Українська  English  Русский  


Inventory reference

ISSN 1812-7231 Klin.inform.telemed. Volume 14, Issue 15, 2019, Pages 67-73


A. Martynenko1, G. Raimondi2, N. Budreiko1


1V. N. Karazin Kharkiv National University, School of Medicine, Ukraine

2University of Roma "Sapienza", Italy

Article title

Robust entropy estimator for heart rate variability

Abstract (resume)

Introduction. Non-linear methods of analysis have found widespread use in the heart rate variability (HRV) technology, when the long-term HRV records are available. Using one of the effective nonlinear methods of analysis of HRV entropy for the standard 5-min HRV records is suppressed by unsatisfactory accuracy of available methods in case of short records (usually, doctors have 300–600 RRs during standard 5-min HRV record), as well as complexity and ambiguity of choosing additional parameters for known methods of calculating entropy ApEn, SampEn, MSE and etc.

The purpose of the work. Building a robust formula for calculating entropy (EnRE) with high accuracy for limited series of RR-intervals observed in a standard 5-minute HRV record, i. e. with N≈300–600. As well as demonstrating the capabilities of the EnRE formula on a series of statistical distributions and in diagnosing the congestive heart failure.

Materials and Methods. We used MIT-BIH long-term HRV records for Normal Sinus Rhythm (NSR) and Congestive Heart Failure (CHF). In order to analyze the accuracy of EnRE, we used the known statistical distributions (Normal, Uniform, Exponential, Lognormal, Pareto) with their precise entropy values.

The results of the study. We have shown the effectiveness of the developed EnRE formula for time series of limited length (N = 300–600) using the example of various types of statistical distributions that simulate human HRV ranges, and also demonstrated high accuracy of classification of cases of NSR and CHF for standard 5 min segments from MIT-BIH database of HRV records, using EnRE and EnRE(sort).

Conclusion. Proposed in the article is generalized form for Robust Entropy Estimator, which allows, for time series of limited length (N= 300–600), to calculate entropy value that differs from a precise one by 0,5–2,9%, as demonstrated for various random distributions. On standard 5-min segments from MIT-BIH database of HRV records, we have shown the usage of EnRE and EnRE (sort) for classification of cases of Normal Sinus Rhythm and Congestive Heart Failure with indicators of quality of division into groups: Se = 0,76, Sp = 0,98, Acc = 0,90.


Hearth rate variability, Entropy, Congestive heart failure


1. Task force of the European society of cardiology and the North American society of pacing and electrophysiology. Heart rate variability — standards of measurement, physiological interpretation, and clinical use. Circulation, 1996. vol. 93, iss. 5, pp.1043–1065.

2. Yabluchansky N., Martynenko A. [Heart Rate Variability for clinical practice]. 2010. Kharkiv, Univer. Press, 131 p. (In Russ.) depositary:

3. Nayak S. K. at all. A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal. J. Healthc. Eng. 2018. Article ID 6920420, 19 p.
PMid:29854361 PMCid:PMC5954865

4. De Godoy M. F. Nonlinear Analysis of Heart Rate Variability: A Comprehensive Review. J.Cardiology and Therapy, 2016, vol. 3, no. 3, pp.528–533.

5. İşler Y., Kuntalp M. Combining classical HRV indices with wavelet entropy measures improves to performance in diagnosing congestive heart failure. Comput. Biol. Med., 2007. iss. 37, pp. 1502–1510.

6. Wood A. J., Cohn J. N. The management of chronic heart failure. N. Engl. J. Med. 1996, iss. 335, pp. 490–498.

7. Nolan J. at all. Prospective study of heart rate variability and mortality in chronic heart. Circulation 1998, vol. 98, pp. 1510–1516.

8. Rector T. S., Cohn J. N. Prognosis in congestive heart failure. Annu. Rev. Med. 1994, vol. 45, pp. 341–350.

9. Arbolishvili G. N. at all. Heart rate variability in chronic heart failure and its role in prognosis of the disease. Kardiologiia [Cardiology]. 2005, vol. 46, pp. 4–11.

10. Smilde T. D. J., van Veldhuisen, D. J. and van den Berg, M. P. Prognostic value of heart rate variability and ventricular arrhythmias during 13-year follow-up in patients with mild to moderate heart failure. Clin. Res. Cardiol. 2009, vol. 98, pp. 233–239.

