An adaptive technique for multiscale approximate entropy (MAE_bin) threshold (r) selection: application to heart rate variability (HRV) and systolic blood pressure variability (SBPV) under postural stress

Abstract

Multiscale approximate entropy (MAE) is used to quantify the complexity of a time series as a function of time scale τ. Approximate entropy (ApEn) tolerance threshold selection ‘r’ is based on either: (1) arbitrary selection in the recommended range (0.1–0.25) times standard deviation of time series (2) or finding maximum ApEn (ApEn_max) i.e., the point where self-matches start to prevail over other matches and choosing the corresponding ‘r’ (r_max) as threshold (3) or computing r_chon by empirically finding the relation between r_max, SD₁/SD₂ ratio and N using curve fitting, where, SD₁ and SD₂ are short-term and long-term variability of a time series respectively. None of these methods is gold standard for selection of ‘r’. In our previous study [1], an adaptive procedure for selection of ‘r’ is proposed for approximate entropy (ApEn). In this paper, this is extended to multiple time scales using MAE_bin and multiscale cross-MAE_bin (XMAE_bin). We applied this to simulations i.e. 50 realizations (n = 50) of random number series, fractional Brownian motion (fBm) and MIX (P) [1] series of data length of N = 300 and short term recordings of HRV and SBPV performed under postural stress from supine to standing. MAE_bin and XMAE_bin analysis was performed on laboratory recorded data of 50 healthy young subjects experiencing postural stress from supine to upright. The study showed that (i) ApEn_bin of HRV is more than SBPV in supine position but is lower than SBPV in upright position (ii) ApEn_bin of HRV decreases from supine i.e. 1.7324 ± 0.112 (mean ± SD) to upright 1.4916 ± 0.108 due to vagal inhibition (iii) ApEn_bin of SBPV increases from supine i.e. 1.5535 ± 0.098 to upright i.e. 1.6241 ± 0.101 due sympathetic activation (iv) individual and cross complexities of RRi and systolic blood pressure (SBP) series depend on time scale under consideration (v) XMAE_bin calculated using ApEn_max is correlated with cross-MAE calculated using ApEn (0.1–0.26) in steps of 0.02 at each time scale in supine and upright position and is concluded that ApEn_0.26 has highest correlation at most scales (vi) choice of ‘r’ is critical in interpreting interactions between RRi and SBP and in ascertaining true complexity of the individual RRi and SBP series.