MUSCLE FORCE MAGNITUDES IN THE HUMAN LEG FOR ISOMETRIC EXERCISES WITH VARIOUS RESULTANT FORCE DIRECTIONS AND JOINT ANGLES

Using a gradient-based numerical optimization routine, the force magnitudes required of 10 major sagittal plane leg muscles to create a constant magnitude isometric resultant force against a fixed surface at the toe directed anteriorly, posteriorly, superiorly, and inferiorly were quantitatively predicted for three sets of joint angles: a straight leg configuration, with the knee flexed, and with both the hip and knee flexed. Comparisons over the conditions studied for each individual system muscle found that the maximum variation occurred in knee and hip extensor forces (up to two orders of magnitude). Comparisons within the set of active muscles for each studied condition identified dominant muscles and muscle functions. All anteriorly-directed and posteriorly-directed resultants required a small number of muscles with common functions (mainly knee or hip extensors) and large force magnitudes (O(1000[Formula: see text]N)). In contrast, a large number of muscles, with wide-ranging synergistic and antagonistic functions, acting across multiple joints with relatively small magnitudes (O(100[Formula: see text]N)) were needed to create the superiorly-directed resultant with flexed hip and knee. With good correlation to experimentally measured trends in the interrelationships between leg joint angles and isometric forces, the systematic muscle force prediction and analysis presented in this work can be used to guide the design of targeted muscle strengthening exercises and study of muscle-specific injury.

Force feedback reinforces muscle synergies in insect legs

The nervous system solves complex biomechanical problems by activating muscles in modular, synergist groups. We have studied how force feedback in substrate grip is integrated with effects of sense organs that monitor support and propulsion in insects. Campaniform sensilla are mechanoreceptors that encode forces as cuticular strains. We tested the hypothesis that integration of force feedback from receptors of different leg segments during grip occurs through activation of specific muscle synergies. We characterized the effects of campaniform sensilla of the feet (tarsi) and proximal segments (trochanter and femur) on activities of leg muscles in stick insects and cockroaches. In both species, mechanical stimulation of tarsal sensilla activated the leg muscle that generates substrate grip (retractor unguis), as well as proximal leg muscles that produce inward pull (tibial flexor) and support/propulsion (trochanteral depressor). Stimulation of campaniform sensilla on proximal leg segments activated the same synergistic group of muscles. In stick insects, the effects of proximal receptors on distal leg muscles changed and were greatly enhanced when animals made active searching movements. In insects, the task-specific reinforcement of muscle synergies can ensure that substrate adhesion is rapidly established after substrate contact to provide a stable point for force generation.

Task-dependent inhibition of slow-twitch soleus and excitation of fast-twitch gastrocnemius do not require high movement speed and velocity-dependent sensory feedback

Although individual heads of triceps surae, soleus (SO) and medial gastrocnemius (MG) muscles, are often considered close functional synergists, previous studies have shown distinct activity patterns between them in some motor behaviors. The goal of this study was to test two hypotheses explaining inhibition of slow SO with respect to fast MG: (1) inhibition occurs at high movement velocities and mediated by velocity-dependent sensory feedback and (2) inhibition depends on the ankle-knee joint moment combination and does not require high movement velocities. The hypotheses were tested by comparing the SO EMG/MG EMG ratio during fast and slow motor behaviors (cat paw shake responses vs. back, straight leg load lifting in humans), which had the same ankle extension-knee flexion moment combination; and during fast and slow behaviors with the ankle extension-knee extension moment combination (human vertical jumping and stance phase of walking in cats and leg load lifting in humans). In addition, SO EMG/MG EMG ratio was determined during cat paw shake responses and walking before and after removal of stretch velocity-dependent sensory feedback by self-reinnervating SO and/or gastrocnemius. We found the ratio SO EMG/MG EMG below 1 (p < 0.05) during fast paw shake responses and slow back load lifting, requiring the ankle extension-knee flexion moment combination; whereas the ratio SO EMG/MG EMG was above 1 (p < 0.05) during fast vertical jumping and slow tasks of walking and leg load lifting, requiring ankle extension-knee extension moments. Removal of velocity-dependent sensory feedback did not affect the SO EMG/MG EMG ratio in cats. We concluded that the relative inhibition of SO does not require high muscle velocities, depends on ankle-knee moment combinations, and is mechanically advantageous for allowing a greater MG contribution to ankle extension and knee flexion moments.

