Optimal sensorimotor transformations for balance

Probabilistic Movement Models Show that Postural Control Precedes and Predicts Volitional Motor Control

Human motor skill learning is driven by the necessity to adapt to new situations. While supportive contacts are essential for many tasks, little is known about their impact on motor learning. To study the effect of contacts an innovative full-body experimental paradigm was established. The task of the subjects was to reach for a distant target while postural stability could only be maintained by establishing an additional supportive hand contact. To examine adaptation, non-trivial postural perturbations of the subjects’ support base were systematically introduced. A novel probabilistic trajectory model approach was employed to analyze the correlation between the motions of both arms and the trunk. We found that subjects adapted to the perturbations by establishing target dependent hand contacts. Moreover, we found that the trunk motion adapted significantly faster than the motion of the arms. However, the most striking finding was that observations of the initial phase of the left arm or trunk motion (100–400 ms) were sufficient to faithfully predict the complete movement of the right arm. Overall, our results suggest that the goal-directed arm movements determine the supportive arm motions and that the motion of heavy body parts adapts faster than the light arms.

A Probabilistic Analysis of Muscle Force Uncertainty for Control

BACKGROUND

We control the movements of our body and limbs through our muscles. However, the forces produced by our muscles depend unpredictably on the commands sent to them. This uncertainty has two sources: irreducible noise in the motor system's processes (i.e., motor noise) and variability in the relationship between muscle commands and muscle outputs (i.e., model uncertainty). Any controller, neural or artificial, benefits from estimating these uncertainties when choosing commands.

METHODS

To examine these benefits, we used an experimental preparation of the rat hindlimb to electrically stimulate muscles and measure the resulting isometric forces. We compare a functional electric stimulation (FES) controller that represents and compensates for uncertainty in muscle forces with a standard FES controller that neglects uncertainty.

RESULTS

Accounting for uncertainty substantially increased the precision of force control.

CONCLUSION

Our study demonstrates the theoretical and practical benefits of representing muscle uncertainty when computing muscle commands.

SIGNIFICANCE

The findings are relevant beyond FES as they highlight the benefits of estimating statistical properties of muscles for both artificial controllers and the nervous system.

Suboptimal Muscle Synergy Activation Patterns Generalize their Motor Function across Postures

We used a musculoskeletal model to investigate the possible biomechanical and neural bases of using consistent muscle synergy patterns to produce functional motor outputs across different biomechanical conditions, which we define as generalizability. Experimental studies in cats demonstrate that the same muscle synergies are used during reactive postural responses at widely varying configurations, producing similarly-oriented endpoint force vectors with respect to the limb axis. However, whether generalizability across postures arises due to similar biomechanical properties or to neural selection of a particular muscle activation pattern has not been explicitly tested. Here, we used a detailed cat hindlimb model to explore the set of feasible muscle activation patterns that produce experimental synergy force vectors at a target posture, and tested their generalizability by applying them to different test postures. We used three methods to select candidate muscle activation patterns: (1) randomly-selected feasible muscle activation patterns, (2) optimal muscle activation patterns minimizing muscle effort at a given posture, and (3) generalizable muscle activation patterns that explicitly minimized deviations from experimentally-identified synergy force vectors across all postures. Generalizability was measured by the deviation between the simulated force direction of the candidate muscle activation pattern and the experimental synergy force vectors at the test postures. Force angle deviations were the greatest for the randomly selected feasible muscle activation patterns (e.g., >100°), intermediate for effort-wise optimal muscle activation patterns (e.g., ~20°), and smallest for generalizable muscle activation patterns (e.g., <5°). Generalizable muscle activation patterns were suboptimal in terms of effort, often exceeding 50% of the maximum possible effort (cf. ~5% in minimum-effort muscle activation patterns). The feasible muscle activation ranges of individual muscles associated with producing a specific synergy force vector was reduced by ~45% when generalizability requirements were imposed. Muscles recruited in the generalizable muscle activation patterns had less sensitive torque-producing characteristics to changes in postures. We conclude that generalization of function across postures does not arise from limb biomechanics or a single optimality criterion. Muscle synergies may reflect acquired motor solutions globally tuned for generalizability across biomechanical contexts, facilitating rapid motor adaptation.

Human upright posture control models based on multisensory inputs; in fast and slow dynamics

Posture control to maintain an upright stance is one of the most important and basic requirements in the daily life of humans. The sensory inputs involved in posture control include visual and vestibular inputs, as well as proprioceptive and tactile somatosensory inputs. These multisensory inputs are integrated to represent the body state (body schema); this is then utilized in the brain to generate the motion. Changes in the multisensory inputs result in postural alterations (fast dynamics), as well as long-term alterations in multisensory integration and posture control itself (slow dynamics). In this review, we discuss the fast and slow dynamics, with a focus on multisensory integration including an introduction of our study to investigate "internal force control" with multisensory integration-evoked posture alteration. We found that the study of the slow dynamics is lagging compared to that of fast dynamics, such that our understanding of long-term alterations is insufficient to reveal the underlying mechanisms and to propose suitable models. Additional studies investigating slow dynamics are required to expand our knowledge of this area, which would support the physical training and rehabilitation of elderly and impaired persons.

