Do humans optimally exploit redundancy to control step variability in walking?

Effects of local and widespread muscle fatigue on movement timing

Repetitive movements can cause muscle fatigue, leading to motor reorganization, performance deficits, and/or possible injury. The effects of fatigue may depend on the type of fatigue task employed, however. The purpose of this study was to determine how local fatigue of a specific muscle group versus widespread fatigue of various muscle groups affected the control of movement timing. Twenty healthy subjects performed an upper extremity low-load work task similar to sawing for 5 continuous minutes both before and after completing a protocol that either fatigued all the muscles used in the task (widespread fatigue) or a protocol that selectively fatigued the primary muscles used to execute the pushing stroke of the sawing task (localized fatigue). Subjects were instructed to time their movements with a metronome. Timing error, movement distance, and speed were calculated for each movement. Data were then analyzed using a goal-equivalent manifold approach to quantify changes in goal-relevant and non-goal-relevant variability. We applied detrended fluctuation analysis to each time series to quantify changes in fluctuation dynamics that reflected changes in the control strategies used. After localized fatigue, subjects made shorter, slower movements and exerted greater control over non-goal-relevant variability. After widespread fatigue, subjects exerted less control over non-goal-relevant variability and did not change movement patterns. Thus, localized and widespread muscle fatigue affected movement differently. Local fatigue may reduce the available motor solutions and therefore cause greater movement reorganization than widespread muscle fatigue. Subjects altered their control strategies but continued to achieve the timing goal after both fatigue tasks.

Dynamic stability of superior vs. inferior body segments in individuals with transtibial amputation walking in destabilizing environments

Interestingly, young and highly active people with lower limb amputation appear to maintain a similar trunk and upper body stability during walking as able-bodied individuals. Understanding the mechanisms underlying how this stability is achieved after lower-leg amputation is important to improve training regimens for improving walking function in these patients. This study quantified how superior (i.e., head, trunk, and pelvis) and inferior (i.e., thigh, shank, and feet) segments of the body respond to continuous visual or mechanical perturbations during walking. Nine persons with transtibial amputation (TTA) and 12 able-bodied controls (AB) walked on a 2 m × 3 m treadmill in a Computer Assisted Rehabilitation Environment (CAREN). Subjects were perturbed by continuous pseudo-random mediolateral movements of either the treadmill platform or the visual scene. TTA maintained a similar local and orbital stability in their superior body segments as AB throughout both perturbation types. However, for their inferior body segments, TTA subjects exhibited greater dynamic instability during perturbed walking. In TTA subjects, these increases in instability were even more pronounced in their prosthetic limb compared to their intact leg. These findings demonstrate that persons with unilateral lower leg amputation maintain upper body stability in spite of increased dynamic instability in their impaired lower leg. Thus, transtibial amputation does significantly impair sensorimotor function, leading to substantially altered dynamic movements of their lower limb segments. However, otherwise relatively healthy patients with unilateral transtibial amputation appear to retain sufficient remaining sensorimotor function in their proximal and contralateral limbs to adequately compensate for their impairment.

Function dictates the phase dependence of vision during human locomotion

In human and animal locomotion, sensory input is thought to be processed in a phase-dependent manner. Here we use full-field transient visual scene motion toward or away from subjects walking on a treadmill. Perturbations were presented at three phases of walking to test 1) whether phase dependence is observed for visual input and 2) whether the nature of phase dependence differs across body segments. Results demonstrated that trunk responses to approaching perturbations were only weakly phase dependent and instead depended primarily on the delay from the perturbation. Recording of kinematic and muscle responses from both right and left lower limb allowed the analysis of six distinct phases of perturbation effects. In contrast to the trunk, leg responses were strongly phase dependent. Leg responses during the same gait cycle as the perturbation exhibited gating, occurring only when perturbations were applied in midstance. In contrast, during the postperturbation gait cycle, leg responses occurred at similar response phases of the gait cycle over a range of perturbation phases. These distinct responses reflect modulation of trunk orientation for upright equilibrium and modulation of leg segments for both hazard accommodation/avoidance and positional maintenance on the treadmill. Overall, these results support the idea that the phase dependence of responses to visual scene motion is determined by different functional tasks during walking.

Detrended fluctuation analysis and adaptive fractal analysis of stride time data in Parkinson's disease: stitching together short gait trials

Variability indicates motor control disturbances and is suitable to identify gait pathologies. It can be quantified by linear parameters (amplitude estimators) and more sophisticated nonlinear methods (structural information). Detrended Fluctuation Analysis (DFA) is one method to measure structural information, e.g., from stride time series. Recently, an improved method, Adaptive Fractal Analysis (AFA), has been proposed. This method has not been applied to gait data before. Fractal scaling methods (FS) require long stride-to-stride data to obtain valid results. However, in clinical studies, it is not usual to measure a large number of strides (e.g., [Formula: see text][Formula: see text] strides). Amongst others, clinical gait analysis is limited due to short walkways, thus, FS seem to be inapplicable. The purpose of the present study was to evaluate FS under clinical conditions. Stride time data of five self-paced walking trials ([Formula: see text] strides each) of subjects with PD and a healthy control group (CG) was measured. To generate longer time series, stride time sequences were stitched together. The coefficient of variation (CV), fractal scaling exponents [Formula: see text] (DFA) and [Formula: see text] (AFA) were calculated. Two surrogate tests were performed: A) the whole time series was randomly shuffled; B) the single trials were randomly shuffled separately and afterwards stitched together. CV did not discriminate between PD and CG. However, significant differences between PD and CG were found concerning [Formula: see text] and [Formula: see text]. Surrogate version B yielded a higher mean squared error and empirical quantiles than version A. Hence, we conclude that the stitching procedure creates an artificial structure resulting in an overestimation of true [Formula: see text]. The method of stitching together sections of gait seems to be appropriate in order to distinguish between PD and CG with FS. It provides an approach to integrate FS as standard in clinical gait analysis and to overcome limitations such as short walkways.

