The Refined Composite Downsampling Permutation Entropy Is a Relevant Tool in the Muscle Fatigue Study Using sEMG Signals

Abstract

Surface electromyography (sEMG) is a valuable technique that helps provide functional and structural information about the electric activity of muscles. As sEMG measures output of complex living systems characterized by multiscale and nonlinear behaviors, Multiscale Permutation Entropy (MPE) is a suitable tool for capturing useful information from the ordinal patterns of sEMG time series. In a previous work, a theoretical comparison in terms of bias and variance of two MPE variants—namely, the refined composite MPE (rcMPE) and the refined composite downsampling (rcDPE), was addressed. In the current paper, we assess the superiority of rcDPE over MPE and rcMPE, when applied to real sEMG signals. Moreover, we demonstrate the capacity of rcDPE in quantifying fatigue levels by using sEMG data recorded during a fatiguing exercise. The processing of four consecutive temporal segments, during biceps brachii exercise maintained at 70% of maximal voluntary contraction until exhaustion, shows that the 10th-scale of rcDPE was capable of better differentiation of the fatigue segments. This scale actually brings the raw sEMG data, initially sampled at 10 kHz, to the specific 0–500 Hz sEMG spectral band of interest, which finally reveals the inner complexity of the data. This study promotes good practices in the use of MPE complexity measures on real data.

On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy

“…Many of the MPE are based on linear preprocessing [ 12 , 30 , 31 , 53 , 54 , 55 ] such as lag operator and/or linear filters and/or downsampling. Firstly, it should be noted that at high scales, the downsampling step of this MPE class may induce spurious patterns reflecting spectral aliasing as Shannon’s theorem is no longer respected [ 3 ].…”

“…Ordinal pattern-based approaches have recently gained attention because of their natural and efficient way to transform a time series into a sequence of symbols with a finite alphabet [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ]. This ordinal pattern sequence is simply obtained by comparing the values of a finite number of neighboring samples and ranking them.…”

“…The probability distribution of ordinal patterns (OP) implicitly captures information about the temporal structure of the time series and thus allows the extraction of several promising ordinal pattern-based indicators. These indicators are useful in a growing number of applications including biomedical signal and image processing [ 6 , 10 , 11 , 15 , 31 , 33 , 38 ], fault bearing diagnosis [ 30 , 39 , 40 , 41 , 42 , 43 , 44 ], financial time series analysis [ 7 ] and engineering physics [ 18 , 35 , 45 , 46 , 47 , 48 , 49 , 50 , 51 ].…”

“…As the PE has the ability to capture hidden dynamics of time series, various extensions of the PE, called multiscale PE (MPE), have been proposed to explore in depth the internal structure of signals at different time scales. Among the MPE techniques, we cite coarse-graining MPE [ 53 ], composite MPE [ 54 ], refined composite MPE [ 12 ], downspamling PE (DPE) [ 55 ], composite DPE [ 31 ], refined composite DPE [ 31 ], hierarchical PE [ 56 ], and data-driven decomposition-based MPE [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 57 , 58 , 59 ]. The main idea of these PE-based techniques is to combine PE with a preprocessing step of the signal of interest in order to reduce the number of patterns related to noise.…”

“…These MPE techniques can be roughly split into two categories regarding the preprocessing step. The first category applies a linear filtering [ 12 , 31 , 53 , 54 , 55 ], whereas the second category uses a nonlinear processing [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 57 , 58 , 59 ]. Despite the widely proven usefulness of these techniques, there is still a need to understand the impact of the preprocessing step on the MPE values and how this impact can significantly alter the interpretation of MPE results.…”