Cerebral Hemodynamic Responses During Dynamic Posturography: Analysis with a Multichannel Near-Infrared Spectroscopy System

To investigate cortical roles in standing balance, cortical hemodynamic activity was recorded from the right hemisphere using near-infrared spectroscopy (NIRS) while subjects underwent the sensory organization test (SOT) protocol that systematically disrupts sensory integration processes (i.e., somatosensory or visual inputs or both). Eleven healthy men underwent the SOT during NIRS recording. Group statistical analyses were performed based on changes in oxygenated hemoglobin concentration in 10 different cortical regions of interest and on a general linear analysis with NIRS statistical parametric mapping. The statistical analyses indicated significant activation in the right frontal operculum (f-Op), right parietal operculum (p-Op), and right superior temporal gyrus (STG), right posterior parietal cortex (PPC), right dorsal and ventral premotor cortex (PMC), and the supplementary motor area (SMA) under various conditions. The activation patterns in response to specific combinations of SOT conditions suggested that (1) f-Op, p-Op, and STG are essential for sensory integration when standing balance is perturbed; (2) the SMA is involved in the execution of volitional action and establishment of new motor programs to maintain postural balance; and (3) the PPC and PMC are involved in the updating and computation of spatial reference frames during instances of sensory conflict between vestibular and visual information.

A model-based approach to predict muscle synergies using optimization: application to feedback control

This paper presents a new model-based method to define muscle synergies. Unlike the conventional factorization approach, which extracts synergies from electromyographic data, the proposed method employs a biomechanical model and formally defines the synergies as the solution of an optimal control problem. As a result, the number of required synergies is directly related to the dimensions of the operational space. The estimated synergies are posture-dependent, which correlate well with the results of standard factorization methods. Two examples are used to showcase this method: a two-dimensional forearm model, and a three-dimensional driver arm model. It has been shown here that the synergies need to be task-specific (i.e., they are defined for the specific operational spaces: the elbow angle and the steering wheel angle in the two systems). This functional definition of synergies results in a low-dimensional control space, in which every force in the operational space is accurately created by a unique combination of synergies. As such, there is no need for extra criteria (e.g., minimizing effort) in the process of motion control. This approach is motivated by the need for fast and bio-plausible feedback control of musculoskeletal systems, and can have important implications in engineering, motor control, and biomechanics.

Standing still: is there a role for the cortex?

In humans, standing still appears so automatic that high-level cortical processes seem unnecessary. However, by measuring cortical activity time-locked to reactive control events arising from naturally occurring instability while standing still, we detected cortical involvement in the form of an evoked N1 potential prior to the onset of balance reactions. Peak amplitude and spectral power of this event-related activity increased as postural challenges and demand for reactive control increased.

Are movement disorders and sensorimotor injuries pathologic synergies? When normal multi-joint movement synergies become pathologic

The intact nervous system has an exquisite ability to modulate the activity of multiple muscles acting at one or more joints to produce an enormous range of actions. Seemingly simple tasks, such as reaching for an object or walking, in fact rely on very complex spatial and temporal patterns of muscle activations. Neurological disorders such as stroke and focal dystonia affect the ability to coordinate multi-joint movements. This article reviews the state of the art of research of muscle synergies in the intact and damaged nervous system, their implications for recovery and rehabilitation, and proposes avenues for research aimed at restoring the nervous system’s ability to control movement.

Neck proprioception shapes body orientation and perception of motion

This review article deals with some effects of neck muscle proprioception on human balance, gait trajectory, subjective straight-ahead (SSA), and self-motion perception. These effects are easily observed during neck muscle vibration, a strong stimulus for the spindle primary afferent fibers. We first remind the early findings on human balance, gait trajectory, SSA, induced by limb, and neck muscle vibration. Then, more recent findings on self-motion perception of vestibular origin are described. The use of a vestibular asymmetric yaw-rotation stimulus for emphasizing the proprioceptive modulation of motion perception from the neck is mentioned. In addition, an attempt has been made to conjointly discuss the effects of unilateral neck proprioception on motion perception, SSA, and walking trajectory. Neck vibration also induces persistent aftereffects on the SSA and on self-motion perception of vestibular origin. These perceptive effects depend on intensity, duration, side of the conditioning vibratory stimulation, and on muscle status. These effects can be maintained for hours when prolonged high-frequency vibration is superimposed on muscle contraction. Overall, this brief outline emphasizes the contribution of neck muscle inflow to the construction and fine-tuning of perception of body orientation and motion. Furthermore, it indicates that tonic neck-proprioceptive input may induce persistent influences on the subject's mental representation of space. These plastic changes might adapt motion sensitiveness to lasting or permanent head positional or motor changes.

Mini-max feedback control as a computational theory of sensorimotor control in the presence of structural uncertainty

We propose a mini-max feedback control (MMFC) model as a robust approach to human motor control under conditions of uncertain dynamics, such as structural uncertainty. The MMFC model is an expansion of the optimal feedback control (OFC) model. According to this scheme, motor commands are generated to minimize the maximal cost, based on an assumption of worst-case uncertainty, characterized by familiarity with novel dynamics. We simulated linear dynamic systems with different types of force fields–stable and unstable dynamics–and compared the performance of MMFC to that of OFC. MMFC delivered better performance than OFC in terms of stability and the achievement of tasks. Moreover, the gain in positional feedback with the MMFC model in the unstable dynamics was tuned to the direction of instability. It is assumed that the shape modulations of the gain in positional feedback in unstable dynamics played the same role as that played by end-point stiffness observed in human studies. Accordingly, we suggest that MMFC is a plausible model that predicts motor behavior under conditions of uncertain dynamics.