The dynamical analysis of inter-trial fluctuations near goal equivalent manifolds

Using the concept of task manifolds, a number of data analysis methods have been used to explain how redundancy influences the structure of variability observed during repeated motor performance. Here we describe investigations that integrate the task manifold perspective with the analysis of inter-trial task dynamics. Goal equivalent manifolds (GEMs), together with optimal control ideas, are used to formulate simple models that serve as experimentally testable hypotheses on how inter-trial fluctuations are generated and regulated. In an experimental context, these phenomenological models allow us to show how error-correcting control is spatiotemporally organized around a given GEM. To illustrate our approach, we apply it to study the variability observed in a virtual shuffleboard task. The geometric stability properties of the inter-trial dynamics near the GEM are extracted from fluctuation time series data. We find that subjects exhibit strong control of fluctuations in an eigendirection transverse to the GEM, whereas they only weakly control fluctuations in an eigendirection nearly, but not exactly, tangent to it. We demonstrate that our dynamical analysis is robust under coordinate transformations, and discuss how our results support a generalized interpretation of the minimum intervention principle that suggests the involvement of competing costs in addition to goal-level error minimization.

Does visual feedback during walking result in similar improvements in trunk control for young and older healthy adults?

BACKGROUND

Most current applications of visual feedback to improve postural control are limited to a fixed base of support and produce mixed results regarding improved postural control and transfer to functional tasks. Currently there are few options available to provide visual feedback regarding trunk motion while walking. We have developed a low cost platform to provide visual feedback of trunk motion during walking. Here we investigated whether augmented visual position feedback would reduce trunk movement variability in both young and older healthy adults.

METHODS

The subjects who participated were 10 young and 10 older adults. Subjects walked on a treadmill under conditions of visual position feedback and no feedback. The visual feedback consisted of anterior-posterior (AP) and medial-lateral (ML) position of the subject's trunk during treadmill walking. Fourier transforms of the AP and ML trunk kinematics were used to calculate power spectral densities which were integrated as frequency bins "below the gait cycle" and "gait cycle and above" for analysis purposes.

RESULTS

Visual feedback reduced movement power at very low frequencies for lumbar and neck translation but not trunk angle in both age groups. At very low frequencies of body movement, older adults had equivalent levels of movement variability with feedback as young adults without feedback. Lower variability was specific to translational (not angular) trunk movement. Visual feedback did not affect any of the measured lower extremity gait pattern characteristics of either group, suggesting that changes were not invoked by a different gait pattern.

CONCLUSIONS

Reduced translational variability while walking on the treadmill reflects more precise control maintaining a central position on the treadmill. Such feedback may provide an important technique to augment rehabilitation to minimize body translation while walking. Individuals with poor balance during walking may benefit from this type of training to enhance path consistency during over-ground locomotion.

Spatio-temporal analysis reveals active control of both task-relevant and task-irrelevant variables

The Uncontrolled Manifold (UCM) hypothesis and Minimal Intervention principle propose that the observed differential variability across task relevant (i.e., task goals) vs. irrelevant (i.e., in the null space of those goals) variables is evidence of a separation of task variables for efficient neural control, ranked by their respective variabilities (sometimes referred to as hierarchy of control). Support for this comes from spatial domain analyses (i.e., structure of) of kinematic, kinetic, and EMG variability. While proponents admit the possibility of preferential as opposed to strictly uncontrolled variables, such distinctions have only begun to be quantified or considered in the temporal domain when inferring control action. Here we extend the study of task variability during tripod static grasp to the temporal domain by applying diffusion analysis. We show that both task-relevant and task-irrelevant parameters show corrective action at some time scales; and conversely, that task-relevant parameters do not show corrective action at other time scales. That is, the spatial fluctuations of fingertip forces show, as expected, greater ranges of variability in task-irrelevant variables (>98% associated with changes in total grasp force; vs. only <2% in task-relevant changes associated with acceleration of the object). But at some time scales, however, temporal fluctuations of task-irrelevant variables exhibit negative correlations clearly indicative of corrective action (scaling exponents <0.5); and temporal fluctuations of task-relevant variables exhibit neutral and positive correlations clearly indicative of absence of corrective action (scaling exponents ≥0.5). In agreement with recent work in other behavioral contexts, these results propose we revise our understanding of variability vis-á-vis task relevance by considering both spatial and temporal features of all task variables when inferring control action and understanding how the CNS confronts task redundancy. Instead of a dichotomy of presence vs. absence of control, we should speak of a continuum of weaker to stronger—and potentially different—control strategies in specific spatiotemporal domains, indicated here by the magnitude of deviation from the 0.5 scaling exponent. Moreover, these results are counter examples to the UCM hypothesis and the Minimal Intervention principle, and the similar nature of control actions across time scales in both task-relevant and task-irrelevant spaces points to a level of modularity not previously recognized.

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.

Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability

It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.

