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Correlation Integral and Frequency Analysis of Cardiovascular Functions

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Open Systems & Information Dynamics

Abstract

To study the dynamics of the cardiovascular system several cardiovascular functions are measured at different sites of the human body. Measured time series of peripheral blood flow, respiration, electrical activity of the heart (ECG), and instantaneous heart rate (IHR) derived from the ECG are analysed in time and frequency domains and in phase space. Correlation integrals are calculated for the original signals and their surrogates. The auto and crosscorrelation functions and the Fourier spectra are also presented. All measured data of the physiological origin are corrupted by noise. To some extent they also contain non-stationarities. Therefore, the correlation integral is first analysed on numerically generated quasi-periodic time series and the effect of added noise is studied. The scale that is corrupted by noise is also analytically examined. An upper dimension which may reliably be estimated is evaluated. The results presented suggest that the calculated correlation integral cannot be used as a quantitative characterization of an attractor reconstructed from measured time series. Hence, only the relative qualitative differences between slopes of the correlation integral of measured time series and their surrogates are analysed. For all measured time series the slopes of their correlation integrals differ from those of their surrogates suggesting deterministic nature of the system that governs cardiovascular dynamics. It is also shown that all time series contain the same five characteristic peaks in their frequency spectra.

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Bibliography

  1. S. Akselrod, D. Gordon, F. A. Ubel, D. C. Shannon, A. C. Berger, and R. J. Cohen, Science 213, 220 (1981).

    Google Scholar 

  2. A. M. Albano, A. Passamante, and M. E. Farrell, Physica D 54, 85 (1991).

    Google Scholar 

  3. A. M. Albano, P. E. Rapp, and A. Passamante, Phys. Rev. E 52, 196 (1995).

    Google Scholar 

  4. R. Badii and A. Politi, J. Stat. Phys. 40, 725 (1985).

    Google Scholar 

  5. M. Bračič and A. Stefanovska, Open Sys. Information Dyn., this issue.

  6. I. Daubechics. Ten Lectures on Wavelets, SIAM, Philadelphia. 1992.

    Google Scholar 

  7. R. W. DeBoer, J. M. Karemaker, and J. Strackee, IEEE Trans. Biomed. Eng. 31, 384 (1984)

    Google Scholar 

  8. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).

    Google Scholar 

  9. J.-P. Eckmann and D. Ruelle, Physica D 56, 185 (1992).

    Google Scholar 

  10. J. D. Farmer and J. J. Sidorovich, Physica D 47, 373 (1991) 373.

    Google Scholar 

  11. A. M. Fraser and H. L. Swinney, Phys. Rev. A 33, 1134 (1986).

    Google Scholar 

  12. L. Glass, Physics Today, August 1996, p. 40.

  13. P. Grassberger and I. Procaccia. Phys. Rev. Lett. 50, 346 (1983).

    Google Scholar 

  14. P. Grassberger and I. Procaccia. Physica D 9, 189 (1983).

    Google Scholar 

  15. P. Grassberger, T. Schriber, and C. Schaffruth, Int. J. Bif. Chaos 1, 521 (1991).

    Google Scholar 

  16. T. M. Griffith, Cardiovascular Research 31, 342.

  17. R. J. Gush and T. A. King, Med. & Biol. Eng. & Comput. 25, 391 (1987).

    Google Scholar 

  18. H. Haken, Advanced Synergetics, Springer-Verlag, Berlin, 1987.

    Google Scholar 

  19. S. M. Hammel, Phys. Lett. A 148, 421 (1990).

    Google Scholar 

  20. H. G. E. Hentschel and I. Procaccia, Physica D 8, 435 (1983).

    Google Scholar 

  21. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rew. A 45, 3403 (1992).