11. Acharya U. R. at all. Application of empirical mode decomposition (EMD) for automated identification of congestive heart failure using heart rate signals. Neural Comput. Appl. 2016, pp. 1–22

12. Yu, S. N., Lee M. Y. Bispectral analysis and genetic algorithm for congestive heart failure recognition based on heart rate variability. Comput. Biol. Med. 2012, vol. 42, pp. 816–825.

13. Narin A., Isler Y., Ozer M. Investigating the performance improvement of hrv indices in chf using feature selection methods based on backward elimination and statistical significance. Comput. Biol. Med. 2013, vol. 45, pp. 72–79.

14. Jong T. L., Chang B., Kuo C. D. Optimal timing in screening patients with congestive heart failure and healthy subjects during circadian observation. Ann. Biomed. Eng. 2011, vol. 39, pp. 835–849.

15. Kumar M., Pachori R. B., Acharya U. R. Use of accumulated entropies for automated detection of congestive heart failure in flexible analytic wavelet transform framework based on short-term HRV signals. Entropy 2017, vol. 19, p. 92,

16. Pincus S. M. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA. 1991, vol. 88, pp. 2297–2301.
PMid:11607165 PMCid:PMC51218

17. Richman J. S., Moorman, J. R. Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol. 2000, iss. 278, pp. H2039–H2049.

18. Humeau-Heurtier A. The multiscale entropy algorithm and its variants: A review. Entropy 2015, vol. 17, pp. 3110–3123.

19. Costa M., Goldberger A. L., Peng C. K. Multiscale entropy analysis of biological signals. Phys. Rev. E. 2005, vol. 71, Article ID 021906.

20. Costa M., Goldberger A.L., Peng C.K. Multiscale entropy analysis of complex physiologic time series. Phys. Rev. Lett. 2002, vol. 89, Article ID 068102.

21. Gao Z. K., Fang P. C., Ding M. S., Jin N. D. Multivariate weighted complex network analysis for characterizing nonlinear dynamic behavior in two-phase flow. Exp. Therm. Fluid Sci. 2015, vol. 60, pp. 157–164.

22. Labate D. at all. Entropic measures of EEG complexity in Alzheimer's disease through a multivariate multiscale approach. IEEE Sens. J. 2013, vol. 13, pp. 3284–3292.

23. Azami H., Escudero J. Refined composite multivariate generalized multiscale fuzzy entropy: A tool for complexity analysis of multichannel signals. Physica A. 2017, iss. 465, pp. 261–276.

24. Zhao L. N., Wei S. S., Tong H., Liu C. Y. Multivariable fuzzy measure entropy analysis for heart rate variability and heart sound amplitude variability. Entropy. 2016, vol. 18, p. 430.

25. Li, P. at all. Multiscale multivariate fuzzy entropy analysis. Acta Phys. Sin. 2013, vol. 62, 120512.

26. Ahmed M. U., Mandic D. P. Multivariate multiscale entropy analysis. IEEE Signal Proc. Lett. 2012, vol. 19, .pp.91–94.

27. Chengyu L., Rui G. Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure. Entropy. 2017, vol. 19, p. 251.

28. Goldberger A. L. at all. Physiobank, physiotoolkit, and physionet: Components of a new research resource for complex physio logic signals. Circulation. 2000, vol. 101, pp. 215–220.

29. Shannon C. E. "A Mathematical Theory of Communication". Bell System Technical Journal. 1948. vol. 27, no 3, pp. 379–423.

30. Lazo A. and Rathie P. "On the entropy of continuous probability distributions". IEEE Transactions on Information Theory. 1978, vol. 24, no. 1.

31. Gini C. Variabilitа e mutabilitа. Reprinted in Pizetti, E.; Salvemini, T., eds. Memorie di metodologica statistica. Rome, Libreria Eredi Virgilio Veschi. 1955. 156 p.

32. Sаnchez-Hechavarrнa M. E. and etc. Introduction of Application of Gini Coefficient to Heart Rate Variability Spectrum for Mental Stress Evaluation. Arq Bras Cardiol. 2019; [online]. ahead print, pp. 0–0.
PMid:31508693 PMCid:PMC7020869

33. Firebaugh G. Empirics of World Income Inequality. American Journal of Sociology. 1999, vol. 104, no. 6, pp. 1597–1630.

34. Shorrocks A. F. The Class of Additively Decomposable Ine quality Measures. Econometrica. 1980, vol. 48, no. 3, pp. 613–625.

Full-text version