Neuromechanical tuning of nonlinear postural control dynamics

Nonlinear dynamics of postural control system under visual-vestibular habituation balance practice: evidence from EEG, EMG and center of pressure signals

Human postural control system is inherently complex with nonlinear interaction among multiple subsystems. Accordingly, such postural control system has the flexibility in adaptation to complex environments. Previous studies applied complexity-based methods to analyze center of pressure (COP) to explore nonlinear dynamics of postural sway under changing environments, but direct evidence from central nervous system or muscular system is limited in the existing literature. Therefore, we assessed the fractal dimension of COP, surface electromyographic (sEMG) and electroencephalogram (EEG) signals under visual-vestibular habituation balance practice. We combined a rotating platform and a virtual reality headset to present visual-vestibular congruent or incongruent conditions. We asked participants to undergo repeated exposure to either congruent (n = 14) or incongruent condition (n = 13) five times while maintaining balance. We found repeated practice under both congruent and incongruent conditions increased the complexity of high-frequency (0.5-20 Hz) component of COP data and the complexity of sEMG data from tibialis anterior muscle. In contrast, repeated practice under conflicts decreased the complexity of low-frequency (<0.5 Hz) component of COP data and the complexity of EEG data of parietal and occipital lobes, while repeated practice under congruent environment decreased the complexity of EEG data of parietal and temporal lobes. These results suggested nonlinear dynamics of cortical activity differed after balance practice under congruent and incongruent environments. Also, we found a positive correlation (1) between the complexity of high-frequency component of COP and the complexity of sEMG signals from calf muscles, and (2) between the complexity of low-frequency component of COP and the complexity of EEG signals. These results suggested the low- or high-component of COP might be related to central or muscular adjustment of postural control, respectively.

Assessing Postural Control From Birth to Adulthood Among Individuals Born Preterm: A Systematic Review

Premature life exposure, meaning an immature central nervous system, presents a significant challenge for the development of postural control and, in turn, overall motor development. Preventing motor delay thus requires identifying, characterizing, and quantifying deficit in postural control as early as possible. In our study, we reviewed the procedures used in past studies to assess postural control among individuals born preterm, specifically the characterization of participants, the instruments and motor tasks involved, the types of data collected and analyzed, and the outcomes. To that end, we performed a literature search on PubMed, Wiley Online Library, Web of Science, and Scopus using Boolean logic and assessed the quality of the studies with a standardized assessment based on the Strengthening the Reporting of Observational Studies in Epidemiology guidelines and the Cochrane Handbook for Systematic Reviews of Interventions. Of 35 potential studies, 24 were included; all evaluated infants born preterm, but six did not include a control group of full-term infants. Although the heterogeneity of measurements, variability of instruments, and divergence in motor tasks examined limit definitive conclusions based on quantitative synthesis and the generalization of the results, most studies revealed dysfunctional postural control among individuals born preterm.

Repetitive head impacts among professional fighters: a pilot study evaluating Traumatic Encephalopathy Syndrome and postural balance

OBJECTIVES

Clinical criteria for Traumatic Encephalopathy Syndrome (ccTES) were developed for research purposes to reflect the clinical symptoms of Chronic Traumatic Encephalopathy (CTE). The aims of this study were to 1) determine whether there was an association between the research diagnosis of TES and impaired postural balance among retired professional fighters, and 2) determine repetitive head impacts (RHI) exposure thresholds among both TES positive and TES negative groups in retired professional fighters when evaluating for balance impairment.

METHODS

This was a pilot study evaluating postural balance among participants of the Professional Athletes Brain Health Study (PABHS). Among the cohort, 57 retired professional fighters met the criteria for inclusion in this study. A generalized linear model with generalized estimating equations was used to compare various balance measures longitudinally between fighters with and without TES.

RESULTS

A significant association was observed between a TES diagnosis and worsening performance on double-leg balance assessments when stratifying by RHI exposure thresholds. Additionally, elevated exposure to RHI was significantly associated with increased odds of developing TES; The odds for TES diagnosis were 563% (95% CI = 113, 1963; p-value = 0.0011) greater among athletes with 32 or more professional fights compared to athletes with less than 32 fights when stratifying by balance measures. Likewise, the odds for TES diagnosis were 43% (95% CI = 10, 102; p-value = 0.0439) greater with worsening double leg stance balance in athletes exposed to 32 or more fights.

CONCLUSION

This pilot study provides preliminary evidence of a relationship between declining postural balance and a TES diagnosis among retired professional fighters with elevated RHI exposure. Further research exploring more complex assessments such as the Functional Gait Assessment may be of benefit to improve clinical understanding of the relationship between TES, RHI, and balance.

Mechanosensory encoding of forces in walking uphill and downhill: force feedback can stabilize leg movements in stick insects

Force feedback could be valuable in adapting walking to diverse terrains, but the effects of changes in substrate inclination on discharges of sensory receptors that encode forces have rarely been examined. In insects, force feedback is provided by campaniform sensilla, mechanoreceptors that monitor forces as cuticular strains. We neurographically recorded responses of stick insect tibial campaniform sensilla to "naturalistic" forces (joint torques) that occur at the hind leg femur-tibia (FT) joint in uphill, downhill, and level walking. The FT joint torques, obtained in a previous study that used inverse dynamics to analyze data from freely moving stick insects, are quite variable during level walking (including changes in sign) but are larger in magnitude and more consistent when traversing sloped surfaces. Similar to vertebrates, insects used predominantly extension torque in propulsion on uphill slopes and flexion torques to brake forward motion when going downhill. Sensory discharges to joint torques reflected the torque direction but, unexpectedly, often occurred as multiple bursts that encoded the rate of change of positive forces (dF/dt) even when force levels were high. All discharges also showed hysteresis (history dependence), as firing substantially decreased or ceased during transient force decrements. These findings have been tested in simulation in a mathematical model of the sensilla (Szczecinski NS, Dallmann CJ, Quinn RD, Zill SN. Bioinspir Biomim 16: 065001, 2021) that accurately reproduced the biological data. Our results suggest the hypothesis that sensory feedback from the femoro-tibial joint indicating force dynamics (dF/dt) can be used to counter the instability in traversing sloped surfaces in animals and, potentially, in walking machines.NEW & NOTEWORTHY Discharges of sensory receptors (campaniform sensilla) in the hind legs of stick insects can differentially signal forces that occur in walking uphill versus walking downhill. Unexpectedly, sensory firing most closely reflects the rate of change of force (dF/dt) even when the force levels are high. These signals have been replicated in a mathematical model of the receptors and could be used to stabilize leg movements both in the animal and in a walking robot.

