Entropy of frequency domain of heart rate variability
Authors: Martynenko Oleksandr , Raimondi Gianfranco , Barsi Luca , Maliarova Liudmila 
Published: April 2023

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.