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Large deviations estimates for the multiscale analysis of heart rate variability

Author

Listed:
  • Loiseau, Patrick
  • Médigue, Claire
  • Gonçalves, Paulo
  • Attia, Najmeddine
  • Seuret, Stéphane
  • Cottin, François
  • Chemla, Denis
  • Sorine, Michel
  • Barral, Julien

Abstract

In the realm of multiscale signal analysis, multifractal analysis provides a natural and rich framework to measure the roughness of a time series. As such, it has drawn special attention of both mathematicians and practitioners, and led them to characterize relevant physiological factors impacting the heart rate variability. Notwithstanding these considerable progresses, multifractal analysis almost exclusively developed around the concept of Legendre singularity spectrum, for which efficient and elaborate estimators exist, but which are structurally blind to subtle features like non-concavity or, to a certain extent, non scaling of the distributions. Large deviations theory allows bypassing these limitations but it is only very recently that performing estimators were proposed to reliably compute the corresponding large deviations singularity spectrum. In this article, we illustrate the relevance of this approach, on both theoretical objects and on human heart rate signals from the Physionet public database. As conjectured, we verify that large deviations principles reveal significant information that otherwise remains hidden with classical approaches, and which can be reminiscent of some physiological characteristics. In particular we quantify the presence/absence of scale invariance of RR signals.

Suggested Citation

  • Loiseau, Patrick & Médigue, Claire & Gonçalves, Paulo & Attia, Najmeddine & Seuret, Stéphane & Cottin, François & Chemla, Denis & Sorine, Michel & Barral, Julien, 2012. "Large deviations estimates for the multiscale analysis of heart rate variability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5658-5671.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5658-5671
    DOI: 10.1016/j.physa.2012.05.069
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    References listed on IDEAS

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    1. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
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    5. Makowiec, Danuta & Dudkowska, Aleksandra & Gała̧ska, Rafał & Rynkiewicz, Andrzej, 2009. "Multifractal estimates of monofractality in RR-heart series in power spectrum ranges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3486-3502.
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    Cited by:

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