An empirical examination of detrended fluctuation analysis for gait data

Effects of metronome walking on long-term attractor divergence and correlation structure of gait: a validation study in older people

This study investigates the effects of metronome walking on gait dynamics in older adults, focusing on long-range correlation structures and long-range attractor divergence (assessed by maximum Lyapunov exponents). Sixty older adults participated in indoor walking tests with and without metronome cues. Gait parameters were recorded using two triaxial accelerometers attached to the lumbar region and to the foot. We analyzed logarithmic divergence of lumbar acceleration using Rosenstein's algorithm and scaling exponents for stride intervals from foot accelerometers using detrended fluctuation analysis (DFA). Results indicated a concomitant reduction in long-term divergence exponents and scaling exponents during metronome walking, while short-term divergence remained largely unchanged. Furthermore, long-term divergence exponents and scaling exponents were significantly correlated. Reliability analysis revealed moderate intrasession consistency for long-term divergence exponents, but poor reliability for scaling exponents. Our results suggest that long-term divergence exponents could effectively replace scaling exponents for unsupervised gait quality assessment in older adults. This approach may improve the assessment of attentional involvement in gait control and enhance fall risk assessment.

Females Present Reduced Minimum Toe Clearance During Walking As Compared to Males in Active Older Adults

BACKGROUND

Physical decline due to aging has been associated with the risk of falls. Minimum toe clearance (MTC) is a gait parameter that might play a role in the mechanism of tripping and falling. However, it is unclear if there are any sex-related effects regarding MTC as people age. The present study investigated if there are sex-related differences in MTC in older active adults.

METHODS

Twenty-three females and 23 males (F: 65.5 ± 4.8 years; M: 61.9 ± 5.2 years) walked on a treadmill at a preferred walking speed, while kinematic data were obtained at a sampling frequency of 100 Hz and up-sampled to 120 and 240 Hz. MTC was calculated from the kinematics data and evaluated concerning its magnitude (ie, MTC and MTC/leg length), the time between left/right MTC (ie, T-MTC), amount of variability (ie, coefficient of variation [CV] and coefficient of variation modified [CVm]), and temporal structure of variability, that is, the complexity of the time series (ie, MTC α, T-MTC α).

RESULTS

No sex effects were found for MTC/leg length, for the amount of variability (ie, CV and CVm), and for the complexity of the time series (MTC α, T-MTC α). However, females exhibited significantly lower MTC and T-MTC after adjusting for walking speed, mass, and age as covariates.

CONCLUSIONS

The reduced MTC in females suggests a potential sex-related disparity in the risk of tripping and falling among active older adults.

Tapping into the human spinal locomotor centres with transspinal stimulation

Human locomotion is controlled by spinal neuronal networks of similar properties, function, and organization to those described in animals. Transspinal stimulation affects the spinal locomotor networks and is used to improve standing and walking ability in paralyzed people. However, the function of locomotor centers during transspinal stimulation at different frequencies and intensities is not known. Here, we document the 3D joint kinematics and spatiotemporal gait characteristics during transspinal stimulation at 15, 30, and 50 Hz at sub-threshold and supra-threshold stimulation intensities. We document the temporal structure of gait patterns, dynamic stability of joint movements over stride-to-stride fluctuations, and limb coordination during walking at a self-selected speed in healthy subjects. We found that transspinal stimulation (1) affects the kinematics of the hip, knee, and ankle joints, (2) promotes a more stable coordination at the left ankle, (3) affects interlimb coordination of the thighs, and (4) intralimb coordination between thigh and foot, (5) promotes greater dynamic stability of the hips, (6) increases the persistence of fluctuations in step length variability, and lastly (7) affects mechanical walking stability. These results support that transspinal stimulation is an important neuromodulatory strategy that directly affects gait symmetry and dynamic stability. The conservation of main effects at different frequencies and intensities calls for systematic investigation of stimulation protocols for clinical applications.

Stride-to-stride variability is altered when running to isochronous visual cueing but remains unaltered with fractal cueing

Running synchronised to external cueing is often implemented in both clinical and training settings, and isochronous cueing has been shown to improve running economy. However, such cueing disregards the natural stride-to-stride fluctuations present in human locomotion which is thought to reflect higher levels of adaptability. The present study aimed to investigate how alterations in the temporal structure of cueing affect stride-to-stride variability during running. We hypothesised that running using cueing with a fractal-like structure would preserve the natural stride-to-stride variability of young adults. Thirteen runners performed four 8-min trials: one uncued (UNC) trial and three cued trials presenting an isochronous (ISO), a fractal (FRC) and a random (RND) structure. Repeated measures ANOVAs were used to identify changes in the dependent variables. We have found no main effect on the cardiorespiratory parameters, whereas a significant main effect was observed in the temporal structure of stride-to-stride variability. During FRC, the participants were able to retain the fractal patterns of their natural locomotor variability observed during the UNC condition, while during the ISO and RND they exhibited more random of fluctuations (i.e., lower values of fractal scaling). Our results demonstrate that cueing based on the natural stride-to-stride fluctuations opens new avenues for training and rehabilitation.

Muscle activity variability patterns and stride to stride fluctuations of older adults are positively correlated during walking

It has been found that fractal-like patterns are present in the temporal structure of the variability of healthy biological rhythms, while pathology and disease lead to their deterioration. Interestingly, it has recently been suggested that these patterns in biological rhythms are related with each other, reflecting overall health or lack of it, due to their interaction. However, the underlying neurophysiological mechanisms responsible for such dependency remain unknown. In addition, this relationship between different elements needs to be first verified before we even pursue understanding their interaction. This study aimed to investigate the relationship between two elements of the neuromuscular system, gait and muscle activity variability patterns in older adults. Twenty-one older adults walked at their preferred walking speed on a treadmill. Inter-stride intervals were obtained through an accelerometer placed on the lateral malleoli to assess the temporal structure of variability of stride-to-stride fluctuations. Inter muscle peak intervals were obtained through the electromyographic signal of the gastrocnemius to assess the temporal structure of the variability of the simultaneous muscle activity. The temporal structure of variability from both signals was evaluated through the detrended fluctuation analysis, while their magnitude of variability was evaluated using the coefficient of variation. The Pearson's Correlation coefficient was used to identify the relationship between the two dependent variables. A significant strong positive correlation was found between the temporal structure of gait and muscle activity patterns. This result suggests that there is an interdependency between biological rhythms that compose the human neuromuscular system.

