Accuracy of gastrocnemius muscles forces in walking and running goats predicted by one-element and two-element Hill-type models

Hill-type models are commonly used to estimate muscle forces during human and animal movement—yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation–deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with “differential” activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r², was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r²=0.26–0.51), and all exhibited some errors (RMSE=9.63–32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.     

A Wavelet-Based Method to Predict Muscle Forces From Surface Electromyography Signals in Weightlifting

The purpose of this study was to develop a wavelet-based method to predict muscle forces from surface electromyography (EMG) signals in vivo.The weightlifting motor task was implemented as the case study.EMG signals of biceps brachii,triceps brachii and deltoid muscles were recorded when the subject carried out a standard weightlifting motor task.The wavelet-based algorithm was used to process raw EMG signals and extract features which could be input to the Hill-type muscle force models to predict muscle forces.At the same time,the musculoskeletal model of subject's weightlifting motor task was built and simulated using the Computed Muscle Control (CMC) method via a motion capture experiment.The results of CMC were compared with the muscle force predictions by the proposed method.The correlation coefficient between two results was 0.99(p＜0.01).However,the proposed method was easier and more efficiency than the CMC method.It has potential to be used clinically to predict muscle forces in vivo.     

Voluntary activation of the triceps surae in prepubertal children

The activation capacities and neuromuscular efficiency (NME) of the triceps surae (TS) of prepubescent children (7–11 years) and adults were evaluated during submaximal and maximal (MVC) isometric plantarflexion to determine whether they varied with age. TS-EMG were obtained by summing-up the rectified electromyograms of the soleus and gastrocnemii muscles; these data were quantified using a sliding average method and normalized with reference to the TS maximal compound action potential (TS-M-wave).

The maximal EMG increased significantly with age in the children, but less than MVC, what led to a significant increase in NME_Max (MVC/TS-EMG_max ratio). The EMG–torque relationship indicated an age-related overactivation of TS at low torque, what led to a lower NME_Sub-max (inverse of the slope of the EMG–torque relationship) for the youngest children. The overactivation of TS was accompanied by contraction of the TA, which decreased with age. The youngest children were also less able to maintain a target torque and muscle activation. Finally, the twitch interpolated method revealed an age-dependant activation deficit. We conclude that central mechanisms are the main cause of the lower torques developed by children and they appear to vary with age in prepubertal children.     

Feasibility of using EMG driven neuromusculoskeletal model for prediction of dynamic movement of the elbow.

Neuromusculoskeletal (NMS) modeling is a valuable tool in orthopaedic biomechanics and motor control research. To evaluate the feasibility of using electromyographic (EMG) signals with NMS modeling to estimate individual muscle force during dynamic movement, an EMG driven NMS model of the elbow was developed. The model incorporates dynamical equation of motion of the forearm, musculoskeletal geometry and musculotendon modeling of four prime elbow flexors and three prime elbow extensors. It was first calibrated to two normal subjects by determining the subject-specific musculotendon parameters using computational optimization to minimize the root mean square difference between the predicted and measured maximum isometric flexion and extension torque at nine elbow positions (0-120 degrees of flexion with an increment of 15 degrees ). Once calibrated, the model was used to predict the elbow joint trajectories for three flexion/extension tasks by processing the EMG signals picked up by both surface and fine electrodes using two different EMG-to-activation processing schemes reported in the literature without involving any trajectory fitting procedures. It appeared that both schemes interpreted the EMG somewhat consistently but their prediction accuracy varied among testing protocols. In general, the model succeeded in predicting the elbow flexion trajectory in the moderate loading condition but over-drove the flexion trajectory under unloaded condition. The predicted trajectories of the elbow extension were noted to be continuous but the general shape did not fit very well with the measured one. Estimation of muscle activation based on EMG was believed to be the major source of uncertainty within the EMG driven model. It was especially so apparently when fine wire EMG signal is involved primarily. In spite of such limitation, we demonstrated the potential of using EMG driven neuromusculoskeletal modeling for non-invasive prediction of individual muscle forces during dynamic movement under certain conditions.     

Total trunk muscle force and spinal compression are lower in asymmetric moments as compared to pure extension moments.

