Abdominal muscles dominate contributions to vertebral joint stiffness during the push-up

The goal of this study was to quantify the relative contributions of each muscle group surrounding the spine to vertebral joint rotational stiffness (VJRS) during the push-up exercise. Upper-body kinematics, three-dimensional hand forces and lumbar spine postures, and 14 channels (bilaterally from rectus abdominis, external oblique, internal oblique, latissimus dorsi, thoracic erector spinae, lumbar erector spinae, and multifidus) of trunk electromyographic (EMG) activity were collected from 11 males and used as inputs to a biomechanical model that determined the individual contributions of 10 muscle groups surrounding the lumbar spine to VJRS at five lumbar vertebral joints (L1-L2 to L5-S1). On average, the abdominal muscles contributed 64.32 +/- 8.50%, 86.55 +/- 1.13%, and 83.84 +/- 1.95% to VJRS about the flexion/extension, lateral bend, and axial twist axes, respectively. Rectus abdominis contributed 43.16 +/- 3.44% to VJRS about the flexion/extension axis at each lumbar joint, and external oblique and internal oblique, respectively contributed 52.61 +/- 7.73% and 62.13 +/- 8.71% to VJRS about the lateral bend and axial twist axes, respectively, at all lumbar joints with the exception of L5-S1. Owing to changes in moment arm length, the external oblique and internal oblique, respectively contributed 55.89% and 50.01% to VJRS about the axial twist and lateral bend axes at L5-S1. Transversus abdominis, multifidus, and the spine extensors contributed minimally to VJRS during the push-up exercise. The push-up challenges the abdominal musculature to maintain VJRS. The orientation of the abdominal muscles suggests that each muscle primarily controls the rotational stiffness about a single axis.     

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.     

Moment arms of the human neck muscles in flexion, bending and rotation

There is a paucity of data available for the moment arms of the muscles of the human neck. The objective of the present study was to measure the moment arms of the major cervical spine muscles in vitro. Experiments were performed on five fresh-frozen human head-neck specimens using a custom-designed robotic spine testing apparatus. The testing apparatus replicated flexion-extension, lateral bending and axial rotation of each individual intervertebral joint in the cervical spine while all other joints were kept immobile. The tendon excursion method was used to measure the moment arms of 30 muscle sub-regions involving 13 major muscles of the neck about all three axes of rotation of each joint for the neutral position of the cervical spine. Significant differences in the moment arm were observed across sub-regions of individual muscles and across the intervertebral joints spanned by each muscle (p<0.05). Overall, muscle moment arms were larger in flexion-extension and lateral bending than in axial rotation, and most muscles had prominent moment arms in at least 2 out of the 3 joint motions investigated. This study emphasizes the importance of detailed representation of a muscle's architecture in prediction of its torque capacity about the individual joints of the cervical spine. The dataset produced may be useful in developing and validating computational models of the human neck.     

In vivo determination of the direction of rotation and moment-angle relationship of individual elbow muscles.

The direction of rotation (DOR) of individual elbow muscles, defined as the direction in which a muscle rotates the forearm relative to the upper arm in three-dimensional space, was studied in vivo as a function of elbow flexion and forearm rotation. Electrical stimulation was used to activate an individual muscle selectively, and the resultant flexion-extension, supination-pronation, and varus-valgus moments were used to determine the DOR. Furthermore, multi-axis moment-angle relationships of individual muscles were determined by stimulating the muscle at a constant submaximal level across different joint positions, which was assumed to result in a constant level of muscle activation. The muscles generate significant moments about axes other than flexion-extension, which is potentially important for actively controlling joint movement and maintaining stability about all axes. Both the muscle DOR and the multi axis moments vary with the joint position systematically. Variations of the DOR and moment-angle relationship across muscle twitches of different amplitudes in a subject were small, while there were considerable variations between subjects.     

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.     

