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Sensitivity of the Wolf’s and Rosenstein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets

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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.

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Acknowledgments

This research was supported by National Institutes of Health (1K99AG033684) and National Institute on Disability and Rehabilitation Research (H133G080023) grants. The authors thank Dr. M. J. Kurz for his technical assistance.

Conflict of interest

The authors disclose any financial and personal relationships with other people or organizations that could inappropriately influenced (bias) this work.

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Authors and Affiliations

  1. Nebraska Biomechanics Core Facility, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE, 68182-0216, USA

    Fabien Cignetti, Leslie M. Decker & Nicholas Stergiou

  2. Environmental, Agricultural and Occupational Health Sciences, College of Public Health, University of Nebraska Medical Center, 985450 Nebraska Medical Center, Omaha, NE, 68198-5450, USA

    Nicholas Stergiou

Authors
  1. Fabien Cignetti
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  2. Leslie M. Decker
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  3. Nicholas Stergiou
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Correspondence to Fabien Cignetti.

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Associate Editor Catherine Disselhorst-Klug oversaw the review of this article.

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Cignetti, F., Decker, L.M. & Stergiou, N. Sensitivity of the Wolf’s and Rosenstein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets. Ann Biomed Eng 40, 1122–1130 (2012). https://doi.org/10.1007/s10439-011-0474-3

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  • DOI: https://doi.org/10.1007/s10439-011-0474-3

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