Comparison of different threshold values r for approximate entropy: application to investigate the heart rate variability between heart failure and healthy control groups

Approximate entropy (ApEn) is widely accepted as a complexity measure of the heart rate variability (HRV) signal, but selecting the criteria for the threshold value r is controversial. This paper aims to verify whether Chon's method of forecasting the r(max) is an appropriate one for the HRV signal. The standard limb lead ECG signals of 120 subjects were recorded for 10 min in a supine position. The subjects were divided into two groups: the heart failure (22 females and 38 males, median age 62.4 +/- 12.6) and healthy control group (33 females and 27 males, median age 51.5 +/- 16.9). Three types of ApEn were calculated: the ApEn(0.2) using the recommended constant r = 0.2, the ApEn(chon) using Chon's method and the ApEn(max) using the true r(max). A Wilcoxon rank sum test showed that the ApEn(0.2) (p = 0.267) and the ApEn(max) (p = 0.813) had no statistical differences between the two groups, while the ApEn(chon) (p = 0.040) had. We generated a synthetic database to study the effect of two influential factors (the signal length N and the ratio of short-and long-term variability sd(1)/sd(2)) on the empirical formula in Chon's method (Chon et al 2009 IEEE Eng. Med. Biol. Mag. 28 18-23). The results showed that the empirical formula proposed by Chon et al is a good method for analyzing the random signal, but not an appropriate tool for analyzing nonlinear signals, such as the logistic or HRV signals.