Advertisement

Fractal Noise in Breathing

  • Bernard Hoop
  • Melvin D. Burton
  • Homayoun Kazemi

Abstract

Our understanding of respiration derives from applications of a variety of physical and life science disciplines, methods, and models to a critical physiological process: exchange and balance of oxygen and carbon dioxide. We know that breathing at rest arises from a diversity of interrelated and interactive physical and chemical mechanisms involving molecular and cellular processes in the brainstem which include-among other phenomena common to the central nervous system-metabolism, synaptic transmission of neurochemicals, neurochemical-mediated alteration of neural cell membrane potential, transmembrane ion conductance, neural electrical signal propagation, and neuromodulation by afferent chemoreceptive and mechanoreceptive inputs.

Keywords

Fractal Dimension Tidal Volume Fractal Brownian Motion Brownian Particle Hurst Exponent 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    West, B.J. Fractal Physiology and Chaos in Medicine. Singapore: World Scientific, 1990.Google Scholar
  2. 2.
    Cannon, W.B. The Wisdom of the Body. New York: Norton, 1963.Google Scholar
  3. 3.
    Feldman, J.L. Neurophysiology of breathing in mammals. In: Handbook of Physiology. The Nervous System. Intrinsic Regulatory Systems of the Brain. Bethesda, MD: Am. Physiol. Soc., 1986, sect. 3, vol. II, chapt. 7, p. 463–524.Google Scholar
  4. 4.
    Richter, D.W., D. Ballantyne, and J.E. Remmers. How is the respiratory rhythm generated? A model. News Physiol. Sci. 1:109–112,1986.Google Scholar
  5. 5.
    Botros, S.M., and E.N. Bruce. Neural network implementation of a three phase model of respiratory rhythm generation. Biol. Cybern. 63:143–153,1990.PubMedCrossRefGoogle Scholar
  6. 6.
    Poon, C.S. Respiratory models and control. In: Physiologic Modeling, Simulation, and Control. New York: CRC Press, 1995, pp. 2404–2421.Google Scholar
  7. 7.
    Khoo, M.C.K. (ed.). Bioengineering Approaches to Pulmonary Physiology and Medicine. New York: Plenum, 1996 (other contributions to this volume).Google Scholar
  8. 8.
    Feder, J. Fractals. New York: Plenum, 1988.Google Scholar
  9. 9.
    Mandelbrot, B.B. The Fractal Geometry of Nature. San Francisco: Freeman, 1983.Google Scholar
  10. 10.
    Ossadnik, S.M., 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. 67:64–70,1994.PubMedGoogle Scholar
  11. 11.
    Turcott, R.G., S.B. Lowen, E. Li, D. Johnson, C. Tsuchitani, and M.C. Teich. A non-stationary Poisson point process describes the sequence of action potentials over long time scales in lateral-superior-olive auditory neurons. Biol. Cybern. 70:209–217,1994.PubMedGoogle Scholar
  12. 12.
    Goetze, T., and J. Brickmann. Self similarity of protein surfaces. Biophys. J. 61:109–118,1992.PubMedCrossRefGoogle Scholar
  13. 13.
    Nogueira, R.A., W.A. Varanda, and L.S. Liebovitch. Hurst analysis in the study of ion channel kinetics. Brazil. J. Med. Biol. Res. 28:491–496, 1995.Google Scholar
  14. 14.
    Onimaru, H., A. Arata, and I. Homma. Intrinsic burst generation of preinspiratory neurons in the medulla of brainstem-spinal cord preparations isolated from newborn rats. Exp. Brain Res. 106:57–68,1995.PubMedCrossRefGoogle Scholar
  15. 15.
    Bianchi, A.L., M. Denavit-Saubie, and J. Champagnat. Central control of breathing in mammals: neuronal circuitry, membrane properties, and neurotransmitters. Physiol. Rev. 75, 1–45,1995.PubMedGoogle Scholar
  16. 16.
    Burton, M.D., M. Nouri, and H. Kazemi. Acetylcholine and central respiratory control: perturbations of acetylcholine synthesis in the isolated brainstem of the neonatal rat. Brain Res. 670:39–47,1995.PubMedCrossRefGoogle Scholar
  17. 17.
    Bassingthwaighte, J.B., L.S. Liebovitch, and B.J. West, Fractal Physiology. New York: Oxford, 1994.Google Scholar
  18. 18.
    Szeto, H.H, P.Y. Cheng, J.A. Decena, Y. Cheng, D. Wu, and G. Dwyer. Fractal properties in fetal breathing dynamics. Am. J. Physiol. 263:R141–R147, 1992.PubMedGoogle Scholar
  19. 19.
    Hoop, B., H. Kazemi, and L. Liebovitch. Rescaled range analysis of resting respiration. CHAOS 3:27–29,1993.PubMedCrossRefGoogle Scholar