Stride-to-Stride Fluctuations of Human Gait Are Affected By Chronobiology: An Exploratory Study

Physiological processes present daily oscillations of ≈24 h, called circadian rhythms. Motor performance, for example, reaches its peak in the afternoon, although this can be affected by chronotype. Certain motor activities, for example, walking, can also be affected by circadian rhythms. Healthy walking exhibits stride-to-stride fluctuations with a fractal-like structure that enables adaptability. While pathology and aging are shown to lead to random-like fluctuations; and, therefore, decreased adaptability; the influence of circadian rhythms remains unknown. This study investigates how these fluctuations present in healthy gait are affected by the time of day and chronotype. Eighteen young adults walk for 10 min every 2 h, from 8 a.m. to 6 p.m. Footswitches are used to determine heel-strike and calculate stride time. Then, detrended fluctuation analysis is used to calculate fractal scaling. A mixed-model Analysis of Variance is used and followed by a backward stepwise elimination process. Tukey's tests are used for pairwise comparisons. The statistical model shows the effect of time during the day (12 p.m. exhibits a higher fractal scaling compared to 8 a.m.); and chronotype (evening-types exhibit higher fractal scaling compared to morning-types). This study reveals the influence of chronobiology on stride-to-stride fluctuations. These findings open new perspectives to integrate circadian medicine in biomechanics.

A guide to Whittle maximum likelihood estimator in MATLAB

The assessment of physiological complexity via the estimation of monofractal exponents or multifractal spectra of biological signals is a recent field of research that allows detection of relevant and original information for health, learning, or autonomy preservation. This tutorial aims at introducing Whittle's maximum likelihood estimator (MLE) that estimates the monofractal exponent of time series. After introducing Whittle's maximum likelihood estimator and presenting each of the steps leading to the construction of the algorithm, this tutorial discusses the performance of this estimator by comparing it to the widely used detrended fluctuation analysis (DFA). The objective of this tutorial is to propose to the reader an alternative monofractal estimation method, which has the advantage of being simple to implement, and whose high accuracy allows the analysis of shorter time series than those classically used with other monofractal analysis methods.

Multifractality in stride-to-stride variations reveals that walking involves more movement tuning and adjusting than running

Introduction: The seemingly periodic human gait exhibits stride-to-stride variations as it adapts to the changing task constraints. The optimal movement variability hypothesis (OMVH) states that healthy stride-to-stride variations exhibit "fractality"-a specific temporal structure in consecutive strides that are ordered, stable but also variable, and adaptable. Previous research has primarily focused on a single fractality measure, "monofractality." However, this measure can vary across time; strideto-stride variations can show "multifractality." Greater multifractality in stride-tostride variations would highlight the ability to tune and adjust movements more. Methods: We investigated monofractality and multifractality in a cohort of eight healthy adults during self-paced walking and running trials, both on a treadmill and overground. Footfall data were collected through force-sensitive sensors positioned on their heels and feet. We examined the effects of self-paced walking vs. running and treadmill vs. overground locomotion on the measure of monofractality, α-DFA, in addition to the multifractal spectrum width, W, and the asymmetry in the multifractal spectrum, WAsym, of stride interval time series. Results: While the α-DFA was larger than 0.50 for almost all conditions, α-DFA was higher in running and locomoting overground than walking and locomoting on a treadmill. Similarly, W was greater while locomoting overground than on a treadmill, but an opposite trend indicated that W was greater in walking than running. Larger WAsym values in the negative direction suggest that walking exhibits more variation in the persistence of shorter stride intervals than running. However, the ability to tune and adjust movements does not differ between treadmill and overground, although both exhibit more variation in the persistence of shorter stride intervals. Discussion: Hence, greater heterogeneity in shorter than longer stride intervals contributed to greater multifractality in walking compared to running, indicated by larger negative WAsym values. Our results highlight the need to incorporate multifractal methods to test the predictions of the OMVH.

Running gait produces long range correlations: A systematic review

BACKGROUND

Walking and running are common forms of locomotion, both of which exhibit variability over many gait cycles. Many studies have investigated the patterns generated from that ebb and flow, and a large proportion suggests human gait exhibits Long Range Correlations (LRCs). LRCs refer to the observation that healthy gait characteristic, like stride times, are positively correlated to themselves over time. Literature on LRCs in walking gait is well known but less attention has been given to LRCs in running gait.

RESEARCH QUESTION

What is the state of the art concerning LRCs in running gait?

METHODS

We conducted a systematic review to identify the typical LRC patterns present in human running gait, in addition to disease, injury, and running surface effects on LRCs. Inclusion criteria were human subjects, running related experiments, computed LRCs, and experimental design. Exclusion criteria were studies on animals, non-humans, walking only, non-running, non-LRC analysis, and non-experiments.

RESULTS

The initial search returned 536 articles. After review and deliberation, our review included 26 articles. Almost every article produced strong evidence for LRCs apparent in running gait and in all running surfaces. Additionally, LRCs tended to decrease due to fatigue, past injury, increased load carriage and seem to be lowest at preferred running speed on a treadmill. No studies investigated disease effects on LRCs in running gait.

SIGNIFICANCE

LRCs seem to increase with deviations away from preferred running speed. Previously injured runners produced decreased LRCs compared to non-injured runners. LRCs also tended to decrease due to an increase in fatigue rate, which has been associated with increased injury rate. Lastly, there is a need for research on the typical LRCs in an overground environment, for which the typical LRCs found in a treadmill environment may or may not transfer.

Effects of Motor Task Difficulty on Postural Control Complexity during Dual Tasks in Young Adults: A Nonlinear Approach

Few studies have evaluated the effect of a secondary motor task on the standing posture based on nonlinear analysis. However, it is helpful to extract information related to the complexity, stability, and adaptability to the environment of the human postural system. This study aimed to analyze the effect of two motor tasks with different difficulty levels in motor performance complexity on the static standing posture in healthy young adults. Thirty-five healthy participants (23.08 ± 3.92 years) performed a postural single task (ST: keep a quiet standing posture) and two motor dual tasks (DT). i.e., mot-DT(A)—perform the ST while performing simultaneously an easy motor task (taking a smartphone out of a bag, bringing it to the ear, and putting it back in the bag)—and mot-DT(T)—perform the ST while performing a concurrent difficult motor task (typing on the smartphone keyboard). The approximate entropy (ApEn), Lyapunov exponent (LyE), correlation dimension (CoDim), and fractal dimension (detrending fluctuation analysis, DFA) for the mediolateral (ML) and anterior-posterior (AP) center-of-pressure (CoP) displacement were measured with a force plate while performing the tasks. A significant difference was found between the two motor dual tasks in ApEn, DFA, and CoDim-AP (p < 0.05). For the ML CoP direction, all nonlinear variables in the study were significantly different (p < 0.05) between ST and mot-DT(T), showing impairment in postural control during mot-DT(T) compared to ST. Differences were found across ST and mot-DT(A) in ApEn-AP and DFA (p < 0.05). The mot-DT(T) was associated with less effectiveness in postural control, a lower number of degrees of freedom, less complexity and adaptability of the dynamic system than the postural single task and the mot-DT(A).

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.

Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm

We analyse the fractal nature of geomagnetic field northward and eastward horizontal components with 1 min resolution measured by the four stations Belsk, Hel, Sodankylä and Hornsund during the period of 22 August–1 September, when the 26 August 2018 geomagnetic storm appeared. To reveal and to quantitatively describe the fractal scaling of the considered data, three selected methods, structure function scaling, Higuchi, and detrended fluctuation analysis are applied. The obtained results show temporal variation of the fractal dimension of geomagnetic field components, revealing differences between their irregularity (complexity). The values of fractal dimension seem to be sensitive to the physical conditions connected with the interplanetary shock, the coronal mass ejection, the corotating interaction region, and the high-speed stream passage during the storm development. Especially, just after interplanetary shock occurrence, a decrease in the fractal dimension for all stations is observed, not straightforwardly visible in the geomagnetic field components data.

