Physiological time-series analysis using approximate entropy and sample entropy

TLDR

Entropy measures the rate of information production in dynamical systems, but conventional estimation methods fail on short, noisy biological data, prompting Pincus to introduce approximate entropy (ApEn) for clinical cardiovascular time series. The authors evaluated cross-ApEn and cross-SampEn to quantify similarity between two distinct cardiovascular time series. Sample entropy (SampEn) consistently matched theoretical expectations across varied conditions, outperforming ApEn and offering more reliable complexity estimates for clinical cardiovascular and other biological time series.

Abstract

Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.