From 1/f noise to multifractal cascades in heartbeat dynamics

Chaos

Volumn 11, Issue 3, 2001, Pages 641-652

  Ivanov, Plamen Ch ^a,b   Nunes Amaral, Luís A ^a,b   Goldberger, Ary L ^b   Havlin, Shlomo ^c   Rosenblum, Michael G ^d   Stanley, H Eugene ^a   Struzik, Zbigniew R ^e  

^a Boston University   (United States)

^b BETH ISRAEL DEACONESS MEDICAL CENTER   (United States)

^c BAR ILAN UNIVERSITY   (Israel)

^d UNIVERSITY OF POTSDAM   (Germany)

^e CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035457767     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1395631     Document Type: Article

References (74)

1. M. F. Shlesinger, "Fractal time and 1/f noise in complex systems," Ann. N.Y. Acad. Sci. 504, 214 (1987).
2. J. B. Bassingthwaighte, L. S. Liebovitch, and B. J. West, Fractal Physiology (Oxford University Press, New York, 1994).
3. Heart Rate Variability, edited by M. Malik and A. J. Camm (Futura. Armonk, NY, 1995).
4. M. Kobayashi and T. Musha, "1/f fluctuation of heartbeat period," IEEE Trans. Biomed. Eng. 29, 456 (1982).
5. J. P. Saul, P. Albrecht, D. Berger, and R. J. Cohen. Computers in Cardiology (IEEE Computer Society, Washington. DC, 1987), p. 419.
6. C-K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, and A. L. Goldberger, "Long-range anti-correlations and non-Gaussian behavior of the heartbeat," Phys. Rev. Lett. 70, 1343 (1993).
7. J. M. Hausdorff, P. L. Purdon, C.-K. Peng, Z. Ladin, J. Y. Wei, and A. L. Goldberger, "Fractal dynamics of human gait: Stability of long-range correlations in stride interval fluctuations," J. Appl. Physiol. 80, 1448 (1996).
8. L. S. Liebovitch, "Fractal analysis of channel mechanisms," Adv. Chem. Ser. 235, 357 (1994); S. B. Lowen, L. S. Liebovitch, and J. A. White, "Fractal ion-channel behavior generates fractal firing patterns in neuronal models," Phys. Rev. E 59, 5970 (1999).
9. L. S. Liebovitch, "Fractal analysis of channel mechanisms," Adv. Chem. Ser. 235, 357 (1994); S. B. Lowen, L. S. Liebovitch, and J. A. White, "Fractal ion-channel behavior generates fractal firing patterns in neuronal models," Phys. Rev. E 59, 5970 (1999).
10. J. Lefebvre, D. A. Goodings, M. V. Kamath, and E. L. Fallen, "Predictability of normal heart rhythms and deterministic chaos," Chaos 3, 267 (1993).
11. Y. Yamamoto, R. L. Hughson, J. R. Sutton, C. S. Houston, A. Cymerman, E. L. Fallen, and M. V. Kamath, "Operation Everest II: An indication of deterministic chaos in human heart rate variability at simulated extreme altitude," Biol. Cybern. 69, 205 (1993).
12. J. K. Kanters, N. H. Holstein-Rathlou, and E. Agner, "Lack of evidence for low-dimensional chaos in heart rate variability," J. Cardiovasc. Electrophysiol. 5, 128 (1994).
13. J. Kurths, A. Voss, P. Saparin, A. Witt, H. J. Kleiner, and N. Wessel, "Quantitative analysis of heart rate variability," Chaos 5, 88 (1995).
14. P. Ch. Ivanov, M. G. Rosenblum, C.-K. Peng, J. Mietus, S. Havlin, H. E. Stanley, and A. L. Goldberger, "Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis," Nature (London) 383, 323 (1996).
15. G. Sugihara, W. Allan, D. Sobel, and K. D. Allan, "Nonlinear control of heart rate variability in human infants," Proc. Natl. Acad. Sci. U.S.A. 93, 2608 (1996).
16. C-S. Poon and C. K. Merrill, "Decrease of cardiac chaos in congestive heart failure," Nature (London) 389, 492 (1997).
17. J. F. Muzy, E. Bacry, and A. Arneodo, "Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method," Phys. Rev. E 47. 875 (1993).
18. P. Ch. Ivanov, L. A. N. Amaral, A. L. Goldberger, S. Havlin, M. G. Rosenblum, Z. Struzik, and H. E. Stanley, "Multifractality in human heartbeat dynamics," Nature (London) 399, 461 (1999).
19. M. Mackey and L. Glass, "Oscillation and chaos in physiological control systems," Science 197, 287 (1977).
20. M. M. Wolf, G. A. Varigos, D. Hunt, and J. G. Sloman, "Sinus arrhythmia in acute myocardial infarction," Med. J. Australia 2, 52 (1978).
21. R. I. Kitney and O. Rompelman. The Study of Heart-Kate Variability (Oxford University Press, London. 1980).