Decreased Postural Complexity in Overweight to Obese Children and Adolescents: A Cross-Sectional Study

Introduction

Although a few studies suggest that young overweight to obese children and adolescents (YO) may have impaired postural control compared to young normal-weight (YN) peers, little information exists about how these two groups differ in the quality of the underlying balance strategies employed. Hence, the aim of the present study was a first comprehensive examination of the structural complexity of postural sways in these two cohorts during quiet bilateral standing.

Methods

Nineteen YO secondary school students (13.0 ± 1.4 years; male = 10, female = 9) were carefully matched to YN controls (13.0 ± 1.5 years) for age, sex, height, and school. Mediolateral (ML) and anteriorposterior (AP) acceleration signals were recorded with an inertial measurement unit (IMU) positioned at the trunk while standing barefoot in two conditions: firm and foam support surface. The magnitude of postural fluctuations was obtained using the root mean square (RMS). The temporal structure of the signals was analyzed via sample entropy (SEn), largest Lyapunov exponent (LyE), and detrended fluctuation analysis (α-DFA) algorithm. Reliability was assessed using a test–retest design.

Results

In both groups, foam standing caused higher postural fluctuations (higher RMS values) and reduced structural complexity (lower SEn values, higher LyE values, higher α-DFA values). In comparison to YN, YO exhibited a higher RMS_AP. Especially in ML direction, the acceleration signals of the YO had higher repeatability (smaller SEn values), greater long-range correlations (higher α-DFA values), and lower local stability (higher LyE values). However, these observations were largely independent of the task difficulty. Except for α-DFA_AP, the IMU approach proved reliable to characterize posture control.

Discussion

Our outcomes confirm postural control deficits in YO compared to their YN peers and indicate impaired regulatory mechanisms reflected as rigidity. Such less complex patterns usually reflect diverse pathologies, are detrimental to compensate for internal or external perturbations, and are attributed to lower adaptability and task performance. Without targeted balance stimuli, YO likely end in a lifelong vicious circle of mutually dependent poor balance regulation and low physical activity.

Adaptive treadmill walking encourages persistent propulsion

BACKGROUND

Adaptive treadmills allow real-time changes in walking speed by responding to changes in step length, propulsion, or position on the treadmill. The stride-to-stride variability, or persistence, of stride time during overground, fixed-speed, and adaptive treadmill walking has been studied, but persistence of propulsion during adaptive treadmill walking remains unknown. Because increased propulsion is often a goal of post-stroke rehabilitation, knowledge of the stride-to-stride variability may aid rehabilitation protocol design.

RESEARCH QUESTION

How do spatiotemporal and propulsive gait variables vary from stride to stride during adaptive treadmill walking, and how do they compare to fixed-speed treadmill walking?

METHODS

Eighteen young healthy subjects walked on an instrumented split-belt treadmill in the adaptive and fixed-speed modes for 10 minutes at their comfortable speed. Kinetic data was collected from the treadmill. Detrended fluctuation analysis was applied to the time series data. Shapiro-Wilk tests assessed normality and one-way repeated measures ANOVAs compared between adaptive, fixed-speed, and randomly shuffled conditions at a Bonferroni-corrected significance level of 0.0055.

RESULTS

Stride time, stride length, step length, and braking impulse were persistent (α > 0.5) in the adaptive and fixed-speed conditions. Adaptive and fixed-speed were different from each other. Stride speed was persistent in the adaptive condition and anti-persistent (α < 0.5) in the fixed-speed condition. Peak propulsive force, peak braking force, and propulsive impulse were persistent in the adaptive condition but not the fixed-speed condition (α ≈ 0.5). Net impulse was non-persistent in the adaptive and fixed-speed conditions. All variables were non-persistent in the shuffled condition.

SIGNIFICANCE

During adaptive treadmill walking, increases in propulsive force and impulse persist for multiple strides. Persistence was stronger on the adaptive treadmill, where increased propulsion translates into increased walking speed. For post-stroke gait rehabilitation where increasing propulsion and speed are goals, the stronger persistence of adaptive treadmill walking may be beneficial.

Long-Range Correlations and Natural Time Series Analyses from Acoustic Emission Signals

This work focuses on analyzing acoustic emission (AE) signals as a means to predict failure in structures. There are two main approaches that are considered: (i) long-range correlation analysis using both the Hurst (H) and the detrended fluctuation analysis (DFA) exponents, and (ii) natural time domain (NT) analysis. These methodologies are applied to the data that were collected from two application examples: a glass fiber-reinforced polymeric plate and a spaghetti bridge model, where both structures were subjected to increasing loads until collapse. A traditional (AE) signal analysis was also performed to reference the study of the other methods. The results indicate that the proposed methods yield reliable indication of failure in the studied structures.

Long-range correlations and stride pattern variability in recreational and elite distance runners during a prolonged run

BACKGROUND

Although movement variability and long-range correlations (LRCs) have been assessed in relation to neuropathology and aging during walking, to date only a few studies have investigated these aspects in subjects of different skill levels during prolonged overground running.

RESEARCH QUESTION

What effect does skill level and run duration have on different stride parameters, measures of variability and long-range correlations?

METHODS

Using a between-subject repeated measures design, we assessed stride mechanics, variability and LRCs in recreational and elite runners over the course of a continuous exhaustive run. All subjects ran at a fixed, pre-determined running speed relative to their maximal performance. Stride parameters were continually recorded using a single foot-mounted inertial measurement unit. It was hypothesized that a significant reduction in the strength of the LRCs would occur over the course of the run and that the observed changes would be more pronounced in the group of recreational runners.

RESULTS

Runners maintained a consistent stride length (SL), stride time (ST) and contact time (CT) during the run, while peak impact acceleration increased. Across groups, long-range correlations significantly decreased over the course of the run, while the magnitude of the variability remained constant. LRCs did not differ significantly between groups.

SIGNIFICANCE

This is the first study to simultaneously investigate the effects of prolonged running and skill level on a range of stride parameters as well as stride-to-stride variability. Generally, long-range correlations were shown to be sensitive to run duration, while the magnitude of the variability did not differ between earlier and later stages of the run. The lack of a group effect on LRCs supports the idea that the mechanisms responsible for the emergence of temporal patterns in the stride pattern are not influenced by skill level.

Self-paced treadmills do not allow for valid observation of linear and nonlinear gait variability outcomes in patients with Parkinson's disease

BACKGROUND

Due to the imposed constant belt speed, motorized treadmills are known to affect linear and nonlinear gait variability outcomes. This is particularly true of patients with Parkinson's Disease where the treadmill can act as an external pacemaker. Self-paced treadmills update the belt speed in response to the subject's walking speed and might, therefore, be a useful tool for measurement of gait variability in this patient population. This study aimed to compare gait variability during walking at self-paced and constant treadmill speeds with overground walking in individuals with PD and individuals with unimpaired gait.

