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Journal of Biological Physics logoLink to Journal of Biological Physics
. 2007 Jan 30;32(6):489–495. doi: 10.1007/s10867-006-9031-y

Two Statistical Methods for Resolving Healthy Individuals and Those with Congestive Heart Failure Based on Extended Self-similarity and a Recursive Method

F Atyabi 1, M A Livari 2, K Kaviani 1,, M Reza Rahimi Tabar 3
PMCID: PMC2651543  PMID: 19669436

Abstract

In this paper we introduce two methods for measuring irregularities in human heartbeat time series (HHTS). First we consider the multi-fractal structure of HHTS to distinguish healthy individuals and from those with congestive heart failure. In this way we modify the Extended Self-Similarity (ESS) method and apply it to HHTS. Our second approach is based on the recursive method, which we use to predict the duration of the next heartbeat by considering a few previous ones. We use standard physiological data and show that these approaches lead to very satisfactory methods to resolve the healthy and CHF individuals. These methods can be used potentially in portable electronic heart alarm systems.

Key words: interbeat, congestive heart failure, extended self-similarity, recursive method

References

  • 1.Kantelhardt, J.W., Koscielny-Bunde, E., Rego, H.H.A., Havlin, S., Bunde, A.: Detecting long-range correlations with detrended fluctuation analysis. Physica A 295, 441 (2001) [DOI]
  • 2.Bunde, A., Havlin, S., Kantelhardt, J.W., Penzel, T., Peter, J.-H., Voigt, K.: Correlated and uncorrelated regions in heart-rate fluctuations during sleep. Phys. Rev. Lett. 85, 3736 (2000) [DOI] [PubMed]
  • 3.Peng, C.-K., Mietus, J., Hausdorff, J.M., Havlin, S., Stanley, H.E., Goldberger, A.L.: Long-range anticorrelations and non-Gaussian behavior of the heartbeat. Phys. Rev. Lett. 70, 1343 (1993) [DOI] [PubMed]
  • 4.Goldberger, A.L. et al.: Fractal mechanisms in neural control: Human heartbeat and gait dynamics in health and disease, http://www.physionet.org/tutorials/fmnc/
  • 5.Karasik, R., Sapir, N., Ashkenazy, Y., Ivanov, P.Ch., Dvir, I., Lavie, P., Havlin, S.: Correlation differences in heartbeat fluctuations during rest and exercise. Phys. Rev. E 66, 062902 (2002) [DOI] [PubMed]
  • 6.Ashkenazy, Y., Ivanov, P.Ch., Havlin, S., Peng, C.-K., Goldberger, A.L., Stanley, H.E.: Magnitude and sign correlations in heartbeat fluctuations. Phys. Rev. Lett. 86, 1900 (2001), (preprint cond-mat/0005365) [DOI] [PubMed]
  • 7.Kantelhardt, J.W., Ashkenazy, Y., Ivanov, P.Ch., Bunde, A., Havlin, S., Penzel, T., Peter, J.-H., Stanley, H.E.: Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments. Phys. Rev., E 65, 051908 (2002), (preprint cond-mat/0012390) [DOI] [PubMed]
  • 8.Feder, J.: Fractals. Plenum, New York (1988)
  • 9.Ivanov, P.Ch., Amaral, L.A.N., Goldberger, A.L., Havlin, S., Rosenblum, M.G., Struzik, Z.R., Stanley, H.E.: Multifractality in human heartbeat dynamics. Nature 399, 461 (1999) [DOI] [PubMed]
  • 10.Benzi, R., Biferale, L., Ciliberto, S., Struglia, M.V., Tripiccione, R.: Generalized scaling in fully developed turbulence. Physica D 96, 162 (1996) [DOI]
  • 11.Bershadskii, A., Screenivasan, K.R.: Extended self-similarity of the small-scale cosmic microwave background anisotropy. Phys. Lett. A 319, 21 (2003) [DOI]
  • 12.Heartbeat database is freely available at the following URL: http://www.physionet.org/physiobank/ database/ecg
  • 13.Smith, S.W.: The Scientist and Engineer’s Guide to Digital Signal Processing, 2nd edn. California Technical Publishing San Diego, California (1999)

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