A method to combine numerical optimization and EMG data for the estimation of joint moments under dynamic conditions

To solve the problem of muscle redundancy at the level of opposing muscle groups, an alternative method to inverse dynamics must be employed. Considering the advantages of existing alternatives, the present study was aimed to compute knee joint moments under dynamic conditions using electromyographic (EMG) signals combined with non-linear constrained optimization in a single routine. The associated mathematical problems accounted for muscle behavior in an attempt to obtain accurate predictions of the resultant moment as well as physiologically realistic estimates of agonist and antagonist moments. The experiment protocol comprised (1) isometric trials to determine the most effective EMG processing for the prediction of the resultant moment and (2) stepping-in-place trials for the calculation of joint moments from processed EMG under dynamic conditions. Quantitative comparisons of the model predictions with the output of a biological-based model, showed that the proposed method (1) produced the most accurate estimates of the resultant moment and (2) avoided possible inconsistencies by enforcing appropriate constraints. As a possible solution for solving the redundancy problem under dynamic conditions, the proposed optimization formulation also led to realistic predictions of agonist and antagonist moments.     

Mechanical correction of dynamometer moment for the effects of segment motion during isometric knee-extension tests

The purpose of this study was to determine the effect of dynamometer and joint axis misalignment on measured isometric knee-extension moments using inverse dynamics based on the actual joint kinematic information derived from the real-time X-ray video and to compare the errors when the moments were calculated using measurements from external anatomical surface markers or obtained from the isokinetic dynamometer. Six healthy males participated in this study. They performed isometric contractions at 90° and 20° of knee flexion, gradually increasing to maximum effort. For the calculation of the actual knee-joint moment and the joint moment relative to the knee-joint center, determined using the external marker, two free body diagrams were used of the Cybex arm and the lower leg segment system. In the first free body diagram, the mean center of the circular profiles of the femoral epicondyles was used as the knee-joint center, whereas in the second diagram, the joint center was assumed to coincide with the external marker. Then, the calculated knee-joint moments were compared with those measured by the dynamometer. The results indicate that 1) the actual knee-joint moment was different from the dynamometer recorded moment (difference ranged between 1.9% and 4.3%) and the moment calculated using the skin marker (difference ranged between 2.5% and 3%), and 2) during isometric knee extension, the internal knee angle changed significantly from rest to the maximum contraction state by about 19°. Therefore, these differences cannot be neglected if the moment-knee-joint angle relationship or the muscle mechanical properties, such as length-tension relationship, need to be determined.     

Predictions of knee and ankle moments of force in walking from EMG and kinematic data

A deterministic model was developed and validated to calculate instantaneous ankle and knee moments during walking using processed EMG from representative muscles, instantaneous joint angle as a correlate of muscle length and angular velocity as a correlate of muscle velocity, and having available total instantaneous joint moments for derivation of certain model parameters. A linear regression of the moment on specifically processed EMG, recorded while each subject performed cycled isometric calibration contractions, yielded the constants for a basic moment-EMG relationship. Using the resultant moment for optimization, the predicted moment was proportionally augmented for longer muscle lengths and reduced for shorter lengths. Similarly, the predicted moment was reduced for shortening velocities and increased if the muscle was lengthening. The plots of moments predicted using the full model and those calculated from link segment mechanics followed each other quite closely. The range of root mean square errors were: 3.2-9.5 Nm for the ankle and 4.7-13.0 Nm for the knee.     