Changes in muscle and joint coordination in learning to direct forces

While it has been suggested that bi-articular muscles have a specialized role in directing external reaction forces, it is unclear how humans learn to coordinate mono- and bi-articular muscles to perform force-directing tasks. Participants were asked to direct pedal forces in a specified target direction during one-legged cycling. We expected that with practice, performance improvement would be associated with specific changes in joint torque patterns and mono- and bi-articular muscular coordination. Nine male participants practiced pedaling an ergometer with only their left leg, and were instructed to always direct their applied pedal force perpendicular to the crank arm (target direction) and to maintain a constant pedaling speed. After a single practice session, the mean error between the applied and target pedal force directions decreased significantly. This improved performance was accompanied by a significant decrease in the amount of ankle angular motion and a smaller increase in knee and hip angular motion. This coincided with a re-organization of lower extremity joint torques, with a decrease in ankle plantarflexor torque and an increase in knee and hip flexor torques. Changes were seen in both mono- and bi-articular muscle activity patterns. The mono-articular muscles exhibited greater alterations, and appeared to contribute to both mechanical work and force-directing. With practice, a loosening of the coupling between bi-articular thigh muscle activation and joint torque co-regulation was observed. The results demonstrated that participants were able to learn a complex and dynamic force-directing task by changing the direction of their applied pedal forces through re-organization of joint torque patterns and mono- and bi-articular muscle coordination.

Enhancement of muscle activity by electrical stimulation in cerebral palsy: a case-control study

The objectives of this study were to compare the effects of low-intensity electrical stimulation of the quadriceps muscle in children with cerebral palsy in the following 2 modes: reconditioning by long-term training of the muscle versus real-time assist to the muscle during motion. To evaluate the force enhancement in the assist mode, we developed a method to dissociate the volitional and the induced components from the total electromyographic signal. The study group, including 5 children with cerebral palsy (mean age, 3.3 years; 0.4 SD), underwent 2 testing sessions: 1 before and 1 after 3-month training by electrical stimulation. Each session included 2 series of trials: 1 with electrical stimulation, as an orthotic assist, and 1 without electrical stimulation. The tests included flexion-extension movements of the knee at a self-selected pace. The results showed that, compared to before training, there was a significant increase in the average motion velocity and a decrease in motion jerk and in knee torque after training in both the electrical stimulation- assisted and -unassisted modes. Of special interest was the significant decrease in quadriceps-hamstrings co-contraction following training by electrical stimulation but not during electrical stimulation-assisted motion. The results obtained for the group with cerebral palsy were statistically different from those of the control group, but this difference decreased after long-term training by electrical stimulation. It was concluded that, in children with cerebral palsy, electrical stimulation is more beneficial in long-term training than when used as a real-time motion assist. Although muscle strength is not affected, more centrally controlled attributes such as co-contraction are improved.

Control of ground reaction forces by hindlimb muscles during cat locomotion

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

Multi-functionality of the cat medical gastrocnemius during locomotion

The functional role of biarticular muscles was investigated based on direct force measurement in the cat medial gastrocnemius (MG) and analysis of hindlimb kinematics and kinetics for the stance phase of level, uphill, and downhill walking. Four primary functional roles of biarticular muscles have been proposed in the past. These functional roles have typically been discussed independently of each other, and biarticular muscles have rarely been assigned more than one functional roles for different phases of the work cycle. The purpose of this study was to elucidate the functional role of the biarticular cat MG during locomotion. It was found that MG forces were primarily associated with the moment requirements at the ankle for most of the stance phase, but also helped to satisfy the moments at the knee in the initial phase of stance. In the second half of stance, MG transferred mechanical energy from the knee to the ankle from the knee to the ankle, while simultaneously producing a substantial amount of mechanical work. Based on these results, we hypothesize that MG's primary function is that of an ankle extensor. However, because of the coupling of the ankle extensor moment with a knee flexor moment in the initial, and a knee extensor moment in the final phase of stance, MG satisfies two joint moments in early stance, and transfers mechanical energy from the knee to the ankle in late stance. We conclude that cat MG has multiple functional roles during the stance phase of locomotion, and speculate that such multi-functionality also exists in other bi- and multi-articular muscles.

