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

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 (ENTA 1/2) 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, ENTA 1/2, 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 ENTA 1/2 and SPD between walking condition, and they exhibited a low correlation. ENTA 1/2 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.