Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability.
ABSTRACT: It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.
Project description: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.
Project description: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.
Project description:Introduction During cyclical steady state ambulation, such as walking, variability in stride intervals can indicate the state of the system. In order to define locomotor system function, observed variability in motor patterns, stride regulation and gait complexity must be assessed in the presence of a perturbation. Common perturbations, especially for military populations, are load carriage and an imposed locomotion pattern known as forced marching (FM). We examined the interactive effects of load magnitude and locomotion pattern on motor variability, stride regulation and gait complexity during bipedal ambulation in recruit-aged females. Methods Eleven healthy physically active females (18–30 years) completed 1-min trials of running and FM at three load conditions: no additional weight/bodyweight (BW), an additional 25% of BW (BW + 25%), and an additional 45% of BW (BW + 45%). A goal equivalent manifold (GEM) approach was used to assess motor variability yielding relative variability (RV; ratio of “good” to “bad” variability) and detrended fluctuation analysis (DFA) to determine gait complexity on stride length (SL) and stride time (ST) parameters. DFA was also used on GEM outcomes to calculate stride regulation. Results There was a main effect of load (p = 0.01) on RV; as load increased, RV decreased. There was a main effect of locomotion (p = 0.01), with FM exhibiting greater RV than running. Strides were regulated more tightly and corrected quicker at BW + 45% compared (p < 0.05) to BW. Stride regulation was greater for FM compared to running. There was a main effect of load for gait complexity (p = 0.002); as load increased gait complexity decreased, likewise FM had less (p = 0.02) gait complexity than running. Discussion This study is the first to employ a GEM approach and a complexity analysis to gait tasks under load carriage. Reduction in “good” variability as load increases potentially exposes anatomical structures to repetitive site-specific loading. Furthermore, load carriage magnitudes of BW + 45% potentially destabilize the system making individuals less adaptable to additional perturbations. This is further evidenced by the decrease in gait complexity, which all participants demonstrated values similarly observed in neurologically impaired populations during the BW + 45% load condition.
Project description:Stride-to-stride time intervals during human walking are characterised by predictability and statistical persistence quantified by sample entropy (SaEn) and detrended fluctuation analysis (DFA) which indicates a time dependency in the gait pattern. However, neither analyses quantify time dependency in a physical or physiological interpretable time scale. Recently, entropic half-life (ENT½) has been introduced as a measure of the time dependency on an interpretable time scale. A novel measure of time dependency, based on DFA, statistical persistence decay (SPD), was introduced. The present study applied SaEn, DFA, ENT½, and SPD in known theoretical signals (periodic, chaotic, and random) and stride-to-stride time intervals during overground and treadmill walking in healthy subjects. The analyses confirmed known properties of the theoretical signals. There was a significant lower predictability (p = 0.033) and lower statistical persistence (p = 0.012) during treadmill walking compared to overground walking. No significant difference was observed for ENT½ and SPD between walking condition, and they exhibited a low correlation. ENT½ showed that predictability in stride time intervals was halved after 11-14 strides and SPD indicated that the statistical persistency was deteriorated to uncorrelated noise after ~50 strides. This indicated a substantial time memory, where information from previous strides affected the future strides.
Project description: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 ?-DFA values are not consistent from trial-to-trial for short stride time series, 2) stride time ?-DFA values from each 3-min trials are not consistent when compared to stride time ?-DFA values from a 15-min trial, and 3) stride time ?-DFA values from the first 150 strides of the 15-min trial are not consistent when compared to ?-DFA values from the full 15-min trial. SIGNIFICANCE:Our results confirm that ?-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.
Project description: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.
Project description:Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.
Project description: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.
Project description:<b>Purpose: </b>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.<br><br><b>Methods: </b>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 (?) long-range scaling coefficient derived from DFA and gait speed were evaluated as outcomes.<br><br><b>Results: </b>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.<br><br><b>Conclusion: </b>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.<br><br><b>Trial registration: </b>The randomized trial component of this study was registered at ClinicalTrials.gov (NCT01340365).
Project description:Walking can be challenging for aging individuals and people with neurological disorders such as Parkinson disease (PD). Gait impairment characterized by reduced speed and higher variability destabilizes gait and increases the risk of falls. External auditory cueing provides an effective strategy to improve gait, as matching footfalls to rhythms typically increases gait speed and elicits larger steps, but the need to synchronize to an outside source often has a detrimental effect on gait variability. Internal cueing in the form of singing may provide an alternative to conventional gait therapy. In the present study, we compare the effects of internal and external cueing techniques on forward and backward walking for both people with PD and healthy controls. Results indicate that internal cueing was associated with improvements in gait velocity, cadence, and stride length in the backward direction, and reduced variability in both forward and backward walking. In comparison, external cueing was associated with minimal improvement in gait characteristics and a decline in gait stability. People with gait impairment due to aging or neurological decline may benefit more from internal cueing techniques such as singing as compared to external cueing techniques.