Direction of foot force for pushes against a fixed pedal: role of effort level

Control of the force exerted by the foot on the ground is critical to human locomotion. During running on a treadmill and pushing against a fixed pedal, humans increased foot force in a linear manner in sagittal plane force space. However, for pushes against a moving pedal, force output was linear for some participants but slightly curved for others. A primary difference between the static and dynamic pedaling studies was that the dynamic study required participants to push with varying peak effort levels, whereas a constant peak effort level was used for the fixed pedal pushes. The present study evaluated the possibility that force direction varied with level of effort. Seated humans pushed against a fixed pedal to a series of force magnitude targets. The force direction varied systematically with effort level consistent with the force path curvature observed for dynamic pedaling.

Foot force direction in an isometric pushing task: prediction by kinematic and musculoskeletal models

The abilities of a kinematic model and a muscle model of the human lower limb to predict the stereotyped direction of the muscular component of foot force produced by seated subjects in a static task were tested and compared. Human subjects ( n=11) performed a quasi-static, lower-limb pushing task against an instrumented bicycle pedal, free to rotate about its own axis, but with the crank fixed. Each pushing trial consisted of applying a force from the resting level to a force magnitude target with the right foot. Ten force target magnitudes were used (200, 250, ..., 650 N) along with 12 pedal positions. For each pushing effort, the muscular contribution to the measured foot force was determined from push onset to peak attained force. This segment was well characterized by a straight line across subjects, pedal positions, and force target magnitudes. The linear nature of the muscular component allowed a characteristic direction to be determined for each trial. A three-joint (hip, knee, and ankle) and a two-joint (hip and knee) net joint torque optimization was applied to a sagittal-plane kinematic model to predict the characteristic force direction. A musculoskeletal model was also used to create a feasible force space (FFS) for the lower limb. This FFS represents the range of possible forces the lower limb could theoretically produce. From this FFS, the direction of the maximum feasible foot force was determined and compared with the characteristic direction of subject performance. The muscle model proved to be the most effective in predicting subject force direction, followed by the three-joint and two-joint net joint torques optimizations. Similarities between the predictions of the kinematic and muscle model were also found.

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

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

Analysis of muscle coordination strategies in cycling

The functional significance of the stereotypical muscle activation patterns used in skilled multi-joint tasks is not well understood. Optimization methods could provide insight into the functional significance of muscle coordination. The purpose of this study was to predict muscle force patterns during cycling by pushing and pulling the pedal using different optimization criteria and compare the predictions with electromyographic (EMG) patterns. To address the purpose of the study, 1) the contribution of muscle length and velocity changes to EMG-muscle force relationships during cycling was examined by comparing joint moments calculated from EMG and inverse dynamics, 2) patterns of individual muscle forces during cycling of five subjects were predicted using 13 different optimization criteria, and 3) the properties of the criterion with the best performance in predicting the normalized EMG were used to explain the features and functional significance of muscle coordination in cycling. It was shown that the criterion that minimizes the sum of muscle stresses cubed demonstrated the best performance in predicting the relative magnitude and patterns of muscle activation. Based on this criterion, it was suggested that the functional significance of muscle coordination strategy in cycling may be minimization of fatigue and/or perceived effort.

Muscle coordination: the discussion continues

In this response, the major criticisms of the target article are addressed. Terminology from the target article that may have caused some confusion is clarified. In particular, the tasks that have the basic features of muscle coordination, as identified in the target article, have been limited in scope. A new metabolic optimization criterion suggested by Alexander (2000) is examined for its ability to predict muscle coordination in walking. Issues concerning the validation of muscle force predictions, the rules of muscle coordination, and the role of directional constraints in coordination of two-joint muscles are discussed. It is shown in particular that even in one-joint systems, the forces predicted by the criterion of Crowninshield and Brand (1981) depend upon the muscle moment arms and the physiological cross-sectional areas in much more complex ways than either previously assumed in the target article, or incorrectly derived by Herzog and Ait-Haddou (2000). It is concluded that the criterion of Crowninshield and Brand qualitatively predicts the basic coordination features of the major one- and two-joint muscles in a number of highly skilled, repetitive motor tasks performed by humans under predictable conditions and little demands on stability and accuracy. A possible functional significance of such muscle coordination may be the minimization of perceived effort, muscle fatigue, and/or energy expenditure.

