An alternative approach to approximate entropy threshold value (r) selection: application to heart rate variability and systolic blood pressure variability under postural challenge

This study presents an alternative approach to approximate entropy (ApEn) threshold value (r) selection. There are two limitations of traditional ApEn algorithm: (1) the occurrence of undefined conditional probability (CPu) where no template match is found and (2) use of a crisp tolerance (radius) threshold 'r'. To overcome these limitations, CPu is substituted with optimum bias setting epsilon(opt) which is found by varying. from (1/N - m) to 1 in the increments of 0.05, where N is the length of the series and m is the embedding dimension. Furthermore, an alternative approach for selection of r based on binning the distance values obtained by template matching to calculate ApEn(bin) is presented. It is observed that ApEn(max), ApEn(chon) and ApEn(bin) converge for epsilon(opt) = 0.6 in 50 realizations (n = 50) of random number series of N = 300. Similar analysis suggests epsilon(opt) = 0.65 and epsilon(opt) = 0.45 for 50 realizations each of fractional Brownian motion and MIX(P) series (Lu et al. in J Clin Monit Comput 22(1):23-29, 2008). epsilon(opt) = 0.5 is suggested for heart rate variability (HRV) and systolic blood pressure variability (SBPV) signals obtained from 50 young healthy subjects under supine and upright position. It is observed that (1) ApEn(bin) of HRV is lower than SBPV, (2) ApEn(bin) of HRV increases from supine to upright due to vagal inhibition and (3) ApEn(bin) of BPV decreases from supine to upright due to sympathetic activation. Moreover, merit of ApEn(bin) is that it provides an alternative to the cumbersome ApEn(max) procedure.