Development of an anatomically based whole‐body musculoskeletal model of the Japanese macaque (Macaca fuscata)

We constructed a three‐dimensional whole‐body musculoskeletal model of the Japanese macaque (Macaca fuscata) based on computed tomography and dissection of a cadaver. The skeleton was modeled as a chain of 20 bone segments connected by joints. Joint centers and rotational axes were estimated by joint morphology based on joint surface approximation using a quadric function. The path of each muscle was defined by a line segment connecting origin to insertion through an intermediary point if necessary. Mass and fascicle length of each were systematically recorded to calculate physiological cross‐sectional area to estimate the capacity of each muscle to generate force. Using this anatomically accurate model, muscle moment arms and force vectors generated by individual limb muscles at the foot and hand were calculated to computationally predict muscle functions. Furthermore, three‐dimensional whole‐body musculoskeletal kinematics of the Japanese macaque was reconstructed from ordinary video sequences based on this model and a model‐based matching technique. The results showed that the proposed model can successfully reconstruct and visualize anatomically reasonable, natural musculoskeletal motion of the Japanese macaque during quadrupedal/bipedal locomotion, demonstrating the validity and efficacy of the constructed musculoskeletal model. The present biologically relevant model may serve as a useful tool for comprehensive understanding of the design principles of the musculoskeletal system and the control mechanisms for locomotion in the Japanese macaque and other primates. Am J Phys Anthropol, 2009. © 2008 Wiley‐Liss, Inc.     

Individual muscle force parameters and fiber operating ranges for elbow flexion-extension and forearm pronation-supination

We have quantified individual muscle force and moment contributions to net joint moments and estimated the operating ranges of the individual muscle fibers over the full range of motion for elbow flexion/extension and forearm pronation/supination. A three dimensional computer graphics model was developed in order to estimate individual muscle contributions in each degree of freedom over the full range of motion generated by 17 muscles crossing the elbow and forearm. Optimal fiber length, tendon slack length, and muscle specific tension values were adjusted within the literature range from cadaver studies such that the net isometric joint moments of the model approximated experimental joint moments within one standard deviation. Analysis of the model revealed that the muscles operate on varying portions of the ascending limb, plateau region, and descending limb of the force-length curve. This model can be used to further understand isometric force and moment contributions of individual muscles to net joint moments of the arm and forearm and can serve as a comprehensive reference for the forces and moments generated by 17 major muscles crossing the elbow and wrist.     

Shoulder muscle function depends on elbow joint position: an illustration of dynamic coupling in the upper limb

Shoulder muscle function has been documented based on muscle moment arms, lines of action and muscle contributions to contact force at the glenohumeral joint. At present, however, the contributions of individual muscles to shoulder joint motion have not been investigated, and the effects of shoulder and elbow joint position on shoulder muscle function are not well understood. The aims of this study were to compute the contributions of individual muscles to motion of the glenohumeral joint during abduction, and to examine the effect of elbow flexion on shoulder muscle function. A three-dimensional musculoskeletal model of the upper limb was used to determine the contributions of 18 major muscles and muscle sub-regions of the shoulder to glenohumeral joint motion during abduction. Muscle function was found to depend strongly on both shoulder and elbow joint positions. When the elbow was extended, the middle and anterior deltoid and supraspinatus were the greatest contributors to angular acceleration of the shoulder in abduction. In contrast, when the elbow was flexed at 90°, the anterior deltoid and subscapularis were the greatest contributors to joint angular acceleration in abduction. This dependence of shoulder muscle function on elbow joint position is explained by the existence of dynamic coupling in multi-joint musculoskeletal systems. The extent to which dynamic coupling affects shoulder muscle function, and therefore movement control, is determined by the structure of the inverse mass matrix, which depends on the configuration of the joints. The data provided may assist in the diagnosis of abnormal shoulder function, for example, due to muscle paralysis or in the case of full-thickness rotator cuff tears.     

Contributions of the individual muscles of the shoulder to glenohumeral joint stability during abduction

The aim of this study was to determine the relative contributions of the deltoid and rotator cuff muscles to glenohumeral joint stability during arm abduction. A three-dimensional model of the upper limb was used to calculate the muscle and joint-contact forces at the shoulder for abduction in the scapular plane. The joints of the shoulder girdle-sternoclavicular joint, acromioclavicular joint, and glenohumeral joint-were each represented as an ideal three degree-of-freedom ball-and-socket joint. The articulation between the scapula and thorax was modeled using two kinematic constraints. Eighteen muscle bundles were used to represent the lines of action of 11 muscle groups spanning the glenohumeral joint. The three-dimensional positions of the clavicle, scapula, and humerus during abduction were measured using intracortical bone pins implanted into one subject. The measured bone positions were inputted into the model, and an optimization problem was solved to calculate the forces developed by the shoulder muscles for abduction in the scapular plane. The model calculations showed that the rotator cuff muscles (specifically, supraspinatus, subscapularis, and infraspinatus) by virtue of their lines of action are perfectly positioned to apply compressive load across the glenohumeral joint, and that these muscles contribute most significantly to shoulder joint stability during abduction. The middle deltoid provides most of the compressive force acting between the humeral head and the glenoid, but this muscle also creates most of the shear, and so its contribution to joint stability is less than that of any of the rotator cuff 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.     

