Fractal Fluctuations in Human Walking: Comparison Between Auditory and Visually Guided Stepping

Visual feedback modulates the 1/f structure of movement amplitude time series

In our prior studies, human participants were required to generate long sequences of targeted hand movement when task difficulty varied between conditions, and where full vision of the hand and target was always available. The movement amplitude-that is, the actual distance travelled-for each movement was measured; consecutive movement amplitude values were formed into time series; then, the time series were submitted to spectral analysis. As task difficulty increased, there was a pink-to-white-noise shift in movement amplitude time-series structure. Those changes could be attributed to a difficulty-induced increase in the need to engage visual feedback processes, which maintain accurate guidance of the hand to the target. The current study was designed to provide a more direct test of the hypothesis that difficulty-induced increases in visual feedback processing modulate movement amplitude time-series structure. To that end, we examined cyclical aiming performance under four unique conditions created from the crossing of two index of difficulty (2 and 5 bits) and two visual feedback (visual feedback and no-visual feedback) conditions. That allowed us to examine how variations in visual feedback quality might influence difficulty-induced changes in time-series structure. In the visual feedback condition, we predicted that the increase in difficulty should result in a pink-to-white-noise shift in time-series structure. If that expected shift resulted from increased engagement of visual feedback processing, then in the no-visual feedback condition-where visual feedback processing was disabled-we should observe a strengthened pink-noise time-series structure that does not change with the increase in difficulty. The current results confirmed those predictions. That provides further support for the hypothesis that engagement of closed-loop visual feedback processing modulates movement amplitude time-series structure.

Application of vibration to the soles increases long-range correlations in the stride parameters during walking

Temporal fluctuations in the stride parameters during human walking exhibit long-range correlations, but these long-range correlations in the stride parameters decrease due to aging or neuromuscular diseases. These observations suggest that any quantified index of the long-range correlation can be regarded as an indicator of gait functionality. Considering the effect of task-relevant sensory feedback on augmenting human motor performance, we devised shoes with active insoles that could deliver noisy vibration to the soles of feet and assessed their efficacy in enhancing the long-range correlations in the stride parameters for healthy young adults. The vibration could be wirelessly controlled using a smartphone. The actuators, control unit, and battery in the devised shoes were light and embedded in the shoes. By virtue of this compactness, the shoes could be easily used for daily walking outside a laboratory. We performed walking experiments with 20 healthy adults and evaluated the effects of sub- and supra-threshold vibration on long-range correlations in stride interval and length. We performed detrended fluctuation analysis to quantify the long-range correlation of temporal changes in stride interval and length. We found that supra-threshold vibration, applied to the soles with the amplitude of 130 % of the sensory threshold, significantly increased the long-range correlations in stride interval and length by 10.3 % (p = 0.009) and 10.1 % (p = 0.021), respectively. On the other hand, sub-threshold vibration with the amplitude of 90 % of the sensory threshold had no significant effect. These results demonstrate that additional somatosensory feedback through barely detectable vibrations, which are supplied by compact shoes with active insoles, can enhance the indices of "healthy" complexity of locomotor function.

Restoring walking ability in older adults with arm-in-arm gait training: study protocol for the AAGaTT randomized controlled trial

CONTEXT

Falls are a significant problem among older adults. While balance and functional exercises have been shown to be effective, it remains unclear whether regular walking has specific effects on reducing the risk of falls.

RATIONALE

Older people who fall frequently have impaired gait patterns. Recent studies have suggested using interpersonal synchronization: while walking arm-in-arm, an older person synchronizes steps with a younger person to reinstate a better gait pattern. This method of gait training may reduce the risk of falls.

OBJECTIVE

The aim is to assess the efficacy of an arm-in-arm gait-training program in older people.

DESIGN

The arm-in-arm gait training trial (AAGaTT) is a single-site, open label, two-arm, randomized controlled trial.

PARTICIPANTS

We will enroll 66 dyads of older people and their younger "gait instructors". The older participants must be > 70 years old with adequate walking ability. They must have experienced a fall in the year prior to study entry.

INTERVENTION

Dyads will walk an indoor course for 30 min either side-by-side without contact (control group) or arm-in-arm while synchronizing their gait (intervention group). The gait training will be repeated three times a week for four weeks.

OUTCOMES

The main outcome will be the walking speed measured in five-minute walking trials performed at baseline and at the end of each intervention week (week 1 - week 4), and at week 7. Gait quality will be assessed using accelerometers. We will also assess perceived physical activity and health using questionnaires. Finally, we will monitor fall incidence over 18 months. We will evaluate whether outcomes are more improved in the intervention group compared to the control group. In addition, interviews will be conducted to assess the perception of the gait training.

EXPECTED RESULTS

Recent advances in the neurophysiology of motor control have shown that synchronizing gait to external cues or to a human partner can increase the efficiency of gait training. The expected benefits of arm-in-arm gait training are: reduced risk of falls, safe treatment with no adverse effects, and high adherence. This gait training program could be a low-cost intervention with positive effects on the health and well-being of seniors.

TRIAL REGISTRATION

ClinicalTrials.gov NCT05627453. Date of registration: 11.25.2022.