    Google Scholar 

  22. R. I. Kitney, T. Fulton, A. McDonald, and D. A. Linkens, J. Biomed. Eng. 7, 217.

  23. E. J. Kostelich and J. A. Yorke, Phys. Rev. A 38, 1649 (1988).

    Google Scholar 

  24. E. J. Kostelich and J. A. Yorke, Physica D 41, 183 (1990).

    Google Scholar 

  25. W. Liebert and H. G. Schuster, Phys. Lett. A 142, 107 (1989).

    Google Scholar 

  26. O. C. J. Lippold, F. R. Winton, Eds., Human Physiology, Churchill Livingstone, Edinburgh, 1979.

    Google Scholar 

  27. J. M. Lipton and K. P. Dubke, Phys. Lett. A 210, 290 (1996).

    Google Scholar 

  28. R. Manè, in: D. A. Rand and L. S. Young, eds., Lecture Notes in Mathematics 898. Springer-Verlag, New York, p. 230, 1981.

    Google Scholar 

  29. M. Möller, W. Lange, F. Mitschke, N. B. Abraham and U. Hübner, Phys. Lett. A 138, 176 (1989).

    Google Scholar 

  30. G. E. Nilsson, T. Tenland and P. A. Öberg, IEEE Trans. Biomed. Eng. 27, p. 597.

  31. A. R. Osborne and A. Provenzale, Physica D 35, 357 (1989).

    Google Scholar 

  32. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980).

    Google Scholar 

  33. K. Pawelzik and H. G. Schuster, Phys. Rev. A 35, 481 (1987).

    Google Scholar 

  34. M. B. Priestley, Non-linear and Non-stationary Time Series Analysis, Academic Press, London, 1991.

    Google Scholar 

  35. M. B. Priestley, Spectral Analysis and Time Series, Academic Press, London, 1994.

    Google Scholar 

  36. I Procaccia, Nature 333, 498 (1988).

    Google Scholar 

  37. J. B. Ramsey and H.-J. Yuan, Phys. Lett. A 134, 287 (1989).

    Google Scholar 

  38. P. E. Rapp, A. M. Albano, T. I. Schmah, and L. A. Farwell, Phys. Rev. A 47, 2289 (1993).

    Google Scholar 

  39. P. E. Rapp, A. M. Albano, I. D. Zimmerman, and M. A. Jiménez-Montaño, Phys. Rev. A 192, 27 (1994).

    Google Scholar 

  40. M. T. Rosenstein, J. J. Collins, and C. J. DeLuca, Physica D 73, 82 (1994).

    Google Scholar 

  41. L. B. Rowel, Human Cardiovascular Control, Oxford University Press, New York, 1993.

    Google Scholar 

  42. M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985).

    Google Scholar 

  43. S. Sato, M. Sano, and Y. Sawada, Prog. Theor. Phys. 77, 1 (1987).

    Google Scholar 

  44. R. F. Schmidt and G. Thews, Human Physiology, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  45. L. A. Smith, Phys. Lett. A 133, 283 (1988). 283.

    Google Scholar 

  46. A. Stefanovska, Dissertation, University of Ljubljana, Ljubljana, 1992.

  47. A. Stefanovska, P. Krošelj, and S. Strle, Open Sys. Information Dyn. 3, 1 (1995).

    Google Scholar 

  48. A. Stefanovska, S. Strle, and P. Krošelj, Phys. Lett. A, in print, 1997.

  49. F. Takens, in: D. A. Rand and L. S. Young, eds., Lecture Notes in Mathematics 898, Springer-Verlag, New York, p. 366, 1981.

    Google Scholar 

  50. J. Theiler, Phys. Rev. A 34, 2427 (1986).

    Google Scholar 

  51. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, Physica D 58, 77 (1992).

    Google Scholar 

  52. A. Wolf, J. B. Swift, H. Swinney, and J. A. Vastano, Physica D 16, 285 (1985).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia

    Aneta Stefanovska & Peter Krošelj

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  1. Aneta Stefanovska
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  2. Peter Krošelj
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Stefanovska, A., Krošelj, P. Correlation Integral and Frequency Analysis of Cardiovascular Functions. Open Systems & Information Dynamics 4, 457–478 (1997). https://doi.org/10.1023/A:1009681002818

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