  20. 20.
    Hoop, B., M.D. Burton, H. Kazemi, and L.S. Liebovitch. Correlation in stimulated respiratory neural noise. CHAOS 5:609–612,1995.PubMedCrossRefGoogle Scholar
  21. 21.
    Tuck, S.A., Y. Yamamoto, and R.L. Hughson. The effects of hypoxia and hyperoxia on the 1/f nature of breath-by-breath ventilatory variability. In: Modelling and Control of Ventilation, edited by S.J.G. Semple and L. Adams. New York: Plenum, 1996 L.Adams and B. J. Whipp. New York: Plenum, 1996, p. 297–302.Google Scholar
  22. 22.
    Lowen, S.B., and M.C. Teich. Fractal renewal processes generate 1/f noise. Phys. Rev. E. 47:992–1001, 1993.CrossRefGoogle Scholar
  23. 23.
    West, B.J., and W. Deering. Fractal physiology for physicists: Levy Statistics. Physics Reports 246:2–100,1994.CrossRefGoogle Scholar
  24. 24.
    Schroeder, M. Fractals, Chaos, Power Laws. New York: Freeman, 1991.Google Scholar
  25. 25.
    Hausdorff, J.M., C.K. Peng, Z. Ladin, J.R. Wei, and A.L. Goldberger. Is walking a random walk: evidence for long-range correlations in stride interval of human gait. J. Appl. Physiol. 78:349–358,1995.PubMedGoogle Scholar
  26. 26.
    Berg, H.C. Random Walks in Biology. Princeton: Princeton University Press, 1983.Google Scholar
  27. 27.
    DeGroot, M.H. Probability and Statistics (2nd ed). Reading: Addison-Wesley, 1989.Google Scholar
  28. 28.
    Voss, R.F. Random fractal forgeries. In: Fundamental Algorithms in Computer Graphics, edited by R.A. Earashaw, Berlin: Springer, pp. 805–835, 1985.Google Scholar
  29. 29.
    Abramowitz, M., and I.A. Stegun (eds). Handbook of Mathematical Functions, AMS 55. Washington DC: Natl. Bureau Stand., 1970 (9th printing), sect. 26.8.Google Scholar
  30. 30.
    Teich, M.C., and S.B. Lowen. Fractal patterns in auditory nerve-spike trains. IEEE Engr. Med. Biol. 13:197–202,1994.CrossRefGoogle Scholar
  31. 31.
    Peng, C.K., S. Havlin, H.E. Stanley, and A.L. Goldberger. Quantification of scaling exponents and crossover phenomena in nonstationary hearbeat time series. CHAOS 5:82–87,1995.PubMedCrossRefGoogle Scholar
  32. 32.
    Hurst, H.E. Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civ. Engrs. 116:770–808, 1951.Google Scholar
  33. 33.
    Feller, W. The asymptotic distribution of the range of sums of independent random variables. Ann. Math. Stat. 22:427–432, 1951.Google Scholar
  34. 34.
    Bassingthwaighte, J.B., and G.M. Raymond. Evaluating rescaled range analysis for time series. Ann. Biomed Engr. 22:432–444,1994.CrossRefGoogle Scholar
  35. 35.
    Bassingthwaighte, J.B. Physiological heterogeneity: fractals link determinism and randomness in structures and functions. News Physiol. Sci. 3:5–10,1988.Google Scholar
  36. 36.
    Bassingthwaighte, J.B., and G.M. Raymond. Evaluation of the dispersional analysis method for fractal time series. Ann. Biomed. Engr. 23:491–505,1995.CrossRefGoogle Scholar
  37. 37.
    Glenny, R.W., H.T. Robertson, S. Yamashiro, and J.B. Bassingthwaighte. Applications of fractal analysis to physiology. J. Appl. Physiol. 70:2351–2367,1991.PubMedGoogle Scholar
  38. 38.
    Schepers, H.E., J.H.G.M. van Beek, and J.B. Bassingthwaighte. Four methods to estimate the fractal dimension from self-affine signals. IEEE Eng. Med Biol Mag. 11(2): 57–64&71.1992.CrossRefGoogle Scholar
  39. 39.
    Lowen, S.B., and M.C. Teich. Estimation and simulation of fractal stochastic point processes. Fractals 3:183–210,1995.CrossRefGoogle Scholar
  40. 40.
    Churilla, M., W.A. Gottschalke, L.S. Liebovitch, L.Y. Selector, A.T. Todorov, and S. Yeandle. Membrane potential fluctuations of human T-lymphocytes have fractal characteristics of fractional Brownian motion. Ann. Biomed Engr. 24:1996 99–108, 1996.Google Scholar
  41. 41.
    Flandrin, P. On the spectrum of fractional Brownian motions. IEEE Trans. Infor. Theor. 35:197–199,1989.CrossRefGoogle Scholar

Copyright information

© Plenum Press 1996

Authors and Affiliations

  • Bernard Hoop
    • 1
  • Melvin D. Burton
    • 1
  • Homayoun Kazemi
    • 1
  1. 1.Pulmonary and Critical Care UnitMedical Services Massachusetts General Hospital, Harvard Medical SchoolBoston

Personalised recommendations