Leveraging a virtual alley with continuously varying width modulates step width variability during self-paced treadmill walking

Increased fall risk in older adults and clinical populations is linked with increased amount and altered temporal structure of step width variability. One approach to rehabilitation seeks to reduce fall risk in older adults by reducing the amount of step width variability and restoring the temporal structure characteristic of healthy young adults. The success of such a program depends on our ability to modulate step width variability effectively. To this end, we investigated how manipulation of the visual walking space in a virtual environment could modulate the amount and temporal structure of step width variability. Nine healthy adults performed self-paced treadmill walking in a virtual alley in a fixed-width Control condition (1.91 m) and two conditions in which the alley's width oscillated sinusoidally at 0.03 Hz: between 0.38 and 1.14 m and 0.38-2.67 m in Narrow and Wide conditions, respectively. The step width time series from each condition was evaluated using: (i) the standard deviation to identify changes in the amount of variability and (ii) the fractal scaling exponent estimated using detrended fluctuation analysis (DFA) to identify changes in the temporal structure of variability in terms of persistence in fluctuations. The Wide condition neither affected the standard deviation nor the fractal scaling exponent of step width time series. The Narrow condition did not affect the standard deviation of step width time series compared to the Control condition but significantly increased its fractal scaling exponent compared to the Control and Wide conditions, suggestive of more persistent fluctuations characteristic of a healthy gait. These results show that virtual reality based rehabilitative intervention can modulate step width variability to potentially reduce fall risk in older adults and clinical populations.

Stride-to-stride time intervals are independently affected by the temporal pattern and probability distribution of visual cues

The temporal structure of the variability of the stride-to-stride time intervals during paced walking is affected by the underlying autocorrelation function (ACF) of the pacing signal. This effect could be accounted for by differences in the underlying probability distribution function (PDF) of the pacing signal. We investigated the isolated and combined effect of the ACF and PDF of the pacing signals on the temporal structure of the stride-to-stride time intervals during visually guided paced overground walking. Ten young, healthy participants completed four walking trials while synchronizing their footstep to a visual pacing signal with a temporal pattern of either pink or white noise (different ACF) and either a Gaussian or normal probability distribution (different PDF). The scaling exponent from the Detrended Fluctuation Analysis was used to quantify the temporal structure of the stride-to-stride time intervals. The ACF and PDF of the pacing signals had independent effects on the scaling exponent of the stride-to-stride time intervals. The scaling exponent was higher during the pink noise pacing trials compared to the white noise pacing trials and higher during the trials with the Gaussian probability distribution compared to the uniform distribution. The results suggest that the sensorimotor system in healthy young individuals has an affinity towards external cues with a pink noise pattern and a Gaussian probability distribution during paced walking.

Adaptive multi-objective control explains how humans make lateral maneuvers while walking

To successfully traverse their environment, humans often perform maneuvers to achieve desired task goals while simultaneously maintaining balance. Humans accomplish these tasks primarily by modulating their foot placements. As humans are more unstable laterally, we must better understand how humans modulate lateral foot placement. We previously developed a theoretical framework and corresponding computational models to describe how humans regulate lateral stepping during straight-ahead continuous walking. We identified goal functions for step width and lateral body position that define the walking task and determine the set of all possible task solutions as Goal Equivalent Manifolds (GEMs). Here, we used this framework to determine if humans can regulate lateral stepping during non-steady-state lateral maneuvers by minimizing errors consistent with these goal functions. Twenty young healthy adults each performed four lateral lane-change maneuvers in a virtual reality environment. Extending our general lateral stepping regulation framework, we first re-examined the requirements of such transient walking tasks. Doing so yielded new theoretical predictions regarding how steps during any such maneuver should be regulated to minimize error costs, consistent with the goals required at each step and with how these costs are adapted at each step during the maneuver. Humans performed the experimental lateral maneuvers in a manner consistent with our theoretical predictions. Furthermore, their stepping behavior was well modeled by allowing the parameters of our previous lateral stepping models to adapt from step to step. To our knowledge, our results are the first to demonstrate humans might use evolving cost landscapes in real time to perform such an adaptive motor task and, furthermore, that such adaptation can occur quickly-over only one step. Thus, the predictive capabilities of our general stepping regulation framework extend to a much greater range of walking tasks beyond just normal, straight-ahead walking.

Characterizing stroke-induced changes in the variability of lower limb kinematics using multifractal detrended fluctuation analysis

Movement variability reflects the adaptation of the neuromuscular control system to internal or external perturbations, but its relationship to stroke-induced injury is still unclear. In this study, the multifractal detrended fluctuation analysis was used to explore the stroke-induced changes in movement variability by analyzing the joint angles in a treadmill-walking task. Eight healthy subjects and ten patients after stroke participated in the experiment, performing a treadmill-walking task at a comfortable speed. The kinematics data of the lower limbs were collected by the motion-capture system, and two indicators, the degree of multifractality (α) and degree of correlation [h(2)], were used to investigate the mechanisms underlying neuromuscular control. The results showed that the knee and ankle joint angles were multifractal and persistent at various scales, and there was a significant difference in the degree of multifractality and the degree of correlation at the knee and ankle joint angles among the three groups, with the values being ranked in the following order: healthy subjects < non-paretic limb < paretic limb. These observations highlighted increased movement variability and multifractal strength in patients after stroke due to neuromotor defects. This study provided evidence that multifractal detrended analysis of the angles of the knee and ankle joints is useful to investigate the changes in movement variability and multifractal after stroke. Further research is needed to verify and promote the clinical applications.

Persistence and anti-persistence in treadmill walking

BACKGROUND

Strong, long-range persistent correlations in stride time (ST) and length (SL) are the fundamental traits of treadmill gait. Our recent work showed that the ST and SL time series' statistical properties originated from the superposition of large-scale trends and small-scale fluctuations (residuals). Trends served as the control manifolds about which ST and SL fluctuated.