The aim of the present study was to test the assumption that asymmetric trunk loading requires a higher total muscle force and consequently entails a higher compression forces on the spine as compared to symmetric loading. When the trunk musculature is modelled in sufficient detail, optimisation shows that there is no mechanical necessity for an increase in total muscle force (or compression force) with task asymmetry. A physiologically based optimisation does also not predict an increase in total muscle force or spinal loading with asymmetry. EMG data on 14 trunk muscles collected in eight subjects showed antagonistic coactivity to be present in both conditions. However, estimates of total muscle force based on the EMG were lower when producing an asymmetric moment. In conclusion, producing an asymmetric moment appears to cause slightly lower forces on the lumbosacral joint as compared to a symmetric moment. Only lateral shear forces increase with asymmetry but these remain well below failure levels.     

Artificial neural network model for the generation of muscle activation patterns for human locomotion.

Skilled locomotor behaviour requires information from various levels within the central nervous system (CNS). Mathematical models have permitted researchers to simulate various mechanisms in order to understand the organization of the locomotor control system. While it is difficult to adequately characterize the numerous inputs to the locomotor control system, an alternative strategy may be to use a kinematic movement plan to represent the complex inputs to the locomotor control system based on the possibility that the CNS may plan movements at a kinematic level. We propose the use of artificial neural network (ANN) models to represent the transformation of a kinematic plan into the necessary motor patterns. Essentially, kinematic representation of the actual limb movement was used as the input to an ANN model which generated the EMG activity of 8 muscles of the lower limb and trunk. Data from a wide variety of gait conditions was necessary to develop a robust model that could accommodate various environmental conditions encountered during everyday activity. A total of 120 walking strides representing normal walking and ten conditions where the normal gait was modified in terms of cadence, stride length, stance width or required foot clearance. The final network was assessed on its ability to predict the EMG activity on individual walking trials as well as its ability to represent the general activation pattern of a particular gait condition. The predicted EMG patterns closely matched those recorded experimentally, exhibiting the appropriate magnitude and temporal phasing required for each modification. Only 2 of the 96 muscle/gait conditions had RMS errors above 0.10, only 5 muscle/gait conditions exhibited correlations below 0.80 (most were above 0.90) and only 25 muscle/gait conditions deviated outside the normal range of muscle activity for more than 25% of the gait cycle. These results indicate the ability of single network ANNs to represent the transformation between a kinematic movement plan and the necessary muscle activations for normal steady state locomotion but they were also able to generate muscle activation patterns for conditions requiring changes in walking speed, foot placement and foot clearance. The abilities of this type of network have implications towards both the fundamental understanding of the control of locomotion and practical realizations of artificial control systems for use in rehabilitation medicine.     

Interpreting muscle function from EMG: lessons learned from direct measurements of muscle force

Electromyography is often used to infer the pattern of productionof force by skeletal muscles. The interpretation of muscle functionfrom the electromyogram (EMG) is challenged by the fact thatfactors such as type of muscle fiber, muscle length, and musclevelocity can all influence the relationship between electricaland mechanical activity of a muscle. Simultaneous measurementsof EMG, muscle force, and fascicle length in hindlimb musclesof wild turkeys allow us to probe the quantitative link betweenforce and EMG. We examined two features of the force–EMGrelationship. First, we measured the relaxation electromechanicaldelay (r-EMD) as the time from the end of the EMG signal totime of the end of force. This delay varied with locomotor speedin the lateral gastrocnemius (LG); it was longer at slow walkingspeeds than for running. This variation in r-EMD was not explainedby differences in muscle length trajectory, as the magnitudeof r-EMD was not correlated with the velocity of shorteningof the muscle during relaxation. We speculate that the longerrelaxation times at slow walking speeds compared with runningmay reflect the longer time course of relaxation in slower musclesfibers. We also examined the relationship between magnitudeof force and EMG across a range of walking and running speeds.We analyzed the force–EMG relationship during the swingphase separately from the force–EMG relationship duringstance phase. During stance, force amplitude (average force)was linearly related to mean EMG amplitude (average EMG). Forcesduring swing phase were lower than predicted from the stancephase force–EMG relationship. The different force–EMGrelationships during the stance and swing phases may reflectthe contribution of passive structures to the development offorce, or a nonlinear force–EMG relationship at low levelsof muscle activity. Together the results suggest that any inferenceof force from EMG must be done cautiously when a broad rangeof activities is considered.     