Perspectives on human-human sensorimotor interactions for the design of rehabilitation robots

Physical interactions between patients and therapists during rehabilitation have served as motivation for the design of rehabilitation robots, yet we lack a fundamental understanding of the principles governing such human-human interactions (HHI). Here we review the literature and pose important open questions regarding sensorimotor interaction during HHI that could facilitate the design of human-robot interactions (HRI) and haptic interfaces for rehabilitation. Based on the goals of physical rehabilitation, three subcategories of sensorimotor interaction are identified: sensorimotor collaboration, sensorimotor assistance, and sensorimotor education. Prior research has focused primarily on sensorimotor collaboration and is generally limited to relatively constrained visuomotor tasks. Moreover, the mechanisms by which performance improvements are achieved during sensorimotor cooperation with haptic interaction remains unknown. We propose that the effects of role assignment, motor redundancy, and skill level in sensorimotor cooperation should be explicitly studied. Additionally, the importance of haptic interactions may be better revealed in tasks that do not require visual feedback. Finally, cooperative motor tasks that allow for motor improvement during solo performance to be examined may be particularly relevant for rehabilitation robotics. Identifying principles that guide human-human sensorimotor interactions may lead to the development of robots that can physically interact with humans in more intuitive and biologically inspired ways, thereby enhancing rehabilitation outcomes.

Mechanisms of motor adaptation in reactive balance control

Balance control must be rapidly modified to provide stability in the face of environmental challenges. Although changes in reactive balance over repeated perturbations have been observed previously, only anticipatory postural adjustments preceding voluntary movements have been studied in the framework of motor adaptation and learning theory. Here, we hypothesized that adaptation occurs in task-level balance control during responses to perturbations due to central changes in the control of both anticipatory and reactive components of balance. Our adaptation paradigm consisted of a Training set of forward support-surface perturbations, a Reversal set of novel countermanding perturbations that reversed direction, and a Washout set identical to the Training set. Adaptation was characterized by a change in a motor variable from the beginning to the end of each set, the presence of aftereffects at the beginning of the Washout set when the novel perturbations were removed, and a return of the variable at the end of the Washout to a level comparable to the end of the Training set. Task-level balance performance was characterized by peak center of mass (CoM) excursion and velocity, which showed adaptive changes with repetitive trials. Only small changes in anticipatory postural control, characterized by body lean and background muscle activity were observed. Adaptation was found in the evoked long-latency muscular response, and also in the sensorimotor transformation mediating that response. Finally, in each set, temporal patterns of muscle activity converged towards an optimum predicted by a trade-off between maximizing motor performance and minimizing muscle activity. Our results suggest that adaptation in balance, as well as other motor tasks, is mediated by altering central sensitivity to perturbations and may be driven by energetic considerations.

Visual reliance for balance control in older adults persists when visual information is disrupted by artificial feedback delays

Sensory information from our eyes, skin and muscles helps guide and correct balance. Less appreciated, however, is that delays in the transmission of sensory information between our eyes, limbs and central nervous system can exceed several 10s of milliseconds. Investigating how these time-delayed sensory signals influence balance control is central to understanding the postural system. Here, we investigate how delayed visual feedback and cognitive performance influence postural control in healthy young and older adults. The task required that participants position their center of pressure (COP) in a fixed target as accurately as possible without visual feedback about their COP location (eyes-open balance), or with artificial time delays imposed on visual COP feedback. On selected trials, the participants also performed a silent arithmetic task (cognitive dual task). We separated COP time series into distinct frequency components using low and high-pass filtering routines. Visual feedback delays affected low frequency postural corrections in young and older adults, with larger increases in postural sway noted for the group of older adults. In comparison, cognitive performance reduced the variability of rapid center of pressure displacements in young adults, but did not alter postural sway in the group of older adults. Our results demonstrate that older adults prioritize vision to control posture. This visual reliance persists even when feedback about the task is delayed by several hundreds of milliseconds.

Quantifying control effort of biological and technical movements: an information-entropy-based approach

In biomechanics and biorobotics, muscles are often associated with reduced movement control effort and simplified control compared to technical actuators. This is based on evidence that the nonlinear muscle properties positively influence movement control. It is, however, open how to quantify the simplicity aspect of control effort and compare it between systems. Physical measures, such as energy consumption, stability, or jerk, have already been applied to compare biological and technical systems. Here a physical measure of control effort based on information entropy is presented. The idea is that control is simpler if a specific movement is generated with less processed sensor information, depending on the control scheme and the physical properties of the systems being compared. By calculating the Shannon information entropy of all sensor signals required for control, an information cost function can be formulated allowing the comparison of models of biological and technical control systems. Exemplarily applied to (bio-)mechanical models of hopping, the method reveals that the required information for generating hopping with a muscle driven by a simple reflex control scheme is only I=32 bits versus I=660 bits with a DC motor and a proportional differential controller. This approach to quantifying control effort captures the simplicity of a control scheme and can be used to compare completely different actuators and control approaches.

Movement variability near goal equivalent manifolds: fluctuations, control, and model-based analysis

Fluctuations in the repeated performance of human movements have been the subject of intense scrutiny because they are generally believed to contain important information about the function and health of the neuromotor system. A variety of approaches has been brought to bear to study these fluctuations. However it is frequently difficult to understand how to synthesize different perspectives to give a coherent picture. Here, we describe a conceptual framework for the experimental study of motor variability that helps to unify geometrical methods, which focus on the role of motor redundancy, with dynamical methods that characterize the error-correcting processes regulating the performance of skilled tasks. We describe how goal functions, which mathematically specify the task strategy being employed, together with ideas from the control of redundant systems, allow one to formulate simple, experimentally testable dynamical models of inter-trial fluctuations. After reviewing the basic theory, we present a list of five general hypotheses on the structure of fluctuations that can be expected in repeated trials of goal-directed tasks. We review recent experimental applications of this general approach, and show how it can be used to precisely characterize the error-correcting control used by human subjects.

