Characterization of statistical persistence in joint angle variation during walking

The objective of this study was to characterize joint angle variation across strides. Specifically, the statistical persistence of variations were quantified using the Hurst exponent. If a time series exhibits statistical persistence, then a parameter which is smaller (or larger) than average will tend to be followed by additional values that are also smaller (or larger) than average. Human walking has statistical persistence between stride durations. Variation in stride duration must arise from variation in the motion of the leg segments during walking. It is unclear, however, if the joint angle variation also exhibits statistical persistence. This study examined kinematic data collected from nine healthy adults walking for 10 min at a self-selected comfortable speed on a treadmill. The joint angle variation in the lower limbs was parameterized using first-order Fourier series which in turn were described by frequency and magnitude coefficients for each stride. To determine if the joint angle variation exhibited statistical persistence, the Hurst exponent was found for each coefficient at each joint. The mean Hurst exponents were 0.54 for the frequency coefficients and 0.61 for the magnitude coefficients. Neither the frequency or magnitude coefficients exhibited statistically significant persistence, although some of the magnitude coefficients were close to reaching statistical significance. This suggests that joint angle variability in healthy adults does not directly produce the statistical persistence observed in stride duration fluctuations.