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Open AccessArticle

Multivariable Fuzzy Measure Entropy Analysis for Heart Rate Variability and Heart Sound Amplitude Variability

by Lina Zhao 1, Shoushui Wei 1,*, Hong Tang 2,* and Chengyu Liu 1,*
1
School of Control Science and Engineering, Shandong University, Jinan 250061, China
2
Department of Biomedical Engineering, Dalian University of Technology, Dalian 116024, China
*
Authors to whom correspondence should be addressed.
Academic Editor: Anne Humeau-Heurtier
Entropy 2016, 18(12), 430; https://doi.org/10.3390/e18120430
Received: 14 October 2016 / Revised: 28 November 2016 / Accepted: 29 November 2016 / Published: 3 December 2016
(This article belongs to the Special Issue Multivariate Entropy Measures and Their Applications)
Simultaneously analyzing multivariate time series provides an insight into underlying interaction mechanisms of cardiovascular system and has recently become an increasing focus of interest. In this study, we proposed a new multivariate entropy measure, named multivariate fuzzy measure entropy (mvFME), for the analysis of multivariate cardiovascular time series. The performances of mvFME, and its two sub-components: the local multivariate fuzzy entropy (mvFEL) and global multivariate fuzzy entropy (mvFEG), as well as the commonly used multivariate sample entropy (mvSE), were tested on both simulation and cardiovascular multivariate time series. Simulation results on multivariate coupled Gaussian signals showed that the statistical stability of mvFME is better than mvSE, but its computation time is higher than mvSE. Then, mvSE and mvFME were applied to the multivariate cardiovascular signal analysis of R wave peak (RR) interval, and first (S1) and second (S2) heart sound amplitude series from three positions of heart sound signal collections, under two different physiological states: rest state and after stair climbing state. The results showed that, compared with rest state, for univariate time series analysis, after stair climbing state has significantly lower mvSE and mvFME values for both RR interval and S1 amplitude series, whereas not for S2 amplitude series. For bivariate time series analysis, all mvSE and mvFME report significantly lower values for after stair climbing. For trivariate time series analysis, only mvFME has the discrimination ability for the two physiological states, whereas mvSE does not. In summary, the new proposed mvFME method shows better statistical stability and better discrimination ability for multivariate time series analysis than the traditional mvSE method. View Full-Text
Keywords: multivariate sample entropy; multivariate fuzzy measure entropy; heart rate variability; heart sound; amplitude variability; cardiovascular time series multivariate sample entropy; multivariate fuzzy measure entropy; heart rate variability; heart sound; amplitude variability; cardiovascular time series
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Zhao, L.; Wei, S.; Tang, H.; Liu, C. Multivariable Fuzzy Measure Entropy Analysis for Heart Rate Variability and Heart Sound Amplitude Variability. Entropy 2016, 18, 430.

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