Some mechanical considerations on muscle coordination

This commentary emphasizes three points of discussion. (a) The terminology: The terms multifunctional, synergisic, antagonistic muscles, and synergistic and antagonistic coactivations are discussed and the conclusion is drawn that they could not be used without mentioning the particular joint motion. (b) The importance of the external joint moments for activation of the muscles is confirmed on the basis of logical and mechanical considerations. Not all-experimental results, however, could be explained by this means. (c) The optimization criterion: Prilutsky's conclusion concerning the predicted muscle force proportionality to the muscle moment arm and PCSA is confirmed using a simple analytical solution of the optimization problem. It is shown, however, that the proportionality to the PCSA is a consequence of the chosen optimization criterion.

Subject specific coordination of two- and one-joint muscles during landings suggests multiple control criteria

The target article, thoughtfully constructed by Dr. Prilutsky, effectively synthesizes available data on multijoint movements regarding coordination patterns of major two- and one-joint muscles, provides evidence for an optimization criterion that predicts critical features of muscle activation patterns, and explores the functional consequences of muscle coordination. This work also provides a clear set of definitions and an organizational framework that is currently needed for a productive interdisciplinary discussion regarding the underlying control mechanisms used during realistic multijoint movements. Although identification of an optimization criterion that predicts muscle recruitment strategies would greatly simplify control logic required for rehabilitation and musculoskeletal modeling, our experimental data during landings indicate more than one criterion may exist. Preliminary review of our experimental landing data suggests the rules identified by Prilutsky apparently hold for some subjects during portions of the landing movements. The presence of more than one muscle activation pattern used to achieve the same NJMs demonstrates there may be more than one optimization criterion that predicts critical features of muscle activation patterns. The functional consequences of more than one control criterion may also prove to be an asset, particularly when adapting to different environmental constraints.

Coordination of two- and one-joint muscles: functional consequences and implications for motor control

The purpose of this paper is three-fold: (a) to summarize available data on coordination of major two- and one-joint muscles in multijoint tasks and identify basic features of muscle coordination, (b) to demonstrate that there may exist an optimization criterion that predicts essential features of electromyographic activity of individual muscles in a variety of tasks, and (c) to address the functional consequences of the observed muscle coordination and underlying mechanisms of its control. The analysis of the literature revealed that basic features of muscle coordination are similar among different voluntary motor tasks and reflex responses. It is demonstrated that these basic features of coordination of one- and two-joint muscles in two-dimensional tasks are qualitatively predicted by minimizing the sum of muscle stresses cubed. Functional consequences of the observed coordination of one- and two-joint muscles are (a) reduction of muscle force as well as stress, mechanical and metabolic energy expenditure, muscle fatigue, and perceived effort; (b) a spring-like behavior of a multi-joint limb during maintenance of an equilibrium posture; and (c) energy transfer between joints via two-joint muscles. A conceptual scheme of connections between motoneuron pools of one- and two-joint muscles, which accounts for the observed muscle coordination, is proposed. An important part of this scheme is the force-dependent inhibition and excitation from two-joint to one-joint synergists and antagonists, respectively.

About weight factors in the non-linear objective functions used for solving indeterminate problems in biomechanics

A lot of non-linear objective criteria are applied for solving the indeterminate problems formulated for different biomechanical models--most of them can be covered by the expression [formula in text]. It might be noted, however, that most of the suggested criteria are not applicable if considerable antagonistic co-contractions exist. This could be an effect of treating the agonistic muscles and their respective antagonists in one and the same manner in the objective function. Using a completely inverse approach (the muscle forces are supposed to be known quantities) and a simple 1DOF model (actuated by three agonistic muscles and one corresponding antagonist) it has been shown which values of the weight factors c(i) may predict different levels of muscle forces from the two antagonistic groups. Three hypothetical border variants for magnitudes of the muscle forces are considered (flexor muscles are only active, extensor muscles are only active, considerable co-contraction of flexors and extensors exists). The main conclusions are: the signs of c(i) at agonistic muscles have to be opposite to the c(i) signs at their antagonists; the signs of the weight factors depend on the direction of the net external joint moment; the closer c(i) to zero, the bigger force will be predicted in the ith muscle.

Is coordination of two-joint leg muscles during load lifting consistent with the strategy of minimum fatigue?