Lower limb vertical stiffness and frontal plane angular impulse during perturbation-induced single limb stance and their associations with gait in individuals post-stroke

After stroke, deficits in paretic single limb stance (SLS) are commonly observed and affect walking performance. During SLS, the hip abductor musculature is critical in providing vertical support and regulating balance. Although disrupted paretic hip abduction torque production has been identified in individuals post-stroke, interpretation of previous results is limited due to the discrepancies in weight-bearing conditions. Using a novel perturbation-based assessment that could induce SLS by removing the support surface underneath one limb, we aim to investigate whether deficits in hip abduction torque production, vertical body support, and balance regulation remain detectable during SLS when controlling for weight-bearing, and whether these measures are associated with gait performance. Our results showed that during the perturbation-induced SLS, individuals post-stroke had lower hip abduction torque, less vertical stiffness, and increased frontal plane angular impulse at the paretic limb compared to the non-paretic limb, while no differences were found between the paretic limb and healthy controls. In addition, vertical stiffness during perturbation-induced SLS was positively correlated with single support duration during gait at the paretic limb and predicted self-selected and fast walking speeds in individuals post-stroke. The findings indicate that reduced paretic hip abduction torque during SLS likely affects vertical support and balance control. Enhancing SLS hip abduction torque production could be an important rehabilitation target to improve walking function for individuals post-stroke.

History-dependent muscle resistance to stretch remains high after small, posturally relevant pre-movements

The contributions of intrinsic muscle fiber resistance during mechanical perturbations to standing and other postural behaviors are unclear. Muscle short-range stiffness is known to vary depending on the current level and history of the muscle's activation, as well as the muscle's recent movement history; this property has been referred to as history dependence or muscle thixotropy. However, we currently lack sufficient data about the degree to which muscle stiffness is modulated across posturally relevant characteristics of muscle stretch and activation. We characterized the history dependence of muscle's resistance to stretch in single, permeabilized, activated, muscle fibers in posturally relevant stretch conditions and activation levels. We used a classic paired muscle stretch paradigm, varying the amplitude of a 'conditioning' triangular stretch-shorten cycle followed by a 'test' ramp-and-hold imposed after a variable inter-stretch interval. We tested low (<15%), intermediate (15-50%) and high (>50%) muscle fiber activation levels, evaluating short-range stiffness and total impulse in the test stretch. Muscle fiber resistance to stretch remained high at conditioning amplitudes of <1% optimal fiber length, L0, and inter-stretch intervals of >1 s, characteristic of healthy standing postural sway. An ∼70% attenuation of muscle resistance to stretch was reached at conditioning amplitudes of >3% L0 and inter-stretch intervals of <0.1 s, characteristic of larger, faster postural sway in balance-impaired individuals. The thixotropic changes cannot be predicted solely on muscle force at the time of stretch. Consistent with the disruption of muscle cross-bridges, muscle resistance to stretch during behavior can be substantially attenuated if the prior motion is large enough and/or frequent enough.

Assisting walking balance using a bio-inspired exoskeleton controller

BACKGROUND

Balance control is important for mobility, yet exoskeleton research has mainly focused on improving metabolic energy efficiency. Here we present a biomimetic exoskeleton controller that supports walking balance and reduces muscle activity.

METHODS

Humans restore balance after a perturbation by adjusting activity of the muscles actuating the ankle in proportion to deviations from steady-state center of mass kinematics. We designed a controller that mimics the neural control of steady-state walking and the balance recovery responses to perturbations. This controller uses both feedback from ankle kinematics in accordance with an existing model and feedback from the center of mass velocity. Control parameters were estimated by fitting the experimental relation between kinematics and ankle moments observed in humans that were walking while being perturbed by push and pull perturbations. This identified model was implemented on a bilateral ankle exoskeleton.

RESULTS

Across twelve subjects, exoskeleton support reduced calf muscle activity in steady-state walking by 19% with respect to a minimal impedance controller (p < 0.001). Proportional feedback of the center of mass velocity improved balance support after perturbation. Muscle activity is reduced in response to push and pull perturbations by 10% (p = 0.006) and 16% (p < 0.001) and center of mass deviations by 9% (p = 0.026) and 18% (p = 0.002) with respect to the same controller without center of mass feedback.

CONCLUSION

Our control approach implemented on bilateral ankle exoskeletons can thus effectively support steady-state walking and balance control and therefore has the potential to improve mobility in balance-impaired individuals.