RESEARCH QUESTION

Do random changes in treadmill belt speed affect the trend properties and ST/SL scaling exponents?

METHODS

We used Multivariate Adaptive Regression Splines (MARS) to determine gait trends during a walk on a treadmill whose belt speed was perturbed by a strong random noise (coefficient of variation was equal to 0.075, 0.1, and 0.13 for treadmill speed 0.8 m/s, 1.2 m/s, and 1.6 m/s, respectively). Then, we calculated the ST/SL scaling exponents of the experimental time series and the corresponding MARS residuals with the madogram estimator.

RESULTS

Except for the ST at the lowest treadmill speed, the normalized trend duration was at least two times greater than that for the unperturbed walk. The Cauchy distribution scale parameter, which served as a measure of the width of SL and ST trend slope distributions, was at v=1.2m/s, almost 50% and 25% smaller than the unperturbed values. The differences were even greater at v=1.6 m/s: 73% and 83%. Apart from ST at v=0.8m/s, the ST/SL scaling indices were close to 0.5. For all speeds, the ST and SL MARS residuals were strongly anti-persistent. At v=1.2m/s, the corresponding scaling exponents were equal to 0.37±0.10 and 0.25±0.09.

SIGNIFICANCE

At normal and moderate treadmill speeds, in the presence of random belt speed perturbations, strongly anti-persistent fluctuations about gentle, persistent trends can lead to weak persistence/antipersistence of ST/SL time series.

The temporal pattern and the probability distribution of visual cueing can alter the structure of stride-to-stride variability

The structure of the stride-to-stride time intervals during paced walking can be altered by the temporal pattern of the pacing cues, however, it is unknown if an altered probability distribution of these cues could also affect stride-to-stride time intervals. We investigated the effect of the temporal pattern and probability distribution of visual pacing cues on the temporal structure of the variability of the stride-to-stride time intervals during walking. Participants completed self-paced walking (SPW) and walking paced by visual cueing that had a temporal pattern of either pink noise presented with a normal distribution (PNND), shuffled pink noise presented with a normal distribution (SPNND), white noise presented with a normal distribution (WNND), and white noise presented with a uniform distribution (WNUD). The temporal structure of the stride-to-stride time intervals was quantified using the scaling exponent calculated from Detrended Fluctuation Analysis. The scaling exponent was higher during the SPW and PNND trials than during the SPNND, WNND and WNUD trials and it was lower during the WNUD trial compared to the SPNND trial. The results revealed that both the temporal pattern and the probability distribution of the visual pacing cues can affect the scaling exponent of the variability of the stride-to-stride time intervals. This information is fundamental in understanding how visual input is involved in the control of gait.

The Untapped Potential of Virtual Reality in Rehabilitation of Balance and Gait in Neurological Disorders

Dynamic systems theory transformed our understanding of motor control by recognizing the continual interaction between the organism and the environment. Movement could no longer be visualized simply as a response to a pattern of stimuli or as a demonstration of prior intent; movement is context dependent and is continuously reshaped by the ongoing dynamics of the world around us. Virtual reality is one methodological variable that allows us to control and manipulate that environmental context. A large body of literature exists to support the impact of visual flow, visual conditions, and visual perception on the planning and execution of movement. In rehabilitative practice, however, this technology has been employed mostly as a tool for motivation and enjoyment of physical exercise. The opportunity to modulate motor behavior through the parameters of the virtual world is often ignored in practice. In this article we present the results of experiments from our laboratories and from others demonstrating that presenting particular characteristics of the virtual world through different sensory modalities will modify balance and locomotor behavior. We will discuss how movement in the virtual world opens a window into the motor planning processes and informs us about the relative weighting of visual and somatosensory signals. Finally, we discuss how these findings should influence future treatment design.

Walking humans trade off different task goals to regulate lateral stepping

People walk in complex environments where they must adapt their steps to maintain balance and satisfy changing task goals. How people do this is not well understood. We recently developed computational models of lateral stepping, based on Goal Equivalent Manifolds that serve as motor regulation templates, to identify how people regulate walking movements from step-to-step. In normal walking, healthy adults strongly maintain step width, but also lateral position on their path. Here, we used this framework to pose empirically-testable hypotheses about how humans might adapt their lateral stepping dynamics when asked to prioritize different stepping goals. Participants walked on a treadmill in a virtual-reality environment under 4 conditions: normal walking and, while given direct feedback at each step, walking while trying to maintain constant step width, constant absolute lateral position, or constant heading (direction). Time series of lateral stepping variables were extracted, and variability and statistical persistence (reflecting step-to-step regulation) quantified. Participants exhibited less variability of the prescribed stepping variable compared to normal walking during each feedback condition. Stepping regulation results supported our models' predictions: to maintain constant step width or position, people either maintained or increased regulation of the prescribed variable, but also decreased regulation of its complement. Thus, people regulated lateral foot placements in predictable and systematic ways determined by specific task goals. Humans regulate stepping movements to not only "just walk" (step without falling), but also to achieve specific goal-directed tasks within a specific environment. The framework and motor regulation templates presented here capture these important interactions.

How persons with transtibial amputation regulate lateral stepping while walking in laterally destabilizing environments

BACKGROUND

Persons with lower limb amputation often experience decreased physical capacity, difficulty walking, and increased fall risk. To either prevent or recover from a loss of balance, one must effectively regulate their stepping movements. It is therefore critical to identify how well persons with amputation regulate stepping. Here, we used a multi-objective control framework based on Goal Equivalent Manifolds to identify how persons with transtibial amputation (TTA) regulate lateral stepping while walking without and with lateral perturbations.