Velocity-dependent cost function for the prediction of force sharing among synergistic muscles in a one degree of freedom model

Prediction of accurate and meaningful force sharing among synergistic muscles is a major problem in biomechanics research. Given a resultant joint moment, a unique set of muscle forces can be obtained from this mathematically redundant system using nonlinear optimization. The classical cost functions for optimization involve a normalization of the muscle forces to the absolute force capacity of the target muscles, usually by the cross-sectional area or the maximal isometric force. In a one degree of freedom model this leads to a functional relationship between moment arms and the predicted muscle forces, such that for constant moment arms, or constant ratios of moment arms, agonistic muscle forces increase or decrease in unison. Experimental studies have shown however that the relationship between muscle forces is highly task-dependent often causing forces to increase in one muscle while decreasing in a functional agonist, likely because of the contractile conditions and contractile properties of the involved muscles. We therefore, suggest a modified cost function that accounts for the instantaneous contraction velocity of the muscles and its effect on the instantaneous maximal force. With this novel objective function, a task-dependent prediction of muscle force distribution is obtained that allows, even in a one degree of freedom system, the prediction of force sharing loops, and simultaneously increasing and decreasing forces for agonist pairs of muscles.     

Experimental muscle pain increases mechanomyographic signal activity during sub-maximal isometric contractions.

This study was designed to investigate the local effect of experimental muscle pain on the MMG and the surface EMG during a range of sub-maximal isometric contractions. Muscle pain was induced by injections of hypertonic saline into the biceps brachii muscle in 12 subjects. Injections of isotonic saline served as a control. Pain intensity and location, MMG and surface EMG from the biceps brachii were assessed during static isometric (0%, 10%, 30%, 50% and, 70% of the maximal voluntary contraction) and ramp isometric (0-50% of the maximal voluntary contraction) elbow flexions. MMG and surface EMG signals were analyzed in the time and frequency domain. Experimentally induced muscle pain induced an increase in root mean square values of the MMG signal while no changes were observed in the surface EMG. Most likely this increase reflects changes in the mechanical contractile properties of the muscle and indicates compensatory mechanisms, i.e. decreased firing rate and increased twitch force to maintain a constant force output in presence of experimental muscle pain. Under well-controlled conditions, MMG recordings may be more sensitive than surface EMG recordings and clinically useful for detecting non-invasively increased muscle mechanical contributions during muscle pain conditions.     

Predicting maximum eccentric strength from surface EMG measurements

The origin of the well-documented discrepancy between maximum voluntary and in vitro tetanic eccentric strength has yet to be fully understood. This study aimed to determine whether surface EMG measurements can be used to reproduce the in vitro tetanic force–velocity relationship from maximum voluntary contractions. Five subjects performed maximal knee extensions over a range of eccentric and concentric velocities on an isovelocity dynamometer whilst EMG from the quadriceps were recorded. Maximum voluntary (MVC) force–length–velocity data were estimated from the dynamometer measurements and a muscle model. Normalised amplitude–length–velocity data were obtained from the EMG signals. Dividing the MVC forces by the normalised amplitudes generated EMG corrected force–length–velocity data. The goodness of fit of the in vitro tetanic force–velocity function to the MVC and EMG corrected forces was assessed. Based on a number of comparative scores the in vitro tetanic force–velocity function provided a significantly better fit to the EMG corrected forces compared to the MVC forces (p?0.05), Furthermore, the EMG corrected forces generated realistic in vitro tetanic force–velocity profiles. A 58±19% increase in maximum eccentric strength is theoretically achievable through eliminating neural factors. In conclusion, EMG amplitude can be used to estimate in vitro tetanic forces from maximal in vivo force measurements, supporting neural factors as the major contributor to the difference between in vitro and in vivo maximal force.     