Voluntary muscle coactivation in quiet standing elicits reciprocal rather than coactive agonist-antagonist control of reactive balance

Muscle coactivation increases in challenging balance conditions as well as with advanced age and mobility impairments. Increased muscle coactivation can occur both in anticipation of (feedforward) and in reaction to (feedback) perturbations, however, the causal relationship between feedforward and feedback muscle coactivation remains elusive. Here, we hypothesized that feedforward muscle coactivation would increase both the body's initial mechanical resistance due to muscle intrinsic properties and the later feedback-mediated muscle coactivation in response to postural perturbations. Young adults voluntarily increased leg muscle coactivation using visual biofeedback before support-surface perturbations. In contrast to our hypothesis, feedforward muscle coactivation did not increase the body's initial intrinsic resistance to perturbations, nor did it increase feedback muscle coactivation. Rather, perturbations with feedforward muscle coactivation elicited a medium- to long-latency increase of feedback-mediated agonist activity but a decrease of feedback-mediated antagonist activity. This reciprocal rather than coactivation effect on ankle agonist and antagonist muscles enabled faster reactive ankle torque generation, reduced ankle dorsiflexion, and reduced center of mass (CoM) motion. We conclude that in young adults, voluntary feedforward muscle coactivation can be independently modulated with respect to feedback-mediated muscle coactivation. Furthermore, our findings suggest feedforward muscle coactivation may be useful for enabling quicker joint torque generation through reciprocal, rather than coactivated, agonist-antagonist feedback muscle activity. As such our results suggest that behavioral context is critical to whether muscle coactivation functions to increase agility versus stability.NEW & NOTEWORTHY Feedforward and feedback muscle coactivation are commonly observed in older and mobility impaired adults and are considered strategies to improve stability by increasing body stiffness prior to and in response to perturbations. In young adults, voluntary feedforward coactivation does not necessarily increase feedback coactivation in response to perturbations. Instead, feedforward coactivation enabled faster ankle torques through reciprocal agonist-antagonist muscle activity. As such, coactivation may promote either agility or stability depending on the behavioral context.

Exoskeletons need to react faster than physiological responses to improve standing balance

Maintaining balance throughout daily activities is challenging because of the unstable nature of the human body. For instance, a person's delayed reaction times limit their ability to restore balance after disturbances. Wearable exoskeletons have the potential to enhance user balance after a disturbance by reacting faster than physiologically possible. However, "artificially fast" balance-correcting exoskeleton torque may interfere with the user's ensuing physiological responses, consequently hindering the overall reactive balance response. Here, we show that exoskeletons need to react faster than physiological responses to improve standing balance after postural perturbations. Delivering ankle exoskeleton torque before the onset of physiological reactive joint moments improved standing balance by 9%, whereas delaying torque onset to coincide with that of physiological reactive ankle moments did not. In addition, artificially fast exoskeleton torque disrupted the ankle mechanics that generate initial local sensory feedback, but the initial reactive soleus muscle activity was only reduced by 18% versus baseline. More variance of the initial reactive soleus muscle activity was accounted for using delayed and scaled whole-body mechanics [specifically center of mass (CoM) velocity] versus local ankle-or soleus fascicle-mechanics, supporting the notion that reactive muscle activity is commanded to achieve task-level goals, such as maintaining balance. Together, to elicit symbiotic human-exoskeleton balance control, device torque may need to be informed by mechanical estimates of global sensory feedback, such as CoM kinematics, that precede physiological responses.

Lifespan changes in postural control

Lifespan development of postural control shows as an inverted U-shaped function with optimal performance in young adults and similar levels of underperformance in children and older adults. However, similarities in children and older adults might conceal differences in underlying control processes. We mapped out age-related differences in postural control using center-of-pressure trajectories of 299 participants ranging from 7 to 81 years old in three tasks: stable stance, compromised vision, and narrowed base of support. Summary statistics (path length, ellipse area) replicated the well-known U-shape function also showing that compromising vision and narrowing the base of support affected older adults more than children. Stabilogram diffusion analysis (SDA) allows to assess postural control performance in terms of diffusion at short (< 1 s) and longer timescales. SDA parameters showed the strongest short-term drift in older adults, especially under compromised vision or narrowed base of support conditions. However, older adults accommodated their poor short-term control by corrective adjustments as reflected in long-term diffusion under eyes closed conditions and initiating anti-persistent behavior earlier compared with children and young adults in tandem stance. We argue that these results highlight the adaptability of the postural control system and warrant a reinterpretation of previous postural control frameworks.

Optimal controllers resembling postural sway during upright stance

The human postural control system can maintain our balance in an upright stance. A simplified control model that can mimic the mechanisms of this complex system and adapt to the changes due to aging and injuries is a significant problem that can be used in clinical applications. While the Intermittent Proportional Derivative (IPD) is commonly used as a postural sway model in the upright stance, it does not consider the predictability and adaptability behavior of the human postural control system and the physical limitations of the human musculoskeletal system. In this article, we studied the methods based on optimization algorithms that can mimic the performance of the postural sway controller in the upright stance. First, we compared three optimal methods (Model Predictive Control (MPC), COP-Based Controller (COP-BC) and Momentum-Based Controller (MBC)) in simulation by considering a feedback structure of the dynamic of the skeletal body as a double link inverted pendulum while taking into account sensory noise and neurological time delay. Second, we evaluated the validity of these methods by the postural sway data of ten subjects in quiet stance trials. The results revealed that the optimal methods could mimic the postural sway with higher accuracy and less energy consumption in the joints compared to the IPD method. Among optimal approaches, COP-BC and MPC show promising results to mimic the human postural sway. The choice of controller weights and parameters is a trade-off between the consumption of energy in the joints and the prediction accuracy. Therefore, the capability and (dis)advantage of each method reviewed in this article can navigate the usage of each controller in different applications of postural sway, from clinical assessments to robotic applications.

Perturbation-based balance training: Principles, mechanisms and implementation in clinical practice

Since the mid-2000s, perturbation-based balance training has been gaining interest as an efficient and effective way to prevent falls in older adults. It has been suggested that this task-specific training approach may present a paradigm shift in fall prevention. In this review, we discuss key concepts and common issues and questions regarding perturbation-based balance training. In doing so, we aim to provide a comprehensive synthesis of the current evidence on the mechanisms, feasibility and efficacy of perturbation-based balance training for researchers and practitioners. We address this in two sections: "Principles and Mechanisms" and "Implementation in Practice." In the first section, definitions, task-specificity, adaptation and retention mechanisms and the dose-response relationship are discussed. In the second section, issues related to safety, anxiety, evidence in clinical populations (e.g., Parkinson's disease, stroke), technology and training devices are discussed. Perturbation-based balance training is a promising approach to fall prevention. However, several fundamental and applied aspects of the approach need to be further investigated before it can be widely implemented in clinical practice.

