Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis.

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q≠1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10×10(-3), 1.11×10(-7), and 5.50×10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis.