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Biofeedback has recently been explored to target deviant lower extremity loading mechanics following anterior cruciate ligament reconstruction (ACLR) to mitigate the development of post traumatic osteoarthritis. The impact this feedback has on the structure of the stride interval dynamics—a barometer of gait system health—however, have yet to be examined. This study was designed to assess how feedback, used to alter lower-extremity loading during gait, affects the structure of stride interval variability by examining long-range stride-to-stride correlations during gait in those with unilateral ACLR. Twelve participants walked under three separate loading conditions: (1) control (i.e., no cue) (2) high loading, and (3) low loading. Baseline vertical ground reaction force (vGRF) data was used to calculate a target 5% change in vGRF for the appropriate loading condition (i.e., high loading was +5% vGRF, low loading was −5% vGRF). The target for the load condition was displayed on a screen along with real-time vGRF values, prescribing changes in stride-to-stride peak vertical ground reaction forces of each limb. From time-series of stride intervals (i.e., duration), we analyzed the mean and standard deviation of stride-to-stride variability and, via detrended fluctuation analysis (i.e., DFA α), temporal persistence for each feedback condition. Both the high and low loading conditions exhibited a change toward more temporally persistent stride intervals (high loading: α =0.92, low loading: α = 0.98) than walking under the control condition (α = 0.78; high vs. control: p = .026, low vs. control: p = .001). Overall, these results indicate that altering lower extremity load changes the temporal persistence of the stride internal dynamics in ACLR individuals, demonstrating the implications of the design of gait training interventions and the influence feedback has on movement strategies.

In recent years, complex models of cardiac regulation have integrated heart rate variability (HRV) as a measure of the cardiac autonomic activity during exercise. Using detrended fluctuation analysis (DFA) technique, the present study examines the influence of cycling cadence and exercise duration on non-linear dynamics of HRV. Sixteen trained cyclists performed a 60-minute exercise bout at 90% of the individual anaerobic threshold on a bicycle ergometer. Cadence was changed every 10 min (90–120–60–120–60–90 rpm). Heart rate (HR) and RR-intervals were recorded continuously during exercise. HRV time domain measures (meanRR, SDNN) and correlation properties were analyzed using short-term scaling exponent alpha1 of DFA. Moreover, blood lactate (La) and rating of perceived exertion (RPE) were recorded at regular intervals at the end of condition. HR, La and RPE increased significantly at 120 rpm compared to 60 rpm. In contrast, all analyzed HRV parameters (meanRR, SDNN, DFA-alpha1) showed a significant decrease during cycling at 120 rpm compared to 60 rpm. The comparison of the first and last 10 min with the same cadence indicates a significant increase in HR and RPE, but also a significant decrease in all analyzed HRV measures. The decrease of HRV values over time and in relation to the increase in cadence indicates a decrease in the overall variability as well as a reduction in complexity of the RR-interval-fluctuations due to the increased organismic demands. Therefore, the decrease of DFA-alpha1 might be associated with a withdrawal of the organismic system aiming at the maintenance of the homeostasis under the control of the central nervous system. In this context, non-linear HRV analyses provide a more systemic view of cardiac regulation during exercise.

Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5–10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50–100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking speed, fractal dynamics increased closer to 1/f when participants were exposed to asymmetric walking. These findings suggest there may not be a relationship between unperturbed preferred or slow speed walking fractal dynamics and gait adaptability. However, the emergent relationship between asymmetric walking fractal dynamics and limb phase adaptation may represent a functional reorganization of the locomotor system (i.e., improved interactivity between degrees of freedom within the system) to be better suited to attenuate externally generated perturbations at various spatiotemporal scales.

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.

Perceptual guidance of movement with simple visual or temporal information can facilitate performance of difficult coordination patterns. Guidance may override coordination constraints that usually limit stability of bimanual coordination to only in-phase and anti-phase. Movement dynamics, however, might not have the same characteristics with and without perceptual guidance. Do visual and auditory guidance produce qualitatively different dynamical organization of movement? An anti-phase wrist flexion and extension coordination task was performed under no specific perceptual guidance, under temporal guidance with a metronome, and under visual guidance with a Lissajous plot. For the time series of amplitudes, periods and relative phases, temporal correlations were measured with Detrended Fluctuation Analysis and complexity levels were measured with multiscale entropy. Temporal correlations of amplitudes and relative phases deviated from the typical 1/f variation towards more random variation under visual guidance. The same was observed for the series of periods under temporal guidance. Complexity levels for all time series were lower in visual guidance, but higher for periods under temporal guidance. Perceptual simplification of the task's goal may produce enhancement of performance, but it is accompanied by changes in the details of movement organization that may be relevant to explain dependence and poor retention after practice under guidance.