The effects of antagonist moment on the resultant knee joint moment during isokinetic testing of the knee extensors

The purpose of this study was to examine the effects of moment of antagonistic muscle on the resultant joint moment during isokinetic eccentric and concentric efforts of the knee extensors. Ten males performed maximum eccentric and concentric knee extension and flexion efforts on a Biodex dynamometer at 0.52 rad · s⁻¹ (30° · s⁻¹). Electromyographic (EMG) activity of vastus medialis and biceps femoris (hamstrings) was also recorded. The antagonistic moment of the hamstrings was determined by recording the integrated EMG (iEMG)/moment relationship at different levels of muscle effort. The iEMG/moment curves were fitted using second-degree polynomials. The polynomials were then used to predict the antagonistic moment exerted by the hamstrings from the antagonist iEMG. The antagonistic moment had a maximum of 42.92 Nm and 28.97 Nm under concentric and eccentric conditions respectively; paired t-tests indicated that this was a significant difference (P < 0.05). These results indicate that the resultant joint moment of knee extensors is the result of both agonist and antagonist muscle activation. The greater antagonist muscle activity under concentric activation conditions may be partly responsible for the lower resultant joint concentric moment of knee extensors compared with the corresponding eccentric activation. The antagonist moment significantly affects comparisons between the isokinetic moments and agonist EMG and in vitro force measurements under different testing (muscle action and angular velocity) conditions. Accepted: 25 February 1997     

Predicting muscle forces in gait from EMG signals and musculotendon kinematics

An EMG-driven muscle model for determining muscle force-time histories during gait is presented. The model, based on Hill's equation (1938), incorporates morphological data and accounts for changes in musculotendon length, velocity, and the level of muscle excitation for both concentric and eccentric contractions. Musculotendon kinematics were calculated using three-dimensional cinematography with a model of the musculoskeletal system. Muscle force-length-EMG relations were established from slow isokinetic calibrations. Walking muscle force-time histories were determined for two subjects. Joint moments calculated from the predicted muscle forces were compared with moments calculated using a linked segment, inverse dynamics approach. Moment curve correlations ranged from r = 0.72 to R = 0.97 and the root mean square (RMS) differences were from 10 to 20 Nm. Expressed as a relative RMS, the moment differences ranged from a low of 23% at the ankle to a high of 72% at the hip. No single reason for the differences between the two moment curves could be identified. Possible explanations discussed include the linear EMG-to-force assumption and how well the EMG-to-force calibration represented excitation for the whole muscle during gait, assumptions incorporated in the muscle modeling procedure, and errors inherent in validating joint moments predicted from the model to moments calculated using linked segment, inverse dynamics. The closeness with which the joint moment curves matched in the present study supports using the modeling approach proposed to determine muscle forces in gait.     

Calibration of EMG to force for knee muscles is applicable with submaximal voluntary contractions.

PURPOSE: In this study, the influence of using submaximal isokinetic contractions about the knee compared to maximal voluntary contractions as input to obtain the calibration of an EMG-force model for knee muscles is investigated. METHODS: Isokinetic knee flexion and extension contractions were performed by healthy subjects at five different velocities and at three contraction levels (100%, 75% and 50% of MVC). Joint angle, angular velocity, joint moment and surface EMG of five knee muscles were recorded. Individual calibration values were calculated according to [C.A.M. Doorenbosch, J. Harlaar, A clinically applicable EMG-force model to quantify active stabilization of the knee after a lesion of the anterior cruciate ligament, Clinical Biomechanics 18 (2003) 142-149] for each contraction level. RESULTS: First, the output of the model, calibrated with the 100% MVC was compared to the actually exerted net knee moment at the dynamometer. Normalized root mean square errors were calculated [A.L. Hof, C.A.N. Pronk, J.A. van Best, Comparison between EMG to force processing and kinetic analysis for the calf muscle moment in walking and stepping, Journal of Biomechanics 20 (1987) 167-187] to compare the estimated moments with the actually exerted moments. Mean RMSD errors ranged from 0.06 to 0.21 for extension and from 0.12 to 0.29 for flexion at the 100% trials. Subsequently, the calibration results of the 50% and 75% MVC calibration procedures were used. A standard signal, representing a random EMG level was used as input in the EMG force model, to compare the three models. Paired samples t-tests between the 100% MVC and the 75% MVC and 50% MVC, respectively, showed no significant differences (p>0.05). CONCLUSION: The application of submaximal contractions of larger than 50% MVC is suitable to calibrate a simple EMG to force model for knee extension and flexion. This means that in clinical practice, the EMG to force model can be applied by patients who cannot exert maximal force.     