Contribution of vision to postural behaviors during continuous support-surface translations

During standing balance, kinematics of postural behaviors have been previously observed to change across visual conditions, perturbation amplitudes, or perturbation frequencies. However, experimental limitations only allowed for independent investigation of such parameters. Here, we adapted a pseudorandom ternary sequence (PRTS) perturbation previously used in rotational support-surface perturbations (Peterka in J Neurophysiol 88(3):1097-1118, 2002) to a translational paradigm, allowing us to concurrently examine the effects of vision, perturbation amplitude, and frequency on balance control. Additionally, the unpredictable PRTS perturbation eliminated effects of feedforward adaptations typical of responses to sinusoidal stimuli. The PRTS perturbation contained a wide spectral bandwidth (0.08-3.67 Hz) and was scaled to 4 different peak-to-peak amplitudes (3-24 cm). Root mean square (RMS) of hip displacement and velocity increased relative to RMS ankle displacement and velocity in the absence of vision across all subjects, especially at higher perturbation amplitudes. Gain and phase lag of center of mass (CoM) sway relative to the perturbation also increased with perturbation frequency; phase lag further increased when vision was absent. Together, our results suggest that visual input, perturbation amplitude, and perturbation frequency can concurrently and independently modulate postural strategies during standing balance. Moreover, each factor contributes to the difficulty of maintaining postural stability; increased difficulty evokes a greater reliance on hip motion. Finally, despite high degrees of joint angle variation across subjects, CoM measures were relatively similar across subjects, suggesting that the CoM is an important controlled variable for balance.

A unifying model of concurrent spatial and temporal modularity in muscle activity

Modularity in the central nervous system (CNS), i.e., the brain capability to generate a wide repertoire of movements by combining a small number of building blocks ("modules"), is thought to underlie the control of movement. Numerous studies reported evidence for such a modular organization by identifying invariant muscle activation patterns across various tasks. However, previous studies relied on decompositions differing in both the nature and dimensionality of the identified modules. Here, we derive a single framework that encompasses all influential models of muscle activation modularity. We introduce a new model (named space-by-time decomposition) that factorizes muscle activations into concurrent spatial and temporal modules. To infer these modules, we develop an algorithm, referred to as sample-based nonnegative matrix trifactorization (sNM3F). We test the space-by-time decomposition on a comprehensive electromyographic dataset recorded during execution of arm pointing movements and show that it provides a low-dimensional yet accurate, highly flexible and task-relevant representation of muscle patterns. The extracted modules have a well characterized functional meaning and implement an efficient trade-off between replication of the original muscle patterns and task discriminability. Furthermore, they are compatible with the modules extracted from existing models, such as synchronous synergies and temporal primitives, and generalize time-varying synergies. Our results indicate the effectiveness of a simultaneous but separate condensation of spatial and temporal dimensions of muscle patterns. The space-by-time decomposition accommodates a unified view of the hierarchical mapping from task parameters to coordinated muscle activations, which could be employed as a reference framework for studying compositional motor control.

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.

Motor primitives and synergies in the spinal cord and after injury--the current state of play

Modular pattern generator elements, also known as burst synergies or motor primitives, have become a useful and important way of describing motor behavior, albeit controversial. It is suggested that these synergy elements may constitute part of the pattern-shaping layers of a McCrea/Rybak two-layer pattern generator, as well as being used in other ways in the spinal cord. The data supporting modular synergies range across species including humans and encompass motor pattern analyses and neural recordings. Recently, synergy persistence and changes following clinical trauma have been presented. These new data underscore the importance of understanding the modular structure of motor behaviors and the underlying circuitry to best provide principled therapies and to understand phenomena reported in the clinic. We discuss the evidence and different viewpoints on modularity, the neural underpinnings identified thus far, and possible critical issues for the future of this area.

Interfacing sensory input with motor output: does the control architecture converge to a serial process along a single channel?

Modular organization in control architecture may underlie the versatility of human motor control; but the nature of the interface relating sensory input through task-selection in the space of performance variables to control actions in the space of the elemental variables is currently unknown. Our central question is whether the control architecture converges to a serial process along a single channel? In discrete reaction time experiments, psychologists have firmly associated a serial single channel hypothesis with refractoriness and response selection [psychological refractory period (PRP)]. Recently, we developed a methodology and evidence identifying refractoriness in sustained control of an external single degree-of-freedom system. We hypothesize that multi-segmental whole-body control also shows refractoriness. Eight participants controlled their whole body to ensure a head marker tracked a target as fast and accurately as possible. Analysis showed enhanced delays in response to stimuli with close temporal proximity to the preceding stimulus. Consistent with our preceding work, this evidence is incompatible with control as a linear time invariant process. This evidence is consistent with a single-channel serial ballistic process within the intermittent control paradigm with an intermittent interval of around 0.5 s. A control architecture reproducing intentional human movement control must reproduce refractoriness. Intermittent control is designed to provide computational time for an online optimization process and is appropriate for flexible adaptive control. For human motor control we suggest that parallel sensory input converges to a serial, single channel process involving planning, selection, and temporal inhibition of alternative responses prior to low dimensional motor output. Such design could aid robots to reproduce the flexibility of human control.