Intra-session and inter-day reliability of forearm surface EMG during varying hand grip forces

Surface electromyography (EMG) is widely used to evaluate forearm muscle function and predict hand grip forces; however, there is a lack of literature on its intra-session and inter-day reliability. The aim of this study was to determine reliability of surface EMG of finger and wrist flexor muscles across varying grip forces. Surface EMG was measured from six forearm flexor muscles of 23 healthy adults. Eleven of these subjects undertook inter-day test–retest. Six repetitions of five randomized isometric grip forces between 0% and 80% of maximum force (MVC) were recorded and normalized to MVC. Intra- and inter-day reliability were calculated through the intraclass correlation coefficient (ICC) and standard error of measurement (SEM).Normalized EMG produced excellent intra-session ICC of 0.90 when repeated measurements were averaged. Intra-session SEM was low at low grip forces, however, corresponding normalized SEM was high (23–45%) due to the small magnitude of EMG signals. This may limit the ability to evaluate finer forearm muscle function and hand grip forces in daily tasks. Combining EMG of functionally related muscles improved intra-session SEM, improving within-subject reliability without taking multiple measurements. Removing and replacing electrodes inter-day produced poor ICC (ICC < 0.50) but did not substantially affect SEM.     

Estimation of muscle fiber conduction velocity from two-dimensional surface EMG recordings in dynamic tasks

The aims of this study are (1) to demonstrate that multi-channel surface electromyographic (EMG) signals can be detected with negligible artifacts during fast dynamic movements with an adhesive two-dimensional (2D) grid of 64 electrodes and (2) to propose a new method for the estimation of muscle fiber conduction velocity from short epochs of 2D EMG recordings during dynamic tasks. Surface EMG signals were collected from the biceps brachii muscle of four subjects with a grid of 13 × 5 electrodes during horizontal elbow flexion/extension movements (range 120–170°) at the maximum speed, repeated cyclically for 2 min. Action potentials propagating between the innervation zone and tendon regions could be detected during the dynamic task. A maximum likelihood method for conduction velocity estimation from the 2D grid using short time intervals was developed and applied to the experimental signals. The accuracy of conduction velocity estimation, assessed from the standard deviation of the residual of the regression line with respect to time, decreased from (range) 0.20–0.33 m/s using one column to 0.02–0.15 m/s when combining five columns of the electrode grid. This novel method for estimation of muscle fiber conduction velocity from 2D EMG recordings provides an estimate which is global in space and local in time, thus representative of the entire muscle yet able to track fast changes over the execution of a task, as is required for assessing muscle properties during fast movements.     

An open source lower limb model: Hip joint validation

Musculoskeletal lower limb models have been shown to be able to predict hip contact forces (HCFs) that are comparable to in vivo measurements obtained from instrumented prostheses. However, the muscle recruitment predicted by these models does not necessarily compare well to measured electromyographic (EMG) signals. In order to verify if it is possible to accurately estimate HCFs from muscle force patterns consistent with EMG measurements, a lower limb model based on a published anatomical dataset (Klein Horsman et al., 2007. Clinical Biomechanics. 22, 239-247) has been implemented in the open source software OpenSim. A cycle-to-cycle hip joint validation was conducted against HCFs recorded during gait and stair climbing trials of four arthroplasty patients (Bergmann et al., 2001. Journal of Biomechanics. 34, 859-871). Hip joint muscle tensions were estimated by minimizing a polynomial function of the muscle forces. The resulting muscle activation patterns obtained by assessing multiple powers of the objective function were compared against EMG profiles from the literature. Calculated HCFs denoted a tendency to monotonically increase their magnitude when raising the power of the objective function; the best estimation obtained from muscle forces consistent with experimental EMG profiles was found when a quadratic objective function was minimized (average overestimation at experimental peak frame: 10.1% for walking, 7.8% for stair climbing). The lower limb model can produce appropriate balanced sets of muscle forces and joint contact forces that can be used in a range of applications requiring accurate quantification of both. The developed model is available at the website https://simtk.org/home/low_limb_london.     

