Adaptive fractal analysis of postural sway Nikita Kuznetsov

Adaptive fractal analysis of postural sway Nikita Kuznetsov 1, Michael Riley 1, Scott Bonnette 1, & Jianbo Gao 2, Illya Vilinsky 3 1 Center for Cognition, Action, & Perception, Department of Psychology, University of Cincinnati, OH 2 Biological Sciences, University of Cincinnati, OH 3 PMB Intelligence LLC, West Lafayette, IN Data + Smoothed polynomial AFA plot w log 2 w 100 0. 26 (0. 10) 1. 04 (0. 15) 0. 22 (0. 07) 0. 21 (0. 04) 0. 17 (0. 06) Relative Energy (% Total within regions) Specifically, Collins and De Luca 2 identified COP signals as a particular type of stochastic process termed fractional Brownian Motion (f. Bm). This model was initially presented by Mandelbrot & Van Ness (1963) to capture the variability of the stock market prices. Increments of f. Bm constitute fractional Gaussian noise (f. Gn)—a stationary stochastic process with long -range correlations identified by the Hurst parameter (H). For from 0 < H < 0. 5 the fluctuations are anti-persistent, for H = 0. 5 they are random, and for 0. 5 < H < 1 they are persistent 2. Adaptive fractal analysis Power Spectrum AFA Result We used adaptive fractal analysis (AFA) to accurately characterize the number of scaling regions in the COP. AFA offers several advantages over DFA 1 (e. g. , it deals with arbitrary background trends and has a direct link to power spectrum energy). See Riley et al. 6 for details. log 2 F(w) Upright stance is supported by a complex interaction of the visual, haptic, and vestibular perceptual systems. Recent studies have utilized methods from random fractal and deterministic dynamics theories to capture the integrative control mechanisms of healthy and pathological upright stance primarily using recordings of center of pressure (COP)1, 2, 3, 4. 80 60 40 20 0 Fast There are more than one scaling regions in COP signals • Slopes of integrated and non-integrated COP signals do not differ by theoretically expected value of 1 • Theoretical limit on H is 1. However, we have observed COP signals with H greater than 1 • Fractal scaling region contains little power spectral energy We hypothesized that COP signals during quiet stance (in both anterior-posterior [AP] and medial-lateral [ML] directions) is not well characterized within the f. Bm-f. Gn framework. Understanding these empirical features of COP signals is important for developing models of normal and pathological postural control and for guiding the interpretation of the fractal measures of postural stability and performance 1, 4. Slow Discussion 1) About 30% of AP COP trials had three scaling regions. 80% of ML COPs had three regions. 2) H values of the intermediate region exceeded However, previous research and our observations raise several issues that have consequences for the immediate application of the f. Gn-f. Bm framework to COP during upright stance: • Intermediate Experimental data Quiet stance 3 trials - 2 minutes each 40 Participants 115 Total COP (for each AP and ML) analyzed 1 in 52% AP and 62% ML recordings. 3) Persistent fractal scaling was limited to a region with about 11% spectral power. These results indicate that other frameworks than f. Bm-f. Gn need to be explored to characterize the variability of the COP. ON-OFF intermittency models look attractive given than they are consistent with the empirical observation of ballistic gastrocnemiusand soleus muscle contractions during stance 5 and a moving set-point model of stance proposed by Zatsiorsky & Duarte 7. References 1 Blázquez, M. T. , Anguiano, M. , de Saavedra, F. A. , Lallena, A. M. , & Carpena, P. (2010). Characterizing the human postural control system using detrended fluctuation analysis. Journal of Computaional and Applied Mathematics, 233, 1478 -1482. 2 Collins, J. J. , & De Luca, C. J. (1993). Open-loop and closed loop control of posture: a random-walk analysis of center of pressure trajectories. Experimental Brain Research, 95, 308– 318. 3 Delignières, D. , K. Torre, and P. L. Bernard. Transition from persistent to anti-persistent correlations in postural sway indicates velocity-based control. PLo. S Computational Biology, 7(2). 4 Kent J. S. , Hong, S. L. , Bolbecker, A. R. , Klaunig, M. J. , Forsyth, J. K. , et al. (2012) Motor Deficits in Schizophrenia Quantified by Nonlinear Analysis of Postural Sway. PLo. S ONE 7(8). 5 Loram, I. D. , C. N. Maganaris, and M. Lakie. Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius. J. Physiol. 654: 295– 311, 2005. 6 Riley, M. A. , Bonnette, S. , Kuznetsov, N. , Wallot, S. , & Gao, J. (2012). A tutorial introduction to adaptive fractal analysis. Frontiers in Fractal Physiology, 3, 1 -10. 7 Zatsiorsky, V. M. , & Duarte, M. (2000). Rambling and trembling in quiet standing. Motor Control, 4, 185– 200.