Annals of Biomedical Engineering

, Volume 30, Issue 5, pp 683–692 | Cite as

Quantifying Fractal Dynamics of Human Respiration: Age and Gender Effects

  • C.-K. Peng
  • Joseph E. Mietus
  • Yanhui Liu
  • Christine Lee
  • Jeffrey M. Hausdorff
  • H. Eugene Stanley
  • Ary L. Goldberger
  • Lewis A. Lipsitz


We sought to quantify the fractal scaling properties of human respiratory dynamics and determine whether they are altered with healthy aging and gender. Continuous respiratory datasets (obtained by inductive plethysmography) were collected from 40 healthy adults (10 young men, 10 young women, 10 elderly men, and 10 elderly women) during 120 min of spontaneous breathing. The interbreath interval (IBI) time series were extracted by a new algorithm and fractal scaling exponents that quantify power-law correlations were computed using detrended fluctuation analysis. Under supine, resting, and spontaneous breathing conditions, both healthy young and elderly subjects had scaling exponents for the IBI time series that indicate long-range (fractal) correlations across multiple time scales. Furthermore, the scaling exponents (mean ± SD) for the IBI time series were significantly (p < 0.03) lower (indicating decreased correlations) in the healthy elderly male 0.60 ± 0.08) compared to the young male (0.68 ± 0.07), young female (0.70 ± 0.07), and elderly female (0.67 ± 0.06) subjects. These results provide evidence for fractal organization in physiologic human breathing cycle dynamics, and for their degradation in elderly men. These findings may have implications for modeling integrated respiratory control mechanisms, quantifying their changes in aging or disease, and assessing the outcome of interventions aimed toward restoring normal physiologic respiratory dynamics. © 2002 Biomedical Engineering Society.

PAC2002: 8719Uv, 8710+e, 0545Df

Aging Chaos theory Long-range correlations Respiration Ventilation 


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  1. 1.
    Bassingthwaighte, J. B., L. S. Liebovitch, and B. J. West. Fractal Physiology. New York: Oxford University Press, 1994.Google Scholar
  2. 2.
    Beran, J. Statistics for Long-Memory Processes. New York: Chapman and Hall, 1994.Google Scholar
  3. 3.
    Buldyrev, S. V., A. L. Goldberger, S. Havlin, C.-K. Peng, M. Simons, and H. E. Stanley. Generalized Lévy walk model for DNA nucleotide sequences. Phys. Rev. E 47:4514–4523, 1993.Google Scholar
  4. 4.
    Dejours, P., R. Puccinelli, J. Armand, and M. Dicharry. Breath-to-breath variations of pulmonary gas exchange in resting man. Respir. Physiol. 1:265–280, 1966.Google Scholar
  5. 5.
    Edwards, R. D., and J. F. Magee. Technical Analysis of Stock Trends, 7th ed. Springfield: Amacom, 1997.Google Scholar
  6. 6.
    Frey, U., M. Silverman, A. L. Barabasi, and B. Suki. Irregularity and power-law distributions in the breathing pattern in preterm and term infants. J. Appl. Physiol. 86:789–797, 1998.Google Scholar
  7. 7.
    Haas, F., S. Distenfeld, and K. Axen. Effects of perceived musical rhythm on respiratory pattern. J. Appl. Physiol. 61:1185–1191, 1986.Google Scholar
  8. 8.
    Hausdorff, J. M., C.-K. Peng, Z. Ladin, J. Y. Wei, and A. L. Goldberger. Is walking a random walk? Evidence for longrange correlations in the stride interval of human gait. J. Appl. Physiol. 78:349–358, 1995.Google Scholar
  9. 9.
    Hausdorff, J. M., and C.-K. Peng. Multiscaled randomness: A possible source of 1/f noise in biology. Phys. Rev. E 54:2154–2157, 1996.Google Scholar
  10. 10.
    Hausdorff, J. M., 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. 80:1448–1457, 1996.Google Scholar
  11. 11.
    Hausdorff, J. M., S. L. Mitchell, R. Firtion, C.-K. Peng, M. E. Cudkowicz, J. Y. Wei, and A. L. Goldberger. Altered fractal dynamics of gait: Reduced stride interval correlations with aging and Huntington's disease. J. Appl. Physiol. 82:262–269, 1997.Google Scholar
  12. 12.
    Ho, K. K. L., G. B. Moody, C.-K. Peng, J. E. Mietus, M. G. Larson, D. Levy, and A. L. Goldberger. Predicting survival in heart failure cases and controls using fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics. Circulation 96:842–848, 1997.Google Scholar
  13. 13.
    Hoop, B., H. Krazemi, and L. Liebovitch. Rescaled range analysis of resting respiration. Chaos 3:27–29, 1993.Google Scholar
  14. 14.
    Hughson, R. L., Y. Yamamoto, and J. O. Fortrat. Is the pattern of breathing at rest chaotic? A test of the Lyapunov exponent. Adv. Exp. Med. Biol. 393:15–19, 1995.Google Scholar
  15. 15.
    Hughson, R. L., Y. Yamamoto, J.-O. Fortrat, R. Leask, and M. S. Fofana. Possible fractal and/or chaotic breathing patterns in resting humans. In: Bioengineering Approaches to Pulmonary Physiology and Medicine, edited by M. C. K. Khoo. New York: Plenum, 1996, pp. 187–196.Google Scholar
  16. 16.
    Ivanov, P. Ch., M. Rosenblum, C.-K. Peng, J. Mietus, S. Havlin, H. E. Stanley, and A. L. Goldberger. Scaling behavior of heartbeat intervals obtained by wavelet-based time series analysis. Nature (London) 383:323–327, 1996.Google Scholar
  17. 17.
    Iyenger, N., C.-K. Peng, R. Morin, A. L. Goldberger, and L. A. Lipsitz. Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics. Am. J. Physiol. 271:R1078-R1084, 1996.Google Scholar
  18. 18.
    Kaplan, D. T., M. I. Furman, S. M. Pincus, S. M. Ryan, L. A. Lipsitz, and A. L. Goldberger. Aging and the complexity of cardiovascular dynamics. Biophys. J. 59:945–949, 1991.Google Scholar
  19. 19.
    Kolmogorov, A. N. Local structure of turbulence in fluid for very large Reynolds numbers. In Translations in Turbulence, edited by S. Friedlander and L. Topper. New York: Interscience, 1961, pp. 151–155.Google Scholar
  20. 20.
    Lefevre, G. R., S. E. Kowalski, L. G. Girling, D. B. Thiessen, and W. A. C. Mutch. Improved arterial oxygenation after oleic acid lung injury in the pig using a computer-controlled mechanical ventilator. Am. J. Respir. Crit. Care Med. 154:1567–1572, 1996.Google Scholar
  21. 21.