Localized muscular fatigue duration, EMG parameters and accuracy of rapid limb movements

While much is known about the physiological basis of local muscular fatigue, little is known about the kinematic and electromyographic (EMG) consequences of brief fatiguing isometric contractions. Five male subjects performed a horizontal elbow flexion-extension reversal movement over 90° in 250 ms to reversal before and after one of five single maximal isometric elbow flexions ranging in duration from 15–120 s. Surface EMG signals were recorded from the biceps brachii, the long head of the triceps, the clavicular portion of the pectoralis major, and the posterior deltoid. Spatial and temporal errors were computed from potentiometer output. During the fatiguing bouts, maximum voluntary force dropped linearly an average of 4% in the 15 s condition and 58% in the 120 s condition relative to maximum force. The associated biceps rectified-integrated EMG signal increased from the onset of each fatigue bout for 15–30 s, then decreased over the remainder of the longer bouts. Following the fatigue bout, subjects undershot the target distance on the first movement trial in all conditions. Following short fatigue durations (i.e. 15–30 s), the peak biceps EMG amplitude was disrupted and movement velocity decreased, but both measures recovered within seconds. As fatigue duration increased, progressive decreases in peak velocity occurred with increased time to reversal, reduced EMG amplitude, and longer recovery times. However, the relative timing of the EMG pattern was maintained suggesting the temporal structure was not altered by fatigue. The findings suggest that even short single isometric contractions can disrupt certain elements of the motor control system.     

Validation of a biodynamic model of pushing and pulling.

Pushing and pulling during manual material handling can increase the compressive forces on the lumbar disc region while creating high shear forces at the shoe-floor interface. A sagittal plane dynamic model derived from previous biomechanical models was developed to predict L5/S1 compressive force and required coefficients of friction during dynamic cart pushing and pulling. Before these predictions could be interpreted, however, it was necessary to validate model predictions against independently measured values of comparable quantities. This experiment used subjects of disparate stature and body mass, while task factors such as cart resistance and walking speed were varied. Predicted ground reaction forces were compared with those measured by a force platform, with correlations up to 0.67. Predicted erector spinae and rectus abdominus muscle forces were compared with muscle forces derived from RMS-EMGs of the respective muscle groups, using a static force build-up regression relationship to transform the dynamic RMS-EMGs to trunk muscle forces. Although correlations were low, this was attributed in part to the use of surface EMG on subjects of widely varied body mass. The biodynamic model holds promise as a tool for analysis of actual industrial pushing and pulling tasks, when carefully applied.     

The dynamical stability of isometrically contracting muscle and its relation to transient force response

The length-tension relation for tetanically contracting muscle indicates that for lengths longer than the resting length, the muscle should be dynamically unstable; i.e. some sarcomeres should lengthen and others shorten. This behavior is not observed experimentally. The theoretical behavior of muscle in this respect is determined both by the length-tension curve, and by the response of muscle to rapid changes in its mechanical state. In this paper it is shown that the force generated after a small step change in length is related to the dynamical stability of muscle. By means of a simple model, the behavior of isometrically contracting muscle is predicted based on in vitro mechanical studies and classical control theory. It is found that inhomogeneities in sarcomere length can develop only after many seconds, and that this relative stability is due entirely to the presence of the muscle transients.     

An EMG-assisted model of loads on the lumbar spine during asymmetric trunk extensions

An EMG-assisted, low-back, lifting model is presented which simulates spinal loading as a function of dynamic, asymmetric, lifting exertions. The purpose of this study has been to develop a model which overcomes the limitations of previous models including static or isokinetic mechanics, inaccurate predictions of muscle coactivity, static interpretation of myoelectric activity, and physiologically unrealistic or variable muscle force per unit area. The present model predicts individual muscle forces from processed EMG data, normalized as a function of trunk angle and asymmetry, and modified to account for muscle length and velocity artifacts. The normalized EMGs are combined with muscle cross-sectional area and intrinsic strength capacity as determined on a per subject basis, to represent tensile force amplitudes. Dynamic internal and external force vectors are employed to predict trunk moments, spinal compression, lateral and anterior shear forces. Data from 20 subjects performing a total of 2160 exertions showed good agreement between predicted and measured values under all trunk angle, asymmetry, velocity, and acceleration conditions. The design represents a significant step toward accurate, fully dynamic modeling of the low-back in multiple dimensions. The benefits of such a model are the insights provided into the effects of motion induced, muscle co-activity on spinal loading in multiple dimensions.     

