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

Abstract

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 (CP_u) where no template match is found and (2) use of a crisp tolerance (radius) threshold 'r'. To overcome these limitations, CP_u is substituted with optimum bias setting ɛ _opt which is found by varying ɛ 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 ɛ _opt = 0.6 in 50 realizations (n = 50) of random number series of N = 300. Similar analysis suggests ɛ _opt = 0.65 and ɛ _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). ɛ _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.

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