RESEARCH QUESTION

When walking in destabilizing environments, do otherwise healthy persons with TTA exhibit greater difficulty regulating lateral stepping due to impaired control? Or do they instead continue to use similar strategies to regulate lateral stepping despite their amputation?

METHODS

Eight persons with unilateral TTA and thirteen able-bodied (AB) controls walked in a virtual environment under three conditions: no perturbations, laterally oscillating visual field, and laterally oscillating treadmill platform. We analyzed step-to-step time series of step widths and absolute lateral body positions. We computed means, standard deviations and Detrended Fluctuation Analysis scaling exponents for each time series and computed how much participants directly corrected step width and position deviations at each step. We compared our results to computational predictions to identify the underlying causes of our experimental findings.

RESULTS

All participants exhibited significantly increased variability, decreased scaling exponents, and tighter direct control when perturbed. Simulations from our stepping regulation models revealed that people responded to the increased variability produced by the imposed perturbations by tightening their control of both step width and lateral position. Participants with TTA exhibited only a few minor differences from AB in lateral stepping regulation, even when subjected to substantially destabilizing lateral perturbations.

SIGNIFICANCE

Since control of stepping is intrinsically multi-objective, developing effective interventions to reduce fall risk in persons with amputation will likely require strategies that adopt multi-objective approaches.

Significance of trends in gait dynamics

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.

Detrended fluctuation analysis of gait dynamics when entraining to music and metronomes at different tempi in persons with multiple sclerosis

In persons with multiple sclerosis (PwMS), synchronizing walking to auditory stimuli such as to music and metronomes have been shown to be feasible, and positive clinical effects have been reported on step frequency and perception of fatigue. Yet, the dynamic interaction during the process of synchronization, such as the coupling of the steps to the beat intervals in music and metronomes, and at different tempi remain unknown. Understanding these interactions are clinically relevant, as it reflects the pattern of step intervals over time, known as gait dynamics. 28 PwMS and 29 healthy controls were instructed to walk to music and metronomes at 6 tempi (0–10% in increments of 2%). Detrended fluctuation analysis was applied to calculate the fractal statistical properties of the gait time-series to quantify gait dynamics by the outcome measure alpha. The results showed no group differences, but significantly higher alpha when walking to music compared to metronomes, and when walking to both stimuli at tempi + 8, + 10% compared to lower tempi. These observations suggest that the precision and adaptation gain differ during the coupling of the steps to beats in music compared to metronomes (continuous compared to discrete auditory structures) and at different tempi (different inter-beat-intervals).

Sensorimotor synchronization during gait is altered by the addition of variability to an external cue

Sensorimotor synchronization has been used in the rehabilitation of gait, yet much remains unknown regarding the optimal use of this technique. The purpose of this study was to test the hypothesis that adding small amounts of variability to the motion of a vertically oscillating treadmill would affect the behavior of healthy walkers. Sixteen young adults walked on a treadmill and pneumatically actuated platform for one control trial (no oscillation) and eight trials in which the walking surface oscillated in the vertical direction under different conditions of variability. During the oscillation trials, the mean frequency of oscillation was equal to the preferred step frequency of the participant, but each individual cycle period was allowed to vary within a pre-determined range from 0% (no variability) to ±25% (high variability) of the mean cycle period. The amount of variance of each cycle period within each condition was drawn randomly from a white noise generator. Synchronization was improved when a small amount of noise was added to the platform motion but synchronization significantly decreased at higher levels of noise. Coefficient of variation of stride duration was relatively unchanged at lower levels of variability, but increased significantly at higher levels of variability. Statistical persistence of stride duration was significantly reduced during all trials with vertical oscillation relative to normal walking, but was not significantly altered by variability in the treadmill oscillation. These results suggest that the addition of a small amount of random variability to the cycle period of an oscillator may enhance sensorimotor synchronization of gait to an external signal. These data may have implications for the use of synchronization in a therapeutic setting.

Auditory and Visual External Cues Have Different Effects on Spatial but Similar Effects on Temporal Measures of Gait Variability

Walking synchronized to external cues is a common practice in clinical settings. Several research studies showed that this popular gait rehabilitation tool alters gait variability. There is also recent evidence which suggests that alterations in the temporal structure of the external cues could restore gait variability at healthy levels. It is unknown, however, if such alterations produce similar effects if the cueing modalities used are different; visual or auditory. The modality could affect gait variability differentially, since there is evidence that auditory cues mostly act in the temporal domain of gait, while visual cues act in the spatial domain of gait. This study investigated how synchronizing steps with visual and auditory cues that are presented with different temporal structures could affect gait variability during treadmill walking. Three different temporal structured stimuli were used, invariant, fractal and random, in both modalities. Stride times, length and speed were determined, and their fractal scaling (an indicator of complexity) and coefficient of variation (CV) were calculated. No differences were observed in the CV, regardless of the cueing modality and the temporal structure of the stimuli. In terms of the stride time's fractal scaling, we observed that the fractal stimulus induced higher values compared to random and invariant stimuli. The same was also observed in stride length, but only for the visual cueing modality. No differences were observed for stride speed. The selection of the cueing modality seems to be an important feature of gait rehabilitation. Visual cues are possibly a better choice due to the dependency on vision during walking. This is particularly evident during treadmill walking, a common practice in a clinical setting. Because of the treadmill effect on the temporal domain of gait, the use of auditory cues can be minimal, compared to visual cues.

