Fractal analyses reveal independent complexity and predictability of gait

Abstract

Locomotion is a natural task that has been assessed for decades and used as a proxy to highlight impairments of various origins. So far, most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent α and the Minkowski fractal dimension D were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. We show that α and D accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity (D) and hence, adaptability. In contrast, walking backward and/or stimulation of the vestibular system decreased D. Furthermore, walking backward increased predictability (α) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures.

Digital Natives and Dual Task: Handling It But Not Immune Against Cognitive-Locomotor Interferences

“…The dual task significantly decreases D in both conditions, which is coherent with the optimal variability framework [28]: Physiological signals -SI time series in the present work -show a maximal complexity in healthy participants, and any deviation from healthy state lowers it. As previously shown by our lab [15], D is a relevant measure of complexity in walking, hence we can state that SI time series complexity is lower because of the dual task. An intuitive argument, related to capacity-sharing model, is that participant's mind is "busy" while talking or solving Raven's matrices, resulting in a lower ability to handle afferent signals needed to optimally adapt their walk and eventually in a lower D. We can safely assume that adding a cognitive load during gait in digital natives has noticeable effects on SI and its stride-to-stride temporal organization.…”

“…In addition to SI, w and DS, several variability parameters have been extracted from the recorded SI time series following the methods of Ref. [15]: The coefficient of variation, CV, the Minkowski fractal dimension, D, and the Hurst exponent, H, defined as follows.…”

“…However, it provides no information on the temporal dynamics of these fluctuations. This is provided by two independent indices D and H [15]. The Minkowski fractal dimension D is computed by resorting to the box-counting method: if N ( ) is the number of square boxes of size needed to fully cover the plot of T (see Fig.…”

Added Value and Clinical Significance of Nonlinear Variability Indices of Walking Stride Interval in Neurodegenerative Diseases

“…Information about the variability of SI are easily provided by linear tools. Nonlinear goes one step beyond by assessing its complexity and predictability [13]. It is challenging to diagnosing neurodegeneration at an early stage.…”

“…The Minkowski's fractal dimension (D) of SI time series has also been proved to be a reliable estimator of complexity over time, see e.g. [13]. Where does the autocorrelations find its origins in the walking cycle ?…”