To determine the effects of speed on gait previous studies have examined young adults walking at different speeds; however, the small number of strides may have influenced the results. The aim of this study was to investigate the immediate and long-term impact of continuous slow walking on the mean, variability and structure of stride-to-stride measures. Fourteen young adults walked at a constant pace on a treadmill at three speeds (preferred walking speed (PWS), 90% and 80% PWS) for 30 min each. Spatiotemporal gait parameters were computed over six successive 5-min intervals. Walking slower significantly decreased stride length, while stride period and width increased. Additionally, stride period and width variability increased. Signal regularity of stride width increased and decreased in stride period. Persistence of stride period and width increased significantly at slower speeds. While several measures changed during 30 min of walking, only stride period variability and signal regularity revealed a significant speed and time interaction. Healthy young adults walking at slower than preferred speeds demonstrated greater persistence and signal regularity of stride period while spatiotemporal changes such as increased stride width and period variability arose. These results suggest that different control processes are involved in adapting to the slower speeds.

Typically, gait rehabilitation uses an invariant stimulus paradigm to improve gait related deficiencies. However, this approach may not be optimal as it does not incorporate gait complexity, or in more precise words, the variable fractal-like nature found in the gait fluctuations commonly observed in healthy populations. Aging which also affects gait complexity, resulting in a loss of adaptability to the surrounding environment, could benefit from gait rehabilitation that incorporates a variable fractal-like stimulus paradigm. Therefore, the present study aimed to investigate the effect of a variable fractal-like visual stimulus on the stride-to-stride fluctuations of older adults during overground walking. Additionally, our study aimed to investigate potential retention effects by instructing the participants to continue walking after turning off the stimulus. Older adults walked 8 min with i) no stimulus (self-paced), ii) a variable fractal-like visual stimulus and iii) an invariant visual stimulus. In the two visual stimuli conditions, the participants walked 8 additional minutes after the stimulus was turned off. Gait complexity was evaluated with the widely used fractal scaling exponent calculated through the detrended fluctuation analysis of the stride time intervals. We found a significant ~20% increase in the scaling exponent from the no stimulus to the variable fractal-like stimulus condition. However, no differences were found when the older adults walked to the invariant stimulus. The observed increase was towards the values found in the past to characterize healthy young adults. We have also observed that these positive effects were retained even when the stimulus was turned off for the fractal condition, practically, acutely restoring gait complexity of older adults. These very promising results should motivate researchers and clinicians to perform clinical trials in order to investigate the potential of visual variable fractal-like stimulus for gait rehabilitation.

Complex systems applications in human movement sciences have increased our understanding of emergent coordination patterns between athletes. In the current study, we take a novel step and propose that movement coordination between athletes is a multiscale phenomenon. Specifically, we investigated so-called "complexity matching" of performance measured in the context of rowing. Sixteen rowers participated in two sessions on rowing ergometers: One individual session of 550 strokes and one dyadic session of 550 strokes side-by-side with a team member. We used evenly-spaced detrended fluctuation analysis (DFA) to calculate the complexity indices (DFA exponents) of the force-peak interval series for each rower in each session. The DFA exponents between team members were uncorrelated in the individual sessions (r = 0.06), but were strongly and significantly correlated when team members rowed together (r = 0.87). Furthermore, we found that complexity matching could not be attributed to the rowers mimicking or locally adapting to each other. These findings contribute to the current theoretical understanding of coordination dynamics in sports.

Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15 min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA a in the baseline condition was 0.77 ± 0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA a = 0.87 ± 0.06) and to the random metronome (DFA a = 0.61 ± 0.10) (both p < .05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon.

Numerous measures of dynamic stability have been proposed to gauge fall risk in the elderly, including stride interval variability and variability of the center of mass. However, these measures have been deemed inadequate because they do not take into account temporal information. Therefore, research on the measurement of dynamic stability has turned to other analysis methods such as stride interval dynamics and the maximum Lyapunov exponent. Stride interval dynamics reflect the statistical persistence of an individual's stride interval time series and the Lyapunov exponent quantifies local dynamic stability - the sensitivity of the system to infinitesimal perturbations. In this study, we compare the ability of these measurement tools to detect changes between overground and compliant-surface walking, a condition known to affect stability, to determine their aptness as measures of dynamic stability. Fourteen able-bodied participants completed three 15 min walks, two overground and one on a compliant surface. Our results show that the Lyapunov exponent may be more sensitive to gait changes than stride interval dynamics and gait variability measures.