Common muscle synergies for balance and walking

Little is known about the integration of neural mechanisms for balance and locomotion. Muscle synergies have been studied independently in standing balance and walking, but not compared. Here, we hypothesized that reactive balance and walking are mediated by a common set of lower-limb muscle synergies. In humans, we examined muscle activity during multidirectional support-surface perturbations during standing and walking, as well as unperturbed walking at two speeds. We show that most muscle synergies used in perturbations responses during standing were also used in perturbation responses during walking, suggesting common neural mechanisms for reactive balance across different contexts. We also show that most muscle synergies using in reactive balance were also used during unperturbed walking, suggesting that neural circuits mediating locomotion and reactive balance recruit a common set of muscle synergies to achieve task-level goals. Differences in muscle synergies across conditions reflected differences in the biomechanical demands of the tasks. For example, muscle synergies specific to walking perturbations may reflect biomechanical challenges associated with single limb stance, and muscle synergies used during sagittal balance recovery in standing but not walking were consistent with maintaining the different desired center of mass motions in standing vs. walking. Thus, muscle synergies specifying spatial organization of muscle activation patterns may define a repertoire of biomechanical subtasks available to different neural circuits governing walking and reactive balance and may be recruited based on task-level goals. Muscle synergy analysis may aid in dissociating deficits in spatial vs. temporal organization of muscle activity in motor deficits. Muscle synergy analysis may also provide a more generalizable assessment of motor function by identifying whether common modular mechanisms are impaired across the performance of multiple motor tasks.

Acceleration feedback improves balancing against reflex delay

A model for human postural balance is considered in which the time-delayed feedback depends on position, velocity and acceleration (proportional-derivative-acceleration (PDA) feedback). It is shown that a PDA controller is equivalent to a predictive controller, in which the prediction is based on the most recent information of the state, but the control input is not involved into the prediction. A PDA controller is superior to the corresponding proportional-derivative controller in the sense that the PDA controller can stabilize systems with approximately 40 per cent larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for detection by sensory receptors results in highly intermittent, complex oscillations that are a typical feature of human postural sway.

Contributions of phase resetting and interlimb coordination to the adaptive control of hindlimb obstacle avoidance during locomotion in rats: a simulation study

Obstacle avoidance during locomotion is essential for safe, smooth locomotion. Physiological studies regarding muscle synergy have shown that the combination of a small number of basic patterns produces the large part of muscle activities during locomotion and the addition of another pattern explains muscle activities for obstacle avoidance. Furthermore, central pattern generators in the spinal cord are thought to manage the timing to produce such basic patterns. In the present study, we investigated sensory-motor coordination for obstacle avoidance by the hindlimbs of the rat using a neuromusculoskeletal model. We constructed the musculoskeletal part of the model based on empirical anatomical data of the rat and the nervous system model based on the aforementioned physiological findings of central pattern generators and muscle synergy. To verify the dynamic simulation by the constructed model, we compared the simulation results with kinematic and electromyographic data measured during actual locomotion in rats. In addition, we incorporated sensory regulation models based on physiological evidence of phase resetting and interlimb coordination and examined their functional roles in stepping over an obstacle during locomotion. Our results show that the phase regulation based on interlimb coordination contributes to stepping over a higher obstacle and that based on phase resetting contributes to quick recovery after stepping over the obstacle. These results suggest the importance of sensory regulation in generating successful obstacle avoidance during locomotion.

Are muscle synergies useful for neural control?

The observation that the activity of multiple muscles can be well approximated by a few linear synergies is viewed by some as a sign that such low-dimensional modules constitute a key component of the neural control system. Here, we argue that the usefulness of muscle synergies as a control principle should be evaluated in terms of errors produced not only in muscle space, but also in task space. We used data from a force-aiming task in two dimensions at the wrist, using an electromyograms (EMG)-driven virtual biomechanics technique that overcomes typical errors in predicting force from recorded EMG, to illustrate through simulation how synergy decomposition inevitably introduces substantial task space errors. Then, we computed the optimal pattern of muscle activation that minimizes summed-squared muscle activities, and demonstrated that synergy decomposition produced similar results on real and simulated data. We further assessed the influence of synergy decomposition on aiming errors (AEs) in a more redundant system, using the optimal muscle pattern computed for the elbow-joint complex (i.e., 13 muscles acting in two dimensions). Because EMG records are typically not available from all contributing muscles, we also explored reconstructions from incomplete sets of muscles. The redundancy of a given set of muscles had opposite effects on the goodness of muscle reconstruction and on task achievement; higher redundancy is associated with better EMG approximation (lower residuals), but with higher AEs. Finally, we showed that the number of synergies required to approximate the optimal muscle pattern for an arbitrary biomechanical system increases with task-space dimensionality, which indicates that the capacity of synergy decomposition to explain behavior depends critically on the scope of the original database. These results have implications regarding the viability of muscle synergy as a putative neural control mechanism, and also as a control algorithm to restore movements.

The inflow of sensory information for the control of standing is graded and bidirectional

The control of upright standing is accomplished through the integration of different sources of sensory information and by providing an appropriate motor program to control both expected and unexpected perturbations imposed on the system. However, the dynamic characteristics of postural sway and its interplay with the regulation of Ia sensory information within the spinal cord are largely unknown. Here, using a stochastic technique for analyzing the dynamics of upright standing, we demonstrate that the changes in the dynamics of postural sway were accompanied by modulation of the soleus H-reflex during quiet standing. While the causality of this relation was not established, the results showed that these changes were independent of the sway of the center of pressure and were bidirectional and purposeful. With this novel perspective, the appropriate reflex gain, which is important for balance control, can be predicted from the dynamic characteristics of postural sway. Our current findings provide the first human behavioral evidence to suggest the contribution of the spinal cord in fulfilling the desired motor programming of a complex task. This contribution is, by conventional guess, carried out through interneuronal adjustments, which are under the control of different brain areas.

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.

