Entropy of frequency domain of heart rate variability

Keywords: hearth rate variability, entropy, frequency-domain, congestive heart failure, atrial fibrillation


Introduction. The heart rate variability (HRV) is based on measuring (time) intervals between R-peaks (of RR-intervals) of an electrocardiogram (ECG) and plotting a rhythmogram on their basis with its subsequent analysis by various mathematical methods which are classified as Time-Domain (TD), Frequency-Domain (FD) and Nonlinear [1, 2]. There are a number of popular Nonlinear methods used in HRV analysis, such as entropy-based measures that mostly applied for TD. Spectral Entropy (SE) is using for Frequency-Domain: it is defined to be the Shannon entropy of the power spectral density (PSD) of the data. An important characteristic of Frequency-Domain studies is sympatho-vagal balance, which has been overlooked by entropy-based analysis. This is due to the fact that good entropy analysis restricted the number of existing HRV data, which is shrinking in FD and also in total spectrum parts. Aim of the research. The goal of this paper is to provide a reliable formula for calculating entropy accurately for Frequency-domain of standard 5-min. HRV records and to show the advantages of such approach for analyzing of sympatho-vagal balance for healthy subjects (NSR), Congestive Heart Failure (CHF) and Atrial Fibrillation (AF) patients. Materials and Methods. We used MIT-BIH long-term HRV records for Normal Sinus Rhythm (NSR), Congestive Heart Failure (CHF) and Atrial Fibrillation (AF). The generalized form of the Robust Entropy Estimator (EnRE) for Frequency-domain of standard 5-min. HRV records was proposed and the key EnRE futures was shown. The difference between means of the two independent selections (NSR and CHF, before and after AF) has been determined by a t-test for independent samples; discriminant analysis and statistical  calculations have been done by using the statistical package IBM SPSS 27. The results of the study. We calculate entropy for all valuable for HRV spectral interval, namely 0–0.4 Hz and to compare with existing results for Spectral Entropy: qualitatively we receive the same distribution number as [14] and significant difference (p < 0.001) between entropy averages for NSR and CHF or AF patients. We define low-frequencies (LF) power spectrum components in the range of 0.04–0.15 Hz and high-frequencies (HF) power spectrum components in the range of 0.15–0.4 Hz [1]. The sympatho-vagal balance is a simple ratio LF/HF [1]. Then, we define an entropy eLF of the LF power spectrum components, an entropy eHF of the HF power spectrum components and entropy based sympatho-vagal balance as a ratio eLF/eHF. The difference between NSR and CHF groups are significant in both cases LF/HF and eLF/eHF with p < 0.001, but in case of eLF/eHF the results are quite better (t = -4.8, compared to LF/HF where t = -4.4). The discriminant analysis shows total classification accuracy for eLF/eHF in 79.3 % (χ2 = 19.4, p < 0.001) and for LF/HF in 72.4 % (χ2 = 16.6, p < 0.001). We applied entropy-based Frequencies-domain analyzing for AF patients and showed that ratio eLF/eHF is significantly higher during AF than before AF (p < 0.001). This is opposite to ordinary LF/HF where difference is insignificant due to high variation of this ratio. Conclusion. Proposed in the article is generalized form for Robust Entropy Estimator EnRE for Frequencies-domain, which allows, for time series of a limited length (standard 5-min. records), to find entropy value of HRV power spectrum (total spectrum, low- and high- frequencies bands). Using the proposed EnRE for MIT-BIH database of HRV records, we show for standard 5 min. HRV records the usage of EnRE of HRV power spectrum and entropy-based sympatho-vagal balance of Normal Sinus Rhythm (NSR) and Congestive Heart Failure (CHF) cases. It is demonstrated, that, entropy-based Frequencies-domain analyzing is applicable for case of Atrial Fibrillation (AF) even during AF episodes. We showed the significant difference (p < 0.001) before and during AF for entropy of total spectrum, as well as for sympatho-vagal balance in form of eLF/eHF.


Download data is not yet available.