Brain and muscle activation patterns during postural control affect static postural control

BACKGROUND

Previous studies have reported existence of coordinated brain and muscle activity patterns that affect postural control. However, differences in these activity patterns that affect postural control are still unclear. The purpose of this study was to clarify brain and muscle activity pattern affecting postural control.

RESEARCH QUESTION

Does the difference in brain and muscle activity patterns during postural control affect postural control ability?

METHOD

Nineteen healthy men (mean age: 24.8 ± 4.1 years, height: 171.8 ± 5.5 cm, and weight: 63.5 ± 12.5 kg) performed a postural control task on a balance board, and their brain and muscle activities and body sway during the task were measured using functional near-infrared spectroscopy, surface electromyography, and three-dimensional accelerometry. Hierarchical cluster analysis was conducted to extract subgroups based on brain and muscle activities and postural control, and correlation analysis was performed to investigate the relationship between brain activity, muscle activity, and postural control.

RESULTS

Two subgroups were found. Subgroup 1 (n = 9) showed higher brain activity in the supplementary motor area (p = 0.04), primary motor cortex (p = 0.04) and stable postural control in the mediolateral (p < 0.01) planes, and subgroup 2 (n = 10) showed higher muscle activity in the tibialis anterior (p < 0.01), a higher shank muscles co-contraction (p = 0.02) and unstable postural control. Furthermore, the supplementary motor area activity is negatively correlated with body sway of mediolateral plane (r = -0.51, p = 0.02), and tibialis anterior activity is positively correlated with body sway on the mediolateral plane (r = 0.62, p = 0.004).

SIGNIFICANCE

Higher brain activity in motor-related areas, lower activity in the lower limb muscles and lower co-contraction of shank muscles were observed in stable postural control. These results will facilitate the planning of new rehabilitation methods for improving postural control ability.

The deep hip muscles are unlikely to contribute to hip stability in the sagittal plane during walking: a stiffness approach

- Objective: This study determined whether the deep hip muscles could contribute to hip stability.

METHODS

Hip stability was defined as rotational hip stiffness in the sagittal plane, which was calculated for walking trials for 12 participants via electromyography (EMG)informed neuromusculoskeletal modelling that included all 22 hip spanning muscles. Three model configurations were compared that differed in the excitations of the deep hip muscles, but were identical in the excitations of all other muscles: (1) deep hip muscles informed by intramuscular EMG measurements (assisted activation); (2) deep hip muscles with simulated zero activation (no activation); (3) deep hip muscles with simulated maximal activation (maximal activation). Sagittal plane rotational hip stiffness over the gait cycle was compared between model configurations using a within-participant analysis of variance via statistical parametric mapping (p<0.05).

RESULTS

Compared to the assisted activation configuration, hip stiffness (mean (95% confidence interval)) was 0.8% (0.7 to 0.9) lower in the no activation configuration, and 3.2% (2.9 to 3.5) higher in the maximal activation configuration over the gait cycle.

CONCLUSION

Regardless of activation level, the deep hip muscles made little contribution to sagittal plane rotational hip stiffness, which casts uncertainty around their assumed function as hip stabilizers.

SIGNIFICANCE

The merit of targeted deep hip muscle strengthening to improve hip stability in rehabilitation programs for remains unclear.

Similar sensorimotor transformations control balance during standing and walking

Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.

The stability of human standing and walking is remarkable, given that from a mechanical point of view standing and walking are highly unstable and therefore require well-coordinated control actions from the central nervous system. The nervous system continuously receives information on the state of the body through sensory inputs, which is processed to generate descending motor commands to the muscles. It remains, however, unclear how the central nervous system uses information from multiple sensors to control walking balance. In standing balance, such sensorimotor transformations have been studied. When standing balance is perturbed, previous studies suggest that the central nervous system estimates the movement of the whole body center of mass to activate muscles and control balance. Here, we investigated whether the same sensorimotor transformations underlie control of walking balance. We found that changes in muscle activity and ankle moments in response to perturbations of walking balance were indeed proportional to center of mass movement. These findings suggest that common processes underlie control of standing and walking balance. Our work is significant because it captures the result of complex underlying neural processes in a simple relation between the body’s center of mass movement and corrective joint moments that can be implemented in the control of prostheses and exoskeletons to support balance control in a human-like manner.

Effects of footedness and stance asymmetry confirm an inter-leg metastable coordination dynamics of standing posture

We investigated the patterns of coordination between the left and right legs that support the task of maintaining an upright standing posture. We used cross-wavelet analyses to assess coordination between the centers of pressure under the left and right feet. We recruited participants with a lateralized functional preference for their right leg, and we manipulated whether these participants stood with symmetric/asymmetric stances and whether their eyes were open or closed. Our hypotheses were derived from the Haken-Kelso-Bunz (HKB) model of interlimb coordination dynamics. Consistent with HKB model predictions, we observed (1) coordination taking the form of metastable, transient epochs of stable phase relations, (2) preferences for in-phase and anti-phase coordination patterns, and (3) changes in pattern stability and phase leads associated with both stance asymmetry and right-side lateral preference. The form and stability of observed coordination patterns were mediated by the availability of visual information. Our findings confirm the existence of a metastable coordination dynamic associated with the task of maintaining upright stance. We discuss the implications of these findings in the context of evaluating the utility of the HKB model for understanding the functional organization of the posture system.