Two independent contributions to step variability during over-ground human walking

Human walking exhibits small variations in both step length and step width, some of which may be related to active balance control. Lateral balance is thought to require integrative sensorimotor control through adjustment of step width rather than length, contributing to greater variability in step width. Here we propose that step length variations are largely explained by the typical human preference for step length to increase with walking speed, which itself normally exhibits some slow and spontaneous fluctuation. In contrast, step width variations should have little relation to speed if they are produced more for lateral balance. As a test, we examined hundreds of overground walking steps by healthy young adults (N = 14, age < 40 yrs.). We found that slow fluctuations in self-selected walking speed (2.3% coefficient of variation) could explain most of the variance in step length (59%, P < 0.01). The residual variability not explained by speed was small (1.5% coefficient of variation), suggesting that step length is actually quite precise if not for the slow speed fluctuations. Step width varied over faster time scales and was independent of speed fluctuations, with variance 4.3 times greater than that for step length (P < 0.01) after accounting for the speed effect. That difference was further magnified by walking with eyes closed, which appears detrimental to control of lateral balance. Humans appear to modulate fore-aft foot placement in precise accordance with slow fluctuations in walking speed, whereas the variability of lateral foot placement appears more closely related to balance. Step variability is separable in both direction and time scale into balance- and speed-related components. The separation of factors not related to balance may reveal which aspects of walking are most critical for the nervous system to control.

Extraction of basic movement from whole-body movement, based on gait variability

The aim of this study was to quantify the step-to-step variability (SSV) in speed-variant and speed-invariant movement components of the whole-body gait pattern during running. These separate aspects of variability can be used to gain insight into the neuromuscular control strategies that are engaged during running. Ten healthy, physically active, male recreational athletes performed five treadmill running trials at five different speeds (range: 1.3–4.9 m/sec). The whole-body movement was separated into principal movements (PM) using a principal component analysis. The PMs were split into two groups: a speed-variant group, where the range of motion (amplitude of PMs) changed with running speed; and a speed-invariant group, where the range of motion was constant across various speeds. The step-to-step variability (SSV) of the two groups was then quantified. The absolute SSV was the summed variability across all gait cycles, whereas the relative SSV was the summed variability divided by the magnitude of the movement. The absolute SSV of the speed-variant movements increased with running speed. By contrast, the relative SSV of the speed-variant group (as normalized to the PM amplitude) decreased asymptotically toward a minimal level as running speed increased. Both the absolute and relative SSV of the speed-invariant movements revealed a minimum at 3.1 m/sec. The whole-body gait pattern during running can be subdivided into speed-variant and speed-invariant movements. An interpretation of the SSV based on minimal intervention theory suggests that speed-variant movements are more tightly controlled, as evidenced by a lower degree of variability compared to the speed-invariant movements.

Application of principal component analysis in clinical gait research: identification of systematic differences between healthy and medial knee-osteoarthritic gait

For a successful completion of a movement task the motor control system has to observe a multitude of internal constraints that govern the coordination of its segments. The purpose of this study was to apply principal component (PC) analysis to detect differences in the segmental coordination between healthy subjects and patients with medial knee osteoarthritis (OA). It was hypothesized that (1) systematic differences in patterns of whole body movement would be identifiable with this method even in small sample sized groups and that (2) these differences will include compensatory movements in the OA patients in both the lower and upper body segments. Marker positions and ground reaction forces of three gait trials of 5 healthy and 5 OA participants with full body marker sets were analyzed using a principal component analysis. Group differences in the PC-scores were determined for the first 10 PC-vectors and a linear combination of those PC-vectors where differences were found defined a discriminant vector. Projecting the original trials onto this discriminant vector yielded significant group differences (t(d=8)=3.011; p=0.017) with greater upper body movement in patients with knee OA that was correlated with the medial-lateral ground reaction force. These results help to characterize the adaptation of whole-body gait patterns to knee OA in a relatively small population and may provide an improved basis for the development of interventions to modify knee load. The PC-based motion analysis offered a highly sensitive approach to identify characteristic whole body patterns of movement associated with pathological gait.

Executive function orchestrates regulation of task-relevant gait fluctuations

Humans apply a minimum intervention principle to regulate treadmill walking, rapidly correcting fluctuations in the task-relevant variable (step speed: SS) while ignoring fluctuations in the task-irrelevant variables (step time: ST; step length: SL). We examined whether the regulation of fluctuations in SS and not in ST and SL depends on high-level, executive function, processes. Young adults walked on a treadmill without a cognitive requirement and while performing the cognitive task of dichotic listening. SS fluctuations became less anti-persistent when performing dichotic listening, meaning that taxing executive function impaired the ability to rapidly correct speed deviations on subsequent steps. Conversely, performing dichotic listening had no effect on SL and ST persistent fluctuations. Findings suggest that high-level brain processes are involved only in regulating gait task-relevant variables.

Directionality in distribution and temporal structure of variability in skill acquisition

Observable structure of variability presents a window into the underlying processes of skill acquisition, especially when the task affords a manifold of solutions to the desired task result. This study examined skill acquisition by analyzing variability in both its distributional and temporal structure. Using a virtual throwing task, data distributions were analyzed by the Tolerance, Noise, Covariation-method (TNC); the temporal structure was quantified by autocorrelation and detrended fluctuation analysis (DFA). We tested four hypotheses: (1) Tolerance and Covariation, not Noise, are major factors underlying long-term performance improvement. (2) Trial-to-trial dynamics in execution space exhibits preferred directions. (3) The direction-dependent organization of variability becomes more pronounced with practice. (4) The anisotropy is in directions orthogonal and parallel to the solution manifold. Results from 13 subjects practicing for 6 days revealed that performance improvement correlated with increasing Tolerance and Covariation; Noise remained relatively constant. Temporal fluctuations and their directional modulation were identified by a novel rotation method that was a priori ignorant about orthogonality. Results showed a modulation of time-dependent characteristics that became enhanced with practice. However, this directionality was not coincident with orthogonal and parallel directions of the solution manifold. A state-space model with two sources of noise replicated not only the observed temporal structure but also its deviations from orthogonality. Simulations suggested that practice-induced changes were associated with an increase in the feedback gain and a subtle weighting of the two noise sources. The directionality in the structure of variability depended on the scaling of the coordinates, a result that highlights that analysis of variability sensitively depends on the chosen coordinates.