METHODS

Thirteen patients with Parkinson's Disease and thirteen healthy controls walked under three conditions: overground, on a treadmill at a constant speed, and using three self-paced treadmill modes. Gait variability was assessed with coefficient of variation (CV), sample entropy (SampEn), and detrended fluctuation analysis (DFA) of stride time and length. Systematic and random error between the conditions was quantified.

RESULTS

For individuals with PD, error in variability measurement was less during self-paced modes compared with constant treadmill speed for stride time but not for stride length. However, there was substantial error for stride time and length variability for all treadmill conditions. For healthy controls the error in measurement associated with treadmill walking was substantially less.

SIGNIFICANCE

The large systematic and random errors between overground and treadmill walking prohibit meaningful gait variability observations in patients with Parkinson's Disease using self-paced or constant-speed treadmills.

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.

Test-Retest Reliability and the Effects of Walking Speed on Stride Time Variability During Continuous, Overground Walking in Healthy Young Adults

Studies have investigated the reliability and effect of walking speed on stride time variability during walking trials performed on a treadmill. The objective of this study was to investigate the reliability of stride time variability and the effect of walking speed on stride time variability, during continuous, overground walking in healthy young adults. Participants completed: (1) 2 walking trials at their preferred walking speed on 1 day and another trial 2 to 4 days later and (2) 1 trial at their preferred walking speed, 1 trial approximately 20% to 25% faster than their preferred walking speed, and 1 trial approximately 20% to 25% slower than their preferred walking speed on a separate day. Data from a waist-mounted accelerometer were used to determine the consecutive stride times for each trial. The reliability of stride time variability outcomes was generally poor (intraclass correlations: .167-.487). Although some significant differences in stride time variability were found between the preferred walking speed, fast, and slow trials, individual between-trial differences were generally below the estimated minimum difference considered to be a real difference. The development of a protocol to improve the reliability of stride time variability outcomes during continuous, overground walking would be beneficial to improve their application in research and clinical settings.

Assessing the Temporal Organization of Walking Variability: A Systematic Review and Consensus Guidelines on Detrended Fluctuation Analysis

Human physiological signals are inherently rhythmic and have a hallmark feature in that even distant intrasignal measurements are related to each other. This relationship is termed long-range correlation and has been recognized as an indicator of the optimal state of the observed physiological systems, among which the locomotor system. Loss of long-range correlations has been found as a result of aging as well as disease, which can be evaluated with detrended fluctuation analysis (DFA). Recently, DFA and the scaling exponent α have been employed for understanding the degeneration of temporal regulation of human walking biorhythms in, for example, Parkinson disease (PD). However, heterogeneous evidence on scaling exponent α values reported in the literature across different population groups has put into question what constitutes a healthy physiological pattern. Therefore, the purpose of this systematic review was to investigate the functional thresholds of scaling exponent α in young vs. older adults, as well as between patients with PD and age-matched asymptomatic controls. Aging and PD exhibited a negative effect size (i.e., led to decreased long-range correlations) of -0.20 and -0.53, respectively. Our meta-analysis based on 14 studies provides evidence that a mean scaling exponent α threshold of 0.86 [2 standard error (0.76, 0.96)] is able to optimally discriminate temporal organization of stride interval between young and old, whereas 0.82 (0.72, 0.92) differentiates patients with PD and age-matched asymptomatic controls. The optimal thresholds presented in this review together with the consensus guidelines for using DFA might allow a more sensitive and reliable application of this metric for understanding human walking physiology than has been achieved to date.

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.

Fractal Analysis of Human Gait Variability via Stride Interval Time Series

Fractal analysis of stride interval time series is a useful tool in human gait research which could be used as a marker for gait adaptability, gait disorder, and fall risk among patients with movement disorders. This study is designed to systematically and comprehensively investigate two practical aspects of fractal analysis which significantly affect the outcome: the series length and the parameters used in the algorithm. The Hurst exponent, scaling exponent, and/or fractal dimension are computed from both simulated and experimental data using three fractal methods, namely detrended fluctuation analysis, box-counting dimension, and Higuchi's fractal dimension. The advantages and drawbacks of each method are discussed, in terms of biases and variability. The results demonstrate that a careful selection of fractal analysis methods and their parameters is required, which is dependent on the aim of study (either analyzing differences between experimental groups or estimating an accurate determination of fractal features). A set of guidelines for the selection of the fractal methods and the length of stride interval time series is provided, along with the optimal parameters for a robust implementation for each method.

Comparison of a portable balance board for measures of persistence in postural sway

Measuring postural sway is important for determining functional ability or risk of falling. Gathering postural sway measures outside of controlled environments is desirable for reaching populations with limited mobility. Previous studies have confirmed the accuracy of the magnitude of postural sway using the Nintendo Wii Balance Board (WBB). However, it is unclear if the WBB can accurately measure persistence of postural sway, i.e., the pattern of center-of-pressure fluctuations over time. The purpose of this study was to compare measures of persistence of postural sway (through detrended fluctuation analysis) using WBB and a force platform (FP). Seventeen healthy individuals performed three standing conditions: eyes open, eyes closed, and one-leg standing. The WBB (30 Hz) was placed on top on the FP (600 Hz) to collect data simultaneously, then the FP data were downsampled to 100 Hz and 30 Hz. The agreement between WBB and FP for measures of postural sway were influenced by the sampling rate and postural sway direction. Intraclass correlation coefficient was excellent (range: 0.953-0.998) for long-term scaling regions in the anterior-posterior direction, but lower (range: 0.352-0.877) and inconsistent for medial-lateral direction and short-term scaling regions. The three comparison groups (WBB at 30 Hz, FP at 30 Hz, and FP at 100 Hz) showed dissimilar abilities in detecting differences in persistence of postural sway. In summary, the WBB is accurate for quantifying persistence of postural sway measurements in long-term scaling regions in the AP direction, but has limitations for short-term scaling regions and the ML direction.

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.

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.

Reliability of the fluctuations within the stride time series measured in runners during treadmill running to exhaustion

BACKGROUND

The fluctuations within stride time series (i.e., stride time variability and complexity) during running exhibit long-range correlation. Detecting the breakdown of the long-range correlation was proposed for monitoring the occurrence of running-related injuries during running. However, the stride time fluctuations were only measured from the unilateral side. In addition, the reliability of the stride time fluctuations of within-subject repeated measures remains largely unknown, particularly during exhaustive running.

PURPOSES

This study investigated between-side and between-day reliabilities of the stride time variability and complexity of right and left sides during an exhaustive running.

METHODS

The stride time variability and complexity of bilateral sides were obtained while 24 healthy participants performed a 31-minute treadmill running at their individual anaerobic threshold speed. Seven of the 24 participants performed the treadmill running test twice at two different days 5-7 days apart. Limits of agreement (LoA) and intraclass correlation coefficient (ICC) were respectively used to assess the absolute and relative between-side and between-day reliabilities.

