Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson's Disease: Stitching Together Short Gait Trials

Abstract

Variability indicates motor control disturbances and is suitable to identify gait pathologies. It can be quantified by linear parameters (amplitude estimators) and more sophisticated nonlinear methods (structural information). Detrended Fluctuation Analysis (DFA) is one method to measure structural information, e.g., from stride time series. Recently, an improved method, Adaptive Fractal Analysis (AFA), has been proposed. This method has not been applied to gait data before. Fractal scaling methods (FS) require long stride-to-stride data to obtain valid results. However, in clinical studies, it is not usual to measure a large number of strides (e.g., strides). Amongst others, clinical gait analysis is limited due to short walkways, thus, FS seem to be inapplicable. The purpose of the present study was to evaluate FS under clinical conditions. Stride time data of five self-paced walking trials ( strides each) of subjects with PD and a healthy control group (CG) was measured. To generate longer time series, stride time sequences were stitched together. The coefficient of variation (CV), fractal scaling exponents (DFA) and (AFA) were calculated. Two surrogate tests were performed: A) the whole time series was randomly shuffled; B) the single trials were randomly shuffled separately and afterwards stitched together. CV did not discriminate between PD and CG. However, significant differences between PD and CG were found concerning and . Surrogate version B yielded a higher mean squared error and empirical quantiles than version A. Hence, we conclude that the stitching procedure creates an artificial structure resulting in an overestimation of true . The method of stitching together sections of gait seems to be appropriate in order to distinguish between PD and CG with FS. It provides an approach to integrate FS as standard in clinical gait analysis and to overcome limitations such as short walkways.

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

“…Differences in the short-range statistical correlations detected in these relatively short recordings may be sufficient to characterize differences in gait dynamics between two groups or experimental conditions as shown by Kirchner et al [16]. The question we sought to answer was how many subjects and trials are required when researchers are limited to collecting only 100–200 strides per trial (this corresponds to 2 to 4 minutes of walking assuming stride time of 1.2 s).…”

Respiratory Variability during Sleep in Methadone Maintenance Treatment Patients

“…We attempted to overcome this by removing all segments shorter than 5 minutes. We also compared our preprocessing approach to estimate α from all segments with an alternative approach 42 and found that they were statistically equivalent (data not shown).…”

Discrimination and Characterization of Parkinsonian Rest Tremors by Analyzing Long-Term Correlations and Multifractal Signatures

“…Several different methods have been developed in the past years to detect fractal and multifractal signatures. Among the many we can cite multifractal detrended fluctuation analysis (MF-DFA) [18], adaptive fractal analysis [22], wavelet transform modulo maxima [28], and wavelet leaders [23]. Fractal and multifractal analysis of time series play a pivotal role in many scientific contexts, such as neuroscience and medicine in general [9,10,37].…”