Fractal analysis of muscle activity patterns during locomotion: pitfalls and how to avoid them

Abstract

Time-dependent physiological data, such as electromyogram (EMG) recordings from multiple muscles, is often difficult to interpret objectively. Here, we used EMG data gathered during mouse locomotion to investigate the effects of calculation parameters and data quality on two metrics for fractal analysis: the Higuchis fractal dimension (HFD) and the Hurst exponent (H). A curve is fractal if it repeats itself at every scale or, in other words, if its shape remains unchanged when zooming in the curve at every zoom level. Many linear and nonlinear analysis methods are available, each of them aiming at the explanation of different data features. In recent years, fractal analysis has become a powerful nonlinear tool to extract information from physiological data not visible to the naked eye. It can present, however, some dangerous pitfalls that can lead to misleading interpretations. To calculate the HFD and the H, we have extracted muscle synergies from normal and mechanically perturbed treadmill locomotion from the hindlimb of adult mice. Then, we used one set per condition (normal and perturbed walking) of the obtained time-dependent coefficients to create surrogate data with different fluctuations over the original mean signal. Our analysis shows that HFD and H are exceptionally sensitive to the presence or absence of perturbations to locomotion. However, both metrics suffer from variations in their value depending on the parameters used for calculations and the presence of quasi-periodic elements in the time series. We discuss those issues giving some simple suggestions to reduce the chance of misinterpreting the outcomes. New & NoteworthyDespite the lack of consensus on how to perform fractal analysis of physiological time series, many studies rely on this technique. Here, we shed light on the potential pitfalls of using the Higuchis fractal dimension and the Hurst exponent. We expose and suggest how to solve the drawbacks of such methods when applied to data from normal and perturbed locomotion by combining in vivo recordings and computational approaches.