RESULTS

The stride time variability and complexity of right and left sides were highly symmetrical (LoA: (-0.500%, 0.459%) and (-0.052, 0.051), respectively; ICC: 0.94 (0.87, 0.97) and 0.98 (0.95, 0.99), respectively). The overall stride time variability and complexity revealed good between-day reliability (LoA: (-1.044%, 0.724%) and (-0.067, 0.115), respectively; ICC: 0.78 (0.45, 0.92) and 0.81 (0.48, 0.93), respectively). However, the segmented stride time complexity showed poor between-day reliability (ICCs<0.40).

CONCLUSION

The findings demonstrated that the stride time series showed equivalent fluctuations between right and left sides and good between-day reliability in fluctuations during exhaustive running. Given the poor between-day reliability in the segmented stride time series, stride time series during exhaustive running could be collected from either right or left side and should be processed as an overall in the future.

Fractal analysis of gait in people with Parkinson's disease: three minutes is not enough

BACKGROUND

The fractal dynamics of gait variability in people with Parkinson's disease has been studied by applying the detrended fluctuation analysis (DFA) to short time series (<200 strides). However, DFA is sensitive to time series length, and it is unclear if DFA results from short time series are reliable and if they reflect the fractal dynamics of longer time series.

RESEARCH QUESTION

Is DFA reliable when applied to short time series?

METHODS

We applied DFA to stride time series from five 3-min trials and one 15-min trial in 12 people with Parkinson's disease, 14 healthy older adults and 14 healthy young adults walking overground. Within each group, intraclass correlations (ICC 3,1) were performed to assess the reliability of i) the five 3-min trials together, ii) each 3-min trials to the 15-min trial, and iii) the first 150 strides from the 15-min trial to the full 15-min trial.

RESULTS

Our three main findings are that 1) stride time α-DFA values are not consistent from trial-to-trial for short stride time series, 2) stride time α-DFA values from each 3-min trials are not consistent when compared to stride time α-DFA values from a 15-min trial, and 3) stride time α-DFA values from the first 150 strides of the 15-min trial are not consistent when compared to α-DFA values from the full 15-min trial.

SIGNIFICANCE

Our results confirm that α-DFA values from 3-min walking trials are not reliable, and that they do not reflect the scale invariant properties of longer time series. This suggests that previous studies assessing the fractal dynamics of gait variability from about 3-min walking must be interpreted with caution. A major clinical implication is that DFA cannot be used to study gait in people unable to perform 500 strides continuously.

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.

Interaction between step-to-step variability and metabolic cost of transport during human walking

Minimizing the metabolic cost of transport can affect selection of the preferred walking speed. While many factors can affect metabolic cost of transport during human walking, its interaction with step-to-step variability is unclear. Here, we aimed to determine the interaction between metabolic cost of transport and step length variability during human walking at different speeds. In particular, two aspects of step length variability were analyzed: the amount of variations ('variations') and the organization of the step-to-step fluctuations ('fluctuations'). Ten healthy, young participants walked on a treadmill at five speeds, ranging from 0.75 to 1.75 m s^-1 Metabolic cost of transport, step length variations (coefficient of variation) and step length fluctuations (quantified via detrended fluctuation analysis) were calculated. A mixed-model ANOVA revealed that variations and walking speed were strong predictors of metabolic cost of transport (R ²=0.917, P<0.001), whereas fluctuations were not. Preferred walking speed (1.05±0.20 m s^-1) was not significantly different from the speed at which metabolic cost of transport was minimized (1.04±0.05 m s^-1; P=0.792), nor from the speed at which fluctuations were most persistent (1.00±0.41 m s^-1; P=0.698). The minimization of variations occurred at a faster speed (1.56±0.17 m s^-1) than the preferred walking speed (P<0.001). Step length variations likely affect metabolic cost of transport because greater variations are indicative of suboptimal, mechanically inefficient steps. Fluctuations have little or no effect on metabolic cost of transport, but still may relate to preferred walking speed.

When Coordinating Finger Tapping to a Variable Beat the Variability Scaling Structure of the Movement and the Cortical BOLD Signal are Both Entrained to the Auditory Stimuli

Rhythmic actions are characterizable as a repeating invariant pattern of movement together with variability taking the form of cycle-to-cycle fluctuations. Variability in behavioral measures is atypically random, and often exhibits serial temporal dependencies and statistical self-similarity in the scaling of variability magnitudes across timescales. Self-similar (i.e. fractal) variability scaling is evident in measures of both brain and behavior. Variability scaling structure can be quantified via the scaling exponent (α) from detrended fluctuation analysis (DFA). Here we study the task of coordinating thumb-finger tapping to the beats of constructed auditory stimuli. We test the hypothesis that variability scaling evident in tap-to-tap intervals as well as in the fluctuations of cortical hemodynamics will become entrained to (i.e. drawn toward) manipulated changes in the variability scaling of a stimulus's beat-to-beat intervals. Consistent with this hypothesis, manipulated changes of the exponent α of the experimental stimuli produced corresponding changes in the exponent α of both tap-to-tap intervals and cortical hemodynamics. The changes in hemodynamics were observed in both motor and sensorimotor cortical areas in the contralateral hemisphere. These results were observed only for the longer timescales of the detrended fluctuation analysis used to measure the exponent α. These findings suggest that complex auditory stimuli engage both brain and behavior at the level of variability scaling structures.

Concurrent Changes of Brain Functional Connectivity and Motor Variability When Adapting to Task Constraints

In behavioral neuroscience, the adaptability of humans facing different constraints has been addressed on one side at the brain level, where a variety of functional networks dynamically support the same performance, and on the other side at the behavioral level, where fractal properties in sensorimotor variables have been considered as a hallmark of adaptability. To bridge the gap between the two levels of observation, we have jointly investigated the changes of network connectivity in the sensorimotor cortex assessed by modularity analysis and the properties of motor variability assessed by multifractal analysis during a prolonged tapping task. Four groups of participants had to produce the same tapping performance while being deprived from 0, 1, 2, or 3 sensory feedbacks simultaneously (auditory and/or visual and/or tactile). Whereas tapping performance was not statistically different across groups, the number of brain networks involved and the degree of multifractality of the inter-tap interval series were significantly correlated, increasing as a function of feedback deprivation. Our findings provide first evidence that concomitant changes in brain modularity and multifractal properties characterize adaptations underlying unchanged performance. We discuss implications of our findings with respect to the degeneracy properties of complex systems, and the entanglement of adaptability and effective adaptation.