22. S. Akselrod, D. Gordon, F. A. Ubel, D. C. Shannon, A. C. Barger, and R. J. Cohen, "Power spectrum analysis of heart rate fluctuation: A quantitative probe of beat-to-beat cardiovascular control," Science 213, 220 (1981).
23. Theory of Heart, edited by L. Glass, P. Hunter, and A. McCulloch (Springer Verlag, New York, 1991).
24. C-K. Peng, S. Havlin, H. E. Stanley, and A. L. Goldberger, "Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series," in Proceedings of the NATO Dynamical Disease Conference, edited by L. Glass, Chaos 5, 82 (1995).
25. P. Ch. Ivanov, M. G. Rosenblum, C.-K. Peng, J. Mietus, S. Havlin, H. E. Stanley, and A. L. Goldberger, "Scaling and universality in heart rate variability distributions," Physica A 249, 587 (1998).
26. Y. Ashkenazy, P. Ch. Ivanov, S. Havlin, C.-K. Peng, A. L. Goldberger, and H. E. Stanley, "Magnitude and sign correlations in heartbeat fluctuations," Phys. Rev. Lett. 86, 1900 (2001).
27. D. Panter, Modulation, Noise and Spectral Analysis (McGraw-Hill, New York, 1965).
28. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1981), Vol. I.
29. R. I. Kitney, D. Linkens, A. C. Selman, and A. A. McDonald, Automedica 4, 141 (1982).
30. A. L. Goldberger, "Non-linear dynamics for clinicians: Chaos theory, fractals, and complexity at the bedside," Lancet 347, 1312 (1996).
31. S. Havlin et al, "Random multiplicative processes and transport in structures with correlated spatial disorder," Phys. Rev. Lett. 61, 1438 (1988).
32. M. F. Shlesinger and B. J. West, Random Fluctuations and Pattern Growth: Experiments and Models (Kluwer Academic, Boston, 1988).
33. M. N. Levy, "Sympathetic-parasympathetic interactions in the heart," Circ. Res. 29, 437 (1971).
34. P. Ch. Ivanov, L. A. N. Amaral, A. L. Goldberger, and H. E. Stanley, "Stochastic feedback and the regulation of biological rhythms," Europhys. Lett. 43, 363 (1998).
35. P. Bernaola-Galvan, P. Ch. Ivanov, L. A. N. Amaral, and H. E. Stanley, "Scale-invariance in the nonstationarity of physiological signals" (http:// xxx.lanl.gov/cond-mat/0005284).
36. P. Bernaola-Galvan, I. Grosse, P. Carpena, J. L. Oliver, R. Roman-Roldan, and H. E. Stanley, "Finding borders between coding and noncoding DNA regions by an entropie segmentation method," Phys. Rev. Lett. 85, 1342 (2000).
37. R. M. Berne and M. N. Levy, Cardiovascular Physiology, 6th ed. (Mosby, St. Louis, 1996).
38. C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, "Mosaic organization of DNA nucleotides," Phys. Rev. E 49, 1685 (1994).
39. K. Hu, P. Ch. Ivanov, C. Zhi, P. Carpena, and H. E. Stanley, "Effects of trends on detrended fluctuation analysis," Phys. Rev. E 64, 011114 (2001).
40. S. V. Buldyrev. A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Matsa, C.-K. Peng, M. Simons, and H. E. Stanley, "Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis," Phys. Rev. E 51, 5084 (1995).
41. S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, H. E. Stanley, and M. Simons, "Fractal landscapes and molecular evolution: Modeling the myosin heavy chain gene family," Biophys. J. 65, 2673 (1993).
42. S. M. Ossadnik, S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, C.-K. Peng, M. Simons, and H. E. Stanley, "Correlation approach to identify coding regions in DNA sequences," Biophys. J. 67, 64 (1994).
43. M. S. Taqqu, V. Teverovksy, and W. Willinger, "Estimators for long-range dependence: An empirical study," Fractals 3, 185 (1996).
44. H. V. Huikuri, K. M. Kessler, E. Terracall, A. Castellanos, M. K. Linnaluoto, and R. J. Myerburg, "Reproducibility and circadian rhythm of heart rate variability in healthy subjects," Am. J. Cardiol. 65, 391 (1990).
45. H. Moelgaard, K. E. Soerensen, and P. Bjerregaard, "Circadian variation and influence of risk factors on heart rate variability in healthy subjects," Am. J. Cardiol. 68, 777 (1991).
46. P. Ch. Ivanov, M. G. Rosenblum, C.-K. Peng, S. Havlin, H. E. Stanley, and A. L. Goldberger, "Wavelets in medicine and physiology," in Wavelets in Physics, edited by H. van der Berg (Cambridge University Press, Cambridge, 1998).