Dynamics of revolution time variability in cycling pattern: voluntary intent can alter the long-range autocorrelations

Long-range dependency has been found in most rhythmic motor signals. The origin of this property is unknown and largely debated. There is a controversy on the influence of voluntary control induced by requiring a pre-determined pace such as asking subjects to step to a metronome. We studied the cycle duration variability of 15 men pedaling on an ergometer at free pace and at an imposed pace (60 rpm). Revolution time was determined based on accelerometer signals (sample frequency 512 Hz). Revolution time variability was assessed by coefficient of variation (CV). The presence of long-range autocorrelations was based on scaling properties of the series variability (Hurst exponent) and the shape of the power spectral density (α exponent). Mean revolution time was significantly lower at freely chosen cadence, while values of CV were similar between both sessions. Long-range autocorrelations were highlighted in all series of cycling patterns. However, Hurst and α exponents were significantly lower at imposed cadence. This study demonstrates the presence of long-range autocorrelations during cycling and that voluntary intent can modulate the interdependency between consecutive cycles. Therefore, cycling may constitute a powerful paradigm to investigate the influence of central control mechanisms on the long-range interdependency characterizing rhythmic motor tasks.

Assessing the stability of human locomotion: a review of current measures

Falling poses a major threat to the steadily growing population of the elderly in modern-day society. A major challenge in the prevention of falls is the identification of individuals who are at risk of falling owing to an unstable gait. At present, several methods are available for estimating gait stability, each with its own advantages and disadvantages. In this paper, we review the currently available measures: the maximum Lyapunov exponent (λS and λL), the maximum Floquet multiplier, variability measures, long-range correlations, extrapolated centre of mass, stabilizing and destabilizing forces, foot placement estimator, gait sensitivity norm and maximum allowable perturbation. We explain what these measures represent and how they are calculated, and we assess their validity, divided up into construct validity, predictive validity in simple models, convergent validity in experimental studies, and predictive validity in observational studies. We conclude that (i) the validity of variability measures and λS is best supported across all levels, (ii) the maximum Floquet multiplier and λL have good construct validity, but negative predictive validity in models, negative convergent validity and (for λL) negative predictive validity in observational studies, (iii) long-range correlations lack construct validity and predictive validity in models and have negative convergent validity, and (iv) measures derived from perturbation experiments have good construct validity, but data are lacking on convergent validity in experimental studies and predictive validity in observational studies. In closing, directions for future research on dynamic gait stability are discussed.

Teaching the principle of biological optimization

Among the important principles in biology that should be taught in biological engineering educational programs is the principle of optimization, what it means, why it is important, and how it comes about. This material can be presented at numerous levels throughout the curriculum. Understanding of this principle can lead biological engineers to expect it in many, if not all, biological system applications. Understanding optimization in biological systems can help understand the predictive power of evolutionary principles and what to expect from living things incorporated in designs.

Random walk of motor planning in task-irrelevant dimensions

The movements that we make are variable. It is well established that at least a part of this variability is caused by noise in central motor planning. Here, we studied how the random effects of planning noise translate into changes in motor planning. Are the random effects independently added to a constant mean end point, or do they accumulate over movements? To distinguish between these possibilities, we examined repeated, discrete movements in various tasks in which the motor output could be decomposed into a task-relevant and a task-irrelevant component. We found in all tasks that the task-irrelevant component had a positive lag 1 autocorrelation, suggesting that the random effects of planning noise accumulate over movements. In contrast, the task-relevant component always had a lag 1 autocorrelation close to zero, which can be explained by effective trial-by-trial correction of motor planning on the basis of observed motor errors. Accumulation of the effects of planning noise is consistent with current insights into the stochastic nature of synaptic plasticity. It leads to motor exploration, which may subserve motor learning and performance optimization.

Proximal versus distal control of two-joint planar reaching movements in the presence of neuromuscular noise

Determining how the human nervous system contends with neuro-motor noise is vital to understanding how humans achieve accurate goal-directed movements. Experimentally, people learning skilled tasks tend to reduce variability in distal joint movements more than in proximal joint movements. This suggests that they might be imposing greater control over distal joints than proximal joints. However, the reasons for this remain unclear, largely because it is not experimentally possible to directly manipulate either the noise or the control at each joint independently. Therefore, this study used a 2 degree-of-freedom torque driven arm model to determine how different combinations of noise and/or control independently applied at each joint affected the reaching accuracy and the total work required to make the movement. Signal-dependent noise was simultaneously and independently added to the shoulder and elbow torques to induce endpoint errors during planar reaching. Feedback control was then applied, independently and jointly, at each joint to reduce endpoint error due to the added neuromuscular noise. Movement direction and the inertia distribution along the arm were varied to quantify how these biomechanical variations affected the system performance. Endpoint error and total net work were computed as dependent measures. When each joint was independently subjected to noise in the absence of control, endpoint errors were more sensitive to distal (elbow) noise than to proximal (shoulder) noise for nearly all combinations of reaching direction and inertia ratio. The effects of distal noise on endpoint errors were more pronounced when inertia was distributed more toward the forearm. In contrast, the total net work decreased as mass was shifted to the upper arm for reaching movements in all directions. When noise was present at both joints and joint control was implemented, controlling the distal joint alone reduced endpoint errors more than controlling the proximal joint alone for nearly all combinations of reaching direction and inertia ratio. Applying control only at the distal joint was more effective at reducing endpoint errors when more of the mass was more proximally distributed. Likewise, controlling the distal joint alone required less total net work than controlling the proximal joint alone for nearly all combinations of reaching distance and inertia ratio. It is more efficient to reduce endpoint error and energetic cost by selectively applying control to reduce variability in the distal joint than the proximal joint. The reasons for this arise from the biomechanical configuration of the arm itself.