Frequency-domain identification of the human controller

System identification techniques applied to experimental human-in-the-loop data provide an objective test of three alternative control-theoretical models of the human control system: non-predictive control, predictive control, and intermittent predictive control. A two-stage approach to the identification of a single-input single-output control system is used: first, the closed-loop frequency response is derived using the periodic property of the experimental data, followed by the fitting of a parametric model. While this approach is well-established for non-predictive and predictive control, it is here used for the first time with intermittent predictive control. This technique is applied to data from experiments with human volunteers who use one of two control strategies, focusing either on position or on velocity, to manually control a virtual, unstable load which requires sustained feedback to maintain position or low velocity. The results show firstly that the non-predictive controller does not fit the data as well as the other two models, and secondly that the predictive and intermittent predictive controllers provide equally good models which cannot be distinguished using this approach. Importantly, the second observation implies that sustained visual manual control is compatible with intermittent control, and that previous results suggesting a continuous control model for the human control system do not rule out intermittent control as an alternative hypothesis. Thirdly, the parameters identified reflect the control strategy adopted by the human controller.

Energy margins in dynamic object manipulation

Many tasks require humans to manipulate dynamically complex objects and maintain appropriate safety margins, such as placing a cup of coffee on a coaster without spilling. This study examined how humans learn such safety margins and how they are shaped by task constraints and changing variability with improved skill. Eighteen subjects used a manipulandum to transport a shallow virtual cup containing a ball to a target without losing the ball. Half were to complete the cup transit in a comfortable target time of 2 s (a redundant task with infinitely many equivalent solutions), and the other half in minimum time (a nonredundant task with one explicit cost to optimize). The safety margin was defined as the ball energy relative to escape, i.e., as an energy margin. The first hypothesis, that subjects converge to a single strategy in the minimum-time task but choose different strategies in the less constrained target-time task, was not supported. Both groups developed individualized strategies with practice. The second hypothesis, that subjects decrease safety margins in the minimum-time task but increase them in the target-time task, was supported. The third hypothesis, that in both tasks subjects modulate energy margins according to their execution variability, was partially supported. In the target-time group, changes in energy margins correlated positively with changes in execution variability; in the minimum-time group, such a relation was observed only at the end of practice, not across practice. These results show that when learning a redundant object manipulation task, most subjects increase their safety margins and shape their movement strategies in accordance with their changing variability.

Muscle coordination is habitual rather than optimal

When sharing load among multiple muscles, humans appear to select an optimal pattern of activation that minimizes costs such as the effort or variability of movement. How the nervous system achieves this behavior, however, is unknown. Here we show that contrary to predictions from optimal control theory, habitual muscle activation patterns are surprisingly robust to changes in limb biomechanics. We first developed a method to simulate joint forces in real time from electromyographic recordings of the wrist muscles. When the model was altered to simulate the effects of paralyzing a muscle, the subjects simply increased the recruitment of all muscles to accomplish the task, rather than recruiting only the useful muscles. When the model was altered to make the force output of one muscle unusually noisy, the subjects again persisted in recruiting all muscles rather than eliminating the noisy one. Such habitual coordination patterns were also unaffected by real modifications of biomechanics produced by selectively damaging a muscle without affecting sensory feedback. Subjects naturally use different patterns of muscle contraction to produce the same forces in different pronation-supination postures, but when the simulation was based on a posture different from the actual posture, the recruitment patterns tended to agree with the actual rather than the simulated posture. The results appear inconsistent with computation of motor programs by an optimal controller in the brain. Rather, the brain may learn and recall command programs that result in muscle coordination patterns generated by lower sensorimotor circuitry that are functionally "good-enough."

Learning about gravity: segmental assessment of upright control as infants develop independent sitting

The question of how infants attain upright sitting is at the core of understanding the development of most functional abilities. Our simple, practical method of securing the hips and different trunk segments while evaluating the infant's ability to vertically align and stabilize the trunk in space contributes a useful method and new insights into the development of upright control. Previous studies have considered the trunk to develop as a single segment. The goal of the present study was to examine how postural control changes across multiple trunk segments during typical development (TD) of sitting balance. For this purpose, electromyography (EMG) and kinematic data were collected at four levels of trunk support (axillae, midribs, waist, hips), in a longitudinal study of eight TD infants (3-9 mo of age). We found that developmental changes in stability were specific to the region of the trunk being investigated, changes in antagonistic muscle activity differed for the anterior-posterior versus the medial-lateral axis, and the relationship between muscle activation and movement changed from erratic attempts to gain upright position to anticipatory graded responses as infants developed upright control through a four-stage behavioral process. This information can be used by researchers to further refine hypotheses regarding this developmental process and by clinicians who wish to develop and test more specific treatment programs for children with postural dysfunction.

Muscle spindle responses to horizontal support surface perturbation in the anesthetized cat: insights into the role of autogenic feedback in whole body postural control

Intact cats and humans respond to support surface perturbations with broadly tuned, directionally sensitive muscle activation. These muscle responses are further sensitive to initial stance widths (distance between feet) and perturbation velocity. The sensory origins driving these responses are not known, and conflicting hypotheses are prevalent in the literature. We hypothesize that the direction-, stance-width-, and velocity-sensitive muscle response during support surface perturbations is driven largely by rapid autogenic proprioceptive pathways. The primary objective of this study was to obtain direct evidence for our hypothesis by establishing that muscle spindle receptors in the intact limb can provide appropriate information to drive the muscle response to whole body postural perturbations. Our second objective was to determine if spindle recordings from the intact limb generate the heightened sensitivity to small perturbations that has been reported in isolated muscle experiments. Maintenance of this heightened sensitivity would indicate that muscle spindles are highly proficient at detecting even small disturbances, suggesting they can provide efficient feedback about changing postural conditions. We performed intraaxonal recordings from muscle spindles in anesthetized cats during horizontal, hindlimb perturbations. We indeed found that muscle spindle afferents in the intact limb generate broadly tuned but directionally sensitive activation patterns. These afferents were also sensitive to initial stance widths and perturbation velocities. Finally, we found that afferents in the intact limb have heightened sensitivity to small perturbations. We conclude that muscle spindle afferents provide an array of important information about biomechanics and perturbation characteristics highlighting their potential importance in generating appropriate muscular response during a postural disturbance.