47. Heart Failure Database (Beth Israel Deaconess Medical Center, Boston, MA). The database now includes 18 healthy subjects (13 female and 5 male, with ages between 20 and 50, average 34.3 years), and 12 congestive heart failure subjects (3 female and 9 male, with ages between 22 and 71, average 60.8 year) in sinus rhythm. Data are freely available at the following URL: http://www.physionet.org.
48. P. Ch. Ivanov, A. Bunde, L. A. N. Amaral, S. Havlin, J. Fritsch-Yelle, R. M. Baevsky, H. E. Stanley, and A. L. Goldberger, "Sleep-wake differences in scaling behavior of the human heartbeat: Analysis of terrestrial and long-term space flight data," Europhys. Lett. 48, 594 (1999).
49. A. L. Goldberger, M. W. Bungo, R. M. Baevsky, B. S. Bennett, D. R. Rigney, J. E. Mietus, G. A. Nikulina, and J. B. Charles, "Heart rate dynamics during long-term space flight: Report on MIR cosmonauts," Am. Heart J. 128, 202 (1994).
50. A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J. H. Peter, and K. Voigt, "Correlated and uncorrelated regions in heart-rate fluctuations during sleep," Phys. Rev. Lett. 85, 3736 (2000).
51. Physics of Complex Systems: Proceedings of the Enrico Fermi School on Physics, Course CXXXIV, edited by F. Mallamace and H. E. Stanley (IOS, Amsterdam, 1997).
52. P. Meakin, Fractals, Scaling and Growth Far from Equilibrium (Cambridge University Press, Cambridge, 1997).
53. H. E. Stanley, "Power laws and universality," Nature (London) 378, 554 (1995).
54. A. Bunde and S. Havlin, Fractals in Science (Springer-Verlag, Berlin, 1994).
55. Fractals and Disordered Systems, 2nd ed., edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1996).
56. T. Vicsek, Fractal Growth Phenomena, 2nd ed. (World Scientific, Singapore, 1993).
57. A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
58. H. Takayasu, Fractals in the Physical Sciences (Manchester University Press, Manchester, UK, 1997).
59. H. E. Hurst, "Long-term storage capacity of reservoirs," Trans. Am. Soc. Civ. Eng. 116, 770 (1951).
60. T. G. Dewey, Fractals in Molecular Biophysics (Oxford University Press, Oxford, 1997).
61. Z. R. Struzik, "Determining local singularity strengths and their spectra with the wavelet transform," Fractals 8(2), 163 (2000).
62. Z. R. Struzik, "Revealing local variability properties of human heartbeat intervals with the local effective Holder exponent," Fractals 9(1), 77 (2001).
63. T. Vicsek and A. L. Barabási, "Multi-affine model for the velocity distribution in fully turbulent flows," J. Phys. A 24, L845 (1991).
64. A.-L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995). Chap. 24.
65. I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992).
66. J. F. Muzy, E. Bacry, and A. Arneodo, "The multifractal formalism revisited with wavelets," Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 245 (1994).
67. L. A. N. Amaral, P. Ch. Ivanov, N. Aoyagi, I. Hidaka, S. Tomono, A. L. Goldberger, H. E. Stanley, and Y. Yamamoto, "Behavioral-independent features of complex heartbeat dynamics," Phys. Rev. Lett. 86, 6026 (2001).
68. L. A. N. Amaral, A. L. Goldberger, P. Ch. Ivanov, and H. E. Stanley, "Scale-independent measures and pathologic cardiac dynamics," Phys. Rev. Lett. 81, 2388 (1998).
69. C. Meneveau and K. R. Sreenivasan, "Simple multifractal cascade model for fully developed turbulence," Phys. Rev. Lett. 59, 1424 (1987).
70. H. E. Stanley and P. Meakin, "Multifractal phenomena in physics and chemistry," Nature (London) 335, 405 (1988).
71. U. Frisch, Turbulence (Cambridge University Press, Cambridge, UK, 1995).
72. L. Glass and C. P. Malta, "Chaos in multiloop negative feedback-systems," J. Theor. Biol. 145(2), 217 (1990).
73. H. Seidel and H. Herzel, "Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex." Physica D 115, 145 (1998).
74. D. C. Lin and R. L. Hughson, "Modeling heart rate variability in healthy humans: A turbulence analogy," Phys. Rev. Lett. 86, 1650 (2001).