Fuzzy entropy (FuzzyEn), a new measure of time series regularity, was proposed and applied to the characterization of surface electromyography (EMG) signals. Similar to the two existing related measures ApEn and SampEn, FuzzyEn is the negative natural logarithm of the conditional probability that two vectors similar for m points remain similar for the next m + 1 points. Importing the concept of fuzzy sets, vectors' similarity is fuzzily defined in FuzzyEn on the basis of exponential function and their shapes. Besides possessing the good properties of SampEn superior to ApEn, FuzzyEn also succeeds in giving the entropy definition in the case of small parameters. Its performance on characterizing surface EMG signals, as well as independent, identically distributed (i.i.d.) random numbers and periodical sinusoidal signals, shows that FuzzyEn can more efficiently measure the regularity of time series. The method introduced here can also be applied to other noisy physiological signals with relatively short datasets.

Understanding the mechanisms that reduce the many degrees of freedom in the musculoskeletal system remains an outstanding challenge. Muscle synergies reduce the dimensionality and hence simplify the control problem. How this is achieved is not yet known. Here we use network theory to assess the coordination between multiple muscles and to elucidate the neural implementation of muscle synergies. We performed connectivity analysis of surface EMG from ten leg muscles to extract the muscle networks while human participants were standing upright in four different conditions. We observed widespread connectivity between muscles at multiple distinct frequency bands. The network topology differed significantly between frequencies and between conditions. These findings demonstrate how muscle networks can be used to investigate the neural circuitry of motor coordination. The presence of disparate muscle networks across frequencies suggests that the neuromuscular system is organized into a multiplex network allowing for parallel and hierarchical control structures.

Abstract:In the present contribution, a complexity measure is proposed to assess surface 1 electromyography (EMG) in the study of muscle fatigue during sustained, isometric muscle 2 contractions. Approximate entropy (ApEn) is believed to provide quantitative information about the 3 complexity of experimental data that is often corrupted with noise, short data-length, and in many cases, 4 has inherent dynamics that exhibit both deterministic and stochastic behaviors. We developed an 5 improved ApEn measure, i.e., fuzziness approximate entropy (fApEn), which utilizes the fuzzy 6 membership function to define the vectors' similarity. Tests were conducted on independent, identically 7 distributed (i.i.d.) Gaussian and uniform noises, a chirp signal, MIX processes, and Rossler, and Henon 8 maps. Compared with the standard ApEn, the fApEn showed better monotonicity, relative consistency, 9 and more robustness to noise when characterizing signals with different complexities. Performance 10 analysis on experimental EMG signals demonstrated that the fApEn significantly decreased during the 11 development of muscle fatigue, which is a similar trend to that of the mean frequency (MNF) of the 12 EMG signal, while the standard ApEn failed to detect this change. Moreover, the fApEn is more 13 sensitive to muscle fatigue than MNF with a larger linear regression slope (significant value p=0.0213). 14 The results suggest that the fApEn of an EMG signal may potentially become a new reliable method for 15 muscle fatigue assessment and be applicable to other short noisy physiological signal analysis. 16 17