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

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

Knee moment outcomes using inverse dynamics and the cross product function in moderate knee osteoarthritis gait: A comparison study

Inverse dynamics are the cornerstone of biomechanical assessments to calculate knee moments during walking. In knee osteoarthritis, these outcomes have been used to understand knee pathomechanics, but the complexity of an inverse dynamic model may limit the uptake of joint moments in some clinical and research structures. The objective was to determine whether discrete features of the sagittal and frontal plane knee moments calculated using inverse dynamics compare to knee moments calculated using a cross product function. Knee moments from 74 people with moderate knee osteoarthritis were assessed after ambulating at a self-selected speed on an instrumented dual belt treadmill. Standardized procedures were used for surface marker placement, gait speed determination and data processing. Net external frontal and sagittal plane knee moments were calculated using inverse dynamics and the three-dimensional position of the knee joint center with respect to the center of pressure was crossed with the three-dimensional ground reaction forces in the cross product function. Correlations were high between outcomes of the moment calculations (r > 0.9) and for peak knee adduction moment, knee adduction moment impulse and difference between peak flexion and extension moments, the cross product function resulted in absolute values less than 10% of those calculated using inverse dynamics in this treadmill walking environment. This computational solution may allow the integration of knee moment calculations to understand knee osteoarthritis gait without data collection or computational complexity.     

Walking on high heels changes muscle activity and the dynamics of human walking significantly

The aim of the study was to investigate the distribution of net joint moments in the lower extremities during walking on high-heeled shoes compared with barefooted walking at identical speed. Fourteen female subjects walked at 4 km/h across three force platforms while they were filmed by five digital video cameras operating at 50 frames/second. Both barefooted walking and walking on high-heeled shoes (heel height: 9 cm) were recorded. Net joint moments were calculated by 3D inverse dynamics. EMG was recorded from eight leg muscles. The knee extensor moment peak in the first half of the stance phase was doubled when walking on high heels. The knee joint angle showed that high-heeled walking caused the subjects to flex the knee joint significantly more in the first half of the stance phase. In the frontal plane a significant increase was observed in the knee joint abductor moment and the hip joint abductor moment. Several EMG parameters increased significantly when walking on high-heels. The results indicate a large increase in bone-on-bone forces in the knee joint directly caused by the increased knee joint extensor moment during high-heeled walking, which may explain the observed higher incidence of osteoarthritis in the knee joint in women as compared with men.     

The effects of fatigue on the resultant joint moment, agonist and antagonist electromyographic activity at different angles during dynamic knee extension efforts.

Examination of the effects of fatigue on antagonist function can provide information on the role of antagonists in limiting the resultant joint moment and stabilizing the knee. Therefore, the purpose of this study was to examine the moment, agonist and antagonist electromyographic (EMG) activity levels at different angular positions during an isokinetic muscular endurance knee extension test. Fifteen healthy males (age 22.6+/-1.9 yr) performed 34 maximal isokinetic concentric efforts of the knee extensors at 120 degrees s(-1). The EMG activity of vastus medialis and biceps femoris was recorded using surface electrodes. The motion ranged from 90 degrees to 0 degrees of knee flexion. The average moment and average EMG (AEMG) at 10-35 degrees, 36-55 degrees and 56-80 degrees angular position intervals were calculated for each repetition. Twenty eight efforts were further analysed. The moment of force demonstrated a decline of 70% at the end of the test. Two-way repeated measures analysis of variance tests indicated that this decline was significant (p < 0.05). No significant effects of angular position on fatigue moment characteristics were found. The agonist (vastus medialis) AEMG during the first repetition demonstrated a significant increase of 40-60% towards the middle part of the test (p < 0.05). In the second part of the test, the VM AEMG at longer muscle lengths was significantly higher compared to the initial efforts whereas the AEMG at short muscle lengths returned to initial values. The antagonist AEMG at all angular positions did not change significantly during the test. The decline in the resultant joint moment could be attributed to the effects of fatigue on the agonist muscle function. The agonist AEMG fatigue-patterns are dependent on the length of the muscle and may be due to alterations in the motor unit recruitment and/or activation failure in the quadriceps muscle. The biceps femoris maintains constant submaximal (21-33% of the maximum) AEMG activity which may play an important role in the stability of the knee joint. The contribution of antagonist activity to the resultant joint moment increases during the last part of an isokinetic concentric muscle endurance test.     

