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Correlation dimension estimates of human postural sway

2013-02-01
Gürses, Senih
Celik, Huseyin
Human postural sway during quiet standing demonstrates a complex structured dynamics, which has been studied by applying numerous methods, such as linear system identification methods, stochastic analysis, and nonlinear system dynamics tools. Although each of the methods applied revealed some particular features of the sway data none of them have succeeded to present a global picture of the quiet stance dynamics, which probably has both stochastic and deterministic properties. In this study we have started applying ergodic theory of dynamical systems to explore statistical characteristic of the sway dynamics observed in successive trials of a subject, different subjects in an age group, and finally different age groups constituted by children, adults, and elderly subjects. Five successive 180-s long trials were performed by each of 28 subjects in four age groups at quiet stance with eyes open. Stationary and ergodic signal characteristics of five successive center of pressure time series collected from a subject in antero-posterior direction (CoPx) were examined. 97% of the trials were found to be stationary by applying Run Test while children and elderly groups demonstrated significant nonstationary behavior. On the other hand 13 out of 24 subjects were found to be nonergodic. We expected to observe differences in complexity of CoPx dynamics due to aging (Farmer, Ott, & Yorke, 1983). However linear metrics such as standard deviation and Fourier spectra of CoPx signals did not show differences due to the age groups. Correlation dimension (D-k) estimates of stationary CoPx signals being an invariant measure of nonlinear system dynamics were computed by using the average displacement method (Eckmann & Ruelle, 1985). Postural dynamics was expanded in m-dimensional space through CoPx signal by introducing optimum time delays, tau(critical). 112 out of 136 stationary CoPx signals for 24 stationary subjects converged to D-k estimates. Average of D-k estimates for children and adult groups was 3.67 +/- 0.28, whereas mean of D-k estimates for elderly subjects was 4.12 +/- 0.59. Nonlinear metrics of postural sway (tau(critical), m(saturated). and D-k estimates) showed significant differences with respect to the age groups. D-k estimates computed from ergodic subjects' CoPx sway trajectories revealed that human quiet standing demonstrates multiple degree of freedom dynamics having a fractal structure with a considerable level of noise embedded in the signal whose characteristics is determined individually for each subject. Furthermore by using ergodic theory of complex systems, we have been able to show that the ability to independently control multiple degrees of freedom has been affected by aging. (C) 2012 Elsevier B.V. All rights reserved.