles. These apparent biomechanical advantages may be a result of the extensor mechanism''s distinctive interconnected fibrous structure, through which the contraction of the intrinsic muscles as flexors of the MCP joint can generate extensions at the DIP and PIP joints.     

Individual muscle contributions to the axial knee joint contact force during normal walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking.     

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.     

Eccentric exercise increases EMG amplitude and force fluctuations during submaximal contractions of elbow flexor muscles.

The purpose of this study was to determine the effect of eccentric exercise on the ability to exert steady submaximal forces with muscles that cross the elbow joint. Eight subjects performed two tasks requiring isometric contraction of the right elbow flexors: a maximum voluntary contraction (MVC) and a constant-force task at four submaximal target forces (5, 20, 35, 50% MVC) while electromyography (EMG) was recorded from elbow flexor and extensor muscles. These tasks were performed before, after, and 24 h after a period of eccentric (fatigue and muscle damage) or concentric exercise (fatigue only). MVC force declined after eccentric exercise (45% decline) and remained depressed 24 h later (24%), whereas the reduced force after concentric exercise (22%) fully recovered the following day. EMG amplitude during the submaximal contractions increased in all elbow flexor muscles after eccentric exercise, with the greatest change in the biceps brachii at low forces (3-4 times larger at 5 and 20% MVC) and in the brachialis muscle at moderate forces (2 times larger at 35 and 50% MVC). Eccentric exercise resulted in a twofold increase in coactivation of the triceps brachii muscle during all submaximal contractions. Force fluctuations were larger after eccentric exercise, particularly at low forces (3-4 times larger at 5% MVC, 2 times larger at 50% MVC), with a twofold increase in physiological tremor at 8-12 Hz. These data indicate that eccentric exercise results in impaired motor control and altered neural drive to elbow flexor muscles, particularly at low forces, suggesting altered motor unit activation after eccentric exercise.     

Contributions of muscles and passive dynamics to swing initiation over a range of walking speeds

Stiff-knee gait is a common walking problem in cerebral palsy characterized by insufficient knee flexion during swing. To identify factors that may limit knee flexion in swing, it is necessary to understand how unimpaired subjects successfully coordinate muscles and passive dynamics (gravity and velocity-related forces) to accelerate the knee into flexion during double support, a critical phase just prior to swing that establishes the conditions for achieving sufficient knee flexion during swing. It is also necessary to understand how contributions to swing initiation change with walking speed, since patients with stiff-knee gait often walk slowly. We analyzed muscle-driven dynamic simulations of eight unimpaired subjects walking at four speeds to quantify the contributions of muscles, gravity, and velocity-related forces (i.e. Coriolis and centrifugal forces) to preswing knee flexion acceleration during double support at each speed. Analysis of the simulations revealed contributions from muscles and passive dynamics varied systematically with walking speed. Preswing knee flexion acceleration was achieved primarily by hip flexor muscles on the preswing leg with assistance from biceps femoris short head. Hip flexors on the preswing leg were primarily responsible for the increase in preswing knee flexion acceleration during double support with faster walking speed. The hip extensors and abductors on the contralateral leg and velocity-related forces opposed preswing knee flexion acceleration during double support.     

Elevation and orientation of external loads influence trunk neuromuscular response and spinal forces despite identical moments at the L5–S1 level

A wide range of loading conditions involving external forces with varying magnitudes, orientations and locations are encountered in daily activities. Here we computed the effect on trunk biomechanics of changes in force location (two levels) and orientation (5 values) in 4 subjects in upright standing while maintaining identical external moment of 15 Nm, 30 N m or 45 Nm at the L5–S1. Driven by measured kinematics and gravity/external loads, the finite element models yielded substantially different trunk neuromuscular response with moderate alterations (up to 24% under 45 Nm moment) in spinal loads as the load orientation varied. Under identical moments, compression and shear forces at the L5–S1 as well as forces in extensor thoracic muscles progressively decreased as orientation of external forces varied from downward gravity (90°) all the way to upward (−25°) orientation. In contrast, forces in local lumbar muscles followed reverse trends. Under larger horizontal forces at a lower elevation, lumbar muscles were much more active whereas extensor thoracic muscle forces were greater under smaller forces at a higher elevation. Despite such differences in activity pattern, the spinal forces remained nearly identical (<6% under 45 Nm moment). The published recorded surface EMG data of extensor muscles trend-wise agreed with computed local muscle forces as horizontal load elevation varied but were overall different from results in both local and global muscles when load orientation altered. Predictions demonstrate the marked effect of external force orientation and elevation on the trunk neuromuscular response and spinal forces and questions attempts to estimate spinal loads based only on consideration of moments at a spinal level.     

