Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

Beyond Inverse Dynamics: Methods for Assessment of Individual Muscle Function during Gait

Three-dimensional motion analysis performed in the modern gait analysis laboratory provides a wealth of information about the kinematics and kinetics of human locomotion, but standard gait analysis is largely restricted to joint-level measures. Three-dimensional joint rotations, joint moments, and joint powers tell us a great deal about gait mechanics, but it is often of interest to know about the roles that muscles play. This narrative review surveys work that has been done, largely over the past four decades, to augment standard gait analysis with muscle-level assessments of function. Often, these assessments have incorporated additional technology such as ultrasound imaging, or complex modeling and simulation techniques. The review discusses measurements of muscle moment arm during walking along with assessment of muscle mechanical advantage, muscle-tendon lengths, and the use of induced acceleration analysis to determine muscle roles. In each section of the review, examples are provided of how the auxiliary analyses have been used to gain potentially useful information about normal and pathological human walking. While this work highlights the potential benefits of adding various measures to gait analysis, it is acknowledged that challenges to implementation remain, such as the need for specialized knowledge and the potential for bias introduced by model choices.

Modern three-dimensional digital methods for studying locomotor biomechanics in tetrapods

Here, we review the modern interface of three-dimensional (3D) empirical (e.g. motion capture) and theoretical (e.g. modelling and simulation) approaches to the study of terrestrial locomotion using appendages in tetrapod vertebrates. These tools span a spectrum from more empirical approaches such as XROMM, to potentially more intermediate approaches such as finite element analysis, to more theoretical approaches such as dynamic musculoskeletal simulations or conceptual models. These methods have much in common beyond the importance of 3D digital technologies, and are powerfully synergistic when integrated, opening a wide range of hypotheses that can be tested. We discuss the pitfalls and challenges of these 3D methods, leading to consideration of the problems and potential in their current and future usage. The tools (hardware and software) and approaches (e.g. methods for using hardware and software) in the 3D analysis of tetrapod locomotion have matured to the point where now we can use this integration to answer questions we could never have tackled 20 years ago, and apply insights gleaned from them to other fields.

Knee extensor force production and discomfort during neuromuscular electrical stimulation of quadriceps with and without gluteal muscle co-stimulation

Purpose

To investigate whether Neuromuscular Electrical Stimulation (NMES) simultaneously applied on the quadriceps (Q) and gluteal (G) muscles, as compared to single Q-stimulation alters the knee extensor force production and discomfort.

Methods

A total of 11 healthy participants (6 females), with normal weight and age between 19 and 54 years were included. The unilateral, isometric maximal voluntary contraction (MVC) was assessed for each participant in an isokinetic dynamometer (Biodex, system 3). NMES was, in a randomized order, applied only on the Q-muscle and on the Q- and G-muscles (QG) simultaneously. NMES-intensity was increased stepwise until the maximal tolerable level was reached regarding discomfort, graded according to the visual analogue scale (VAS). VAS and the % of MVC produced by NMES, were registered for each level, expressed as median (inter-quartile range).

Results

The maximum tolerated NMES-intensity applied on Q compared to QG resulted in equally high discomfort, 8.0 (6.0–9.0) vs 8.0 (6.3–9.0), and in equivalent knee extensor force production, 36.7 (29.9–47.5) and 36.2 (28.9–49.3), respectively, in % of MVC. At 20% of MVC, NMES applied on Q compared to QG resulted in equal acceptable discomfort, 3.0 (2.0–4.5) vs 3.0 (3–5.5), and comparable intensity levels, 41.5 (38.0–45.8) vs 43.5 (37.0–48.8), respectively.

Conclusions

Simultaneous QG-NMES, as compared to single Q-NMES, does not seem to affect the knee extensor force production or discomfort. Q-NMES, without voluntary muscle contraction, can with an acceptable level of discomfort result in at least 20% of MVC.

Lower extremity joints and their contributions to whole limb extension

Lower extremity multi-joint strength curves tend not to evaluate individual joint contributions to endpoint force in maximum effort isometric whole limb extension. Therefore, the purpose of this study was to measure the contribution of the hip, knee, and ankle to vertical ground reaction force in maximum effort isometric whole limb extension at various postures. An effect of posture on the contributions of the hip, knee, and ankle to vertical ground reaction force was found (F_(3,96) = 85.31, p < 0.0001; F_(3,96) = 21.32, p < 0.0001; F_(3,96) = 130.61, p < 0.0001 for the hip, knee, and ankle, respectively). The hip and knee contributed most to vertical endpoint force when the lower limb was in a flexed posture, and their contributions decreased when posture was extended. Conversely, the ankle contributed least when the limb was flexed, but its contribution increased as posture was changed from flexed to more extended. In comparison to recent research involving induced acceleration analysis, it appears that the hip, knee, and ankle utilize the same force allocation strategy in multi-joint maximum effort isometric leg extensions and activities of daily living.