Gait Recognition via Deep Learning of the Center-of-Pressure Trajectory

The fact that every human has a distinctive walking style has prompted a proposal to use gait recognition as an identification criterion. Using end-to-end learning, I investigated whether the center-of-pressure (COP) trajectory is sufficiently unique to identify a person with high certainty. Thirty-six adults walked for 30 min on a treadmill equipped with a force platform that continuously recorded the positions of the COP. The raw two-dimensional signals were sliced into segments of two gait cycles. A set of 20,250 segments from 30 subjects was used to configure and train convolutional neural networks (CNNs). The best CNN classified a separate set containing 2250 segments with an overall accuracy of 99.9%. A second set of 4500 segments from the six remaining subjects was then used for transfer learning. Several small subsamples of this set were selected randomly and used to fine tune the pretrained CNNs. Training with two segments per subject was sufficient to achieve 100% accuracy. The results suggest that every person produces a unique trajectory of underfoot pressures while walking and that CNNs can learn the distinctive features of these trajectories. By applying a pretrained CNN (transfer learning), a couple of strides seem enough to learn and identify new gaits. However, these promising results should be confirmed in a larger sample under realistic conditions.

Effect of sampling frequency on fractal fluctuations during treadmill walking

The temporal dynamics of stride-to-stride fluctuations in steady-state walking reveal important information about locomotor control and can be quantified using so-called fractal analyses, notably the detrended fluctuation analysis (DFA). Gait dynamics are often collected during treadmill walking using 3-D motion capture to identify gait events from kinematic data. The sampling frequency of motion capture systems may impact the precision of event detection and consequently impact the quantification of stride-to-stride variability. This study aimed i) to determine if collecting multiple walking trials with different sampling frequency affects DFA values of spatiotemporal parameters during treadmill walking, and ii) to determine the reliability of DFA values across downsampled conditions. Seventeen healthy young adults walked on a treadmill while their gait dynamics was captured using different sampling frequency (60, 120 and 240 Hz) in each condition. We also compared data from the highest sampling frequency to downsampled versions of itself. We applied DFA to the following time series: step length, time and speed, and stride length, time and speed. Reliability between experimental conditions and between downsampled conditions were measured with 1) intraclass correlation estimates and their 95% confident intervals, calculated based on a single-measurement, absolute-agreement, two-way mixed-effects model (ICC 3,1), and 2) Bland-Altman bias and limits of agreement. Both analyses revealed a poor reliability of DFA results between conditions using different sampling frequencies, but a relatively good reliability between original and downsampled spatiotemporal variables. Collectively, our results suggest that using sampling frequencies of 120 Hz or 240 Hz provide similar results, but that using 60 Hz may alter DFA values. We recommend that gait kinematics should be collected at around 120 Hz, which provides a compromise between event detection accuracy and processing time.

Complexity of human walking: the attractor complexity index is sensitive to gait synchronization with visual and auditory cues

Background

During steady walking, gait parameters fluctuate from one stride to another with complex fractal patterns and long-range statistical persistence. When a metronome is used to pace the gait (sensorimotor synchronization), long-range persistence is replaced by stochastic oscillations (anti-persistence). Fractal patterns present in gait fluctuations are most often analyzed using detrended fluctuation analysis (DFA). This method requires the use of a discrete times series, such as intervals between consecutive heel strikes, as an input. Recently, a new nonlinear method, the attractor complexity index (ACI), has been shown to respond to complexity changes like DFA, while being computed from continuous signals without preliminary discretization. Its use would facilitate complexity analysis from a larger variety of gait measures, such as body accelerations. The aim of this study was to further compare DFA and ACI in a treadmill experiment that induced complexity changes through sensorimotor synchronization.

Methods

Thirty-six healthy adults walked 30 min on an instrumented treadmill under three conditions: no cueing, auditory cueing (metronome walking), and visual cueing (stepping stones). The center-of-pressure trajectory was discretized into time series of gait parameters, after which a complexity index (scaling exponent alpha) was computed via DFA. Continuous pressure position signals were used to compute the ACI. Correlations between ACI and DFA were then analyzed. The predictive ability of DFA and ACI to differentiate between cueing and no-cueing conditions was assessed using regularized logistic regressions and areas under the receiver operating characteristic curves (AUC).

Results

DFA and ACI were both significantly different among the cueing conditions. DFA and ACI were correlated (Pearson’s r = 0.86). Logistic regressions showed that DFA and ACI could differentiate between cueing/no cueing conditions with a high degree of confidence (AUC = 1.00 and 0.97, respectively).

Conclusion

Both DFA and ACI responded similarly to changes in cueing conditions and had comparable predictive power. This support the assumption that ACI could be used instead of DFA to assess the long-range complexity of continuous gait signals. However, future studies are needed to investigate the theoretical relationship between DFA and ACI.

Years of running experience influences stride-to-stride fluctuations and adaptive response during step frequency perturbations in healthy distance runners

RESEARCH QUESTION

The current study investigated stride-to-stride fluctuations of step rate and contact time in response to enforced step frequency perturbations as well as adaptation and de-adaptation behavior.

METHODS

Forty distance runners ran at a self-selected speed and were asked to match five different enforced step frequencies (150, 160, 170, 180, and 190 beats per min). The influence of experience was explored, because running is a skill that presumably gets better with practice, and increased years of running experience is protective against injury. Detrended fluctuation analysis was used to determine the strength of long-range correlations in gait fluctuations at baseline, during the perturbation, and post-perturbation. Adaptive response was measured by the ability to match, rate of matching, and aftereffect of step frequency perturbations.