Trunk muscle contributions of to L4–5 joint rotational stiffness following sudden trunk lateral bend perturbations

The purpose of this research was to investigate the contributions of individual muscles to joint rotational stiffness and total joint rotational stiffness about the lumbar spine’s L_4–5 joint prior to, and following, sudden dynamic lateral perturbations to the trunk. Kinematic and surface EMG data were collected while subjects maintained a kneeling posture on a robotic platform, while restrained so that motions caused by the perturbation were transferred to the pelvis, causing motion of the trunk and head. The robotic platform caused sudden inertial trunk lateral perturbations to the right or left, with or without timing and direction knowledge. An EMG-driven model of the lumbar spine was used to calculate the muscle forces and contributions to joint rotational stiffness during the perturbations. Data showed 95% and 106% increases in total joint rotational stiffness_, about the lateral bend and axial twist axes, when subjects had knowledge of the timing of the perturbation. Also, the contralateral muscles exhibited a significantly larger total joint rotational stiffness about the lateral bend axis, and earlier surface EMG responses, than the ipsilateral muscles. The results indicate that, when the timing of the perturbation was unknown, subjects relied more on delayed muscle forces following the perturbation to stiffen the L_4–5 joint.     

Contributions of individual muscles to hip joint contact force in normal walking

The human hip joint withstands high contact forces during daily activity and is therefore susceptible to injury and structural deterioration over time. Knowledge of muscle-force contributions to hip joint loading may assist in the development of strategies to prevent and manage conditions such as osteoarthritis, femoro-acetabular impingement and fracture. The main aim of this study was to determine the contributions of individual muscles to hip contact force in normal walking. Muscle contributions to hip contact force were calculated based on a previously published dynamic optimization solution for normal walking, which provided the time histories of joint motion, ground reaction forces, and muscle forces during the stance and swing phases of gait. The force developed by each muscle plus its contribution to the ground reaction force were used to determine the muscle’s contribution to hip contact force. Muscles were the major contributors to hip contact force, with gravitational and centrifugal forces combined contributing less than 5% of the total contact force. Four muscles that span the hip – gluteus medius, gluteus maximus, iliopsoas, and hamstrings – contributed most significantly to the three components of the hip contact force and hip contact impulse (integral of hip contact force over time). Three muscles that do not span the hip – vasti, soleus, and gastrocnemius – also contributed substantially to hip joint loading. These results provide additional insight into lower-limb muscle function during walking and may also be relevant to studies of cartilage degeneration and bone remodelling at the hip.     

Neuromechanical control of the forearm muscles during gripping with sudden flexion and extension wrist perturbations

The purpose of this study was to investigate how gripping modulates forearm muscle co-contraction prior to and during sudden wrist perturbations. Ten males performed a sub-maximal gripping task (no grip, 5% and 10% of maximum) while a perturbation forced wrist flexion or extension. Wrist joint angles and activity from 11 muscles were used to determine forearm co-contraction and muscle contributions to wrist joint stiffness. Co-contraction increased in all pairs as grip force increased (from no grip to 10% grip), corresponding to a 36% increase in overall wrist joint stiffness. Inclusion of individual muscle contributions to wrist joint stiffness enhanced the understanding of forearm co-contraction. The extensor carpi radialis longus (ECRL) and brevis had the largest stiffness contributions (34.5 ± 1.3% and 20.5 ± 2.3%, respectively), yet muscle pairs including ECRL produced the lowest co-contraction. The muscles contributing most to wrist stiffness were consistent across conditions (ECRL for extensors; Flexor Digitorum Superficialis for flexors), suggesting enhanced contributions rather than muscular redistribution. This work provides investigation of the neuromuscular response to wrist perturbations and gripping demands by considering both co-contraction and muscle contributions to joint stiffness. Individual muscle stiffness contributions can be used to enhance the understanding of forearm muscle control during complex tasks.     

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 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.     

Orderly recruitment among motoneurons supplying different muscles.