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.

Somatosensory control of balance during locomotion in decerebrated cat

Postmammillary decerebrated cats can generate stepping on a moving treadmill belt when the brain stem or spinal cord is stimulated tonically and the hindquarters are supported both vertically and laterally. While adequate propulsion seems to be generated by the hindlimbs under these conditions, the ability to sustain equilibrium during locomotion has not been examined extensively. We found that tonic epidural spinal cord stimulation (5 Hz at L5) of decerebrated cats initiated and sustained unrestrained weight-bearing hindlimb stepping for extended periods. Detailed analyses of the relationships among hindlimb muscle EMG activity and trunk and limb kinematics and kinetics indicated that the motor circuitries in decerebrated cats actively maintain equilibrium during walking, similar to that observed in intact animals. Because of the suppression of vestibular, visual, and head-neck-trunk sensory input, balance-related adjustments relied entirely on the integration of somatosensory information arising from the moving hindquarters. In addition to dynamic balance control during unperturbed locomotion, sustained stepping could be reestablished rapidly after a collapse or stumble when the hindquarters switched from a restrained to an unrestrained condition. Deflecting the body by pulling the tail laterally induced adaptive modulations in the EMG activity, step cycle features, and left-right ground reaction forces that were sufficient to maintain lateral stability. Thus the brain stem-spinal cord circuitry of decerebrated cats in response to tonic spinal cord stimulation can control dynamic balance during locomotion using only somatosensory input.

Robustness of muscle synergies underlying three-dimensional force generation at the hand in healthy humans

Previous studies using advanced matrix factorization techniques have shown that the coordination of human voluntary limb movements may be accomplished using combinations of a small number of intermuscular coordination patterns, or muscle synergies. However, the potential use of muscle synergies for isometric force generation has been evaluated mostly using correlational methods. The results of such studies suggest that fixed relationships between the activations of pairs of muscles are relatively rare. There is also emerging evidence that the nervous system uses independent strategies to control movement and force generation, which suggests that one cannot conclude a priori that isometric force generation is accomplished by combining muscle synergies, as shown in movement control. In this study, we used non-negative matrix factorization to evaluate the ability of a few muscle synergies to reconstruct the activation patterns of human arm muscles underlying the generation of three-dimensional (3-D) isometric forces at the hand. Surface electromyographic (EMG) data were recorded from eight key elbow and shoulder muscles during 3-D force target-matching protocols performed across a range of load levels and hand positions. Four synergies were sufficient to explain, on average, 95% of the variance in EMG datasets. Furthermore, we found that muscle synergy composition was conserved across biomechanical task conditions, experimental protocols, and subjects. Our findings are consistent with the view that the nervous system can generate isometric forces by assembling a combination of a small number of muscle synergies, differentially weighted according to task constraints.

Variant and invariant features characterizing natural and reverse whole-body pointing movements

Previous investigations showed that kinematics and muscle activity associated with natural whole-body movements along the gravity direction present modular organizations encoding specific aspects relative to both the motor plans and the motor programmes underlying movement execution. It is, however, still unknown whether such modular structures characterize also the reverse movements, when the displacement of a large number of joints is required to take the whole body back to a standing initial posture. To study what motor patterns are conserved across the reversal of movement direction, principal component analysis and non-negative matrix factorization were therefore applied, respectively, to the time series describing the temporal evolution of the elevation angles associated with all the body links and to the electromyographic signals of both natural and reverse whole-body movements. Results revealed that elevation angles were highly co-varying in time and that despite some differences in the global parameters characterizing the different movements (indicating differences in high-level variable associated with the selected motor plans), the level of joint co-variation did not change across movement direction. In contrast, muscle organization of the forward whole-body pointing tasks was found to be different with respect to that characterizing the reverse movements. Such results agree with previous findings, according to which the central nervous system exploits, dependently on the direction of motion, different motor plans for the execution of whole-body movements. However, in addition, this study shows how such motor plans are translated into different muscle strategies that equivalently assure a high level of co-variation in the joint space.

Blood alcohol concentration at 0.06 and 0.10% causes a complex multifaceted deterioration of body movement control

Alcohol-related falls are recognized as a major contributor to the occurrence of traumatic brain injury. The control of upright standing balance is complex and composes of contributions from several partly independent mechanisms such as appropriate information from multiple sensory systems and correct feedback and feed forward movement control. Analysis of multisegmented body movement offers a rarely used option for detecting the fine motor problems associated with alcohol intoxication. The study aims were to investigate whether (1) alcohol intoxication at 0.06 and 0.10% blood alcohol concentration (BAC) affected the body movements under unperturbed and perturbed standing; and (2) alcohol affected the ability for sensorimotor adaptation. Body movements were recorded in 25 participants (13 women and 12 men, mean age 25.1 years) at five locations (ankle, knee, hip, shoulder, and head) during quiet standing and during balance perturbations from pseudorandom pulses of calf muscle vibration over 200s with eyes closed or open. Tests were performed at 0.00, 0.06, and 0.10% BAC. The study revealed several significant findings: (1) an alcohol dose-specific effect; (2) a direction-specific stability decrease from alcohol intoxication; (3) a movement pattern change related to the level of alcohol intoxication during unperturbed standing and perturbed standing; (4) a sensorimotor adaptation deterioration with increased alcohol intoxication; and (5) that vision provided a weaker contribution to postural control during alcohol intoxication. Hence, alcohol intoxication at 0.06 and 0.10% BAC causes a complex multifaceted deterioration of human postural control.