RESULTS

The structure of stride-to-stride fluctuations for step rate and contact time did not change during the perturbation or post-perturbation compared to baseline. However, fluctuations in step rate were affected by the level of perturbation. Runners with the most experience had a less persistent structural gait pattern for both step rate and contact time at baseline. Highly experienced runners also demonstrated the best adaptive response. They better matched the enforced step frequency, reached the enforced step frequency sooner, and returned to preferred step frequency more quickly following removal of the perturbation.

SIGNIFICANCE

These findings indicate baseline locomotor flexibility may be beneficial to achieve task demands and return to a stable state once the task is complete. Increased locomotor flexibility may also be a contributing factor for reduced injury risk in experienced runners.

Synchronization dynamics modulates stride-to-stride fluctuations when walking to an invariant but not to a fractal-like stimulus

Walking with different types of cueing/stimulus (i.e. auditory, visual) has been shown to alter gait variability, thus emerging as an innovative therapeutical tool to restore abnormal gait variability in clinical populations. However, the majority of the research in this area has focused on auditory stimuli while visual stimuli are an understudied alternative that needs more attention, particularly due to the natural dependence on vision during walking. Furthermore, the time differences between the occurrences of the walking steps and the sensory cues, also known as asynchronies, have also received minimal attention, even though the ability to synchronize with different stimuli is of great importance. This study investigated how synchronizing to visual stimuli with different temporal structures could affect gait variability and the respective asynchronies. Participants performed four 15-min walking trials around an indoor track while wearing insole footswitches for the following conditions: a) self-paced walking, and b) walking with glasses that instructed the subjects to step in sync with a virtual moving bar. The stepping occurences of the moving bar were presented in three different ways b1) non-variable, b2) variable and b3) random. Stride times and asynchronies were determined, and the mean values along with the fractal scaling (an indicator of the complexity) in their time series, were calculated. The fractal scaling of the stride times was unaltered when participants walked with the variable stimulus as compared to the self-paced walking condition; while fractal scaling was significantly decreased during the non-variable and random conditions, indicating a loss of complexity for these two conditions. No differences were observed in the means or the fractal scaling of the asynchronies. The correlation analysis between stride times and asynchronies revealed a strong relationship for the non-variable condition but a weak relationship for both variable and random conditions. Taken together, the present study results supports the idea of an existing internal timekeeper that exhibits complexity. We have shown that this complex pattern is similar regardless of the stimulus condition, suggesting that the system's complexity is likely to be expressed at the task performance level - asyncrhonies - when walking to a stimulus. Thus, future research in sensoriomotor gait synchronization should focus and further explore the role of the asynchronies, as it may be of clinical significance.

Tightening Up the Control of Treadmill Walking: Effects of Maneuverability Range and Acoustic Pacing on Stride-to-Stride Fluctuations

The correlational structure of stride-to-stride fluctuations differs between healthy and pathological gait. Uncorrelated and anti-persistent stride-to-stride fluctuations are believed to indicate pathology whereas persistence represents healthy functioning. However, this reading can be questioned because the correlational structure changes with task constraints, like acoustic pacing, signifying the tightness of control over particular gait parameters. We tested this “tightness-of-control interpretation” by varying the maneuverability range during treadmill walking (small, intermediate, and large walking areas), with and without acoustic pacing. Stride-speed fluctuations exhibited anti-persistence, suggesting that stride speeds were tightly controlled, with a stronger degree of anti-persistence for smaller walking areas. Constant-speed goal-equivalent-manifold decompositions revealed simultaneous control of stride times and stride lengths, especially for smaller walking areas to limit stride-speed fluctuations. With acoustic pacing, participants followed both constant-speed and constant-stride-time task goals. This was reflected by a strong degree of anti-persistence around the stride-time by stride-length point that uniquely satisfied both goals. Our results strongly support the notion that anti-persistence in stride-to-stride fluctuations reflect the tightness of control over the associated gait parameter, while not tightly regulated gait parameters exhibit statistical persistence. We extend the existing body of knowledge by showing quantitative changes in anti-persistence of already tightly regulated stride-speed fluctuations.

Humans use multi-objective control to regulate lateral foot placement when walking

A fundamental question in human motor neuroscience is to determine how the nervous system generates goal-directed movements despite inherent physiological noise and redundancy. Walking exhibits considerable variability and equifinality of task solutions. Existing models of bipedal walking do not yet achieve both continuous dynamic balance control and the equifinality of foot placement humans exhibit. Appropriate computational models are critical to disambiguate the numerous possibilities of how to regulate stepping movements to achieve different walking goals. Here, we extend a theoretical and computational Goal Equivalent Manifold (GEM) framework to generate predictive models, each posing a different experimentally testable hypothesis. These models regulate stepping movements to achieve any of three hypothesized goals, either alone or in combination: maintain lateral position, maintain lateral speed or “heading”, and/or maintain step width. We compared model predictions against human experimental data. Uni-objective control models demonstrated clear redundancy between stepping variables, but could not replicate human stepping dynamics. Most multi-objective control models that balanced maintaining two of the three hypothesized goals also failed to replicate human stepping dynamics. However, multi-objective models that strongly prioritized regulating step width over lateral position did successfully replicate all of the relevant step-to-step dynamics observed in humans. Independent analyses confirmed this control was consistent with linear error correction and replicated step-to-step dynamics of individual foot placements. Thus, the regulation of lateral stepping movements is inherently multi-objective and balances task-specific trade-offs between competing task goals. To determine how people walk in their environment requires understanding both walking biomechanics and how the nervous system regulates movements from step-to-step. Analogous to mechanical “templates” of locomotor biomechanics, our models serve as “control templates” for how humans regulate stepping movements from each step to the next. These control templates are symbiotic with well-established mechanical templates, providing complimentary insights into walking regulation.

