Adaptive Fractal Analysis Reveals Limits to Fractal Scaling in Center of Pressure Trajectories

Abstract

Abstract-Fractal time series analysis methods are commonly used for analyzing center of pressure (COP) signals with the goal of revealing the underlying neuromuscular processes for upright stance control. The use of fractal methods is often coupled with the assumption that the COP is an instance of fractional Gaussian noise (fGn) or fractional Brownian motion (fBm). Our purpose was to evaluate the applicability of the fGn-fBm framework to the COP in light of several characteristics of COP signals revealed by a new method, adaptive fractal analysis (AFA). AFA quantifies how the variance of the residuals to fits of a globally smooth trend signal scales with the time scale at which the fits are performed. Application of AFA to COP signals revealed that there are potentially three fractal scaling regions in the COP as opposed to one as expected from a pure fGn or fBm process. The scaling region at the fastest scale was antipersistent and spanned~30-90 ms, the intermediate was persistent and spanned~200 ms-1.9 s, and the slowest was anti-persistent and spanned~5-40 s. The intermediate fractal scaling region was the most clearly defined, but it only contributed around 11% of the total spectral energy of the COP signal, indicating that other features of the COP signal contribute more importantly to the overall dynamics. Also, more than half of the Hurst exponents estimated for the intermediate region were greater than the theoretically expected range [0,1] for fGn-fBm processes. These results suggest the fGn-fBm framework is not appropriate for modeling COP signals. ON-OFF intermittency might provide a better modeling framework for the COP, and multiscale approaches may be more appropriate for analyzing COP data.

Comparing Postural Stability Entropy Analyses to Differentiate Fallers and Non-fallers

“…COP data were calculated using the force plate data and were down-sampled to 100 Hz to reflect the upper limit for sampling postural stability data 29 . Traditional COP measures of 95% ellipsoidal area, COP velocity, ML standard deviation ( x SD) and AP standard deviation ( y SD) were calculated and compared to the entropy methods.…”

Test–retest reliability and responsiveness of centre of pressure measurements in patients with hip osteoarthritis

“…-Fractal indicators 43,44 : Detrended Fluctuation Analysis exponent (DFA) Hurst rescaled range analysis exponent (H R/S ) of the anteroposterior and mediolateral oscillations.…”

Multifractal analysis of information processing in hippocampal neural ensembles during working memory under Δ9-tetrahydrocannabinol administration

“…Many techniques can compute the singularity spectrum, such as Wavelet Transform Modulus Maximus (WTMM; Arneodo et al, 1993), Adaptive Detrended Fluctuation Analysis (AFA; Kuznetsov et al, 2012; Riley et al, 2012), Arbitrary-Order Hilbert Spectral Analysis (AOHSA; Huang et al, 2011), Empirical Mode Decomposition (EMD; Flandrin and Goncalves, 2004; Goncalves et al, 2007), Multifractal Detrended Fluctuation Analysis (MFDFA; Ihlen, 2012; Kantelhardt et al, 2002; Oświecimka et al, 2006), and Wavelet Leaders-based Multifractal Analysis (WLMA; Jaffard et al, 2007; Serrano and Figliola, 2009; Wendt et al, 2007; Wendt and Abry, 2007). WLMA has many advantages over the other methods: it is computationally efficient, it is able to deal with a broader range of singularity types, and it is able to estimate the Hölder exponents in regions of low variability.…”