Effects of kinematic complexity and number of muscles on musculoskeletal model robustness to muscle dysfunction

The robustness of motor outputs to muscle dysfunction has been investigated using musculoskeletal modeling, but with conflicting results owing to differences in model complexity and motor tasks. Our objective was to systematically study how the number of kinematic degrees of freedom, and the number of independent muscle actuators alter the robustness of motor output to muscle dysfunction. We took a detailed musculoskeletal model of the human leg and systematically varied the model complexity to create six models with either 3 or 7 kinematic degrees of freedom and either 14, 26, or 43 muscle actuators. We tested the redundancy of each model by quantifying the reduction in sagittal plane feasible force set area when a single muscle was removed. The robustness of feasible force set area to the loss of any single muscle, i.e. general single muscle loss increased with the number of independent muscles and decreased with the number of kinematic degrees of freedom, with the robust area varying from 1% and 52% of the intact feasible force set area. The maximum sensitivity of the feasible force set to the loss of any single muscle varied from 75% to 26% of the intact feasible force set area as the number of muscles increased. Additionally, the ranges of feasible muscle activation for maximum force production were largely unconstrained in many cases, indicating ample musculoskeletal redundancy even for maximal forces. We propose that ratio of muscles to kinematic degrees of freedom can be used as a rule of thumb for estimating musculoskeletal redundancy in both simulated and real biomechanical systems.

A Systematic Review on Muscle Synergies: From Building Blocks of Motor Behavior to a Neurorehabilitation Tool

The central nervous system (CNS) is believed to utilize specific predefined modules, called muscle synergies (MS), to accomplish a motor task. Yet questions persist about how the CNS combines these primitives in different ways to suit the task conditions. The MS hypothesis has been a subject of debate as to whether they originate from neural origins or nonneural constraints. In this review article, we present three aspects related to the MS hypothesis: (1) the experimental and computational evidence in support of the existence of MS, (2) algorithmic approaches for extracting them from surface electromyography (EMG) signals, and (3) the possible role of MS as a neurorehabilitation tool. We note that recent advances in computational neuroscience have utilized the MS hypothesis in motor control and learning. Prospective advances in clinical, medical, and engineering sciences and in fields such as robotics and rehabilitation stand to benefit from a more thorough understanding of MS.

Neuromechanical principles underlying movement modularity and their implications for rehabilitation

Neuromechanical principles define the properties and problems that shape neural solutions for movement. Although the theoretical and experimental evidence is debated, we present arguments for consistent structures in motor patterns, i.e., motor modules, that are neuromechanical solutions for movement particular to an individual and shaped by evolutionary, developmental, and learning processes. As a consequence, motor modules may be useful in assessing sensorimotor deficits specific to an individual and define targets for the rational development of novel rehabilitation therapies that enhance neural plasticity and sculpt motor recovery. We propose that motor module organization is disrupted and may be improved by therapy in spinal cord injury, stroke, and Parkinson's disease. Recent studies provide insights into the yet-unknown underlying neural mechanisms of motor modules, motor impairment, and motor learning and may lead to better understanding of the causal nature of modularity and its underlying neural substrates.

Three-dimensional ankle moments and nonlinear summation of rat triceps surae muscles

The Achilles tendon and epimuscular connective tissues mechanically link the triceps surae muscles. These pathways may cause joint moments exerted by each muscle individually not to sum linearly, both in magnitude and direction. The aims were (i) to assess effects of sagittal plane ankle angle (varied between 150° and 70°) on isometric ankle moments, in both magnitude and direction, exerted by active rat triceps surae muscles, (ii) to assess ankle moment summation between those muscles for a range of ankle angles and (iii) to assess effects of sagittal plane ankle angle and muscle activation on Achilles tendon length. At each ankle angle, soleus (SO) and gastrocnemius (GA) muscles were first excited separately to assess ankle-angle moment characteristics and subsequently both muscles were excited simultaneously to investigate moment summation. The magnitude of ankle moment exerted by SO and GA, the SO direction in the transverse and sagittal planes, and the GA direction in the transverse plane were significantly affected by ankle angle. SO moment direction in the frontal and sagittal planes were significantly different from that of GA. Nonlinear magnitude summation varied between 0.6±2.9% and −3.6±2.9%, while the nonlinear direction summation varied between 0.3±0.4° and −0.4±0.7° in the transverse plane, between 0.5±0.4° and 0.1±0.4° in the frontal plane, and between 3.0±7.9° and 0.3±2.3° in the sagittal plane. Changes in tendon length caused by SO contraction were significantly lower than those during contraction of GA and GA+SO simultaneously. Thus, moments exerted by GA and SO sum nonlinearly both in the magnitude and direction. The limited degree of nonlinear summation may be explained by different mechanisms acting in opposite directions.