Orbital stability analysis in biomechanics: a systematic review of a nonlinear technique to detect instability of motor tasks

Falls represent a heavy economic and clinical burden on society. The identification of individual chronic characteristics associated with falling is of fundamental importance for the clinicians; in particular, the stability of daily motor tasks is one of the main factors that the clinicians look for during assessment procedures. Various methods for the assessment of stability in human movement are present in literature, and methods coming from stability analysis of nonlinear dynamic systems applied to biomechanics recently showed promise. One of these techniques is orbital stability analysis via Floquet multipliers. This method allows to measure orbital stability of periodic nonlinear dynamic systems and it seems a promising approach for the definition of a reliable motor stability index, taking into account for the whole task cycle dynamics. Despite the premises, its use in the assessment of fall risk has been deemed controversial. The aim of this systematic review was therefore to provide a critical evaluation of the literature on the topic of applications of orbital stability analysis in biomechanics, with particular focus to methodologic aspects. Four electronic databases have been searched for articles relative to the topic; 23 articles were selected for review. Quality of the studies present in literature has been assessed with a customised quality assessment tool. Overall quality of the literature in the field was found to be high. The most critical aspect was found to be the lack of uniformity in the implementation of the analysis to biomechanical time series, particularly in the choice of state space and number of cycles to include in the analysis.

Persistent and anti-persistent pattern in stride-to-stride variability of treadmill walking: influence of rhythmic auditory cueing

It has been observed that long time series of Stride Time (ST), Stride Length (SL) and Stride Speed (SS=SL/ST) exhibited statistical persistence (long-range auto-correlation) in overground walking. Rhythmic auditory cueing induced anti-persistent (or anti-correlated) patterns in ST series, while SL and SS remained persistent. On the other hand, it has been shown that SS became anti-persistent in treadmill walking, while ST and SL remained persistent. The aim of this study was to analyze the effect of the combination of treadmill walking (imposed speed) and auditory cueing (imposed cadence) on gait dynamics. Twenty middle-aged subjects performed 6×5 min walking trials at various imposed speeds on an instrumented treadmill. Freely chosen walking cadences were measured during the first three trials, and then imposed accordingly in the last three trials by using a metronome. Detrended fluctuation analysis (DFA) was performed on the times series of ST, SL, and SS. Treadmill induced anti-persistent dynamics in the time series of SS, but preserved the persistence of ST and SL. On the contrary, all the three parameters were anti-persistent under dual-constraints condition. Anti-persistent dynamics may be related to a tighter control: deviations are followed by a rapid over-correction, which produces oscillations around target values. Under single constraint condition, while SS is tightly regulated in order to follow the treadmill speed, redundancy between ST and SL would likely allow persistent pattern to occur. Conversely, under dual constraint conditions, the absence of redundancy among SL, ST and SS would explain the generalized anti-persistent pattern.

Persistence of motor-equivalent postural fluctuations during bipedal quiet standing

Theoretical and empirical work indicates that the central nervous system is able to stabilize motor performance by selectively suppressing task-relevant variability (TRV), while allowing task-equivalent variability (TEV) to occur. During unperturbed bipedal standing, it has previously been observed that, for task variables such as the whole-body center of mass (CoM), TEV exceeds TRV in amplitude. However, selective control (and correction) of TRV should also lead to different temporal characteristics, with TEV exhibiting higher temporal persistence compared to TRV. The present study was specifically designed to test this prediction. Kinematics of prolonged quiet standing (5 minutes) was measured in fourteen healthy young participants, with eyes closed. Using the uncontrolled manifold analysis, postural variability in six sagittal joint angles was decomposed into TEV and TRV with respect to four task variables: (1) center of mass (CoM) position, (2) head position, (3) trunk orientation and (4) head orientation. Persistence of fluctuations within the two variability components was quantified by the time-lagged auto-correlation, with eight time lags between 1 and 128 seconds. The pattern of results differed between task variables. For three of the four task variables (CoM position, head position, trunk orientation), TEV significantly exceeded TRV over the entire 300 s-period.The autocorrelation analysis confirmed our main hypothesis for CoM position and head position: at intermediate and longer time delays, TEV exhibited higher persistence than TRV. Trunk orientation showed a similar trend, while head orientation did not show a systematic difference between TEV and TRV persistence. The combination of temporal and task-equivalent analyses in the present study allow a refined characterization of the dynamic control processes underlying the stabilization of upright standing. The results confirm the prediction, derived from computational motor control, that task-equivalent fluctuations for specific task variables show higher temporal persistence compared to task-relevant fluctuations.

Trial-to-trial dynamics and learning in a generalized, redundant reaching task

If humans exploit task redundancies as a general strategy, they should do so even if the redundancy is decoupled from the physical implementation of the task itself. Here, we derived a family of goal functions that explicitly defined infinite possible redundancies between distance (D) and time (T) for unidirectional reaching. All [T, D] combinations satisfying any specific goal function defined a goal-equivalent manifold (GEM). We tested how humans learned two such functions, D/T = c (constant speed) and D·T = c, that were very different but could both be achieved by neurophysiologically and biomechanically similar reaching movements. Subjects were never explicitly shown either relationship, but only instructed to minimize their errors. Subjects exhibited significant learning and consolidation of learning for both tasks. Initial error magnitudes were higher, but learning rates were faster, for the D·T task than for the D/T task. Learning the D/T task first facilitated subsequent learning of the D·T task. Conversely, learning the D·T task first interfered with subsequent learning of the D/T task. Analyses of trial-to-trial dynamics demonstrated that subjects actively corrected deviations perpendicular to each GEM faster than deviations along each GEM to the same degree for both tasks, despite exhibiting significantly greater variance ratios for the D/T task. Variance measures alone failed to capture critical features of trial-to-trial control. Humans actively exploited these abstract task redundancies, even though they did not have to. They did not use readily available alternative strategies that could have achieved the same performance.