Role of muscle coactivation in adaptation of standing posture during arm reaching

The ability to maintain stable, upright standing in the face of perturbations is a critical component of daily life. A common strategy for resisting perturbations and maintaining stability is muscle coactivation. Although arm muscle coactivation is often used during adaptation of seated reaching movements, little is known about postural muscle activation during concurrent adaptation of arm and standing posture to novel perturbations. In this study we investigate whether coactivation strategies are employed during adaptation of standing postural control, and how these strategies are prioritized for adaptation of standing posture and arm reaching, in two different postural stability conditions. Healthy adults practiced planar reaching movements while grasping the handle of a robotic arm and standing on a force plate; the robotic arm generated a velocity-dependent force field that created novel perturbations in the forward (more stable) or backward (less stable) direction. Surprisingly, the degree of arm and postural adaptation was not influenced by stability, with similar adaptation observed between conditions in the control of both arm movement and standing posture. We found that an early coactivation strategy can be used in postural adaptation, similar to what is observed in adaptation of arm reaching movements. However, the emergence of a coactivation strategy was dependent on perturbation direction. Despite similar adaptation in both directions, postural coactivation was largely specific to forward perturbations. Backward perturbations led to less coactivation and less modulation of postural muscle activity. These findings provide insight into how postural stability can affect prioritization of postural control objectives and movement adaptation strategies.NEW & NOTEWORTHY Muscle coactivation is a key strategy for modulating movement stability; this is centrally important in the control of standing posture. Our study investigates the little-known role of coactivation in adaptation of whole body standing postural control. We demonstrate that an early coactivation strategy can be used in postural adaptation, but muscle activation strategies may differ depending on postural stability conditions.

Yank: the time derivative of force is an important biomechanical variable in sensorimotor systems

The derivative of force with respect to time does not have a standard term in physics. As a consequence, the quantity has been given a variety of names, the most closely related being 'rate of force development'. The lack of a proper name has made it difficult to understand how different structures and processes within the sensorimotor system respond to and shape the dynamics of force generation, which is critical for survival in many species. We advocate that ∂[Formula: see text]/∂t be termed 'yank', a term that has previously been informally used and never formally defined. Our aim in this Commentary is to establish the significance of yank in how biological motor systems are organized, evolve and adapt. Further, by defining the quantity in mathematical terms, several measurement variables that are commonly reported can be clarified and unified. In this Commentary, we first detail the many types of motor function that are affected by the magnitude of yank generation, especially those related to time-constrained activities. These activities include escape, prey capture and postural responses to perturbations. Next, we describe the multi-scale structures and processes of the musculoskeletal system that influence yank and can be modified to increase yank generation. Lastly, we highlight recent studies showing that yank is represented in the sensory feedback system, and discuss how this information is used to enhance postural stability and facilitate recovery from postural perturbations. Overall, we promote an increased consideration of yank in studying biological motor and sensory systems.

The Maximum Lyapunov Exponent During Walking and Running: Reliability Assessment of Different Marker-Sets

The maximum Lyapunov exponent (MLE) has often been suggested as the prominent measure for evaluation of dynamic stability of locomotion in pathological and healthy population. Although the popularity of the MLE has increased in the last years, there is scarce information on the reliability of the method, especially during running. The purpose of the current study was, thus, to examine the reliability of the MLE during both walking and running. Sixteen participants walked and ran on a treadmill completing two measurement blocks (i.e., two trials per day for three consecutive days per block) separated by 2 months on average. Six different marker-sets on the trunk were analyzed. Intraday, interday and between blocks reliability was assessed using the intraclass correlation coefficient (ICC) and the root mean square difference (RMSD). The MLE was on average significantly higher (p < 0.001) in running (1.836 ± 0.080) compared to walking (1.386 ± 0.207). All marker-sets showed excellent ICCs (>0.90) during walking and mostly good ICCs (>0.75) during running. The RMSD ranged from 0.023 to 0.047 for walking and from 0.018 to 0.050 for running. The reliability was better when comparing MLE values between blocks (ICCs: 0.965–0.991 and 0.768–0.961; RMSD: 0.023–0.034 and 0.018–0.027 for walking and running respectively), and worse when considering trials of the same day (ICCs: 0.946–0.980 and 0.739–0.844; RMSD: 0.042–0.047 and 0.045–0.050 for walking and running respectively). Further, different marker-sets affect the reliability of the MLE in both walking and running. Our findings provide evidence that the assessment of dynamic stability using the MLE is reliable in both walking and running. More trials spread over more than 1 day should be considered in study designs with increased demands of accuracy independent of the locomotion condition.

Movement goals encoded within the cortex and muscle synergies to reduce redundancy pre and post-stroke. The relevance for gait rehabilitation and the prescription of walking-aids. A literature review and scholarly discussion

Current knowledge of neural and neuromuscular processes controlling gait and movement as well as an understanding of how these mechanisms change following stroke is an important basis for the development of effective rehabilitation interventions. To support the translation of findings from basic research into useful treatments in clinical practice, up-to-date neuroscience should be presented in forms accessible to all members of the multidisciplinary team. In this review we discuss aspects of cortical control of gait and movement, muscle synergies as a way of translating cortical commands into specific muscle activity and as an efficient means of reducing neural and musculoskeletal redundancy. We discuss how these mechanisms change following stroke, potential consequences for gait rehabilitation, and the prescription and use of walking-aids as well as areas requiring further research.

Muscle synergies obtained from comprehensive mapping of the primary motor cortex forelimb representation using high-frequency, long-duration ICMS

Simplifying neuromuscular control for movement has previously been explored by extracting muscle synergies from voluntary movement electromyography (EMG) patterns. The purpose of this study was to investigate muscle synergies represented in EMG recordings associated with direct electrical stimulation of single sites in primary motor cortex (M1). We applied single-electrode high-frequency, long-duration intracortical microstimulation (HFLD-ICMS) to the forelimb region of M1 in two rhesus macaques using parameters previously found to produce forelimb movements to stable spatial end points (90-150 Hz, 90-150 μA, 1,000-ms stimulus train lengths). To develop a comprehensive representation of cortical output, stimulation was applied systematically across the full extent of M1. We recorded EMG activity from 24 forelimb muscles together with movement kinematics. Nonnegative matrix factorization (NMF) was applied to the mean stimulus-evoked EMG, and the weighting coefficients associated with each synergy were mapped to the cortical location of the stimulating electrode. Synergies were found for three data sets including 1) all stimulated sites in the cortex, 2) a subset of sites that produced stable movement end points, and 3) EMG activity associated with voluntary reaching. Two or three synergies accounted for 90% of the overall variation in voluntary movement EMG whereas four or five synergies were needed for HFLD-ICMS-evoked EMG data sets. Maps of the weighting coefficients from the full HFLD-ICMS data set show limited regional areas of higher activation for particular synergies. Our results demonstrate fundamental NMF-based muscle synergies in the collective M1 output, but whether and how the central nervous system might coordinate movements using these synergies remains unclear.NEW & NOTEWORTHY While muscle synergies have been investigated in various muscle activity sets, it is unclear whether and how synergies may be organized in the cortex. We have investigated muscle synergies resulting from high-frequency, long-duration intracortical microstimulation (HFLD-ICMS) applied throughout M1. We compared HFLD-ICMS synergies to synergies from voluntary movement. While synergies can be identified from M1 stimulation, they are not clearly related to voluntary movement synergies and do not show an orderly topographic organization across M1.