Gait Dynamics in Parkinson's Disease: Short Gait Trials "Stitched" Together Provide Different Fractal Fluctuations Compared to Longer Trials

The fractal analysis of stride-to-stride fluctuations in walking has become an integral part of human gait research. Fractal analysis of stride time intervals can provide insights into locomotor function and dysfunction, but its application requires a large number of strides, which can be difficult to collect from people with movement disorders such as Parkinson's disease. It has recently been suggested that "stitching" together short gait trials to create a longer time series could be a solution. The objective of this study was to determine if scaling exponents from "stitched" stride time series were similar to those from continuous, longer stride time series. Fifteen young adults, fourteen older adults, and thirteen people with Parkinson's disease walked around an indoor track in three blocks: one time 15 min, five times 3 min, and thirty times 30 s. Stride time intervals were determined from gait events recorded with instrumented insoles, and the detrended fluctuation analysis was applied to each stride time series of 512 strides. There was no statistically significant difference between scaling exponents in the three blocks, but intra-class correlation revealed very low between-blocks reliability of scaling exponents. This result challenges the premise that the stitching procedure could provide reliable information about gait dynamics, as it suggests that fractal analysis of stitched time series does not capture the same dynamics as gait recorded continuously. The stitching procedure cannot be considered as a valid alternative to the collection of continuous, long trials. Further studies are recommended to determine if the application of fractal analysis is limited by its own methodological considerations (i.e., long time series), or if other solutions exists to obtain reliable scaling exponents in populations with movement disorders.

Stride-to-stride variability and complexity between novice and experienced runners during a prolonged run at anaerobic threshold speed

BACKGROUND

Motor control, related to running performance and running related injuries, is affected by progression of fatigue during a prolonged run. Distance runners are usually recommended to train at or slightly above anaerobic threshold (AT) speed for improving performance. However, running at AT speed may result in accelerated fatigue. It is not clear how one adapts running gait pattern during a prolonged run at AT speed and if there are differences between runners with different training experience.

PURPOSES

To compare characteristics of stride-to-stride variability and complexity during a prolonged run at AT speed between novice runners (NR) and experienced runners (ER).

METHODS

Both NR (n = 17) and ER (n = 17) performed a treadmill run for 31 min at his/her AT speed. Stride interval dynamics was obtained throughout the run with the middle 30 min equally divided into six time intervals (denoted as T1, T2, T3, T4, T5 and T6). Mean, coefficient of variation (CV) and scaling exponent alpha of stride intervals were calculated for each interval of each group.

RESULTS

This study revealed mean stride interval significantly increased with running time in a non-linear trend (p<0.001). The stride interval variability (CV) maintained relatively constant for NR (p = 0.22) and changed nonlinearly for ER (p = 0.023) throughout the run. Alpha was significantly different between groups at T2, T5 and T6, and nonlinearly changed with running time for both groups with slight differences.

SIGNIFICANCE

These findings provided insights into how the motor control system adapts to progression of fatigue and evidences that long-term training enhances motor control. Although both ER and NR could regulate gait complexity to maintain AT speed throughout the prolonged run, ER also regulated stride interval variability to achieve the goal.

Transitions in persistence of postural dynamics depend on the velocity and structure of postural perturbations

The sensorimotor system prefers sway velocity information when maintaining upright posture. Sway velocity has a unique characteristic of being persistent on a short time-scale and anti-persistent on a longer time-scale. The time where the transition from persistence to anti-persistence occurs provides information about how sway velocity is controlled. It is, however, not clear what factors affect shifts in this transition point. This research investigated postural responses to support surface movements of different temporal correlations and movement velocities. Participants stood on a force platform that was translated according to three different levels of temporal correlation. White noise had no correlation, pink noise had moderate correlation, and sine wave movements had very strong correlation. Each correlation structure was analyzed at five different average movement velocities (0.5, 1.0, 2.0, 3.0, and 4.0 cm·s^-1), as well as one trial of quiet stance. Center of pressure velocity was analyzed using fractal analysis to determine the transition from persistent to anti-persistent behavior, as well as the strength of persistence. As movement velocity increased, the time to transition became longer for the sine wave and shorter for the white and pink noise movements. Likewise, during the persistent time-scale, the sine wave resulted in the strongest correlation, while white and pink noise had weaker correlations. At the highest three movement velocities, the strength of persistence was lower for the white noise compared to pink noise movements. These results demonstrate that the predictability and velocity of support surface oscillations affect the time-scale threshold between persistent and anti-persistent postural responses. Consequently, whether a feedforward or feedback control is utilized for appropriate postural responses may also be determined by the predictability and velocity of environmental stimuli. The study provides new insight into flexibility and adaptability in postural control. This information has implications for the design of rehabilitative protocols in neuromuscular control.

Gait Complexity and Regularity Are Differently Modulated by Treadmill Walking in Parkinson's Disease and Healthy Population

Variability raises considerable interest as a promising and sensitive marker of dysfunction in physiology, in particular in neurosciences. Both internally (e.g., pathology) and/or externally (e.g., environment) generated perturbations and the neuro-mechanical responses to them contribute to the fluctuating dynamics of locomotion. Defective internal gait control in Parkinson's disease (PD), resulting in typical timing gait disorders, is characterized by the breakdown of the temporal organization of stride duration variability. Influence of external cue on gait pattern could be detrimental or advantageous depending on situations (healthy or pathological gait pattern, respectively). As well as being an interesting rehabilitative approach in PD, treadmills are usually implemented in laboratory settings to perform instrumented gait analysis including gait variability assessment. However, possibly acting as an external pacemaker, treadmill could modulate the temporal organization of gait variability of PD patients which could invalidate any gait variability assessment. This study aimed to investigate the immediate influence of treadmill walking (TW) on the temporal organization of stride duration variability in PD and healthy population. Here, we analyzed the gait pattern of 20 PD patients and 15 healthy age-matched subjects walking on overground and on a motorized-treadmill (randomized order) at a self-selected speed. The temporal organization and regularity of time series of walking were assessed on 512 consecutive strides and assessed by the application of non-linear mathematical methods (i.e., the detrended fluctuation analysis and power spectral density; and sample entropy, for the temporal organization and regularity of gait variability, respectively). A more temporally organized and regular gait pattern seems to emerge from TW in PD while no influence was observed on healthy gait pattern. Treadmill could afford the necessary framework to regulate gait rhythmicity in PD. Overall, the results support the hypothesis of a greater dependence to regulatory inputs as an explanatory factor of treadmill influence observed in PD. Also, since treadmill misrepresents the gait as more healthy than it is, the present findings underline that gait analysis using treadmill devices should be cautiously considered in PD and especially for gait variability assessment in gait lab.

Fractal Dynamics, Variability, and Coordination in Human Locomotion

In human locomotion, the magnitude of gait variability is a strong predictor of fall risk and frailty due to aging and disease. Beyond variability magnitude, the past two decades have provided emerging alternative methodologies for studying biological variability. Specifically, coordination variability has been found to be critically important within a healthy, adaptive system. While many activities aim to minimize end-point variability, greater coordination variability indicates a more flexible system, and is greater in experts compared to novices, or healthy compared to diseased individuals. Finally, variability structure (i.e., fractal dynamics) may describe the overall adaptive capacity of the locomotor system. We provide empirical support that fractal dynamics are associated with step length symmetry during challenging split-belt treadmill walking. Individuals whose fractal scaling approached 1/f fractal scaling during constrained walking also exhibited the best gait adaptability performance. Importantly, this relation between fractality and gait adaptability was not observed in unperturbed preferred speed walking.

