Sample entropy parametric estimation for heart rate variability analysis

Aims: Sample Entropy (SampEn) is a powerful approach for characterizing heart rate variability regularity. On the other hand, autoregressive (AR) models have been employed for maximum-entropy spectral estimation for more than 40 years. The aim of this study is to explore the feasibility of a parametric approach for SampEn estimation through AR models. We re-analyze the Physionet paroxysmal Atrial Fibrillation (AF) database, where RR series are provided before and after an AF episode, for 25 patients. In particular, we selected short RR series, close to AF episodes, to fit an AR model. Then, theoretical values of SampEn, based on each AR model, were analytically derived (SE th) and also estimated numerically (SEsyn). The value of SampEn (SErr), computed on the 50 RR series with r=0.2×STD, m=1 and N=120, were within the standard range of SEsyn in 30 cases (39 for SEth). This figure increased to 82% of cases, if shorter series were selected (N=75), and if RR series were replaced by surrogates with Gaussian amplitude distribution. Interestingly, without removing ectopic beats, every estimate of SampEn considered was significantly different between pre- and post- AF (SErr: p=0.02; SEsyn: p=0.0024; SEth: p=0.023). When an AR model is appropriate and theoretical estimates differ from numerical ones, a parametric approach might enlighten additional information brought by SampEn.