Control of ground reaction forces by hindlimb muscles during cat locomotion

It has been proposed that biarticular muscles are primarily responsible for the control of the direction of external forces, as their activation is closely related and highly sensitive to the direction of external forces. This functional role for biarticular muscles has been supported qualitatively by experimental evidence, but has never been tested quantitatively for lack of a mathematical/mechanical formulation of this theory and the difficulty of measuring individual muscle forces during voluntary movements. The purposes of this study were: (1) to define rules for muscular coordination based on the control of external forces; (2) to develop a model of the cat hindlimb that allows for the calculation of the magnitude and direction of the ground reaction forces (GRFs) produced by individual hindlimb muscles; and (3) to test if the coordination of mono- and biarticular cat hindlimb muscles is related to the control of the resultant GRF. We measured the GRF, hindlimb kinematics, selected muscle forces and activations during cat locomotion. Then, the measured muscle forces were used as input to the hindlimb model to compute the muscle-induced GRF. We assume that if activation (and possibly force) increased as the muscle-induced component of GRF approximated the resultant GRF, then that muscle was used by the central nervous system (CNS) to help control the direction of the external GRF. During cat walking, medial gastrocnemius (MG) and plantaris (PL) forces increased with increasing proximity to the GRF, while soleus (SOL) forces and vastus lateralis (VL) activations did not. SOL and VL activation were most strongly related to the vertical and parallel (braking/accelerating) component of the GRF, respectively. We concluded from these results that MG and PL are primarily responsible for the control of the direction of the GRF, while SOL primarily functions as an anti-gravity muscle, and VL as an acceleration/deceleration muscle.     

Prediction of handgrip forces using surface EMG of forearm muscles.

Evaluation of handgrip forces constitutes an essential component of ergonomic evaluation (e.g. of hand tools), but is difficult to perform at the workplace. The present study describes a series of experiments on 8 healthy male subjects to determine the validity of linear regression models using the surface electromyography (EMG) of up to 6 forearm muscles to predict handgrip forces. For isometric gripping tasks, normalized EMG to grip force calibrations using a series of dynamic force bursts up to 300 N resulted in a valid prediction of grip forces based on the EMG of 6 forearm muscles. Absolute differences between observed and predicted grip force were small (between 27 and 41 N) which shows that the proposed method might be used for the ergonomic evaluation of the use of hand tools. The EMG - handgrip force model appeared to be minimally affected by grip width, i.e. a model for 67 mm grip width was able to validly predict grip forces for 59 and 75 mm grip widths. Furthermore, it was shown that of the 6 forearm muscles studied at least 3 have to be assessed to arrive at a sufficient level of validity, while it seems to be irrelevant which 3 of those 6 forearm muscles are assessed.     

Joint moments and contact forces in the foot during walking

The net force and moment of a joint have been widely used to understand joint disease in the foot. Meanwhile, it does not reflect the physiological forces on muscles and contact surfaces. The objective of the study is to estimate active moments by muscles, passive moments by connective tissues and joint contact forces in the foot joints during walking. Joint kinematics and external forces of ten healthy subjects (all males, 24.7 ± 1.2 years) were acquired during walking. The data were entered into the five-segment musculoskeletal foot model to calculate muscle forces and joint contact forces of the foot joints using an inverse dynamics-based optimization. Joint reaction forces and active, passive and net moments of each joint were calculated from muscle and ligament forces. The maximum joint reaction forces were 8.72, 4.31, 2.65, and 3.41 body weight (BW) for the ankle, Chopart’s, Lisfranc and metatarsophalangeal joints, respectively. Active and passive moments along with net moments were also obtained. The maximum net moments were 8.6, 8.4, 5.4 and 0.8%BW∙HT, respectively. While the trend of net moment was very similar between the four joints, the magnitudes and directions of the active and passive moments varied between joints. The active and passive moments during walking could reveal the roles of muscles and ligaments in each of the foot joints, which was not obvious in the net moment. This method may help narrow down the source of joint problems if applied to clinical studies.     

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.     