A satisficing and bricoleur approach to sensorimotor cognition

In this manuscript I present a set of neural processing principles and evolutionary constraints that should be taken into account in the characterization of sensorimotor cognition. I review evidence supporting the choice of the set of principles, and then I assess how such principles apply to two cases, object perception-action and peripersonal space. The aim is to emphasize the importance of focusing cognitive models on how evolution shapes functional paths to adaptations, as well as to adopt fitness maximization analyses of cognitive functions. Such an approach contrasts with the widespread reverse-engineering assumption that the neural system comprises a set of specialized circuits designed to comply with its assumed functions. The evidence presented in the manuscript points to the fact that neural systems should not be seen as a seat of optimal processes and circuits addressing particular problems in sensorimotor cognition, but as a set of satisficing and tinkered components, mostly not addressing the problems that are supposed to solve, but solving them as secondary effects of the engaged processes. I conclude with a corollary of the challenges lying ahead of the proposed approach.

Step-to-step variability in treadmill walking: influence of rhythmic auditory cueing

While walking, human beings continuously adjust step length (SpL), step time (SpT), step speed (SpS = SpL/SpT) and step width (SpW) by integrating both feedforward and feedback mechanisms. These motor control processes result in correlations of gait parameters between consecutive strides (statistical persistence). Constraining gait with a speed cue (treadmill) and/or a rhythmic auditory cue (metronome), modifies the statistical persistence to anti-persistence. The objective was to analyze whether the combined effect of treadmill and rhythmic auditory cueing (RAC) modified not only statistical persistence, but also fluctuation magnitude (standard deviation, SD), and stationarity of SpL, SpT, SpS and SpW. Twenty healthy subjects performed 6 × 5 min. walking tests at various imposed speeds on a treadmill instrumented with foot-pressure sensors. Freely-chosen walking cadences were assessed during the first three trials, and then imposed accordingly in the last trials with a metronome. Fluctuation magnitude (SD) of SpT, SpL, SpS and SpW was assessed, as well as NonStationarity Index (NSI), which estimates the dispersion of local means in the times series (SD of 20 local means over 10 steps). No effect of RAC on fluctuation magnitude (SD) was observed. SpW was not modified by RAC, what is likely the evidence that lateral foot placement is separately regulated. Stationarity (NSI) was modified by RAC in the same manner as persistent pattern: Treadmill induced low NSI in the time series of SpS, and high NSI in SpT and SpL. On the contrary, SpT, SpL and SpS exhibited low NSI under RAC condition. We used relatively short sample of consecutive strides (100) as compared to the usual number of strides required to analyze fluctuation dynamics (200 to 1000 strides). Therefore, the responsiveness of stationarity measure (NSI) to cued walking opens the perspective to perform short walking tests that would be adapted to patients with a reduced gait perimeter.

Gait variability is altered in older adults when listening to auditory stimuli with differing temporal structures

Gait variability in the context of a deterministic dynamical system may be quantified using nonlinear time series analyses that characterize the complexity of the system. Pathological gait exhibits altered gait variability. It can be either too periodic and predictable, or too random and disordered, as is the case with aging. While gait therapies often focus on restoration of linear measures such as gait speed or stride length, we propose that the goal of gait therapy should be to restore optimal gait variability, which exhibits chaotic fluctuations and is the balance between predictability and complexity. In this context, our purpose was to investigate how listening to different auditory stimuli affects gait variability. Twenty-seven young and 27 elderly subjects walked on a treadmill for 5 min while listening to white noise, a chaotic rhythm, a metronome, and with no auditory stimulus. Stride length, step width, and stride intervals were calculated for all conditions. Detrended Fluctuation Analysis was then performed on these time series. A quadratic trend analysis determined that an idealized inverted-U shape described the relationship between gait variability and the structure of the auditory stimuli for the elderly group, but not for the young group. This proof-of-concept study shows that the gait of older adults may be manipulated using auditory stimuli. Future work will investigate which structures of auditory stimuli lead to improvements in functional status in older adults.

Use of motor abundance in young and older adults during dual-task treadmill walking

Motor abundance allows individuals to perform any task reliably while being variable in movement's particulars. The study investigated age-related differences in this feature when young adults (YA) and older adults (OA) performed challenging tasks, namely treadmill walking alone and while performing a cognitive task. A goal function for treadmill walking was first defined, i.e., maintain constant speed at each step, which led to a goal equivalent manifold (GEM) containing all combinations of step time and step length that equally satisfied the function. Given the GEM, amounts of goal-equivalent and non-goal-equivalent variability were afterwards determined and used to define an index providing information about the set of effective motor solutions relative to the GEM. The set was limited in OA compared to YA in treadmill walking alone, indicating that OA made less flexible use of motor abundance than YA. However, this differentiation between YA and OA disappeared when concurrently performing the cognitive task. It is proposed that OA might have benefited from cognitive compensation.

Extracting synergies in gait: using EMG variability to evaluate control strategies

There has been extensive debate as to whether muscle synergies in motor tasks reflect underlying neural organization or simply correlations in muscle activity that are imposed by the task. One possible means of distinguishing these two alternatives is through the analysis of variability in the electromyogram (EMG). Here, we simulated EMG in eight lower-limb muscles and introduced hypothetical neural coupling between specific muscle groups. Neural coupling was simulated by introducing correlations in the neural activation commands to different muscles (positive, negative, or zero coupling). When the entire EMG signal was used for analysis, the extracted synergies reflected only simultaneous muscle activity, regardless of the neural coupling between the muscles. On the other hand, examining the variability in the EMG after subtracting the ensemble average was successful in identifying the simulated neural coupling. The extracted synergies from these two methods were also different when we analyzed data from participants during treadmill walking. The results emphasize the importance of examining EMG variability to understand the neural basis of muscle synergies.