Motor unit

Movement is accomplished by the controlled activation of motor unit populations. Our understanding of motor unit physiology has been derived from experimental work on the properties of single motor units and from computational studies that have integrated the experimental observations into the function of motor unit populations. The article provides brief descriptions of motor unit anatomy and muscle unit properties, with more substantial reviews of motoneuron properties, motor unit recruitment and rate modulation when humans perform voluntary contractions, and the function of an entire motor unit pool. The article emphasizes the advances in knowledge on the cellular and molecular mechanisms underlying the neuromodulation of motoneuron activity and attempts to explain the discharge characteristics of human motor units in terms of these principles. A major finding from this work has been the critical role of descending pathways from the brainstem in modulating the properties and activity of spinal motoneurons. Progress has been substantial, but significant gaps in knowledge remain.

Long-latency muscle activity reflects continuous, delayed sensorimotor feedback of task-level and not joint-level error

In both the upper and lower limbs, evidence suggests that short-latency electromyographic (EMG) responses to mechanical perturbations are modulated based on muscle stretch or joint motion, whereas long-latency responses are modulated based on attainment of task-level goals, e.g., desired direction of limb movement. We hypothesized that long-latency responses are modulated continuously by task-level error feedback. Previously, we identified an error-based sensorimotor feedback transformation that describes the time course of EMG responses to ramp-and-hold perturbations during standing balance (Safavynia and Ting 2013; Welch and Ting 2008, 2009). Here, our goals were 1) to test the robustness of the sensorimotor transformation over a richer set of perturbation conditions and postural states; and 2) to explicitly test whether the sensorimotor transformation is based on task-level vs. joint-level error. We developed novel perturbation trains of acceleration pulses such that perturbations were applied when the body deviated from the desired, upright state while recovering from preceding perturbations. The entire time course of EMG responses (∼4 s) in an antagonistic muscle pair was reconstructed using a weighted sum of center of mass (CoM) kinematics preceding EMGs at long-latency delays (∼100 ms). Furthermore, CoM and joint kinematic trajectories became decorrelated during perturbation trains, allowing us to explicitly compare task-level vs. joint feedback in the same experimental condition. Reconstruction of EMGs was poorer using joint kinematics compared with CoM kinematics and required unphysiologically short (∼10 ms) delays. Thus continuous, long-latency feedback of task-level variables may be a common mechanism regulating long-latency responses in the upper and lower limbs.

Practical limits on muscle synergy identification by non-negative matrix factorization in systems with mechanical constraints

Statistical decomposition, including non-negative matrix factorization (NMF), is a convenient tool for identifying patterns of structured variability within behavioral motor programs, but it is unclear how the resolved factors relate to actual neural structures. Factors can be extracted from a uniformly sampled, low-dimension command space. In practical application, the command space is limited, either to those activations that perform some task(s) successfully or to activations induced in response to specific perturbations. NMF was applied to muscle activation patterns synthesized from low dimensional, synergy-like control modules mimicking simple task performance or feedback activation from proprioceptive signals. In the task-constrained paradigm, the accuracy of control module recovery was highly dependent on the sampled volume of control space, such that sampling even 50% of control space produced a substantial degradation in factor accuracy. In the feedback paradigm, NMF was not capable of extracting more than four control modules, even in a mechanical model with seven internal degrees of freedom. Reduced access to the low-dimensional control space imposed by physical constraints may result in substantial distortion of an existing low dimensional controller, such that neither the dimensionality nor the composition of the recovered/extracted factors match the original controller.