Evaluation of the influence of muscle deactivation on other muscles and joints during gait motion

When any muscle in the human musculoskeletal system is damaged, other muscles and ligaments tend to compensate for the role of the damaged muscle by exerting extra effort. It is beneficial to clarify how the roles of the damaged muscles are compensated by other parts of the musculoskeletal system from the following points of view: From a clinical point of view, it will be possible to know how the abnormal muscle and joint forces caused by the acute compensations lead to further physical damage to the musculoskeletal system. From the viewpoint of rehabilitation, it will be possible to know how the role of the damaged muscle can be compensated by extra training of the other muscles. A method to evaluate the influence of muscle deactivation on other muscles and joints is proposed in this report. Methodology based on inverse dynamics and static optimization, which is applicable to arbitrary motion was used in this study. The evaluation method was applied to gait motion to obtain matrices representing (1) the dependence of muscle force compensation and (2) the change to bone-on-bone contact forces. These matrices make it possible to evaluate the effects of deactivation of one of the muscles of the musculoskeletal system on the forces exerted by other muscles as well as the change to the bone-on-bone forces when the musculoskeletal system is performing the same motion. Through observation of this matrix, it was found that deactivation of a muscle often results in increment/decrement of force developed by muscles with completely different primary functions and bone-on-bone contact force in different parts of the body. For example, deactivation of the iliopsoas leads to a large reduction in force by the soleus. The results suggest that acute deactivation of a muscle can result in damage to another part of the body. The results also suggest that the whole musculoskeletal system must go through extra retraining in the case of damage to certain muscles.     

Spinal loads and trunk muscles forces during level walking – A combined in vivo and in silico study on six subjects

During level walking, lumbar spine is subjected to cyclic movements and intricate loading of the spinal discs and trunk musculature. This study aimed to estimate the spinal loads (T12–S1) and trunk muscles forces during a complete gait cycle.Six men, 24–33 years walk barefoot at self-selected speed (4–5 km/h). 3D kinematics and ground reaction forces were recorded using a motion capturing system and two force plates, implemented in an inverse dynamic musculoskeletal model to predict the spinal loads and trunk muscles forces. Additionally, the sensitivity of the intra-abdominal pressure and lumbar segment rotational stiffness was investigated.Peak spinal loads and trunk muscle forces were between the gait instances of heel strike and toe off. In L4–L5 segment, sensitivity analysis showed that average peak compressive, antero-posterior and medio-lateral shear forces were 130–179%, 2–15% and 1–6%, with max standard deviation (±STD) of 40%, 6% and 3% of the body weight. Average peak global muscles forces were 24–55% (longissimus thoracis), 11–23% (iliocostalis thoracis), 12–16% (external oblique), 17–25% (internal oblique) and 0–8% (rectus abdominus) of body weight whereas, the average peak local muscles forces were 11–19% (longissimus lumborum), 14–31% (iliocostalis lumborum) and 12–17% (multifidus). Maximum ± STD of the global and local muscles forces were 13% and 8% of the body weight.Large inter-individual differences were found in peak compressive and trunk muscles forces whereas the sensitivity analysis also showed a substantial variation.     

Occlusal force and craniofacial biomechanics during growth in rhesus monkeys

The masticatory muscles in 132 anesthetized male and female rhesus monkeys ranging in age from juvenile to adult were unilaterally stimulated. Muscle forces and speeds were measured with a bite force transducer positioned at the incisors, premolars, and molars during twitch and tetanic contractions. Lateral cephalographs of all animals were used to estimate the orientation and mechanical advantage of the masticatory muscles. Results showed that maximal occlusal forces increased at a greater rate than body weight during growth. However, maximal occlusal forces increased isometrically relative to mandibular length. Mean forces at the incisors ranged from 70.3 newtons (n) in juveniles up to 139.9 n in adult males. Forces at the molars were 2-2.5 times greater than at the incisors. Time-to-peak tension decreased with increasing body size from 44.1 msec in juveniles to 37.4 msec in adult females to 31.0 msec in adult males. Regression analysis showed that adult males have faster muscles than adult females or juveniles even when corrected for body size. Temporalis and masseter orientation was found to change little throughout growth. The mechanical advantage of the masseter and temporalis muscles for producing occlusal forces on the distal molars improved between juveniles and adults, which is contrary to findings of Oyen et al. (Growth 43:174-187, 1979). Among adults, females had a greater mechanical advantage of the masseter muscles than males.