Variation of respiratory resistance suggests optimization of airway caliber

Physiologically optimized processes, such as respiration, walking, and cardiac function, usually show a range of variability about the optimized value. Airway resistance has, in the past, been noted as variable, and this variability has been connected to pulmonary disease (e.g., asthma). A hypothesis was presented many years ago that postulated airway resistance as an optimized parameter in healthy individuals, and we have noticed that respiratory measurements made with the airflow perturbation device (APD) tend to be variable in nature. It was posited that this variability indicates that respiratory resistance is optimized similarly to other physiological processes. Fifty subjects with a wide range of demographics volunteered to have 100 measurements made of their respiratory resistances. Resistances were separated into inhalation and exhalation phases. These were plotted and shown to have frequency distributions that were consistent with expectations for an optimized process. The frequency distributions were not quite symmetrical, being skewed slightly toward upper resistances. Comparison between subject data and data from a mechanical respiratory analog showed that subject resistance variation is overwhelmingly from the respiratory system and not from the APD.

Dynamic margins of stability during human walking in destabilizing environments

Understanding how humans maintain stability when walking, particularly when exposed to perturbations, is key to preventing falls. Here, we quantified how imposing continuous, pseudorandom anterior-posterior (AP) and mediolateral (ML) oscillations affected the control of dynamic walking stability. Twelve subjects completed five 3-minute walking trials in the Computer Assisted Rehabilitation ENvironment (CAREN) system under each of 5 conditions: no perturbation (NOP), AP platform (APP) or visual (APV) or ML platform (MLP) or visual (MLV) oscillations. We computed AP and ML margins of stability (MOS) for each trial. Mean MOS(ml) were consistently slightly larger during all perturbation conditions than during NOP (p≤0.038). Mean MOS(ap) for the APP, MLP and MLV oscillations were significantly smaller than during NOP (p<0.0005). Variability of both MOS(ap) and MOS(ml) was significantly greater during the MLP and MLV oscillations than during NOP (p<0.0005). We also directly quantified how the MOS on any given step affected the MOS on the following step using first-return plots. There were significant changes in step-to-step MOS(ml) dynamics between experimental conditions (p<0.0005). These changes suggested that subjects may have been trying to control foot placement, and consequently stability, during the perturbation conditions. Quantifying step-to-step changes in margins of dynamic stability may be more useful than mean MOS in assessing how individuals control walking stability.

Impaired endogenously evoked automated reaching in Parkinson's disease

Intended reaches triggered by exogenous targets often coexist with spontaneous, automated movements that are endogenously activated. It has been posited that Parkinson's disease (PD) primarily impairs automated movements, but it is unknown to what extent this may affect multijoint/limb control, particularly when patients are off their dopaminergic medications. Here we tested nine human patients with PD while off dopaminergic medication versus nine age-matched normal controls (NCs). Participants performed intentional reaches forward to a target in a dark room and then transitioned back to their initial posture. Upon target flash, three forms of guidance were used: (1) memory with eyes closed, (2) continuous target vision only, and (3) vision of their moving finger only. The trajectories of their arm joints were measured and their joint velocities decomposed into the (intended) task-relevant and the (spontaneous) task-incidental degrees of freedom (DOF). We also measured the balance between these two subsets of DOF as these movements unfolded. In PD patients we found that the incidental DOF values were abnormally variable during the retracting movements and prevailed over the task-relevant DOF values. By contrast, their forward intentional motions were abnormally dominated by the task-relevant components. Moreover, the patients abruptly transitioned between voluntary and automated modes of joint control, and, unlike NCs, the type of visual guidance differentially affected their postural trajectories. These findings lend support to an emerging view that there is a loss of automated control in PD patients that contributes to impairments in voluntary control, and that basal ganglia-cortical circuits are critical for the maintenance and balance of multijoint control.

Stable walking with asymmetric legs

Asymmetric leg function is often an undesired side-effect in artificial legged systems and may reflect functional deficits or variations in the mechanical construction. It can also be found in legged locomotion in humans and animals such as after an accident or in specific gait patterns. So far, it is not clear to what extent differences in the leg function of contralateral limbs can be tolerated during walking or running. Here, we address this issue using a bipedal spring-mass model for simulating walking with compliant legs. With the help of the model, we show that considerable differences between contralateral legs can be tolerated and may even provide advantages to the robustness of the system dynamics. A better understanding of the mechanisms and potential benefits of asymmetric leg operation may help to guide the development of artificial limbs or the design novel therapeutic concepts and rehabilitation strategies.

Influence of simulated neuromuscular noise on the dynamic stability and fall risk of a 3D dynamic walking model

Measures that can predict risk of falling are essential for enrollment of older adults into fall prevention programs. Local and orbital stability directly quantify responses to very small perturbations and are therefore putative candidates for predicting fall risk. However, research to date is not conclusive on whether and how these measures relate to fall risk. Testing this empirically would be time consuming or may require high risk tripping experiments. Simulation studies therefore provide an important tool to initially explore potential measures to predict fall risk. This study performed simulations with a 3D dynamic walking model to explore if and how dynamic stability measures predict fall risk. The model incorporated a lateral step controller to maintain lateral stability. Neuronal noise of increasing amplitude was added to this controller to manipulate fall risk. Short-term (λ(S)(*)) local instability did predict fall risk, but long-term (λ(L)(*)) local instability and orbital stability (maxFM) did not. Additionally, λ(S)(*) was an early predictor for fall risk as it started increasing before fall risk increased. Therefore, λ(S)(*) could be a very useful tool to identify older adults whose fall risk is about to increase, so they can be enrolled in fall prevention programs before they actually fall.