Contribution of muscle short-range stiffness to initial changes in joint kinetics and kinematics during perturbations to standing balance: A simulation study

Simulating realistic musculoskeletal dynamics is critical to understanding neural control of muscle activity evoked in sensorimotor feedback responses that have inherent neural transmission delays. Thus, the initial mechanical response of muscles to perturbations in the absence of any change in muscle activity determines which corrective neural responses are required to stabilize body posture. Muscle short-range stiffness, a history-dependent property of muscle that causes a rapid and transient rise in muscle force upon stretch, likely affects musculoskeletal dynamics in the initial mechanical response to perturbations. Here we identified the contributions of short-range stiffness to joint torques and angles in the initial mechanical response to support surface translations using dynamic simulation. We developed a dynamic model of muscle short-range stiffness to augment a Hill-type muscle model. Our simulations show that short-range stiffness can provide stability against external perturbations during the neuromechanical response delay. Assuming constant muscle activation during the initial mechanical response, including muscle short-range stiffness was necessary to account for the rapid rise in experimental sagittal plane knee and hip joint torques that occurs simultaneously with very small changes in joint angles and reduced root mean square errors between simulated and experimental torques by 56% and 47%, respectively. Moreover, forward simulations lacking short-range stiffness produced unreasonably large joint angle changes during the initial response. Using muscle models accounting for short-range stiffness along with other aspects of history-dependent muscle dynamics may be important to advance our ability to simulate inherently unstable human movements based on principles of neural control and biomechanics.

Hip and ankle responses for reactive balance emerge from varying priorities to reduce effort and kinematic excursion: A simulation study

Although standing balance is important in many daily activities, there has been little effort in developing detailed musculoskeletal models and simulations of balance control compared to other whole-body motor activities. Our objective was to develop a musculoskeletal model of human balance that can be used to predict movement patterns in reactive balance control. Similar to prior studies using torque-driven models, we investigated how movement patterns during a reactive balance response are affected by high-level task goals (e.g., reducing center-of-mass movement, maintaining vertical trunk orientation, and minimizing effort). We generated 23 forward dynamics simulations where optimal muscle excitations were found using cost functions with different weights on minimizing these high-level goals. Variations in hip and ankle angles observed experimentally (peak hip flexion=7.9-53.1°, peak dorsiflexion=0.5-4.7°) could be predicted by varying the priority of these high-level goals. More specifically, minimizing center-of-mass motion produced a hip strategy (peak hip flexion and ankle dorsiflexion angles of 45.5° and 2.3°, respectively) and the response shifted towards an ankle strategy as the priority to keep the trunk vertical was increased (peak hip and ankle angles of 13.7° and 8.5°, respectively). We also found that increasing the priority to minimize muscle stress always favors a hip strategy. These results are similar to those from sagittal-plane torque-driven models. Our muscle-actuated model facilitates the investigation of neuromechanical interactions governing reactive balance control to predict muscle activity and movement patterns based on interactions between neuromechanical elements such as spinal reflexes, muscle short-range stiffness, and task-level sensorimotor feedback.

Mechanical effort predicts the selection of ankle over hip strategies in nonstepping postural responses

Experimental studies have shown that a continuum of ankle and hip strategies is used to restore posture following an external perturbation. Postural responses can be modeled by feedback control with feedback gains that optimize a specific objective. On the one hand, feedback gains that minimize effort have been used to predict muscle activity during perturbed standing. On the other hand, hip and ankle strategies have been predicted by minimizing postural instability and deviation from upright posture. It remains unclear, however, whether and how effort minimization influences the selection of a specific postural response. We hypothesize that the relative importance of minimizing mechanical work vs. postural instability influences the strategy used to restore upright posture. This hypothesis was investigated based on experiments and predictive simulations of the postural response following a backward support surface translation. Peak hip flexion angle was significantly correlated with three experimentally determined measures of effort, i.e., mechanical work, mean muscle activity and metabolic energy. Furthermore, a continuum of ankle and hip strategies was predicted in simulation when changing the relative importance of minimizing mechanical work and postural instability, with increased weighting of mechanical work resulting in an ankle strategy. In conclusion, the combination of experimental measurements and predictive simulations of the postural response to a backward support surface translation showed that the trade-off between effort and postural instability minimization can explain the selection of a specific postural response in the continuum of potential ankle and hip strategies.

