![]() ![]() Unfortunately, the implementation of DFA to stride interval time series is not yet standardized and varies considerably between studies, in which decisions are usually made on an ad hoc or subjective basis. The results from such studies should therefore be interpreted with caution.īesides the length of time series under consideration, another practical aspect of DFA that significantly affects the analysis outcome is the set of parameters used in the algorithm: the box size range, the box size increment, and the order of polynomial fits for a detrending operation. Such relatively long recordings, however, are difficult to collect from older adults or clinical populations, and thus the vast majority of previous studies have collected stride interval time series in these populations for only 2–5 min (i.e., between 100 and 250 strides) ( Moon et al., 2016). Some studies have even suggested that DFA cannot give reliable results with time series shorter than 4,096 data points ( Eke et al., 2002). Previous studies using simulated and/or experimental signals have shown that estimation accuracy is directly related to the series length, and lengths of around 500–600 data points or less, corresponding to the number of stride intervals from approximately 10–12 min of self-paced walking, yield questionable results due to the high bias and variance in the estimation of the scaling exponent ( Damouras et al., 2010 Marmelat and Meidinger, 2019). As a result, these measures could be used as a marker for gait adaptability, gait disorder, and fall risk among patients with movement disorders, such as Parkinson's disease (PD), amyotrophic lateral sclerosis (ALS), and Huntington's disease (HD).Īlthough DFA has become the de facto standard for analyzing statistical persistence in gait data, it too is sensitive to the length of the time series, which remains a significant limitation. Specifically, scaling exponent-like quantities, including the DFA's scaling exponent and the Hurst exponent, show normal human walking produces persistent stride time fluctuations and a drift toward randomness is observed with aging and neurological disorders ( Hausdorff et al., 1997, 2000). (1996) and provides reasonably accurate results for short time series as compared to other classical methods for estimating the Hurst exponent ( Delignieres et al., 2006). This may be because DFA was used by the pioneering works of Hausdorff et al. While many methods of fractal analysis exist to explore long-range autocorrelations in stride interval time series, detrended fluctuation analysis (DFA) has been the most commonly used. More advanced, nonlinear analysis methods, derived from chaos theory, have therefore been proposed to analyze the temporal organization of gait variability ( Chau, 2001). In other words, the variability of stride intervals (or gait variability) could be treated as a meaningful and interpretable metric of gait. However, steady-state walking could be characterized by the presence of subtle variations observed in stride intervals (the time period between consecutive initial contacts of the same foot). Gait analysis has been generally studied using traditional linear analysis methods, adopting biomechanical models in which variability was not of interest (e.g., comparing the means of spatio-temporal gait parameters between groups). 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. 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). The advantages and drawbacks of each method are discussed, in terms of biases and variability. 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. 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. 2Department of Electrical and Computer Engineering, Faculty of Engineering, University of New Brunswick, Fredericton, NB, Canadaįractal 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. ![]() 1Institute of Biomedical Engineering, University of New Brunswick, Fredericton, NB, Canada.Angkoon Phinyomark 1 * Robyn Larracy 1,2 Erik Scheme 1,2
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