Multiple sclerosis affects the frequency content in the vertical ground reaction forces during walking

BACKGROUND

Multiple sclerosis is a progressive neurological disease that results in a high incident of gait disturbance. Exploring the frequency content of the ground reaction forces generated during walking may provide additional insights to gait in patients with multiple sclerosis that could lead to specific tools for differential diagnosis. The purpose of this study was to investigate differences in the frequency content of these forces in an effort to contribute to improved clinical management of this disease.

METHODS

Eighteen patients and eighteen healthy controls walked across a 10 meter long walkway. The anterior-posterior and vertical ground reaction forces generated during the stance phase of gait were evaluated in the frequency domain using fast Fourier transformation. T-tests were utilized for comparison of median frequency, the 99.5% frequency, and the frequency bandwidth between patients and healthy controls and also for comparisons between patients with mild and moderate severity.

FINDINGS

Patients with multiple sclerosis had significantly lower 99.5% frequency (P=0.006) and median frequency (P<0.001) in the vertical ground reaction force. No differences were found in the anterior-posterior reaction force frequency content. There were no differences between patients with mild and moderate severity.

INTERPRETATION

The lower frequency content suggests lesser vertical oscillation of the center of gravity. Lack of differences between severities may suggest presence of differences prior to currently established diagnosis timelines. Analysis of the frequency content may potentially serve to provide earlier diagnostic assessment of this debilitating disease.

Rhythmic dynamics and synchronization via dimensionality reduction: application to human gait

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system.

The many roles of vision during walking

Vision can improve bipedal upright stability during standing and locomotion. However, during locomotion, vision supports additional behaviors such as gait cycle modulation, navigation, and obstacle avoidance. Here, we investigate how the multiple roles of vision are reflected in the dynamics of trunk control as the neural control problem changes from a fixed to a moving base of support. Subjects were presented with either low- or high-amplitude broadband visual stimuli during standing posture or while walking on a treadmill at 1 km/h and 5 km/h. Frequency response functions between visual scene motion (input) and trunk kinematics (output) revealed little or no change in the gain of trunk orientation in the standing posture and walking conditions. However, a dramatic increase in gain was observed in trunk (hip and shoulder) horizontal displacement from posture to locomotion. Such increases in gain may be interpreted as an increased coupling to visual scene motion. However, we believe that the increased gain reflects a decrease in stability due to a change of the control problem from standing to locomotion. Indeed, keeping the body upright with the use of vision during walking is complicated by the additional locomotor processes at work. Unlike during standing, vision plays many roles during locomotion, providing information for upright stability as well as body position relative to the external environment.

Influence of simulated neuromuscular noise on movement variability and fall risk in a 3D dynamic walking model

People at risk of falling exhibit increased gait variability, which may predict future falls. However, the causal mechanisms underlying these correlations are not well known. Increased neuronal noise associated with aging likely leads to increased gait variability, which could in turn lead to increased fall risk. This paper presents a model of how changes in neuromuscular noise independently affect gait variability and probability of falling, and aims to determine the extent to which changes in gait variability directly predict fall risk. We used a dynamic walking model that incorporates a lateral step controller to maintain lateral stability. Noise was applied to this controller to approximate neuromuscular noise in humans. Noise amplitude was varied between low amplitudes that did not induce falls and high amplitudes for which the model always fell. With increases in noise amplitude, the model fell more often and after fewer steps. Gait variability increased with noise amplitude and predicted increased probability of falling. Importantly, these relationships were not linear. At either low gait variability or very high gait variability, small increases in noise and variability affected probability of falling very little. Conversely, at intermediate noise and/or variability levels, the same small increases resulted in large increases in probability of falling. Our results validate the idea that age-related increases in neuromuscular noise likely play a direct contributing role in increasing fall risk. However, neuromuscular noise remains only one of many important factors that need to be considered. These findings have important implications for fall prevention research and practice.

Re-interpreting detrended fluctuation analyses of stride-to-stride variability in human walking

Detrended fluctuation analyses (DFA) have been widely used to quantify stride-to-stride temporal correlations in human walking. However, significant questions remain about how to properly interpret these statistical properties physiologically. Here, we propose a simpler and more parsimonious interpretation than previously suggested. Seventeen young healthy adults walked on a motorized treadmill at each of 5 speeds. Time series of consecutive stride lengths (SL) and stride times (ST) were recorded. Time series of stride speeds were computed as SS=SL/ST. SL and ST exhibited strong statistical persistence (α≫0.5). However, SS consistently exhibited slightly anti-persistent (α<0.5) dynamics. We created three surrogate data sets to directly test specific hypotheses about possible control processes that might have generated these time series. Subjects did not choose consecutive SL and ST according to either independently uncorrelated or statistically independent auto-regressive moving-average (ARMA) processes. However, cross-correlated surrogates, which preserved both the auto-correlation and cross-correlation properties of the original SL and ST time series successfully replicated the means, standard deviations, and (within computational limits) DFA α exponents of all relevant gait variables. These results suggested that subjects controlled their movements according to a two-dimensional ARMA process that specifically sought to minimize stride-to-stride variations in walking speed (SS). This interpretation fully agrees with experimental findings and also with the basic definitions of statistical persistence and anti-persistence. Our findings emphasize the necessity of interpreting DFA α exponents within the context of the control processes involved and the inherent biomechanical and neuro-motor redundancies available.