Persistence and anti-persistence in treadmill walking

Background Long-range persistent correlations in stride time (ST) and length (SL) are the fundamental traits of treadmill gait. Our recent work showed that the ST and SL time series’ statistical properties originated from the superposition of large-scale trends and small-scale fluctuations (residuals). Trends served as the control manifolds about which ST and SL fluctuated. The scaling exponents of the residuals were slightly smaller than 0.5. Research question Do random changes in treadmill belt speed affect the trend properties and scaling exponents of ST/SL residuals? Methods We used Multivariate Adaptive Regression Splines (MARS) to determine gait trends during a walk on a treadmill whose belt speed was perturbed by a strong random noise. Then, we calculated the scaling exponents of MARS residuals with the madogram estimator. Results Except for the ST at the lowest treadmill speed v = 0.8 m/s, the normalized trend duration was at least three times greater than that for the unperturbed walk. The Cauchy distribution scale parameter, which served as a measure of the width of SL and ST trend slope distributions, was at v = 1.2 m/s, almost 50% and 25% smaller than the unperturbed values. The differences were even greater at v = 1.6 m/s: 73% and 83%. For all speeds, the ST and SL MARS residuals were strongly anti-persistent. At v = 1.2 m/s, the corresponding scaling exponents were equal to 0.37±0.10 and 0.25±0.09. Apart from ST at v = 0.8 m/s, the ST/SL scaling indices were close to 0.5. Significance Persistence of gait parameters is closely related to the properties of their trends. Longer trends with a gentle slope and strong anti-persistence of ST/SL residuals are the manifestations or tight control required during the perturbed treadmill walk.