Neuromechanical model of praying mantis explores the role of descending commands in pre-strike pivots

Praying mantises hunt by standing on their meso- and metathoracic legs and using them to rotate and translate (together, 'pivot') their bodies toward prey. We have developed a neuromechanical software model of the praying mantis Tenodera sinensis to use as a platform for testing postural controllers that the animal may use while hunting. Previous results showed that a feedforward model was insufficient for capturing the diversity of posture observed in the animal (Szczecinski et al 2014 Biomimetic and Biohybrid Syst. 3 296-307). Therefore we have expanded upon this model to make a flexible controller with feedback that more closely mimics the animal. The controller actuates 24 joints in the legs of a dynamical model to orient the head and translate the thorax toward prey. It is controlled by a simulation of nonspiking neurons assembled as a highly simplified version of networks that may exist in the mantid central complex and thoracic ganglia. Because of the distributed nature of these networks, we hypothesize that descending commands that orient the mantis toward prey may be simple direction-of-intent signals, which are turned into motor commands by the structure of low-level networks in the thoracic ganglia. We verify this through a series of experiments with the model. It captures the speed and range of mantid pivots as reported in other work (Yamawaki et al 2011 J. Insect Physiol. 57 1010-6). It is capable of pivoting toward prey from a variety of initial postures, as seen in the animal. Finally, we compare the model's joint kinematics during pivots to preliminary 3D kinematics collected from Tenodera.

Advanced age brings a greater reliance on visual feedback to maintain balance during walking

We implemented a virtual reality system to quantify differences in the use of visual feedback to maintain balance during walking between healthy young (n=12, mean age: 24 years) and healthy old (n=11, 71 years) adults. Subjects walked on a treadmill while watching a speed-matched, virtual hallway with and without mediolateral visual perturbations. A motion capture system tracked center of mass (CoM) motion and foot kinematics. Spectral analysis, detrended fluctuation analysis, and local divergence exponents quantified old and young adults' dynamic response to visual perturbations. Old and young adults walked normally with comparable CoM spectral characteristics, lateral step placement temporal persistence, and local divergence exponents. Perturbed visual flow induced significantly larger changes in mediolateral CoM motion in old vs. young adults. Moreover, visual perturbations disrupted the control of lateral step placement and compromised local dynamic stability more significantly in old than young adults. Advanced age induces a greater reliance on visual feedback to maintain balance during waking, an effect that may compensate for degradations in somatosensation. Our findings are relevant to the early diagnosis of sensory-induced balance impairments and also point to the potential use of virtual reality to evaluate sensory rehabilitation and balance training programs for old adults.

Body stability and muscle and motor cortex activity during walking with wide stance

Biomechanical and neural mechanisms of balance control during walking are still poorly understood. In this study, we examined the body dynamic stability, activity of limb muscles, and activity of motor cortex neurons [primarily pyramidal tract neurons (PTNs)] in the cat during unconstrained walking and walking with a wide base of support (wide-stance walking). By recording three-dimensional full-body kinematics we found for the first time that during unconstrained walking the cat is dynamically unstable in the forward direction during stride phases when only two diagonal limbs support the body. In contrast to standing, an increased lateral between-paw distance during walking dramatically decreased the cat's body dynamic stability in double-support phases and prompted the cat to spend more time in three-legged support phases. Muscles contributing to abduction-adduction actions had higher activity during stance, while flexor muscles had higher activity during swing of wide-stance walking. The overwhelming majority of neurons in layer V of the motor cortex, 82% and 83% in the forelimb and hindlimb representation areas, respectively, were active differently during wide-stance walking compared with unconstrained condition, most often by having a different depth of stride-related frequency modulation along with a different mean discharge rate and/or preferred activity phase. Upon transition from unconstrained to wide-stance walking, proximal limb-related neuronal groups subtly but statistically significantly shifted their activity toward the swing phase, the stride phase where most of body instability occurs during this task. The data suggest that the motor cortex participates in maintenance of body dynamic stability during locomotion.

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.

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.

Dynamic stability of a human standing on a balance board

The neuromuscular system used to stabilize upright posture in humans is a nonlinear dynamical system with time delays. The analysis of this system is important for improving balance and for early diagnosis of neuromuscular disease. In this work, we study the dynamic coupling between the neuromuscular system and a balance board-an unstable platform often used to improve balance in young athletes, and older or neurologically impaired patients. Using a simple inverted pendulum model of human posture on a balance board, we describe a surprisingly broad range of divergent and oscillatory CoP/CoM responses associated with instabilities of the upright equilibrium. The analysis predicts that a variety of sudden changes in the stability of upright postural equilibrium occurs with slow continuous deterioration in balance board stiffness, neuromuscular gain, and time delay associated with the changes in proprioceptive/vestibular/visual-neuromuscular feedback. The analysis also provides deeper insight into changes in the control of posture that enable stable upright posture on otherwise unstable platforms.

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.

Anticipated synchronization and the predict-prevent control method in the FitzHugh-Nagumo model system

We study the synchronization region of two unidirectionally coupled FitzHugh-Nagumo systems, in a master-slave configuration, under the influence of external forcing terms. In the particular region where the slave anticipates the dynamics of the master system, we observe that the synchronization is robust to the different types of forcings. We then use the predict-prevent control method to suppress unwanted pulses in the master system by using the information of the slave output. We find that this method is more efficient than the direct control method based on the master dynamics. Finally, we observe that a perfect matching between the parameters of the master and the slave is not necessary for the control to be efficient. Moreover, this parameter mismatch can, in some cases, improve the control.

Leg muscles that mediate stability: mechanics and control of two distal extensor muscles during obstacle negotiation in the guinea fowl

Here, we used an obstacle treadmill experiment to investigate the neuromuscular control of locomotion in uneven terrain. We measured in vivo function of two distal muscles of the guinea fowl, lateral gastrocnemius (LG) and digital flexor-IV (DF), during level running, and two uneven terrains, with 5 and 7 cm obstacles. Uneven terrain required one step onto an obstacle every four to five strides. We compared both perturbed and unperturbed strides in uneven terrain to level terrain. When the bird stepped onto an obstacle, the leg became crouched, both muscles acted at longer lengths and produced greater work, and body height increased. Muscle activation increased on obstacle strides in the LG, but not the DF, suggesting a greater reflex contribution to LG. In unperturbed strides in uneven terrain, swing pre-activation of DF increased by 5 per cent compared with level terrain, suggesting feed-forward tuning of leg impedance. Across conditions, the neuromechanical factors in work output differed between the two muscles, probably due to differences in muscle-tendon architecture. LG work depended primarily on fascicle length, whereas DF work depended on both length and velocity during loading. These distal muscles appear to play a critical role in stability by rapidly sensing and responding to altered leg-ground interaction.