    Lipsitz, L. A., G. B. Mietus, G. B. Moody, and A. L. Goldberger. Spectral characteristics of heart rate variability before and during postural tilt. Relations to aging and risk of syncope. Circulation 81:1803–1810, 1990.Google Scholar
  22. 22.
    Lipsitz, L. A. Clinical physiology of aging. In: Textbook of Internal Medicine, 3rd ed., edited by W. N. Kelley. Philadelphia: Lippincott, 1996, pp. 110–119.Google Scholar
  23. 23.
    Lipsitz, L. A., S. M. Pincus, R. J. Morin, S. Tong, L. P. Eberle, M. Phyllis, and P. M. Gootman. Preliminary evidence for the evolution in complexity of heart rate dynamics during autonomic maturation in neonatal swine. J. Auton Nerv. Syst. 65:1–9, 1997.Google Scholar
  24. 24.
    Mäkikallio, T. H., T. Seppänen, K. E. J. Airaksinen, J. Koistinen, M. P. Tulppo, C.-K. Peng, A. L. Goldberger, and H. V. Huikuri. Dynamic analysis of heart rate may predict subsequent ventricular tachycardia after myocardial infarction. Am. J. Cardiol. 80:779–783, 1997.Google Scholar
  25. 25.
    Mandelbrot, B. B. The Fractal Geometry of Nature. San Francisco: Freeman, 1982.Google Scholar
  26. 26.
    Montroll, E. W., and M. F. Shlesinger. The wonderful world of random walks. In: Nonequilibrium Phenomena II. From Stochastics to Hydrodynamics, edited by J. L. Lebowitz and E. W. Montroll. Amsterdam: North-Holland, 1984, pp. 1–121.Google Scholar
  27. 27.
    Mutch, W. A. C., S. Harms, M. R. Graham, S. E. Kowalski, L. G. Girling, and G. R. Lefevre. Biologically variable or naturally noisy mechanical ventilation recruits atelectatic lung. Am. J. Respir. Crit. Care Med. 162:319–323, 2000.Google Scholar
  28. 28.
    Peng, C.-K., S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger. Mosaic organization of DNA nucleotides. Phys. Rev. E 49:1685–1689, 1994.Google Scholar
  29. 29.
    Peng, C.-K., S. Havlin, H. E. Stanley, and A. L. Goldberger. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5:82–87, 1995.Google Scholar
  30. 30.
    Pomeranz, B., R. Macaulay, M. A. Caudill, I. Kutz, D. Adam, D. Gordon, K. M. Kilborn, A. C. Barger, D. C. Shannon, R. J. Cohen, and H. Benson. Assessment of autonomic function in humans by heart rate spectral analysis. Am. J. Physiol. 248:H151-H153, 1985.Google Scholar
  31. 31.
    Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. Cambridge, U.K.: Cambridge University Press, 1993.Google Scholar
  32. 32.
    Ryan, S. M., A. L. Goldberger, S. M. Pincus, J. E. Mietus, and L. A. Lipsitz. Gender and age-related differences in heart rate dynamics: Are women more complex than men? J. Am. Coll. Cardiol. 24:1700–1707, 1994.Google Scholar
  33. 33.
    Simpson, D. M., and R. Wicks. Spectral analysis of heart rate indicates reduced baroreceptor-related heart rate variability in elderly persons. J. Gerontol. 43:M21-M24, 1988.Google Scholar
  34. 34.
    Small, M., K. Judd, M. Lowe, and S. Stick. Is breathing in infants chaotic? Dimension estimates for respiratory patterns during quiet sleep. J. Appl. Physiol. 86:359–376, 1999.Google Scholar
  35. 35.
    Suki, B., A. M. Alencar, M. K. Sujeer, K. R. Lutchen, J. J. Collins, J. S. Andrade, E. P. Ingenito, S. Zapperi, and H. E. Stanley. Life support system benefits from noise. Nature (London) 393:127–128, 1998.Google Scholar
  36. 36.
    Szeto, H. H., P. Y. Cheng, J. A. Decena, Y. Cheng, D. L. Wu, and G. Dwyer. Fractal properties in fetal breathing dynamics. Am. J. Physiol. 263:R141-R147, 1992.Google Scholar
  37. 37.
    Taqqu, M. S., V. Teverovksy, and W. Willinger. Estimators for long-range dependence: An empirical study. Fractals 3:785–798, 1996.Google Scholar

Copyright information

© Biomedical Engineering Society 2002

Authors and Affiliations

  • C.-K. Peng
    • 1
  • Joseph E. Mietus
    • 1
  • Yanhui Liu
    • 2
  • Christine Lee
    • 1
  • Jeffrey M. Hausdorff
    • 1
    • 3
  • H. Eugene Stanley
    • 2
  • Ary L. Goldberger
    • 1
  • Lewis A. Lipsitz
    • 3
    • 4
  1. 1.Margret and H.A. Rey Institute for Nonlinear Dynamics in Medicine, Beth Israel Deaconess Medical CenterHarvard Medical SchoolBoston
  2. 2.Center for Polymer Studies and Department of PhysicsBoston UniversityBoston
  3. 3.Gerontology Division of Beth Israel Deaconess Medical CenterHarvard Medical SchoolBoston
  4. 4.Research and Training Institute of the Hebrew Rehabilitation Center for AgedBoston

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