Surrogate multivariate Hurst exponent analysis of gait dynamics

The analysis of complex patterns in human gait dynamics typically relies on measuring stride intervals. Several studies have revealed that the dynamics of stride intervals exhibit fractal characteristics that depend on health, age, and task conditions. However, with current measurement devices, other gait parameters such as the swing and stance intervals can also be measured. This prompts the question of whether multivariate analysis provides a more detailed view of gait dynamics. This work aims to use multivariate rescaled range (MR/S) analysis to characterize the fractality of the combined behavior of the stride, stance, and swing intervals in terms of the Hurst exponent, which is an index of the fractality of a time series. The MR/S method was equipped with a surrogate data analysis, to refer to a corrected Hurst exponent, which is defined as a distance to randomness. Datasets of neurodegenerative conditions (amyotrophic lateral sclerosis, Huntington's disease and Parkinson's disease) from Physionet were used to evaluate the ability of MR/S analysis to characterize different phases of gait dynamics. An index of distance to randomness relative to a 95 % confidence interval obtained from surrogate data was introduced to alleviate biased estimation of the Hurst exponent for relatively small samples. The results showed that the distance to randomness of stance and stride intervals was higher (p < 0.05) than that of swing intervals. On the other hand, the stride interval discriminated (p < 0.05) the control conditions from the neurodegenerative conditions. In contrast, the swing interval discriminated (p < 0.05) the Parkinson's disease from ALS and Huntington's disease. Overall, the results indicate that multivariate analysis is a suitable approach for a detailed characterization of the impact of different gait phases on gait dynamics.