Refined generalized multiscale entropy analysis for physiological signals

Multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields. However, it only takes into account the information of mean values (first moment) in coarse-graining procedure. Then generalized multiscale entropy (MSEn) considering higher moments to coarse-grain a time series was proposed and MSE sigma 2 has been implemented. However, the MSE sigma 2 sometimes may yield an imprecise estimation of entropy or undefined entropy, and reduce statistical reliability of sample entropy estimation as scale factor increases. For this purpose, we developed the refined model, RMSE sigma 2, to improve MSEG(sigma 2). Simulations on both white noise and 1/f noise show that RMSE sigma 2 provides higher entropy reliability and reduces the occurrence of undefined entropy, especially suitable for short time series. Besides, we discuss the effect on RMSE sigma 2 analysis from outliers, data loss and other concepts in signal processing. We apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects, patients with congestive heart failure and patients with atrial fibrillation respectively, compared to several popular complexity metrics. The results demonstrate that RMSE sigma 2 measured complexity (a) decreases with aging and diseases, and (b) gives significant discrimination between different physiological/pathological states, which may facilitate clinical application. (C) 2017 Elsevier B.V. All rights reserved.