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.
Annals of Biomedical Engineering
Cignetti, Fabien; Decker, Leslie M.; and Stergiou, Nicholas, "Sensitivity of the Wolf’s and Rostein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets" (2012). Journal Articles. 80.