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 15 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 Higuchi's 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 20 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 25 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 30 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 35 Submitted Manuscript 3 Higuchi's 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.

Lower complexity of motor primitives ensures robust control of high-speed human locomotion

“…To assess the local complexity [44] of motor primitives, we calculated the Higuchi's fractal dimension (HFD), assuming that these time series exhibit self-affinity properties [11,20,21,[45][46][47][48]. Following the procedure first described by Higuchi [20], for each motor primitive H(t)[H (1), 455 H(n)], k sets of new time series must be constructed, where k is an integer interval time and 2 < k < k max :…”

“…For each trial, the HFD 465 of the primitives obtained by NMF was calculated separately and then averaged, so that each trial ultimately consisted of one HFD value [11]. Following suggestions from previous studies, k max was chosen as the most linear part of the log-log plot, which in our data led us to choose k max = 10 [48,49].…”

Muscle Activation Patterns Are More Constrained and Regular in Treadmill Than in Overground Human Locomotion

“…Then, we analyzed the motor modules, or the weighted contributions of each muscle activity, and the timing characteristics of motor primitives, which are the time-dependent components of muscle synergies (Santuz et al, 2018a). Lastly, we used fractal analysis to compute the Hurst exponent of motor primitives, in order to gain deeper insight into their temporal structure (Santuz and Akay, 2020). By using these tools, we recently found that both internal and external perturbations applied to human and murine locomotion affect the timing of motor primitives, despite minor changes in the number and composition of motor modules (Santuz et al, 2018a(Santuz et al, , 2019(Santuz et al, , 2020aSantuz and Akay, 2020).…”

“…Lastly, we used fractal analysis to compute the Hurst exponent of motor primitives, in order to gain deeper insight into their temporal structure (Santuz and Akay, 2020). By using these tools, we recently found that both internal and external perturbations applied to human and murine locomotion affect the timing of motor primitives, despite minor changes in the number and composition of motor modules (Santuz et al, 2018a(Santuz et al, , 2019(Santuz et al, , 2020aSantuz and Akay, 2020). Specifically, we could systematically associate a relatively longer duration of motor primitives (i.e., increased width of the signal) in genetically modified mice lacking proprioceptive feedback from muscle spindles (Santuz et al, 2019), in aging humans as compared to young (Santuz et al, 2020a), and in young adults walking and running on uneven terrain (Santuz et al, 2018a), on unstable ground (Santuz et al, 2020a), or running at extremely high speeds (Santuz et al, 2020b).…”

“…Here, we aimed at uncovering some neuromotor control features of overground and treadmill locomotion using a novel combination of machine learning and fractal analysis. Based on our previous findings on perturbed and unperturbed locomotion (Akay et al, 2018;Santuz et al, 2019Santuz et al, , 2020aSantuz and Akay, 2020), we hypothesized that: (a) treadmill, as compared to overground, would perturb more the locomotor system due to the increased sensory and spatial constraints; and (b) the neural control of treadmill locomotion would be forced to be more regular by the aforementioned constraints, thus resulting in motor primitives having a Hurst exponent lower in treadmill than in overground.…”