The purpose of this study was to examine if strong correlations reported for a back lift task between activity (EMG) of two-joint rectus femoris (RF), hamstrings (HA), and gastrocnemius (GA) and the difference in the joint moments could be predicted by minimizing an objective function of minimum fatigue. Four subjects lifted barbell weights (9 and 18 kg) using a back lift technique at three speeds normal, slow, and fast. Recorded ground reaction forces and coordinates of the leg joints were used to calculate the resultant joint moments. Surface EMG of five muscles crossing the knee joint were also recorded. Forces of nine muscles were calculated using static optimization and a minimum fatigue criterion. Relationships (i) (RF EMG-HA EMG) vs (knee moment hip moment) and (ii) GA EMG vs. (ankle moment knee moment) were closely related (coefficients of determination were typically 0.9 and higher). Qualitatively similar relationships were predicted by minimizing fatigue. Gastrocnemius and hamstrings had the agonistic action at both joints they cross during load lifting, and their activation and predicted forces increased with increasing flexion knee moments and extension ankle and hip moments. The rectus femoris typically had the antagonistic action at the knee and hip, and its activation and predicted force were low. Patterns of predicted muscle forces were qualitatively similar to the corresponding EMG envelopes (except in phases of low joint moments where accuracy of determining joint moments was presumably poor). It was suggested that muscle coordination in load lifting is consistent with the strategy of minimum muscle fatigue.

Forms of forward quadrupedal locomotion. II. A comparison of posture, hindlimb kinematics, and motor patterns for upslope and level walking

To gain insight into the neural mechanisms controlling different forms of quadrupedal walking of normal cats, data on postural orientation, hindlimb kinematics, and motor patterns of selected hindlimb muscles were assessed for four grades of upslope walking, from 25 to 100% (45 degrees incline), and compared with similar data for level treadmill walking (0.6 m/s). Kinematic data for the hip, knee, ankle, and metatarsophalangeal joints were obtained from digitizing ciné film that was synchronized with electromyographic (EMG) records from 13 different hindlimb muscles. Cycle periods, the structure of the step cycle, and paw-contact sequences were similar at all grades and typical of lateral-sequence walking. Also, a few half-bound and transverse gallop steps were assessed from trials at the 100% grade; these steps had shorter cycle periods than the walking steps and less of the cycle (68 vs. 56%) was devoted to stance. Each cat assumed a crouched posture at the steeper grades of upslope walking and stride length decreased, whereas the overall position of the stride shifted caudally with respect to the hip joint. At the steeper grades, the range and duration of swing-related flexion increased at all joints, the stance-phase yield was absent at the knee and ankle joints, and the range of stance-phase extension at knee and ankle joints increased. Patterns of muscle activity for upslope and level walking were similar with some notable exceptions. At the steeper grades, the EMG activity of muscles with swing-related activity, such as the digit flexor muscle, the flexor digitorum longus (FDL), and the knee flexor muscle, the semitendinosus (ST), was prolonged and continued well into midswing. The EMG activity of stance-related muscles also increased in amplitude with grade, and three muscles not active during the stance phase of level walking had stance activity that increased in amplitude and duration at the steepest grades; these muscles were the ST, FDL, and extensor digitorum brevis. Overall the changes in posture, hindlimb kinematics, and the activity patterns of hindlimb muscles during upslope walking reflected the need to continually move the body mass forward and upward during stance and to ensure that the paw cleared the inclined slope during swing. The implications of these changes for the neural control of walking and expected changes in hindlimb kinetics for slope walking are discussed.

Activation patterns of mono- and bi-articular arm muscles as a function of force and movement direction of the wrist in humans

1. In order to explain the task-dependent activation of muscles, we have investigated the hypothesis that mono- and bi-articular muscles have a different functional role in the control of multijoint movements. According to this hypothesis, bi-articular muscles are activated in a way to control the direction of external force. The mono-articular muscles are thought to be activated to contribute to joint torque mainly during shortening movements. 2. To investigate this hypothesis, surface electromyographic (EMG) recordings were obtained from several mono- and bi-articular arm muscles during voluntary slow movements of the wrist in a horizontal plane against an external force. The direction of force produced at the wrist and the direction of movement of the wrist were varied independently. 3. The results revealed distinct differences between the activation patterns of mono- and bi-articular muscles. The activation of the bi-articular muscles was not affected by movement direction, but appeared to vary exclusively with the direction of force. 4. The mono-articular muscles showed significantly more EMG activity for movements in a specific direction, which equalled the movement direction corresponding to the largest shortening velocity of the muscle. The EMG activity decreased gradually for movements in other directions. This direction-dependent activation appeared to be independent of the direction of the external force.