The delayed and noisy nervous system: implications for neural control

Recent advances in the study of delay differential equations draw attention to the potential benefits of the interplay between random perturbations ('noise') and delay in neural control. The phenomena include transient stabilizations of unstable steady states by noise, control of fast movements using time-delayed feedback and the occurrence of long-lived delay-induced transients. In particular, this research suggests that the interplay between noise and delay necessitates the use of intermittent, discontinuous control strategies in which corrective movements are made only when controlled variables cross certain thresholds. A potential benefit of such strategies is that they may be optimal for minimizing energy expenditures associated with control. In this paper, the concepts are made accessible by introducing them through simple illustrative examples that can be readily reproduced using software packages, such as XPPAUT.

Task-level feedback can explain temporal recruitment of spatially fixed muscle synergies throughout postural perturbations

Recent evidence suggests that complex spatiotemporal patterns of muscle activity can be explained with a low-dimensional set of muscle synergies or M-modes. While it is clear that both spatial and temporal aspects of muscle coordination may be low dimensional, constraints on spatial versus temporal features of muscle coordination likely involve different neural control mechanisms. We hypothesized that the low-dimensional spatial and temporal features of muscle coordination are independent of each other. We further hypothesized that in reactive feedback tasks, spatially fixed muscle coordination patterns-or muscle synergies-are hierarchically recruited via time-varying neural commands based on delayed task-level feedback. We explicitly compared the ability of spatially fixed (SF) versus temporally fixed (TF) muscle synergies to reconstruct the entire time course of muscle activity during postural responses to anterior-posterior support-surface translations. While both SF and TF muscle synergies could account for EMG variability in a postural task, SF muscle synergies produced more consistent and physiologically interpretable results than TF muscle synergies during postural responses to perturbations. Moreover, a majority of SF muscle synergies were consistent in structure when extracted from epochs throughout postural responses. Temporal patterns of SF muscle synergy recruitment were well-reconstructed by delayed feedback of center of mass (CoM) kinematics and reproduced EMG activity of multiple muscles. Consistent with the idea that independent and hierarchical low-dimensional neural control structures define spatial and temporal patterns of muscle activity, our results suggest that CoM kinematics are a task variable used to recruit SF muscle synergies for feedback control of balance.

Modules in the brain stem and spinal cord underlying motor behaviors

Previous studies using intact and spinalized animals have suggested that coordinated movements can be generated by appropriate combinations of muscle synergies controlled by the central nervous system (CNS). However, which CNS regions are responsible for expressing muscle synergies remains an open question. We address whether the brain stem and spinal cord are involved in expressing muscle synergies used for executing a range of natural movements. We analyzed the electromyographic (EMG) data recorded from frog leg muscles before and after transection at different levels of the neuraxis-rostral midbrain (brain stem preparations), rostral medulla (medullary preparations), and the spinal-medullary junction (spinal preparations). Brain stem frogs could jump, swim, kick, and step, while medullary frogs could perform only a partial repertoire of movements. In spinal frogs, cutaneous reflexes could be elicited. Systematic EMG analysis found two different synergy types: 1) synergies shared between pre- and posttransection states and 2) synergies specific to individual states. Almost all synergies found in natural movements persisted after transection at rostral midbrain or medulla but not at the spinal-medullary junction for swim and step. Some pretransection- and posttransection-specific synergies for a certain behavior appeared as shared synergies for other motor behaviors of the same animal. These results suggest that the medulla and spinal cord are sufficient for the expression of most muscle synergies in frog behaviors. Overall, this study provides further evidence supporting the idea that motor behaviors may be constructed by muscle synergies organized within the brain stem and spinal cord and activated by descending commands from supraspinal areas.

Modelling human balance using switched systems with linear feedback control

We are interested in understanding the mechanisms behind and the character of the sway motion of healthy human subjects during quiet standing. We assume that a human body can be modelled as a single-link inverted pendulum, and the balance is achieved using linear feedback control. Using these assumptions, we derive a switched model which we then investigate. Stable periodic motions (limit cycles) about an upright position are found. The existence of these limit cycles is studied as a function of system parameters. The exploration of the parameter space leads to the detection of multi-stability and homoclinic bifurcations.

Stability in a frontal plane model of balance requires coupled changes to postural configuration and neural feedback control

Postural stability depends on interactions between the musculoskeletal system and neural control mechanisms. We present a frontal plane model stabilized by delayed feedback to analyze the effects of altered stance width on postural responses to perturbations. We hypothesized that changing stance width alters the mechanical dynamics of the body and limits the range of delayed feedback gains that produce stable postural behaviors. Surprisingly, mechanical stability was found to decrease as stance width increased due to decreased effective inertia. Furthermore, due to sensorimotor delays and increased leverage of hip joint torque on center-of-mass motion, the magnitudes of the stabilizing delayed feedback gains decreased as stance width increased. Moreover, the ranges of the stable feedback gains were nonoverlapping across different stance widths such that using a single neural feedback control strategy at both narrow and wide stances could lead to instability. The set of stable feedback gains was further reduced by constraints on foot lift-off and perturbation magnitude. Simulations were fit to experimentally measured kinematics, and the identified feedback gains corroborated model predictions. In addition, analytical gain margin of the linearized system was found to predict step transitions without the need for simulation. In conclusion, this model offers a method to dissociate the complex interactions between postural configuration, delayed sensorimotor feedback, and nonlinear foot lift-off constraints. The model demonstrates that stability at wide stances can only be achieved if delayed neural feedback gains decrease. This model may be useful in explaining both expected and paradoxical changes in stance width in healthy and neurologically impaired individuals.