Sensorimotor feedback based on task-relevant error robustly predicts temporal recruitment and multidirectional tuning of muscle synergies

We hypothesized that motor outputs are hierarchically organized such that descending temporal commands based on desired task-level goals flexibly recruit muscle synergies that specify the spatial patterns of muscle coordination that allow the task to be achieved. According to this hypothesis, it should be possible to predict the patterns of muscle synergy recruitment based on task-level goals. We demonstrated that the temporal recruitment of muscle synergies during standing balance control was robustly predicted across multiple perturbation directions based on delayed sensorimotor feedback of center of mass (CoM) kinematics (displacement, velocity, and acceleration). The modulation of a muscle synergy's recruitment amplitude across perturbation directions was predicted by the projection of CoM kinematic variables along the preferred tuning direction(s), generating cosine tuning functions. Moreover, these findings were robust in biphasic perturbations that initially imposed a perturbation in the sagittal plane and then, before sagittal balance was recovered, perturbed the body in multiple directions. Therefore, biphasic perturbations caused the initial state of the CoM to differ from the desired state, and muscle synergy recruitment was predicted based on the error between the actual and desired upright state of the CoM. These results demonstrate that that temporal motor commands to muscle synergies reflect task-relevant error as opposed to sensory inflow. The proposed hierarchical framework may represent a common principle of motor control across motor tasks and levels of the nervous system, allowing motor intentions to be transformed into motor actions.

Review and perspective: neuromechanical considerations for predicting muscle activation patterns for movement

Muscle coordination may be difficult or impossible to predict accurately based on biomechanical considerations alone because of redundancy in the musculoskeletal system. Because many solutions exist for any given movement, the role of the nervous system in further constraining muscle coordination patterns for movement must be considered in both healthy and impaired motor control. On the basis of computational neuromechanical analyses of experimental data combined with modeling techniques, we have demonstrated several such neural constraints on the temporal and spatial patterns of muscle activity during both locomotion and postural responses to balance perturbations. We hypothesize that subject-specific and trial-by-trial differences in muscle activation can be parameterized and understood by a hierarchical and low-dimensional framework that reflects the neural control of task-level goals. In postural control, we demonstrate that temporal patterns of muscle activity may be governed by feedback control of task-level variables that represent the overall goal-directed motion of the body. These temporal patterns then recruit spatially-fixed patterns of muscle activity called muscle synergies that produce the desired task-level biomechanical functions that require multijoint coordination. Moreover, these principles apply more generally to movement, and in particular to locomotor tasks in both healthy and impaired individuals. Overall, understanding the goals and organization of the neural control of movement may provide useful reduced dimension parameter sets to address the degrees-of-freedom problem in musculoskeletal movement control. More importantly, however, neuromechanical analyses may lend insight and provide a framework for understanding subject-specific and trial-by-trial differences in movement across both healthy and motor-impaired populations.

Forelimb muscle activity during equine locomotion

Few quantitative data exist to describe the activity of the distal muscles of the equine forelimb during locomotion, and there is an incomplete understanding of the functional roles of the majority of the forelimb muscles. Based on morphology alone it would appear that the larger proximal muscles perform the majority of work in the forelimb, whereas the smaller distal muscles fulfil supplementary roles such as stabilizing the joints and positioning the limb for impact with the ground. We measured the timing and amplitude of the electromyographic activity of the intrinsic muscles of the forelimb in relation to the phase of gait (stance versus swing) and the torque demand placed on each joint during walking, trotting and cantering. We found that all forelimb muscles, except the extensor carpi radialis (ECR), were activated just prior to hoof-strike and deactivated during stance. Only the ECR was activated during swing. The amplitudes of muscle activation typically increased as gait speed increased. However, the amplitudes of muscle activation were not proportional to the net joint torques, indicating that passive structures may also contribute significantly to torque generation. Our results suggest that the smaller distal muscles help to stabilize the forelimb in early stance, in preparation for the passive structures (tendons and ligaments) to be stretched. The distal forelimb muscles remain active throughout stance only during canter, when the net torques acting about the distal forelimb joints are highest. The larger proximal muscles activate in a complex coordination to position and stabilize the shoulder and elbow joints during ground contact.

Optimization of muscle activity for task-level goals predicts complex changes in limb forces across biomechanical contexts

