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Introducing Statistical Persistence Decay: A Quantification of Stride-to-Stride Time Interval Dependency in Human Gait

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Abstract

Stride-to-stride time intervals during human walking are characterised by predictability and statistical persistence quantified by sample entropy (SaEn) and detrended fluctuation analysis (DFA) which indicates a time dependency in the gait pattern. However, neither analyses quantify time dependency in a physical or physiological interpretable time scale. Recently, entropic half-life (ENT½) has been introduced as a measure of the time dependency on an interpretable time scale. A novel measure of time dependency, based on DFA, statistical persistence decay (SPD), was introduced. The present study applied SaEn, DFA, ENT½, and SPD in known theoretical signals (periodic, chaotic, and random) and stride-to-stride time intervals during overground and treadmill walking in healthy subjects. The analyses confirmed known properties of the theoretical signals. There was a significant lower predictability (p = 0.033) and lower statistical persistence (p = 0.012) during treadmill walking compared to overground walking. No significant difference was observed for ENT½ and SPD between walking condition, and they exhibited a low correlation. ENT½ showed that predictability in stride time intervals was halved after 11–14 strides and SPD indicated that the statistical persistency was deteriorated to uncorrelated noise after ~50 strides. This indicated a substantial time memory, where information from previous strides affected the future strides.

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Acknowledgments

Funding for this project was provided by NASA Nebraska EPSCoR and the National Institutes of Health (P20 GM109090).

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Authors and Affiliations

  1. Julius Wolff Institute for Biomechanics and Musculoskeletal Regeneration, Charité – Universitätsmedizin Berlin, Berlin, Germany

    P. C. Raffalt

  2. Department of Biomedical Sciences, University of Copenhagen, Copenhagen, Denmark

    P. C. Raffalt

  3. Center for Research in Human Movement Variability, Department of Biomechanics, University of Nebraska Omaha, Omaha, NE, USA

    J. M. Yentes

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Correspondence to J. M. Yentes.

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Associate Editor Thurmon E. Lockhart oversaw the review of this article.

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Raffalt, P.C., Yentes, J.M. Introducing Statistical Persistence Decay: A Quantification of Stride-to-Stride Time Interval Dependency in Human Gait. Ann Biomed Eng 46, 60–70 (2018). https://doi.org/10.1007/s10439-017-1934-1

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  • DOI: https://doi.org/10.1007/s10439-017-1934-1

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