Fuzzy approximate entropy analysis of chaotic and natural complex systems: detecting muscle fatigue using...

In the present contribution, a complexity measure is proposed to assess surface electromyography (EMG) in the study of muscle fatigue during sustained, isometric muscle contractions. Approximate entropy (ApEn) is believed to provide quantitative information about the complexity of experimental data that is often corrupted with noise, short data length, and in many cases, has inherent dynamics that exhibit both deterministic and stochastic behaviors. We developed an improved ApEn measure, i.e., fuzzy approximate entropy (fApEn), which utilizes the fuzzy membership function to define the vectors' similarity. Tests were conducted on independent, identically distributed (i.i.d.) Gaussian and uniform noises, a chirp signal, MIX processes, Rossler equation, and Henon map. Compared with the standard ApEn, the fApEn showed better monotonicity, relative consistency, and more robustness to noise when characterizing signals with different complexities. Performance analysis on experimental EMG signals demonstrated that the fApEn significantly decreased during the development of muscle fatigue, which is a similar trend to that of the mean frequency (MNF) of the EMG signal, while the standard ApEn failed to detect this change. Moreover, fApEn of EMG demonstrated a better robustness to the length of the analysis window in comparison with the MNF of EMG. The results suggest that the fApEn of an EMG signal may potentially become a new reliable method for muscle fatigue assessment and be applicable to other short noisy physiological signal analysis.