Knee muscle forces during walking and running in patellofemoral pain patients and pain-free controls

One proposed mechanism of patellofemoral pain, increased stress in the joint, is dependent on forces generated by the quadriceps muscles. Describing causal relationships between muscle forces, tissue stresses, and pain is difficult due to the inability to directly measure these variables in vivo. The purpose of this study was to estimate quadriceps forces during walking and running in a group of male and female patients with patellofemoral pain (n=27, 16 female; 11 male) and compare these to pain-free controls (n=16, 8 female; 8 male). Subjects walked and ran at self-selected speeds in a gait laboratory. Lower limb kinematics and electromyography (EMG) data were input to an EMG-driven musculoskeletal model of the knee, which was scaled and calibrated to each individual to estimate forces in 10 muscles surrounding the joint. Compared to controls, the patellofemoral pain group had greater co-contraction of quadriceps and hamstrings (p=0.025) and greater normalized muscle forces during walking, even though the net knee moment was similar between groups. Muscle forces during running were similar between groups, but the net knee extension moment was less in the patellofemoral pain group compared to controls. Females displayed 30–50% greater normalized hamstring and gastrocnemius muscle forces during both walking and running compared to males (p<0.05). These results suggest that some patellofemoral pain patients might experience greater joint contact forces and joint stresses than pain-free subjects. The muscle force data are available as supplementary material.     

A comparison of the triceps surae and residual muscle moments at the ankle during cycling

The rigid linked system model and principles of inverse dynamics have been widely used to calculate residual muscle moments during various activities. EMG driven models and optimization algorithms have also been presented in the literature in efforts to estimate skeletal muscle forces and evaluate their possible contribution to the residual muscle moment. Additionally, skeletal muscle-tendon forces have been measured, directly, in both animals and humans. The purpose of this investigation was to calculate the moment produced by the triceps surae muscles and compare it to the residual muscle moment at the ankle during cycling at three power outputs (90, 180 and 270 W). Inferences were made regarding the potential contribution made by each triceps surae component to the tendon force using EMG and muscle-tendon length changes. A buckle-type transducer was surgically implanted on the right Achilles tendon of one male subject. Achilles tendon forces measured in vivo were multiplied by their corresponding moment arms to yield the triceps surae moment during the three working conditions. Moment arm lengths were obtained in a separate experiment using magnetic resonance imaging (MRI). Pedal reaction forces, body segment accelerations (determined from high speed film), and appropriate mass parameters served as input to the inverse solution. The triceps surae moment was temporally in phase with and consistently represented approximately 65% of the residual muscle moment at the ankle. These data demonstrate the feasibility of using implanted transducers in human subjects and provide a greater understanding of musculoskeletal mechanics during normal human movements.     

Prediction of antagonistic muscle forces using inverse dynamic optimization during flexion/extension of the knee.

This paper examined the feasibility of using different optimization criteria in inverse dynamic optimization to predict antagonistic muscle forces and joint reaction forces during isokinetic flexion/extension and isometric extension exercises of the knee. Both quadriceps and hamstrings muscle groups were included in this study. The knee joint motion included flexion/extension, varus/valgus, and internal/external rotations. Four linear, nonlinear, and physiological optimization criteria were utilized in the optimization procedure. All optimization criteria adopted in this paper were shown to be able to predict antagonistic muscle contraction during flexion and extension of the knee. The predicted muscle forces were compared in temporal patterns with EMG activities (averaged data measured from five subjects). Joint reaction forces were predicted to be similar using all optimization criteria. In comparison with previous studies, these results suggested that the kinematic information involved in the inverse dynamic optimization plays an important role in prediction of the recruitment of antagonistic muscles rather than the selection of a particular optimization criterion. Therefore, it might be concluded that a properly formulated inverse dynamic optimization procedure should describe the knee joint rotation in three orthogonal planes.     