Tradeoff between stability and maneuverability during whole-body movements

BACKGROUND

Understanding how stability and/or maneuverability affects motor control strategies can provide insight on moving about safely in an unpredictable world. Stability in human movement has been well-studied while maneuverability has not. Further, a tradeoff between stability and maneuverability during movement seems apparent, yet has not been quantified. We proposed that greater maneuverability, the ability to rapidly and purposefully change movement direction and speed, is beneficial in uncertain environments. We also hypothesized that gaining maneuverability comes at the expense of stability and perhaps also corresponds with decreased muscle coactivation.

MATERIALS AND METHODS

We used a goal-directed forward lean movement task that integrated both stability and maneuverability. Subjects (n = 11) used their center of pressure to control a cursor on a computer monitor to reach a target. We added task uncertainty by shifting the target anterior-posterior position mid-movement. We used a balance board with a narrow beam that reduced the base of support in the medio-lateral direction and defined stability as the probability that subjects could keep the balance board level during the task.

RESULTS

During the uncertainty condition, subjects were able to change direction of their anterior-posterior center of pressure more rapidly, indicating that subjects were more maneuverable. Furthermore, medio-lateral center of pressure excursions also approached the edges of the beam and reduced stability margins, implying that subjects were less stable (i.e. less able to keep the board level). On the narrow beam board, subjects increased muscle coactivation of lateral muscle pairs and had greater muscle activity in the left leg. However, there were no statistically significant differences in muscle activity amplitudes or coactivation with uncertainty.

CONCLUSIONS/SIGNIFICANCE

These results demonstrate that there is a tradeoff between stability and maneuverability during a goal-directed whole-body movement. Tasks with added uncertainty could help individuals learn to be more maneuverable yet sufficiently stable.

Common muscle synergies for control of center of mass and force in nonstepping and stepping postural behaviors

We investigated muscle activity, ground reaction forces, and center of mass (CoM) acceleration in two different postural behaviors for standing balance control in humans to determine whether common neural mechanisms are used in different postural tasks. We compared nonstepping responses, where the base of support is stationary and balance is recovered by returning CoM back to its initial position, with stepping responses, where the base of support is enlarged and balance is recovered by pushing the CoM away from the initial position. In response to perturbations of the same direction, these two postural behaviors resulted in different muscle activity and ground reaction forces. We hypothesized that a common pool of muscle synergies producing consistent task-level biomechanical functions is used to generate different postural behaviors. Two sets of support-surface translations in 12 horizontal-plane directions were presented, first to evoke stepping responses and then to evoke nonstepping responses. Electromyographs in 16 lower back and leg muscles of the stance leg were measured. Initially (∼100-ms latency), electromyographs, CoM acceleration, and forces were similar in nonstepping and stepping responses, but these diverged in later time periods (∼200 ms), when stepping occurred. We identified muscle synergies using non-negative matrix factorization and functional muscle synergies that quantified correlations between muscle synergy recruitment levels and biomechanical outputs. Functional muscle synergies that produce forces to restore CoM position in nonstepping responses were also used to displace the CoM during stepping responses. These results suggest that muscle synergies represent common neural mechanisms for CoM movement control under different dynamic conditions: stepping and nonstepping postural responses.

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.

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.

Rotated balance in humans due to repetitive rotational movement

We show how asymmetries in the movement patterns during the process of regaining balance after perturbation from quiet stance can be modeled by a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. In our model, which is an adaption of the model of Stirling and Zakynthinaki (2004), the critical curve, defining the set of maximum angles one can lean to and still correct to regain balance, can be rotated and skewed so as to model the effects of a repetitive training of a rotational movement pattern. For the purposes of our study a rotation and a skew matrix is applied to the critical curve of the model. We present here a linear stability analysis of the modified model, as well as a fit of the model to experimental data of two characteristic "asymmetric" elite athletes and to a "symmetric" elite athlete for comparison. The new adapted model has many uses not just in sport but also in rehabilitation, as many work place injuries are caused by excessive repetition of unaligned and rotational movement patterns.

Modeling the basin of attraction as a two-dimensional manifold from experimental data: applications to balance in humans

We present a method of modeling the basin of attraction as a three-dimensional function describing a two-dimensional manifold on which the dynamics of the system evolves from experimental time series data. Our method is based on the density of the data set and uses numerical optimization and data modeling tools. We also show how to obtain analytic curves that describe both the contours and the boundary of the basin. Our method is applied to the problem of regaining balance after perturbation from quiet vertical stance using data of an elite athlete. Our method goes beyond the statistical description of the experimental data, providing a function that describes the shape of the basin of attraction. To test its robustness, our method has also been applied to two different data sets of a second subject and no significant differences were found between the contours of the calculated basin of attraction for the different data sets. The proposed method has many uses in a wide variety of areas, not just human balance for which there are many applications in medicine, rehabilitation, and sport.

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.

Introduction to focus issue: bipedal locomotion--from robots to humans

Running and walking, collectively referred to as bipedal locomotion, represent self-organized behaviors generated by a spatially distributed dynamical system operating under the constraint that a person must be able to move without falling down. The organizing principles involve both forces actively regulated by the nervous system and those generated passively by the biomechanical properties of the musculoskeletal system and the environment in which the movements occur. With the development of modern motion capture and electrophysiological techniques it has become possible to explore the dynamical interplay between the passive and active controllers of locomotion in a manner that directly compares observation to predictions made by relevant mathematical and computer models. Consequently, many of the techniques initially developed to study nonlinear dynamical systems, including stability analyses, phase resetting and entrainment properties of limit cycles, and fractal and multifractal analysis, have come to play major roles in guiding progress. This Focus Issue discusses bipedal locomotion from the point of view of dynamical systems theory with the goal of stimulating discussion between the dynamical systems, physics, biomechanics, and neuroscience communities.