Significance of trends in gait dynamics

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.Author summary: During treadmill walking, the subject’s stride time (ST) and stride length (SL) must yield a stride speed (SS) which can fluctuate over a narrow range centered on the treadmill belt’s speed. The fact that both ST and SL are persistent is an intriguing property of human gait. For persistent fluctuations any deviation from the mean value is likely to be followed by a deviation in the same direction. To trace the origin of such persistence, we used a novel approach to determine trends in spatio-temporal gait parameters. We find that the trends of ST and SL of a subject are strongly correlated and are statistically independent of their corresponding residuals. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The persistence of gait parameters stems from superposition of large scale trends and small scale fluctuations.