The Heart Rate Variability Signal

Among Rhythms, Noise and Chaos
  • Sergio Cerutti
  • Maria G. Signorini


Heart rate variability (HRV) signal is supposed to be the effect of a variety of different controls acting through linear and non-linear mechanisms. In this paper, non-linear dynamic components of HRV signals are analyzed by the evaluation of invariant characteristics of the system attractor obtained from time series: correlation dimension, entropy, self-similarity parameter H, and Lyapunov exponents. The results confirm that nonlinear dynamics are involved in the HRV signal generating mechanism.


Fractal Dimension Heart Rate Variability Lyapunov Exponent Power Spectral Density Singular Value Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Abarbanel, H., Brown. R., Sidorowich, J. J.. Tsimring, L.. 1993, The analysis of observed chaotic data in physical systems. Reviews of Modern Physics. 65: 4.MathSciNetGoogle Scholar
  2. Akselrod, S., Gordon, D., Ubel, F. A., Shannon, D. C., Barger. A. C., Cohen, R. J., 1981, Power spectrum analysis of heart rate fluctuations: A quantitative probe ofbeat-to-beat cardiovascular control, Science 213: 220–222.Google Scholar
  3. Baselli, G., Cerutti, S., Civardi, S., Liberati, D., Lombardi, F., Malliani, A., Pagani. M., 1986, Spectral and cross-spectral analysis of heart rate and blood varibility signals, Comps. and Biomed. Res. 19: 520.Google Scholar
  4. Bianchi, A., Bontempi, B., Cerutti, S., Gianoglio, P., Coml. G., and Natali Sora, M. G., 1990, Spectral analysis of heart rate variability signal and respiration in diabetic subjects, Med. & Biol. Eng. & Comp. 28: 205–211.Google Scholar
  5. Broomhead, D. S., and King, G. P., 1986, Extracting qualitative dynamics from experimental data, Phvsica D 20: 217–236.MathSciNetzbMATHCrossRefGoogle Scholar
  6. Brown, R., Bryan, P., and Abarbanel, H. D. I., I99I,Computing the Lyapunov spectrum of a dynamical system from an observed time series, Phys. Rev A, 43,:2787–2805.Google Scholar
  7. Cerutti, S., Bianchi, A., and Signorini, M. G., 1991, Spectral analysis of variability signals in cardiovascular system. In: Cerutti, S., and Minuco G. (cds.), Spectral Analysis of Heart Rate Variability Signal: Methodological and Clinical Aspects, La Goliardica Pavese: Pavia. pp. 3 1–43.Google Scholar
  8. Cerutti, S., Bartoli, F, Baselli, G, 1985, AR identification and spectral estimate applied to the R-R interval measurements, Int. J. Biomed. Comput. 16: 201–215.CrossRefGoogle Scholar
  9. Cerutti, S., Baselli, G.. Bianchi, A., Mainardi, L., Signorini, M.G., and Malliani. A.. 1994, Cardiovascular variability signals:from signal processing to modelling complex physiological interactions. Automedica 16: 45–69.Google Scholar
  10. Eckmann, J. P., Kamphorst, O. S., Ruelle. D., Ciliberto, S., 1986, Lyapunov exponents from time series, Pin’s. Rev. A 34: 4971–4979.MathSciNetGoogle Scholar
  11. Eckmann, J. P., Ruelle, D., 1985, Ergodic theory of chaos and strange attractors. Rev. Mod. Phvs. 57:617–656. Glass, L., Mackey, M. C., 1979, Pathological conditions resulting from instabilities in physiological control systems. Ann. N.Y Acad. Sci., 316: 214–235.Google Scholar
  12. Goldberger, A. L.. Rigney, D. R., West, B. J., 1990. Chaos and fractals in human physiology. Scientific Am. 260: 27–33.Google Scholar
  13. Grassberger, P., Procaccia, I.. 1984, Dimensions and entropies of strange attractors from a fluctuating dynamics approach, Phvsica D 13: 34–54.MathSciNetzbMATHCrossRefGoogle Scholar
  14. Grassberger, P., Procaccia, I. 1983. Measuring the strangeness of strange attractors. Phvsica 9D:189–208. Hyndman, B.W., Kitney, R. I., Sayers, B. M. A., 1971. Spontaneous rhythms in physiological control systems Nature 233: 339.Google Scholar
  15. Kaplan, J. L., Yorke, J. A., 1979, Chaotic behaviour of multidimensional difference equations: Lecture Notes in Mathematics, vol. 730, ( Springer, Berlin ) pp. 228–287.Google Scholar
  16. Keshner, M. S., 1982, 1/f noise, IEEE Trans. Biomed. Eng. 70: 212–218.Google Scholar
  17. Kleiger, R.E., Miller, J.P., Bigger, J.T., Moss, A.J., and the Multicenter Postinfarction Research Group, 1987, Decreased heart rate variability and its association with increased mortality after acute myocardial infarction, Am. J. Cardiol. 59: 256–262.CrossRefGoogle Scholar
