Adaptive fractal analysis of postural sway

1
Adaptive fractal analysis of postural sway
Nikita Kuznetsov1, Michael Riley1, Scott
Bonnette1, Jianbo Gao2, Illya Vilinsky3
1Center for Cognition, Action, Perception,
Department of Psychology, University of
Cincinnati, OH 2Biological Sciences, University
of Cincinnati, OH 3PMB Intelligence LLC, West
Lafayette, IN
AFA Result
Power Spectrum

• 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.
• Specifically, Collins and De Luca2 identified COP
  signals as a particular type of stochastic
  process termed fractional Brownian Motion (fBm).
  This model was initially presented by Mandelbrot
  Van Ness (1963) to capture the variability of
  the stock market prices. Increments of fBm
  constitute fractional Gaussian noise (fGn)a
  stationary stochastic process with long-range
  correlations identified by the Hurst parameter
  (H). For from 0 lt H lt 0.5 the fluctuations are
  anti-persistent, for H  0.5 they are random, and
  for 0.5 lt H lt 1 they are persistent2.
• However, previous research and our observations
  raise several issues that have consequences for
  the immediate application of the fGn-fBm
  framework to COP during upright stance
• There are more than one scaling regions in COP
  signals
• Slopes of integrated and non-integrated COP
  signals do not differ by the 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 used adaptive fractal analysis (AFA) to
accurately characterize the number of scaling
regions in the COP. AFA offers several advantages
over DFA1 (e.g., it deals with arbitrary
background trends and has a direct link to power
spectrum energy). See Riley et al.6 for details.
Adaptive fractal analysis
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
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 fBm-fGn 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 stance5 and a moving
set-point model of stance proposed by Zatsiorsky
Duarte7.
Experimental data
References
Quiet stance 3 trials - 2 minutes each 40
Participants 115 Total COP (for each AP and ML)
analyzed
We hypothesized that COP signals during quiet
stance (in both anterior-posterior AP and
medial-lateral ML directions) is not well
characterized within the fBm-fGn framework.
1Blázquez, 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. 2Collins, 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, 308318. 3Delignières, D., K.
Torre, and P. L. Bernard. Transition from
persistent to anti-persistent correlations in
postural sway indicates velocity-based control.
PLoS Computational Biology, 7(2). 4Kent 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. PLoS ONE 7(8). 5Loram, I. D., C.
N. Maganaris, and M. Lakie. Human postural sway
results from frequent, ballistic bias impulses by
soleus and gastrocnemius. J. Physiol.
654295311, 2005. 6Riley, 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. 7Zatsiorsky, V. M., Duarte, M. (2000).
Rambling and trembling in quiet standing. Motor
Control, 4, 185200.
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 performance1,4.