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

A. Porta, S. Guzzetti, N. Montano, R. Furlan, M. Pagani, A. Malliani, S. Cerutti

Research output: Contribution to journalArticlepeer-review


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). We 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 we 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.

Original languageEnglish
Pages (from-to)1282-1291
Number of pages10
JournalIEEE Transactions on Biomedical Engineering
Issue number11
Publication statusPublished - 2001


  • Autonomic control
  • Conditional entropy
  • Corrected conditional entropy
  • Heart rate variability
  • Pattern analysis
  • Regularity index
  • Shannon entropy
  • Symbolic dynamics

ASJC Scopus subject areas

  • Biomedical Engineering


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