Author Biographies

Oleksandr Martynenko, V. N. Karazin Kharkiv National University

D.Sc., Ph.D., Full Professor, Department of Hygiene and Social Medicine, School of Medicine, V. N. Karazin Kharkiv National University, 6, Svobody sq., Kharkiv, Ukraine, 61022

Gianfranco Raimondi, Sapienza University of Rome (Italy)

MD, PhD, Prof., Sapienza University of Rome (Italy), 5, Piazzale Aldo Moro, Rome, Italy, 00185

Luca Barsi, Sapienza University of Rome (Italy), Rome, Italy

PhD, Rome, Italy, 00185

Liudmila Maliarova, V. N. Karazin Kharkiv National University

Assistant, Department of hygiene and social medicine, School of Medicine, V. N. Karazin Kharkiv National University, 6, Svobody sq., Kharkiv, Ukraine, 61022


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;93(5):1043–1065. DOI: https://www.ahajournals.org/doi/10.1161/01.CIR.93.5.1043

Iabluchanskyi M, Martynenko A, Bydreiko N, Yabluchansky A. Heart Rate Variability for medical scientists and doctors. Kharkiv: V. N. Karazin Univer. Press; 2022. 131 p. DOI: https://doi.org/10.13140/RG.2.2.32435.91685/1

Pincus SM. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA, 1991;88: 2297–2301. DOI: https://doi.org/10.1073/pnas.88.6.2297

Richman JS, Moorman JR. Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol. 2000; 278: H2039–H2049. DOI: https://doi.org/10.1152/ajpheart.2000.278.6.H2039

Humeau-Heurtier A. The multiscale entropy algorithm and its variants: A review. Entropy. 2015;17: 3110–3123. DOI: https://doi.org/10.3390/e17053110

Costa M, Goldberger AL, Peng CK. Multiscale entropy analysis of biological signals. Phys. Rev. E. 2005 71:021906. DOI: https://doi.org/10.1103/PhysRevE.71.021906

Costa M, Goldberger AL, Peng CK. Multiscale entropy analysis of complex physiologic time series. Phys. Rev. Lett. 2002;89:068102. DOI: https://doi.org/10.1103/PhysRevLett.89.068102

Gao ZK, Fang PC, Ding MS, Jin ND. Multivariate weighted complex network analysis for characterizing nonlinear dynamic behavior in two-phase flow. Exp. Therm. Fluid Sci. 2015;60:157–164. DOI: https://doi.org/10.1016/j.expthermflusci.2014.09.008

Labate D. et al. Entropic measures of eeg complexity in alzheimer’s disease through a multivariate multiscale approach. IEEE Sens. J. 2013;13:3284–3292.

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

Zhao LN, Wei SS, Tong H, Liu CY. Multivariable fuzzy measure entropy analysis for heart rate variability and heart sound amplitude variability. Entropy. 2016; 18: 430, DOI: https://doi.org/10.3390/e18120430

Li P. et al. Multiscale multivariate fuzzy entropy analysis. Acta Phys. Sin. 2013;62:120512.

Ahmed MU, Mandic DP. Multivariate multiscale entropy analysis. IEEE Signal Proc. Lett. 2012;19: 91–94.

Madhavi CHR. Estimation of Spectral Entropy of HRV Data and its Application to Depression and Thyroid Subjects to Predict Cardiac Risk. Biomed Pharmacol J. 2018; 11 (3). DOI : https://dx.doi.org/10.13005/bpj/1532

Martynenko A, Raimondi G, Budreiko N. Robust Entropy Estimator for Heart Rate Variability. Klin. Inform. Telemed. 2019;14(15):67-73. DOI: https://doi.org/10.31071/kit2019.15.06

Goldberger A, Amaral L, Glass L, Hausdorff J, Ivanov PC, Mark R, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation [Online]. 2000;101(23):e215–e220.

Moody GB, Mark RG. A new method for detecting atrial fibrillation using R-R intervals. Computers in Cardiology. 1983;10:227-230.

Tsai CH, Ma HP, Lin YT, et al. Usefulness of heart rhythm complexity in heart failure detection and diagnosis. Sci Rep. 2020;10:14916. DOI: https://doi.org/10.1038/s41598-020-71909-8

Liu G, Wang L, Wang Q, Zhou G, Wang Y, et al. A New Approach to Detect Congestive Heart Failure Using Short-Term Heart Rate Variability Measures. 2014;PLoS ONE 9(4): e93399. DOI: https://doi.org/10.1371/journal.pone.0093399

How to Cite
Martynenko, O., Raimondi, G., Barsi, L., & Maliarova, L. (2022). Entropy of frequency domain of heart rate variability. The Journal of V. N. Karazin Kharkiv National University, Series "Medicine&quot;, (45). https://doi.org/10.26565/2313-6693-2022-45-01