Virtually all movements involve the recruitment of motor units from multiple muscles. Given the functional diversity of motor units (motoneurons and the muscle fibers they supply), the effective production of specific movements undoubtedly depends upon some principle(s) to organize the ensemble of active motor units. The principle acting to organize the recruitment of motor units within muscles is the size principle, whereby the first motor units to be recruited have the smallest values for axonal conduction velocity and contractile force, and are the slowest to contract and fatigue. Here we consider the possibility that the size principle applies in the recruitment of motor units across muscles, i.e., that regardless of their muscles of origin, active motor units are recruited in rank order, for example, from low to high conduction velocity. The benefits of orderly recruitment across muscles could be similar to the acknowledged advantages of orderly recruitment within muscles. One benefit is that the neural process involved in organizing active motor units would be simplified. In a muscle-based scheme, the size principle would organize only those motor units within individual muscles, leaving the nervous system with the additional task of coordinating the relative activities of motor units from different muscles. By contrast, in an ensemble-based scheme, orderly recruitment of all motor units according to the size principle would automatically coordinate motor units both within and across motor nuclei. Another potential benefit is the provision for movements with smooth trajectory, the result of interleaving the divergent torque contributions made by motor units from muscles that differ in their orientations about joints. Otherwise, if order were restricted within muscles, the torque trajectory of a joint would change unevenly as participating muscles begin contracting at different times and grade activity at different rates. These considerations support speculation that motor units recruited from co-contracting muscles are collectively recruited according to the size principle.     

Quantitative functional anatomy of the lower limb with application to human gait

A scheme was developed to classify muscles according to their primary, secondary and tertiary functions, e.g. a muscle which produces primarily a flexion moment may also produce secondary abduction and tertiary internal rotation moments. The functions of muscles crossing the hip and knee joints were computed based upon the changing relative positions of joint centers and muscle origins and insertions during one gait cycle. The function of several of the major muscles crossing the hip and knee joints is reported for the different limb positions corresponding to normal gait. It was found that the amount of force necessary to produce a given moment about a joint was dependent upon the limb position. In addition, the muscle functions changed significantly with limb position. Electrical stimulation of muscles of a paralyzed subject gave qualitative support to the results.     

Muscle contributions to mediolateral and anteroposterior foot placement during walking

Foot placement is critical to balance control during walking and is primarily controlled by muscle force generation. Although gluteus medius activity has been associated with mediolateral foot placement, how other muscles contribute to foot placement is not clear. Furthermore, although dynamic walking models have suggested that anteroposterior foot placement can be passively controlled, the extent to which muscles actively contribute to anteroposterior foot placement has not been determined. The objective of this study was to identify individual muscle contributions to mediolateral and anteroposterior foot placement during walking in healthy adults. Dynamic simulations of walking were developed for six older adults and a segmental power analysis was performed to determine the individual muscle contributions to the mediolateral and anteroposterior power delivered to the foot segment. The simulations revealed the ipsilateral swing limb gluteus medius, iliopsoas, rectus femoris and hamstrings and the contralateral stance limb gluteus medius and ankle plantarflexors were primary contributors to both mediolateral and anteroposterior foot placement. Muscle contributions to foot placement were found to be highly influenced by their contributions to pelvis power, which was dominated by those muscles crossing the hip joint. Thus, impaired balance control may be improved by focusing rehabilitation interventions on optimizing the coordination of those muscles crossing the hip joint and the ankle plantarflexors.     

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.     

A method for determining lower extremity muscle-tendon lengths during flexion/extension movements

A study was conducted to examine the relationship between muscle-tendon lengths of 16 lower extremity muscles and the flexion angle(s) of the joint(s) they cross. Anthropometric data from six subjects were obtained. Various lower extremity joint flexion angle combinations were simulated for each subject using computer software. For each simulated lower extremity position, muscle origin and insertion locations were determined based on averaged cadaveric origin/insertion information and individual anthropometric parameters. Corresponding muscle-tendon lengths were computed and normalized to segment lengths. Regression equations were derived which allow normalized muscle-tendon lengths to be estimated from known joint flexion angles. The regression equations obtained for biarticular muscles fit the data quite well giving correlation coefficients greater than 0.92. The correlation coefficients for the equations describing normalized single joint muscle-tendon lengths range from 0.77 to 0.97. The equations were then validated by comparing predicted lengths to those reported by previous investigations. Confirming the utility of the equations, the comparisons were excellent for both uniarticular and biarticular muscles. Used in conjunction with velocity data (obtained by differentiating the length data) and electromyogram recordings, these equations enable a detailed analysis of muscle function.