Sensitivity of the wolf's and rosenstein's algorithms to evaluate local dynamic stability from small gait data sets

Fabien Cignetti, Leslie M. Decker, Nicholas Stergiou

Research output: Contribution to journalArticle

46 Scopus citations

Abstract

The Wolf's (W-algorithm) and Rosenstein's (R-algorithm) algorithms have been used to quantify local dynamic stability (largest Lyapunov exponent, λ 1) in gait, with prevalence of the latter one that is considered more suitable for small data sets. However, such a claim has never been investigated. To address it, the λ 1 of the Lorenz attractor was estimated using small data sets and varied delays and embedding dimensions. Overall, the λ 1 estimates from the R-algorithm got closer to the theoretical exponent than those from the W-algorithm. The W-algorithm also overestimated λ 1 while the R-algorithm underestimated it, overlooking the attractor convergences and divergences, respectively. Local dynamic stability was then examined from 1-, 2- and 3-min long gait time series of younger (YA) and older adults (OA). The OA were found more locally unstable than the YA regardless of time series length with the W-algorithm but only for the longest time series with the R-algorithm. The lack of sensitivity to capture age-related decline in local dynamic stability from shorter time series is proposed to result from a drawback of the R-algorithm that overlooks the expansion of the attractor trajectories. The W-algorithm is advocated for use when examining local dynamic stability with small gait data sets.

Original languageEnglish (US)
Pages (from-to)1122-1130
Number of pages9
JournalAnnals of biomedical engineering
Volume40
Issue number5
DOIs
StatePublished - May 1 2012

Keywords

  • Aging
  • Delay embedding
  • Largest Lyapunov exponent
  • Walking

ASJC Scopus subject areas

  • Biomedical Engineering

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