# Determination of Sample Entropy and Fuzzy Measure Entropy Parameters for Distinguishing Congestive Heart Failure from Normal Sinus Rhythm Subjects

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School of Control Science and Engineering, Shandong University, Jingshi Road 17923, Jinan 250061, China

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Department of Cardiology, School Hospital of Shandong University, Jingshi Road 17923, Jinan 250061, China

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School of Information Technology and Electrical Engineering, University of Queensland, Queensland, 4072, Australia

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Authors to whom correspondence should be addressed.

Academic Editor: Raúl Alcaraz Martínez

Received: 14 July 2015 / Revised: 9 August 2015 / Accepted: 17 August 2015 / Published: 10 September 2015

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF) from normal sinus rhythm (NSR) subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn) and recently proposed fuzzy measure entropy (FuzzyMEn) is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (>2 s) and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed for each RR segment under different parameter combinations: m of 1, 2, 3 and 4, and r of 0.10, 0.15, 0.20 and 0.25 respectively. The statistical significance between NSR and CHF groups under each combination of m, r and N was observed. The results demonstrated that the selection of m, r and N plays a critical role in determining the SampEn and FuzzyMEn outputs. Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein, r

_{L}= r_{G}= r) are for FuzzyMEn (in addition to setting n_{L}= 3 and n_{G}= 2) were recommended to yield the fine classification results for the NSR and CHF groups.