Estimation of cat medial gastrocnemius fascicle lengths during dynamic contractions

In typical muscle models, it is often assumed that the contractile element (fascicle) length depends exclusively on the instantaneous muscle-tendon length and the instantaneous muscle force. In order to test whether the instantaneous fascicle length during dynamic contractions can be predicted from muscle-tendon length and force, fascicle lengths, muscle-tendon lengths, and muscle forces were directly measured in cat medial gastrocnemii during isometric and dynamic contractions. Two theoretical muscle models were developed: model A was based on force-time data obtained during the activation phase and model D on force-time data obtained during the deactivation phase of isometric contractions. To test the models, instantaneous fascicle lengths were predicted from muscle-tendon lengths and forces during dynamic contractions that simulated cat locomotion for speeds ranging from 0.4 to 1.6m/s. The theoretically predicted fascicle lengths were compared with the experimentally measured fascicle lengths. It was found that fascicle lengths were not uniquely associated with muscle-tendon lengths and forces; that is, for a given muscle-tendon length and force, fascicle lengths varied depending on the contractile history. Consequently, models A and D differed in fascicle length predictions; model D (maximum average error=8.5%) was considerably better than model A (maximum average error=22.3%). We conclude from this study that it is not possible to predict the exact fascicle lengths from muscle-tendon lengths and forces alone, however, adequate predictions seem possible based on such a model. The relationship between fascicle length and muscle force and muscle-tendon length is complex and highly non-linear, thus, it appears unlikely that accurate fascicle length predictions can be made without some reference contractions in which fascicle length, muscle-tendon length, and force are measured simultaneously.     

Relationship between EMG signals and force in human vastus lateralis muscle using multiple bipolar wire electrodes.

This paper describes the relationship between knee extension force and EMG signals detected by multiple bipolar wire electrodes inserted into the human vastus lateralis muscle under isometric conditions. Six healthy male volunteers participated in this study. Eight pairs of bipolar wire electrodes were inserted into the right vastus lateralis muscle and the EMG data were simultaneously detected and analyzed. The EMG raw data and individual force-IEMG relations were influenced by the location of the electrode inserted into the muscle. The force and IEMG relationship averaged across subjects detected from the eight electrodes, however, showed almost the same linear correlation in spite of different electrode locations. No linear correlation was observed between MdF and the knee extension force. This result suggests that, if all of the muscle fibers participate in the same action at the same time, the averaged normalized IEMG from any places using wire electrodes could reflect the total activities of that muscle even if the muscle is large.     

Lumbar spinal muscle activation synergies predicted by multi-criteria cost function

The hypothesis that control of lumbar spinal muscle synergies is biomechanically optimized was studied by comparing EMG data with an analytical model with a multi-component cost function that could include (1) trunk displacements, (2) intervertebral displacements, (3) intervertebral forces; (4) sum of cubed muscle stresses, and (5) eigenvalues for the first two spinal buckling modes. The model's independent variables were 180 muscle forces. The 36 displacements of 6 vertebrae were calculated from muscle forces and the spinal stiffness. Calculated muscle activation was compared with EMG data from 14 healthy human subjects who performed isometric voluntary ramped maximum efforts at angles of 0 degrees, 45 degrees, 90 degrees, 135 degrees and 180 degrees to the right from the anterior direction. Muscle activation at each angle was quantified as the linear regression slope of the RMS EMG versus external force relationship, normalized by the maximum observed EMG.There was good agreement between the analytical model and EMG data for the dorsal muscles when the model included either minimization of intervertebral displacements or minimization of intervertebral forces in its cost function, but the model did not predict a realistic level of abdominal muscles activation. Agreement with EMG data was improved with the sum of the cubed muscle stresses added to the cost function. Addition of a cost function component to maximize the trunk stability produced higher levels of antagonistic muscle activation at low efforts than at greater efforts. It was concluded that the muscle activation strategy efficiently limits intervertebral forces and displacements, and that costs of higher muscle stresses are taken into account, but stability does not appear to be maximized. Trunk muscles are apparently not controlled solely to optimize any one of the biomechanical costs considered here.