Dynamic joint and muscle forces during knee isokinetic exercise

Isokinetic exercise has been commonly used in knee rehabilitation, conditioning and research in the past two decades. Although many investigators have used various experimental and theoretical approaches to study the muscle and joint force involved in isokinetic knee extension and flexion exercises, only a few of these studies have actually distinguished between the tibiofemoral joint forces and muscle forces. Therefore, the objective of this study was to specify, via an eletromyography(EMG)-driven muscle force model of the knee, the magnitude of the tibiofemoral joint and muscle forces acting during isokinetic knee extension and flexion exercises. Fifteen subjects ranging from 21 to 36 years of age volunteered to participate in this study. A Kin Com exercise machine (Chattecx Corporation, Chattanooga, TN, U.S.A.) was used as the loading device. An EMG-driven muscle force model was used to predict muscle forces, and a biomechanical model was used to analyze two knee joint constraint forces; compression and shear force. The methods used in this study were shown to be valid and reliable (r > 0.84 andp < 0.05). The effects on the tibiofemoral joint force during knee isokinetic exercises were compared with several functional activities that were investigated by earlier researchers. The muscle forces generated during knee isokinetic exercise were also obtained. Based on the findings obtained in this study, several therapeutic justifications for knee rehabilitation are proposed.     

Lower extremity control and dynamics during backward angular impulse generation in forward translating tasks

Observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control. When comparing two forward translating tasks performed with and without backward angular impulse, we have learned that both trunk-leg coordination and reaction force-time characteristics are significantly different between tasks. This led us to hypothesize that differences in trunk-leg coordination and reaction force generation would induce between-task differences in the control of the lower extremity joints during impulse generation phase of the tasks. Eight highly skilled performers executed a series of forward jumps with and without backward rotation (reverse somersault and reverse timer, respectively). Sagittal plane kinematics, reaction forces, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. Lower extremity joint kinetics were calculated using inverse dynamics. The results demonstrated between-task differences in the relative angles between the lower extremity segments and the net joint forces/reaction force and the joint angular velocity profiles. Significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer. Between-task differences in lower extremity joint kinetics were regulated by selectively activating the bi-articular muscles crossing the knee and hip. These results indicate that between-task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem.     

The relation between the resultant moments at a joint and the moments measured by an isokinetic dynamometer

Isokinetic dynamometers have frequently been used to determine in vivo properties of human skeletal muscles. In these investigations the moments recorded by the dynamometer were often (implicitly) assumed to be the same as the joint moments produced by muscles. This assumption may have contributed to the conflicting results about in vivo muscle properties of human skeletal muscles that are reported in the literature. The purpose of this paper is to present a method for calculating the resultant joint moments from the moments recorded using a Cybex II dynamometer and to determine the differences between these two moments for some typical exercise conditions. The differences between these these moments are shown to be due to (a) gravitational effects, (b) inertial effects, and (c) non-rigidity of the Cybex arm/shank-foot system. The results obtained suggest that the moments recorded using the dynamometer should not be used to derive muscle properties without taking into account the relationship between the resultant joint moments and the moments measured using an isokinetic dynamometer.     

Effect of contraction form and contraction velocity on the differences between resultant and measured ankle joint moments