When we walk, we walk in real-world contexts and with specific goal to achieve. Side-to-side movements are paramount because walking bipeds (humans, animals, robots, etc.) are inherently more unstable laterally. This is particularly important in older adults as sideways falls greatly increase hip fracture risk. Additionally, we normally walk on paths that limit (more or less) our lateral movements. Appropriately regulating lateral stepping movements is thus critical to achieving successful locomotion in any such context. Here, we use appropriate models to test competing hypotheses about how humans regulate lateral stepping movements from each step to the next to identify what task goals they try to achieve. Our work both bridges and unifies perspectives from dynamic walking and computational motor control to provide a coherent theoretical and computational framework from which to study motor regulation in the context of goal-directedness across a wide range of walking tasks and/or conditions.

Maximum Lyapunov exponent revisited: Long-term attractor divergence of gait dynamics is highly sensitive to the noise structure of stride intervals

BACKGROUND

The local dynamic stability method (maximum Lyapunov exponent) can assess gait stability. Two variants of the method exist: the short-term divergence exponent (DE), and the long-term DE. Only the short-term DE can predict fall risk. However, the significance of long-term DE has been unclear so far. Some studies have suggested that the complex, fractal-like structure of fluctuations among consecutive strides correlates with long-term DE. The aim, therefore, was to assess whether the long-term DE is a gait complexity index.

METHODS

The study reanalyzed a dataset of trunk accelerations from 100 healthy adults walking at preferred speed on a treadmill for 10 min. By interpolation, the stride intervals were modified within the acceleration signals for the purpose of conserving the original shape of the signal, while imposing a known stride-to-stride fluctuation structure. Four types of hybrid signals with different noise structures were built: constant, anti-correlated, random, and correlated (fractal). Short- and long-term DEs were then computed.

RESULTS

The results show that long-term DEs, but not short-term DEs, are sensitive to the noise structure of stride intervals. For example, it was that observed that random hybrid signals exhibited significantly lower long-term DEs than hybrid correlated signals did (0.100 vs 0.144, i.e. a 44% difference). Long-term DEs from constant hybrid signals were close to zero (0.006). Conversely, short-term DEs of anti-correlated, random, and correlated hybrid signals were closely grouped (2.49, 2.50, and 2.51).

CONCLUSIONS

The short-term DE and the long-term DE, although they are both computed from divergence curves, should not be interpreted in a similar way. The long-term DE is very likely an index of gait complexity, which may be associated with gait automaticity or cautiousness. Consequently, to better differentiate between short- and long-term DEs, the use of the term attractor complexity index (ACI) is proposed for the latter.

Effect of Rhythmic Auditory Cueing on Aging Gait: A Systematic Review and Meta-Analysis

Rhythmic auditory cueing has been widely used in gait rehabilitation over the past decade. The entrainment effect has been suggested to introduce neurophysiological changes, alleviate auditory-motor coupling and reduce cognitive-motor interferences. However, a consensus as to its influence over aging gait is still warranted. A systematic review and meta-analysis was carried out to analyze the effects of rhythmic auditory cueing on spatiotemporal gait parameters among healthy young and elderly participants. This systematic identification of published literature was performed according to PRISMA guidelines, from inception until May 2017, on online databases: Web of science, PEDro, EBSCO, MEDLINE, Cochrane, EMBASE, and PROQUEST. Studies were critically appraised using PEDro scale. Of 2789 records, 34 studies, involving 854 (499 young/355 elderly) participants met our inclusion criteria. The meta-analysis revealed enhancements in spatiotemporal parameters of gait i.e. gait velocity (Hedge's g: 0.85), stride length (0.61), and cadence (1.1), amongst both age groups. This review, for the first time, evaluates the effects of auditory entrainment on aging gait and discusses its implications under higher and lower information processing constraints. Clinical implications are discussed with respect to applications of auditory entrainment in rehabilitation settings.

Characterization of Noise Signatures of Involuntary Head Motion in the Autism Brain Imaging Data Exchange Repository

The variability inherently present in biophysical data is partly contributed by disparate sampling resolutions across instrumentations. This poses a potential problem for statistical inference using pooled data in open access repositories. Such repositories combine data collected from multiple research sites using variable sampling resolutions. One example is the Autism Brain Imaging Data Exchange repository containing thousands of imaging and demographic records from participants in the spectrum of autism and age-matched neurotypical controls. Further, statistical analyses of groups from different diagnoses and demographics may be challenging, owing to the disparate number of participants across different clinical subgroups. In this paper, we examine the noise signatures of head motion data extracted from resting state fMRI data harnessed under different sampling resolutions. We characterize the quality of the noise in the variability of the raw linear and angular speeds for different clinical phenotypes in relation to age-matched controls. Further, we use bootstrapping methods to ensure compatible group sizes for statistical comparison and report the ranges of physical involuntary head excursions of these groups. We conclude that different sampling rates do affect the quality of noise in the variability of head motion data and, consequently, the type of random process appropriate to characterize the time series data. Further, given a qualitative range of noise, from pink to brown noise, it is possible to characterize different clinical subtypes and distinguish them in relation to ranges of neurotypical controls. These results may be of relevance to the pre-processing stages of the pipeline of analyses of resting state fMRI data, whereby head motion enters the criteria to clean imaging data from motion artifacts.

Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill

This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation.

Dynamics of Stride Interval Characteristics during Continuous Stairmill Climbing

It has been shown that statistical persistence in stride intervals characteristics exist during walking, running and cycling and were speed-dependent among healthy young adults. The purpose of this study was to determine if such statistical persistence in stride time interval, stride length and stride speed also exists during self-paced continuous stairmill climbing and if the strength is dependent on stepping rate. Stride time, stride length, and stride speed were collected from nine healthy participants during 3 min of stairmill climbing at 100, 110, and 120% of their preferred stepping rate (PSR) and 5 min of treadmill walking at preferred walking speed (PWS). The amount of variability (assessed by standard deviation and coefficient of variation) and dynamics (assessed by detrended fluctuation analysis and sample entropy) of the stride time, stride length, and stride speed time series were investigated. The amounts of variability were significantly higher during stairmill climbing for the stride time, stride length, and stride speed and did only change with increased stepping rate for stride speed. In addition to a more irregular pattern during stairmill climbing, the detrended fluctuation analysis (DFA) revealed that the stride length fluctuations were statistical anti-persistent for all subjects. On a group level both stride time and stride speed fluctuations were characterized by an uncorrelated pattern which was more irregular compared to that during treadmill walking. However, large inter-participant differences were observed for these two variables. In addition, the dynamics did not change with increase in stepping rate.

Monitoring of Gait Quality in Patients With Chronic Pain of Lower Limbs

Severe injuries of lower extremities often lead to chronic pain and reduced walking abilities. We postulated that measuring free-living gait can provide further information about walking ability in complement to clinical evaluations. We sought to validate a method that characterizes free gaits with a wearable sensor. Over one week, 81 healthy controls (HC) and 66 chronic lower limb pain patients (CLLPP) hospitalized for multidisciplinary rehabilitation wore a simple accelerometer (Actigraph). In the acceleration signals, steady 1-min walks detected numbered 7,835 (5,085 in CLLPP and 2,750 in HC). Five gait quality measures were assessed: movement intensity, cadence, stride regularity, and short-term and long-term local dynamic stability. Gait quality variables differed significantly between CLLPP and HC (4%-26%). Intraclass correlation coefficients revealed moderate to high repeatability (0.71-0.91), which suggests that seven days of measurement are sufficient to assess average gait patterns. Regression analyses showed significant association (R² = 0.44) between the gait quality variables and a clinical evaluation of walking ability, i.e., the 6-min walk test. Overall, the results show that the method is easy to implement, valid (high concurrent validity), and reliable to assess walking abilities ecologically.

Asymmetry of short-term control of spatio-temporal gait parameters during treadmill walking

Optimization of energy cost determines average values of spatio-temporal gait parameters such as step duration, step length or step speed. However, during walking, humans need to adapt these parameters at every step to respond to exogenous and/or endogenic perturbations. While some neurological mechanisms that trigger these responses are known, our understanding of the fundamental principles governing step-by-step adaptation remains elusive. We determined the gait parameters of 20 healthy subjects with right-foot preference during treadmill walking at speeds of 1.1, 1.4 and 1.7 m/s. We found that when the value of the gait parameter was conspicuously greater (smaller) than the mean value, it was either followed immediately by a smaller (greater) value of the contralateral leg (interleg control), or the deviation from the mean value decreased during the next movement of ipsilateral leg (intraleg control). The selection of step duration and the selection of step length during such transient control events were performed in unique ways. We quantified the symmetry of short-term control of gait parameters and observed the significant dominance of the right leg in short-term control of all three parameters at higher speeds (1.4 and 1.7 m/s).

Does Nordic Walking restore the temporal organization of gait variability in Parkinson's disease?

BACKGROUND

Gait disorders of Parkinson's disease (PD) are characterized by the breakdown of the temporal organization of stride duration variability that was tightly associated to dynamic instability in PD. Activating the upper body during walking, Nordic Walking (NW) may be used as an external cueing to improve spatiotemporal parameters of gait, such as stride length or gait variability, in PD. The aim of this study was to evaluate the beneficial effects of NW on temporal organization of gait variability and spatiotemporal gait variables in PD.

METHODS

Fourteen mild to moderate PD participants and ten age-matched healthy subjects performed 2 × 12 min overground walking sessions (with and without pole in a randomized order) at a comfortable speed. Gait speed, cadence, step length and temporal organization (i.e. long-range autocorrelations; LRA) of stride duration variability were studied on 512 consecutive gait cycles using a unidimensional accelerometer placed on the malleola of the most affected side in PD patients and of the dominant side in healthy controls. The presence of LRA was determined using the Rescaled Range Analysis (Hurst exponent) and the Power Spectral Density (α exponent). To assess NW and disease influences on gait, paired t-tests, Z-score and a two-way (pathological condition x walking condition) ANOVA repeated measure were used.

RESULTS

Leading to significant improvement of LRA, NW enhances step length and reduces gait cadence without any change in gait speed in PD. Interestingly, LRA and step length collected from the NW session are similar to that of the healthy population.

CONCLUSION

This cross-sectional controlled study demonstrates that NW may constitute a powerful way to struggle against the randomness of PD gait and the typical gait hypokinesia. Involving a voluntary intersegmental coordination, such improvement could also be due to the upper body rhythmic movements acting as rhythmical external cue to bypass their defective basal ganglia circuitries.

ETHICS COMMITTEE'S REFERENCE NUMBER

B403201318916 TRIAL REGISTRATION: NCT02419768.