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

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.