Parametric estimation of sample entropy in heart rate variability analysis

• A parametric approach based on autoregressive models is proposed for sample entropy.
• Theoretical analytical results, which were derived, help in guiding the process.
• A feasibility study of the technique was performed on synthetic and real series.
• When the parametric approach is suitable, nonlinearities are unlikely.
• On the contrary, a failure of the parametric approach is an index of nonlinearity.

In this paper, a detailed study on the possibility and significance of performing a parametric estimation of sample entropy (SampEn) is proposed. SampEn is a non-linear metric, meant to quantify regularity of a time series. It is widely employed on biomedical signals, especially on heart rate variability. Results relevant to approximate entropy, a related index, are also reported.An analytical expression for SampEn of an autoregressive (AR) model is derived first. Then we study the feasibility of a parametric estimation of SampEn through AR models, both on synthetic and real series. RR series of different lengths are fitted to an AR model and then expected values of SampEn (SampEnμ) are estimated.Values of SampEn, computed from real beat-to-beat interval time series (obtained from 72 normal subjects and 29 congestive heart failure patients), with m = 1 and r = 0.2, are within the standard range of SampEnμ more than 83% (for series length N = 75) and 28% (for N = 1500) of the cases. Surrogate data have been employed to verify if departures from Gaussianity are to account for the mismatch.The work supports the finding that when numerical and parametric estimates of SampEn agree, SampEn is mainly influenced by linear properties of the series. A disagreement, on the contrary, might point those cases where SampEn is truly offering new information, not readily available with traditional temporal and spectral parameters.