Correlation dimension estimates of human postural sway Senih Gurses a,b,⇑ , Huseyin Celik a a Department of Engineering Sciences, Middle East Technical University, 06800 Ankara, Turkey b BIOMATEN Center of Excellence in Biomaterials and Tissue Engineering, Middle East Technical University, 06800 Ankara, Turkey article info Article history: Available online xxxx PsycINFO classification: 2221 2240 2320 2330 2540 Keywords: Postural sway Center-of-pressure Ergodicity Correlation dimension Optimum time delay Aging abstract Human postural sway during quiet standing demonstrates a com- plex 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 pic- ture of the quiet stance dynamics, which probably has both sto- chastic 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 succes- sive 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 succes- sive center of pressure time series collected from a subject in ante- ro-posterior direction (CoP x ) 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 nonerg- odic. We expected to observe differences in complexity of CoP x dynamics due to aging (Farmer, Ott, & Yorke, 1983). However lin- ear metrics such as standard deviation and Fourier spectra of CoP x signals did not show differences due to the age groups. Correlation dimension (D k ) estimates of stationary CoP x signals being an invariant measure of nonlinear system dynamics were computed by using the average displacement method (Eckmann & Ruelle, 0167-9457/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.humov.2012.07.007 ⇑ Corresponding author at: Department of Engineering Sciences, Middle East Technical University, 06800 Ankara, Turkey. Tel.: +90 312 210 44 61; fax: +90 312 210 44 62. E-mail address: senih@metu.edu.tr (S. Gurses). Human Movement Science xxx (2013) xxx–xxx Contents lists available at SciVerse ScienceDirect Human Movement Science journal homepage: www.elsevier.com/locate/humov Please cite this article in press as: Gurses, S., & Celik, H. Correlation dimension estimates of human postural sway. Human Movement Science (2013), http://dx.doi.org/10.1016/j.humov.2012.07.007