Power-Law Exponent Modulated Multiscale Entropy: A Complexity Measure Applied to Physiologic Time Series

Wei Han,Yili Yan,Kangning Xie,Chi Tang,Zunjing Zhang,Erping Luo

doi:10.1109/access.2020.3000439

Abstract

Quantifying the complexity of physiologic time series has long attracted interest from researchers. The multiscale entropy (MSE) algorithm is a prevailing method to quantify the complexity of signals in a variety of research fields. However, the MSE method assigns increased complexity to the mixed signal of a physiologic time series added with white noise, although the mixed signal should become less complex due to the broken correlation. In addition, the MSE method needs users to visually examine its scale dependence (shape) to better characterize the complexity of a physiologic process, which is sometimes not feasible. In this paper, we proposed a new method, namely the power-law exponent modulated multiscale entropy (pMSE), as a complexity measure for physiologic time series. We tested the pMSE method on simulated data and real-world physiologic interbeat interval time series and demonstrated that it could solve the above two difficulties of the MSE method. We expect that the proposed pMSE method or its future variants could serve as a useful complement to the MSE method for the complexity analysis of physiologic time series.

Highlights

It has attracted considerable attentions to quantify the ‘‘complexity’’ of physiologic time series in the attempt to distinguish different conditions, e.g., between the healthy and the diseased, or between the young and the elderly [1], [2]
Complexity values to physiologic time series than to periodic and (2) to random time series [7], [8]; (3) it should assign higher complexity values to a physiologic time series than to its shuffled surrogate, due to broken temporal correlations [7]; (4) it should assign reduced complexity values to the physiologic time series added with white noise, which is completely random; (5) it should assign high complexity values to healthy physiologic time series and low complexity values to the diseased [1], [8], [9]
Combining the two types of complexity measures, we propose a new complexity measure, which can overcome the weakness of the multiscale entropy (MSE) method and can meet the five criteria mentioned above, can provide a direct complexity measure for physiologic time series

Summary

INTRODUCTION

It has attracted considerable attentions to quantify the ‘‘complexity’’ of physiologic time series in the attempt to distinguish different conditions, e.g., between the healthy and the diseased, or between the young and the elderly [1], [2]. A lot of indices have been employed including various entropy-based measures, e.g., approximate entropy [10], permutation entropy [11] and sample entropy [12] These conventional entropy-based measures, which quantify the irregularity of time series, assign the highest complexity values to white noise, are not satisfactory in describing physiologic complexity. To solve this problem, Costa et al have devised a new measure, multiscale entropy (MSE), to identify complexity in physiologic systems [9], [13] by calculating sample entropy on multiple scales of the coarse-grained version. We average pMSE over all scales to get an overall vision of the underlying complexity of the time series in question

THE RELATIONSHIP BETWEEN MSE AND β

A MULTISCALE COMPLEXITY MEASURE

COMPLEXITY ANALYSIS OF SIMULATED POWER-LAW PROCESS

DISCUSSION

Findings

CONCLUSION