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Multiscale entropy (MSE) has been a prevalent algorithm to quantify thecomplexity of fluctuations in the local mean value of biomedical time series.Recent developments in the field have tried to improve the MSE by reducing itsvariability in large scale factors. On the other hand, there has been recentinterest in using other statistical moments than the mean, i.e. variance, inthe coarse-graining step of the MSE. Building on these trends, here weintroduce the so-called refined composite multiscale fuzzy entropy based on thestandard deviation (RCMFE{\sigma}) to quantify the dynamical properties ofspread over multiple time scales. We demonstrate the dependency of theRCMFE{\sigma}, in comparison with other multiscale approaches, on severalstraightforward signal processing concepts using a set of synthetic signals. Wealso investigate the complementarity of using the standard deviation instead ofthe mean in the coarse-graining process using magnetoencephalograms inAlzheimer disease and publicly available electroencephalograms recorded fromfocal and non-focal areas in epilepsy. Our results indicate that RCMFE{\sigma}offers complementary information to that revealed by classical coarse-grainingapproaches and that it has superior performance to distinguish different typesof physiological activity.

Refined Multiscale Fuzzy Entropy based on Standard Deviation for Biomedical Signal Analysis