  18. Kobayashy, M., and Musha, T., 1982, 1/f fluctuations of heartbeat period. IEEE Transaction BM F-29:456–464.Google Scholar
  19. Lombardi, F., Sandrone, G., Perpuner, S., Sala. M. Garimoldi, M. Cerutti, S., Baselli, G.. Pagani, M., andGoogle Scholar
  20. Malliani, A., 1987, Heart rate variability as an index of sympatho-vagal interaction after acute myocardial infarction, Am. J. Cardiol. 60: 1239–1245.CrossRefGoogle Scholar
  21. Malliani, A., Pagani, M., Lombardi, F., and Cerutti, S.. 1991, Cardiovascular neural regulation explored in the frequency domain, Circulation 84: 482–1492.CrossRefGoogle Scholar
  22. Mandelbrot, B., 1983, The Fractal Geometry of the Nature, W.H. Freeman, New York.Google Scholar
  23. Mortara, A., La Rovere, M.T., Signorini, M.G., Pantaleo, P., Pinna. G., Martinelli, L., Ceconi, C., Cerutti, S.. and Tavazzi, L., 1994, Can power spectral analysis of heart rate variability identify a high risk subgroup of congestive heart failure patients with excessive sympathetic activation? A pilot study before and after heart transplantation, Br Heart J. 71: 422–430.Google Scholar
  24. Osborne, A. R, and Provenzale, A., 1989, Finite correlation dimension for stochastic systems with power-law spectra, Physica D 35: 357–381.MathSciNetzbMATHCrossRefGoogle Scholar
  25. Pagani, M., Lombardi, F., Guzzetti, S., Rimoldi, O., Furlan, R., Pizzinelli, P., Sandrone,G., Malfatto,G., Dell’Orto,S., Piccaluga,E., Turiel,M., Basclli,G., Cerutti. S., and Malliani, A., 1986, Power spectral analysis of a beat-to-beat heart rate and blood pressure variability as a possible marker of sympatho vagal interaction in man and conscious dog, Circ.Res 59: 178–193.Google Scholar
  26. Pagani, M., Malfatto. G.. Pierini, S., Casati, R., Masu, A. M., Poli, M., Guzzetti, S., Lombardi, F.,Cerutti, S., and Malliani, A., 1988, Spectral analysis of heart rate variability in the assessment of autonomic diabetic neuropathy, J. Auton. Nerv. Syst. 23: 143–153.Google Scholar
  27. Penaz, J., Roukenz, J.. and Van der Waal, H. J., 1968, Spectral analysis of some spontaneous rhythms in the circulation. In: Crischel, H., and Tiedt, N. (eds.), Biokybernetik, Bd.I., Karl Marx Univ., Leipzig, pp. 233–241.Google Scholar
  28. Provenzale, A., Smith, L.A., Vio, R., and Murante, G., 1992, Distinguishing between low dimensional dynamics and randomness in measured time series, Physica D 58: 31–49.CrossRefGoogle Scholar
  29. Rompelman, O., Coenen, A. J. R. M., and Kitney, R. J., 1977, Measurement of heart rate variability: part 1. Comparative study of heart rate variability analysis methods, Med. & Biol. Eng. & Comp. 15: 223.CrossRefGoogle Scholar
  30. Saul, J. P., Albrecht, P., Berger, R. D., and Cohen, R. J., 1988, Analysis of long term heart rate variability: methods, 1/f scaling and implications, Proc. IEEE Computers in Cardiology. Conf., ( IEEE Computer Society Press, Washington ), pp. 419–422.Google Scholar
  31. Sayers, B. Mc A., 1973, Analysis of heart rate variability, Ergonomics 16: 17.CrossRefGoogle Scholar
  32. Signorini, M.G., 1995, Studio di Modelli di caos deterministico con applicazione al sistema cardiovascolare, Ph.D Thesis, Politecnico Univ. Milano, Italy.Google Scholar
  33. Takens, F., 1981, Detecting strange attractors in turbulence, In: Rand, D. A., and Young, L. S. (eds.) Dynamical Systems and Turbulence: Lecture Notes in Mathematics. Springer, Berlin, vol. 898, pp. 366–381. Theiler, J., and Eubank, S., 1993, Don’t bleach chaotic data, Chaos 3: 771–782.Google Scholar
  34. Theiler, J., 1991. Some comments on the correlation dimension of noise, Phys. Lett. A 155: 480–493.MathSciNetCrossRefGoogle Scholar
  35. West, B. J., Goldberger, A.L., Rovner, G., and Bhargava, V., 1985, Nonlinear dynamics of heartbeat (I), Physica I7D:198–206.Google Scholar
  36. West, B. J., 1990. Fractal Physiology and Chaos in Medicine, World Scient. Publishing Co. Pte. Ltd.Google Scholar
  37. Wolf A., Swift, B. J.. Swinney, H.L.,Vastano, J. A., 1985, Determining Lyapunov exponents from time series, Phys lea I6D:285–317.Google Scholar
  38. Zetterberg, L. H., 1969, Estimation parameters for a linear difference equation with application to EEG analysis, Math. Biosc. 5: 227–275.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Sergio Cerutti
    • 1
  • Maria G. Signorini
    • 1
  1. 1.Biomedical Engineering DepartmentPolytechnic UniversityMilanoItaly

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