Optimality principles have been proposed as a general framework for understanding motor control in animals and humans largely based on their ability to predict general features movement in idealized motor tasks. However, generalizing these concepts past proof-of-principle to understand the neuromechanical transformation from task-level control to detailed execution-level muscle activity and forces during behaviorally-relevant motor tasks has proved difficult. In an unrestrained balance task in cats, we demonstrate that achieving task-level constraints center of mass forces and moments while minimizing control effort predicts detailed patterns of muscle activity and ground reaction forces in an anatomically-realistic musculoskeletal model. Whereas optimization is typically used to resolve redundancy at a single level of the motor hierarchy, we simultaneously resolved redundancy across both muscles and limbs and directly compared predictions to experimental measures across multiple perturbation directions that elicit different intra- and interlimb coordination patterns. Further, although some candidate task-level variables and cost functions generated indistinguishable predictions in a single biomechanical context, we identified a common optimization framework that could predict up to 48 experimental conditions per animal (n = 3) across both perturbation directions and different biomechanical contexts created by altering animals' postural configuration. Predictions were further improved by imposing experimentally-derived muscle synergy constraints, suggesting additional task variables or costs that may be relevant to the neural control of balance. These results suggested that reduced-dimension neural control mechanisms such as muscle synergies can achieve similar kinetics to the optimal solution, but with increased control effort (≈2×) compared to individual muscle control. Our results are consistent with the idea that hierarchical, task-level neural control mechanisms previously associated with voluntary tasks may also be used in automatic brainstem-mediated pathways for balance.

Directional constraint of endpoint force emerges from hindlimb anatomy

Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb.

The brain in its body: motor control and sensing in a biomechanical context

Although it is widely recognized that adaptive behavior emerges from the ongoing interactions among the nervous system, the body, and the environment, it has only become possible in recent years to experimentally study and to simulate these interacting systems. We briefly review work on molluscan feeding, maintenance of postural control in cats and humans, simulations of locomotion in lamprey, insect, cat and salamander, and active vibrissal sensing in rats to illustrate the insights that can be derived from studies of neural control and sensing within a biomechanical context. These studies illustrate that control may be shared between the nervous system and the periphery, that neural activity organizes degrees of freedom into biomechanically meaningful subsets, that mechanics alone may play crucial roles in enforcing gait patterns, and that mechanics of sensors is crucial for their function.

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.

A feedback model reproduces muscle activity during human postural responses to support-surface translations

Although feedback models have been used to simulate body motions in human postural control, it is not known whether muscle activation patterns generated by the nervous system during postural responses can also be explained by a feedback control process. We investigated whether a simple feedback law could explain temporal patterns of muscle activation in response to support-surface translations in human subjects. Previously, we used a single-link inverted-pendulum model with a delayed feedback controller to reproduce temporal patterns of muscle activity during postural responses in cats. We scaled this model to human dimensions and determined whether it could reproduce human muscle activity during forward and backward support-surface perturbations. Through optimization, we found three feedback gains (on pendulum acceleration, velocity, and displacement) and a common time delay that allowed the model to best match measured electromyographic (EMG) signals. For each muscle and each subject, the entire time courses of EMG signals during postural responses were well reconstructed in muscles throughout the lower body and resembled the solution derived from an optimal control model. In ankle muscles, >75% of the EMG variability was accounted for by model reconstructions. Surprisingly, >67% of the EMG variability was also accounted for in knee, hip, and pelvis muscles, even though motion at these joints was minimal. Although not explicitly required by our optimization, pendulum kinematics were well matched to subject center-of-mass (CoM) kinematics. Together, these results suggest that a common set of feedback signals related to task-level control of CoM motion is used in the temporal formation of muscle activity during postural control.

Neuromechanics of muscle synergies for posture and movement

Recent research suggests that the nervous system controls muscles by activating flexible combinations of muscle synergies to produce a wide repertoire of movements. Muscle synergies are like building blocks, defining characteristic patterns of activation across multiple muscles that may be unique to each individual, but perform similar functions. The identification of muscle synergies has strong implications for the organization and structure of the nervous system, providing a mechanism by which task-level motor intentions are translated into detailed, low-level muscle activation patterns. Understanding the complex interplay between neural circuits and biomechanics that give rise to muscle synergies will be crucial to advancing our understanding of neural control mechanisms for movement.

Optimal sensorimotor transformations for balance

Here we have identified a sensorimotor transformation that is used by a mammalian nervous system to produce a multijoint motor behavior. Using a simple biomechanical model, a delayed-feedback rule based on an optimal tradeoff between postural error and neural effort explained patterns of muscle activation in response to a sudden loss of balance in cats. Following the loss of large sensory afferents, changes in these muscle-activation patterns reflected an optimal reweighting of sensory feedback gains to minimize postural instability. Specifically, a loss of center-of-mass-acceleration information, which allowed for a rapid initial rise in the muscle activity in intact animals, was absent after large-fiber sensory neuropathy. Our results demonstrate that a simple and flexible neural feedback control strategy coordinates multiple muscles over time via a small set of extrinsic, task-level variables during complex multijoint natural movements.