On the Relevance of Computing a Local Version of Sample Entropy in Cardiovascular Control Analysis

Alberto Porta, Vlasta Bari, Beatrice De Maria, Beatrice Cairo, Emanuele Vaini, Mara Malacarne, Massimo Pagani, Daniela Lucini

Research output: Contribution to journalArticlepeer-review


Objective: Traditional definition of sample entropy (SampEn), here referred to as global SampEn (GSampEn), provides a conditional entropy estimate that blurs the local statistical properties of the time series. We hypothesized that a local version of SampEn (LSampEn) might be more powerful in presence of determinism than GSampEn. Methods: LSampEn was computed by calculating the probability of the current sample conditioned on each reference pattern and averaging it over all reference patterns. The improved ability of LSampEn compared to GSampEn was demonstrated by simulating deterministic periodic, deterministic chaotic and linear stochastic dynamics corrupted by additive noise and over real cardiovascular variability series recorded from 16 healthy subjects (max-min age range: 22-58 years) during incremental bicycle ergometer exercise. Results: We found that: i) LSampEn is more robust in describing deterministic periodic or nonlinear features in presence of additive noise than GSampEn; ii) in association with a surrogate approach LSampEn is more powerful in detecting nonlinear dynamics than GSampEn; iii) LSampEn and GSampEn are equivalent in presence of stochastic linear dynamics; iv) only LSampEn can detect the decrease of complexity of heart period variability during bicycle exercise being a likely hallmark of sympathetic activation. Conclusion: LSampEn preserves the GSampEn capability in characterizing the complexity of short sequences but improves its reliability in presence of deterministic patterns featuring sharp state transitions and nonlinear dynamics. Significance: Variations of complexity can be measured with a greater statistical power over short series using LSampEn especially when nonlinear features are present.

Original languageEnglish
JournalIEEE Transactions on Biomedical Engineering
Publication statusAccepted/In press - Jul 2 2018


  • autonomic nervous system
  • Bicycles
  • Biomedical monitoring
  • Complexity
  • Complexity theory
  • conditional entropy
  • Entropy
  • heart rate variability
  • incremental bicycle ergometer exercise
  • Predictive models
  • rehabilitation
  • sport medicine
  • Standards
  • Uncertainty

ASJC Scopus subject areas

  • Biomedical Engineering


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