During a maximal isometric plantar flexion effort the moment measured at the dynamometer differs from the resultant ankle joint moment. The present study investigated the effects of contraction form and contraction velocity during isokinetic plantar/dorsal flexion efforts on the differences between resultant and measured moments due to the misalignment between ankle and dynamometer axes. Eleven male subjects (age: 31+/-6 years, mass: 80.6+/-9.6 kg, height: 178.4+/-7.4 cm) participated in this study. All subjects performed isometric-shortening-stretch-isometric contractions induced by electrical stimulation at three different angular velocities (25 degrees /s, 50 degrees /s and 100 degrees /s) on a customised dynamometer. The kinematics of the leg were recorded using the vicon 624 system with eight cameras operating at 250 Hz. The resultant moments at the ankle joint were calculated through inverse dynamics. The relative differences between resultant and measured ankle joint moments due to axis misalignment were fairly similar in all phases of the isometric-shortening-stretch-isometric contraction (in average 5-9% of the measured moment). Furthermore these findings were independent of the contraction velocity. During dynamic plantar/dorsal flexion contractions the differences between measured and resultant joint moment are high enough to influence conclusions regarding the mechanical response of ankle extensor muscles. However the relative differences were not increased during dynamic contractions as compared to isometric contractions.     

Effects of agonist and antagonist muscle fatigue on muscle coactivation around the knee in pubertal boys.

In many activities the knee joint flexes and extends actively with the involvement of both knee extensor and flexor muscle groups. Consequently the examination of the muscle activity during reciprocal movements may provide useful information on the function of these two muscle groups during fatigued conditions. Therefore, the purpose of this study was to examine the activity of antagonist muscles during a reciprocal isokinetic fatigue test of the knee extensors and flexors. Fifteen healthy pubertal males (age 13.8+/-0.8 years) performed 22 maximal isokinetic concentric efforts of the knee extensors at 60 degrees s(-1). The EMG activity of vastus medialis (VM), vastus lateralis (VL) and biceps femoris (BF) was recorded using surface electrodes. The motion ranged from 100 to 0 degrees of knee flexion. The average moment and average EMG (AEMG) at 10-30 degrees, 31-50 degrees, 51-70 degrees and 71-90 degrees angular position intervals were calculated for each repetition. Twenty efforts were further analyzed. Two-way repeated measures analysis of variance (ANOVA) tests indicated a significant decline of moment during the test (p<0.025). The VM and VL AEMG at longer muscle lengths increased significantly as the test progressed whereas the AEMG at short muscle lengths (10-30 degrees ) did not significantly change. The agonist AEMG of BF during the first repetition demonstrated a significant increase after the ninth repetition (p<0.025). The antagonist AEMG of all muscles did not change significantly during the test. These results indicate that there is consistent antagonist activity during both extension and flexion phases of an isokinetic reciprocal fatigue test. It can be concluded that during an isokinetic reciprocal fatigue test, both knee extensors and flexors are fatigued. However, this condition does not have a significant effect on the EMG patterns of these muscles when acting as antagonists during the test.     

Hybrid neuromusculoskeletal modeling to best track joint moments using a balance between muscle excitations derived from electromyograms and optimization

Current electromyography (EMG)-driven musculoskeletal models are used to estimate joint moments measured from an individual?s extremities during dynamic movement with varying levels of accuracy. The main benefit is the underlying musculoskeletal dynamics is simulated as a function of realistic, subject-specific, neural-excitation patterns provided by the EMG data. The main disadvantage is surface EMG cannot provide information on deeply located muscles. Furthermore, EMG data may be affected by cross-talk, recording and post-processing artifacts that could adversely influence the EMG?s information content. This limits the EMG-driven model?s ability to calculate the multi-muscle dynamics and the resulting joint moments about multiple degrees of freedom. We present a hybrid neuromusculoskeletal model that combines calibration, subject-specificity, EMG-driven and static optimization methods together. In this, the joint moment tracking errors are minimized by balancing the information content extracted from the experimental EMG data and from that generated by a static optimization method. Using movement data from five healthy male subjects during walking and running we explored the hybrid model?s best configuration to minimally adjust recorded EMGs and predict missing EMGs while attaining the best tracking of joint moments. Minimally adjusted and predicted excitations substantially improved the experimental joint moment tracking accuracy than current EMG-driven models. The ability of the hybrid model to predict missing muscle EMGs was also examined. The proposed hybrid model enables muscle-driven simulations of human movement while enforcing physiological constraints on muscle excitation patterns. This might have important implications for studying pathological movement for which EMG recordings are limited.