Body fluctuations during both quiet standing and walking exhibit temporal correlations that reflect mechanisms of balance control. However, knowledge about the relationship between the temporal structures observed during standing and walking is limited. The goal of the present study was (1) to investigate temporal correlations in the fluctuations of the center of body mass acceleration (ACC) in standing and walking, and (2) to test the hypothesis that the degree of the temporal correlation for the two tasks is similar and correlated across participants. Seventeen young, healthy participants stood and walked for 10 min on a treadmill equipped with two force platforms. The temporal correlations of the ACC in the anteroposterior (ACC(AP)), mediolateral (ACC(ML)), and two-dimensional (ACC(2D)) directions were evaluated using the scaling index (alpha) as calculated with Detrended Fluctuation Analysis. The scaling indices of ACC fluctuations during standing and walking were categorized as stationary signals which are temporally correlated (0.5

Participants were asked to walk and run continuously (5 min trials) at speeds associated with preferred gait transition speeds. During slow running the local dynamic stability of the head was decreased compared with fast walking, with the reverse being true for the local dynamic stability of the ankle. The standard deviation of relative phase of the knee and ankle also was greater during slow running than fast walking. These findings for stability were mirrored in the detrended fluctuation analysis of the peak to peak interval of the head and ankle. Taken collectively these results support the proposition that larger long range correlations in the stride interval are associated with decreases in measures of stability.

During free walking, gait is automatically adjusted to provide optimal mechanical output and minimal energy expenditure; gait parameters, such as cadence, fluctuate from one stride to the next around average values. It was described that this fluctuation exhibited long-range correlations and fractal-like patterns. In addition, it was suggested that these long-range correlations disappeared if the participant followed the beep of metronome to regulate his or her pace. Until now, these fractal fluctuations were only observed for stride interval, because no technique existed to adequately analyze an extended time of free walking. The aim of the present study was to measure walking speed (WS), step frequency (SF) and step length (SL) with high accuracy (1 cm) satellite positioning method (global positioning system or GPS) in order to detect long-range correlations in the stride-to-stride fluctuations. Eight participants walked 30 min under free and constrained (metronome) conditions. Under free walking conditions, DFA (detrended fluctuation analysis) and surrogate data tests showed that the fluctuation of WS, SL and SF exhibited a fractal pattern (i.e., scaling exponent alpha: 0.5alpha1) in a large majority of participants (7/8). Under constrained conditions (metronome), SF fluctuations became significantly anti-correlated (alpha0.5) in all participants. However, the scaling exponent of SL and WS was not modified. We conclude that, when the walking pace is controlled by an auditory signal, the feedback loop between the planned movement (at supraspinal level) and the sensory inputs induces a continual shifting of SF around the mean (persistent anti-correlation), but with no effect on the fluctuation dynamics of the other parameters (SL, WS).

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

Treadmills are commonly implemented in rehabilitation and laboratory settings to facilitate gait analysis and training. However, while this locomotor modality is often used with children, its effect on pediatric stride interval dynamics is unknown. This study investigated the stride interval persistence of 30 asymptomatic children after completion of three to six 10-min walking trials comprised of: (i) overground walking (OW), (ii) unsupported treadmill walking (UTW), and (iii) handrail-supported treadmill walking (STW). The primary outcome measure was α, a quantifier of stride interval persistence obtained from detrended fluctuation analysis. Preferred walking speed, number of strides taken, stride interval duration, and stride interval coefficient of variation were also assessed. Stride interval persistence was significantly diminished during both treadmill walking conditions, compared to overground walking, with the largest decrease in α during UTW. Preferred speed, number of strides, and stride interval duration also differed between overground and treadmill walking, and older children demonstrated reduced stride interval variability compared to younger children. The observed treadmill and age effects on stride parameters may be due to a combination of differing locomotor constraints between overground and treadmill walking and developmental differences in sensory processing, cerebellar plasticity, and corticospinal involvement in locomotion.

Data sequences acquired from bio-systems such as human gait data, heart rate interbeat data, or DNA sequences exhibit complex dynamics that is frequently described by a long-memory or power-law decay of autocorrelation function. One way of characterizing that dynamics is through scale invariant statistics or "fractal-like" behavior. For quantifying scale invariant parameters of physiological signals several methods have been proposed. Among them the most common are detrended fluctuation analysis, sample mean variance analyses, power spectral density analysis, R/S analysis, and recently in the realm of the multifractal approach, wavelet analysis. In this paper it is demonstrated that embedding the time series data in the high-dimensional pseudo-phase space reveals scale invariant statistics in the simple fashion. The procedure is applied on different stride interval data sets from human gait measurements time series (Physio-Bank data library). Results show that introduced mapping adequately separates long-memory from random behavior. Smaller gait data sets were analyzed and scale-free trends for limited scale intervals were successfully detected. The method was verified on artificially produced time series with known scaling behavior and with the varying content of noise. The possibility for the method to falsely detect long-range dependence in the artificially generated short range dependence series was investigated.