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.

Can Tai Chi training impact fractal stride time dynamics, an index of gait health, in older adults? Cross-sectional and randomized trial studies

Purpose

To determine if Tai Chi (TC) has an impact on long-range correlations and fractal-like scaling in gait stride time dynamics, previously shown to be associated with aging, neurodegenerative disease, and fall risk.

Methods

Using Detrended Fluctuation Analysis (DFA), this study evaluated the impact of TC mind-body exercise training on stride time dynamics assessed during 10 minute bouts of overground walking. A hybrid study design investigated long-term effects of TC via a cross-sectional comparison of 27 TC experts (24.5 ± 11.8 yrs experience) and 60 age- and gender matched TC-naïve older adults (50–70 yrs). Shorter-term effects of TC were assessed by randomly allocating TC-naïve participants to either 6 months of TC training or to a waitlist control. The alpha (α) long-range scaling coefficient derived from DFA and gait speed were evaluated as outcomes.

Results

Cross-sectional comparisons using confounder adjusted linear models suggest that TC experts exhibited significantly greater long-range scaling of gait stride time dynamics compared with TC-naïve adults. Longitudinal random-slopes with shared baseline models accounting for multiple confounders suggest that the effects of shorter-term TC training on gait dynamics were not statistically significant, but trended in the same direction as longer-term effects although effect sizes were very small. In contrast, gait speed was unaffected in both cross-sectional and longitudinal comparisons.

Conclusion

These preliminary findings suggest that fractal-like measures of gait health may be sufficiently precise to capture the positive effects of exercise in the form of Tai Chi, thus warranting further investigation. These results motivate larger and longer-duration trials, in both healthy and health-challenged populations, to further evaluate the potential of Tai Chi to restore age-related declines in gait dynamics.

Trial registration

The randomized trial component of this study was registered at ClinicalTrials.gov (NCT01340365).

Impact of series length on statistical precision and sensitivity of autocorrelation assessment in human locomotion

Long-range autocorrelations (LRA) are a robust feature of rhythmic movements, which may provide important information about neural control and potentially constitute a powerful marker of dysfunction. A clear difficulty associated with the assessment of LRA is that it requires a large number of cycles to generate reliable results. Here we investigate how series length impacts the reliability of LRA assessment. A total of 94 time series extracted from walking or cycling tasks were re-assessed with series length varying from 64 to 512 data points. LRA were assessed using an approach combining the rescaled range analysis or the detrended fluctuation analysis (Hurst exponent, H), along with the shape of the power spectral density (α exponent). The statistical precision was defined as the ability to obtain estimates for H and α that are consistent with their theoretical relationship, irrespective of the series length. The sensitivity consisted of testing whether significant differences between experimental conditions found in the original studies when considering 512 data points persisted with shorter series. We also investigate the use of evenly-spaced diffusion plots as a methodological improvement of original version of methods for short series. Our results show that the reliable assessment of LRA requires 512 data points, or no shorter than 256 data points provided that more robust methods are considered such as the evenly-spaced algorithms. Such series can be reasonably obtained in clinical populations with moderate, or even more severe, gait impairments and open the perspective to extend the use of LRA assessment as a marker of gait stability applicable to a broad range of locomotor disorders.

Power considerations for the application of detrended fluctuation analysis in gait variability studies

The assessment of gait variability using stochastic signal processing techniques such as detrended fluctuation analysis (DFA) has been shown to be a sensitive tool for evaluation of gait alterations due to aging and neuromuscular disease. However, previous studies have suggested that the application of DFA requires relatively long recordings (600 strides), which is difficult when working with clinical populations or older adults. In this paper we propose a model for predicting DFA variance in experimental data and conduct a Monte Carlo simulation to estimate the sample size and number of trials required to detect a change in DFA scaling exponent. We illustrate the model in a simulation to detect a difference of 0.1 (medium effect) between two groups of subjects when using short gait time series (100 to 200 strides) in the context of between- and within-subject designs. We assumed that the variance of DFA scaling exponent arises due to individual differences, time series length, and experimental error. Results showed that sample sizes required to achieve acceptable power of 80% are practically feasible, especially when using within-subject designs. For example, to detect a group difference in the DFA scaling exponent of 0.1, it would require either 25 subjects and 2 trials per subject or 12 subjects and 4 trials per subject using a within-subject design. We then compared plausibility of such power predictions to the empirically observed power from a study that required subjects to synchronize with a persistent fractal metronome. The results showed that the model adequately predicted the empirical pattern of results. Our power simulations could be used in conjunction with previous design guidelines in the literature when planning new gait variability experiments.

The effects of altering attentional demands of gait control on the variability of temporal and kinematic parameters

The purpose of this study was to investigate the effects of cognitive and visuomotor tasks on gait control in terms of the magnitude and temporal structure of the variability in stride time and lower-limb kinematics measured using inertial sensors. Fourteen healthy young subjects walked on a treadmill for 15min at a self-selected gait speed in the three conditions: normal walking without a concurrent task; walking while performing a cognitive task; and walking while performing a visuomotor task. The time series data of stride time and peak shank angular velocity were generated from acceleration and angular velocity data recorded from both shanks. The mean, coefficient of variation, and fractal scaling exponent α of the time series of these variables and the standard deviation of shank angular velocity over the entire stride cycle were calculated. The cognitive task had an effect on long-range correlations in stride time but not on lower-limb kinematics. The temporal structure of variability in stride time became more random in the cognitive task. The visuomotor task had an effect on lower-limb kinematics. Subjects controlled their swing limb with greater variability and had a more complex adaptive lower-limb movement pattern in the visuomotor task. The effects of the dual tasks on gait control were different for stride time and lower-limb kinematics. These findings suggest that the temporal structure of variability and lower-limb kinematics are useful parameters to detect a change in gait pattern and provide further insight into gait control.

Gait dynamics when wearing a treadmill safety harness

Nonlinear dynamics quantifies gait variability patterns, which can be useful in evaluating functional ability. A commonly used nonlinear technique is detrended fluctuation analysis (DFA). Safety support structures have previously been shown to alter DFA during gait. However, the effect of a nonweight-supporting treadmill harness on DFA during gait has yet to be determined. The purpose of this study was to determine whether a nonweight-supporting harness influenced the DFA alpha metric (DFA α) of variables typically used to examine gait function. Twenty participants (10 young adults and 10 older adults) were recruited for this study. Each participant completed one testing session on a treadmill consisting of three conditions: (1) no harness, (2) harnessed, but not attached to the support frame, and (3) harnessed and attached to the support frame. Participants walked for 15 min at the same self-selected speed for each condition. The gait variables of stride time, stride length, and step width for each condition were analyzed using DFA α to examine gait function. There were no significant interactions between age group and condition for DFA α of each variable. Additionally, there were no main effects for DFA α for age group or condition. These data indicate that a nonweight-supporting harness can be used for safety without impeding the emergence of natural gait dynamics when stride time, stride length, and step width are the primary variables of interest.

