Entropy, entropy rate, and pattern classification as tools to typify complexity in short heart period variability series

An integrated approach to the complexity analysis of short heart period variability series (∼300 cardiac beats) is proposed and applied to healthy subjects during the sympathetic activation induced by head-up tilt and during the driving action produced by controlled respiration (10, 15, and 20 breaths/min, CR10, CR15, and CR20 respectively). The approach relies on: 1) the calculation of Shannon entropy (SE) of the distribution of patterns lasting three beats; 2) the calculation of a regularity index based on an entropy rate (i.e., the conditional entropy); 3) the classification of frequent deterministic patterns (FDPs) lasting three beats. A redundancy reduction criterion is proposed to group FDPs in four categories according to the number and type or of heart period changes: a) no variation (0V); b) one variation (1V); and c) two like variations (2LV); 4) two unlike variations (2UV). The authors found that: 1) the SE decreased during tilt due to the increased percentage of missing patterns; 2) the regularity index increased during tilt and CR10 as patterns followed each other according to a more repetitive scheme; and 3) during CR10, SE and regularity index were not redundant as the regularity index significantly decreased while SE remained unchanged. Concerning pattern analysis the authors found that: a) at rest mainly three classes (0V, 1V, and 2LV) were detected; b) 0V patterns were more likely during tilt; c) 1V and 2LV patterns were more frequent during CR10; and d) 2UV patterns were more likely during CR20. The proposed approach based on quantification of complexity allows a full characterization of heart period dynamics and the identification of experimental conditions known to differently perturb cardiovascular regulation.