Assessing sample entropy of physiological signals by the norm component matrix algorithm: application on muscular signals during isometric contraction

Abstract

Sample Entropy (SampEn) is a popular method for assessing the unpredictability of biological signals. Its calculation requires to preliminarily set the tolerance threshold r and the embedding dimension m. Even if most studies select m=2 and r=0.2 times the signal standard deviation, this choice is somewhat arbitrary. Effects of different r and m values on SampEn have been rarely assessed, because of the high computational burden of this task. Recently, however, a fast algorithm for estimating correlation sums (Norm Component Matrix, NCM) has been proposed that allows calculating SampEn quickly over wide ranges of r and m. The aim of our work is to describe the structure of SampEn of physiological signals with different complex dynamics as a function of m and r and in relation to the correlation sum. In particular, we investigate whether the criterion of "maximum entropy" for selecting r previously proposed for Approximate Entropy, also applies to SampEn; and whether information from correlation sums provides indications for the choice of r and m. For this aim we applied the NCM algorithm on electromyographic and mechanomyographic signals during isometric muscle contraction, estimating SampEn over wide ranges of r (0.01 ≤ r ≤ 5) and m (from 1 to 11). Results indicate that the "maximum entropy" criterion to select r in Approximate Entropy cannot be applied to SampEn. However, the analysis of correlation sums alternatively suggests to choose r that at any m maximizes the number of "escaping vectors", i.e., data points effectively contributing to the SampEn estimation.