Assessing interactions among multiple physiological systems during walking outside a laboratory: An Android based gait monitor

Gait function is traditionally assessed using well-lit, unobstructed walkways with minimal distractions. In patients with subclinical physiological abnormalities, these conditions may not provide enough stress on their ability to adapt to walking. The introduction of challenging walking conditions in gait can induce responses in physiological systems in addition to the locomotor system. There is a need for a device that is capable of monitoring multiple physiological systems in various walking conditions. To address this need, an Android-based gait-monitoring device was developed that enabled the recording of a patient's physiological systems during walking. The gait-monitoring device was tested during self-regulated overground walking sessions of fifteen healthy subjects that included 6 females and 9 males aged 18-35 years. The gait-monitoring device measures the patient's stride interval, acceleration, electrocardiogram, skin conductance and respiratory rate. The data is stored on an Android phone and is analyzed offline through the extraction of features in the time, frequency and time-frequency domains. The analysis of the data depicted multisystem physiological interactions during overground walking in healthy subjects. These interactions included locomotion-electrodermal, locomotion-respiratory and cardiolocomotion couplings. The current results depicting strong interactions between the locomotion system and the other considered systems (i.e., electrodermal, respiratory and cardiovascular systems) warrant further investigation into multisystem interactions during walking, particularly in challenging walking conditions with older adults.

Wearing a Wetsuit Alters Upper Extremity Motion during Simulated Surfboard Paddling

Surfers often wear wetsuits while paddling in the ocean. This neoprene covering may be beneficial to upper extremity movement by helping to improve proprioceptive acuity, or it may be detrimental by providing increased resistance. The purpose of this study was to evaluate the effects of wearing a wetsuit on muscle activation, upper extremity motion, heart rate, and oxygen consumption during simulated surfboard paddling in the laboratory. Twelve male, recreational surfers performed two paddling trials at a constant workload on a swim bench ergometer both with and without a wetsuit. Kinematic data and EMG were acquired from the right arm via motion capture, and oxygen consumption and heart rate were recorded with a metabolic cart and heart rate monitor. Wearing a wetsuit had no significant effect on oxygen consumption or heart rate. A significant increase in EMG activation was observed for the middle deltoid but not for any of the other shoulder muscle evaluated. Finally, approximate entropy and estimates of the maximum Lyapunov exponent increased significantly for vertical trajectory of the right wrist (i.e. stroke height) when a wetsuit was worn. These results suggest that a 2mm wetsuit has little effect on the energy cost of paddling at lower workloads but does affect arm motion. These changes may be the result of enhanced proprioceptive acuity due to mechanical compression from the wetsuit.

A Validated Smartphone-Based Assessment of Gait and Gait Variability in Parkinson's Disease

Background

A well-established connection exists between increased gait variability and greater fall likelihood in Parkinson’s disease (PD); however, a portable, validated means of quantifying gait variability (and testing the efficacy of any intervention) remains lacking. Furthermore, although rhythmic auditory cueing continues to receive attention as a promising gait therapy for PD, its widespread delivery remains bottlenecked. The present paper describes a smartphone-based mobile application (“SmartMOVE”) to address both needs.

Methods

The accuracy of smartphone-based gait analysis (utilizing the smartphone’s built-in tri-axial accelerometer and gyroscope to calculate successive step times and step lengths) was validated against two heel contact–based measurement devices: heel-mounted footswitch sensors (to capture step times) and an instrumented pressure sensor mat (to capture step lengths). 12 PD patients and 12 age-matched healthy controls walked along a 26-m path during self-paced and metronome-cued conditions, with all three devices recording simultaneously.

Results

Four outcome measures of gait and gait variability were calculated. Mixed-factorial analysis of variance revealed several instances in which between-group differences (e.g., increased gait variability in PD patients relative to healthy controls) yielded medium-to-large effect sizes (eta-squared values), and cueing-mediated changes (e.g., decreased gait variability when PD patients walked with auditory cues) yielded small-to-medium effect sizes—while at the same time, device-related measurement error yielded small-to-negligible effect sizes.

Conclusion

These findings highlight specific opportunities for smartphone-based gait analysis to serve as an alternative to conventional gait analysis methods (e.g., footswitch systems or sensor-embedded walkways), particularly when those methods are cost-prohibitive, cumbersome, or inconvenient.

How to Sync to the Beat of a Persistent Fractal Metronome without Falling Off the Treadmill?

In rehabilitation, rhythmic acoustic cues are often used to improve gait. However, stride-time fluctuations become anti-persistent with such pacing, thereby deviating from the characteristic persistent long-range correlations in stride times of self-paced walking healthy adults. Recent studies therefore experimented with metronomes with persistence in interbeat intervals and successfully evoked persistent stride-time fluctuations. The objective of this study was to examine how participants couple their gait to a persistent metronome, evoking persistently longer or shorter stride times over multiple consecutive strides, without wandering off the treadmill. Twelve healthy participants walked on a treadmill in self-paced, isochronously paced and non-isochronously paced conditions, the latter with anti-persistent, uncorrelated and persistent correlations in interbeat intervals. Stride-to-stride fluctuations of stride times, stride lengths and stride speeds were assessed with detrended fluctuation analysis, in conjunction with an examination of the coupling between stride times and stride lengths. Stride-speed fluctuations were anti-persistent for all conditions. Stride-time and stride-length fluctuations were persistent for self-paced walking and anti-persistent for isochronous pacing. Both stride times and stride lengths changed from anti-persistence to persistence over the four non-isochronous metronome conditions, accompanied by an increasingly stronger coupling between these gait parameters, with peak values for the persistent metronomes. These results revealed that participants were able to follow the beat of a persistent metronome without falling off the treadmill by strongly coupling stride-length fluctuations to the stride-time fluctuations elicited by persistent metronomes, so as to prevent large positional displacements along the treadmill. For self-paced walking, in contrast, this coupling was very weak. In combination, these results challenge the premise that persistent metronomes in gait rehabilitation would evoke stride-to-stride dynamics reminiscent of self-paced walking healthy adults. Future studies are recommended to include an analysis of the interrelation between stride times and stride lengths in addition to the correlational structure of either one in isolation.

Multi-complexity ensemble measures for gait time series analysis: application to diagnostics, monitoring and biometrics

Previously, we have proposed to use complementary complexity measures discovered by boosting-like ensemble learning for the enhancement of quantitative indicators dealing with necessarily short physiological time series. We have confirmed robustness of such multi-complexity measures for heart rate variability analysis with the emphasis on detection of emerging and intermittent cardiac abnormalities. Recently, we presented preliminary results suggesting that such ensemble-based approach could be also effective in discovering universal meta-indicators for early detection and convenient monitoring of neurological abnormalities using gait time series. Here, we argue and demonstrate that these multi-complexity ensemble measures for gait time series analysis could have significantly wider application scope ranging from diagnostics and early detection of physiological regime change to gait-based biometrics applications.