Fractal variability versus pathologic periodicity: Complexity loss and stereotypy in disease

Perspectives in Biology and Medicine

Volumn 40, Issue 4, 1997, Pages 543-561

  Goldberger, Ary L ^a  

^a HARVARD MEDICAL SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISEASE ACTIVITY; OSCILLATION; PATHOLOGY; PERIODICITY; PREDICTION; PRIORITY JOURNAL; REVIEW; STEREOTYPY;

EID: 0030666547     PISSN: 00315982     EISSN: None     Source Type: Journal    
DOI: 10.1353/pbm.1997.0063     Document Type: Review

References (42)

1. GOLDBERGER, A. L. Non-linear dynamics for clinicians: Chaos theory, fractals, and complexity at the bedside. Lancet 347:1312-1314, 1996.
2. WEST, B. J., and GOLDBERGER, A. L. Physiology in fractal dimensions. Am. Scientist. 75:354-365, 1987.
3. GOLDBERGER, A. L.; RIGNEY, D. R.; and WEST, B. J. Chaos and fractals in human physiology. Sci. Am. 262:40-49, 1990.
4. GLASS, L., and MACKEY, M. C. From Clocks to Chaos: The Rhythms of Life. Princeton: Princeton Univ. Press, 1988.
5. BASSINGTHWAIGHTE, J. B.; LIEBOVITCH, L. S.; and WEST, B. J. Fractal Physiology. New York: Oxford Univ. Press, 1994.
6. KAPLAN, D. T., and GLASS, L. Understanding Nonlinear Dynamics. New York: Springer-Verlag, 1995.
7. MANDELBROT, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, 1982.
8. WEIBEL, E. R. Fractal geometry: A design principle for living organisms. Am. J. Physiol. 261 (Lung Cell Mol Physiol 5):L361-369, 1991.
9. ABBOUD, S.; BERENFELD, O.; and SADEH, D. Simulation of high-resolution QRS complex using a ventricular model with a fractal conduction system: Effects of ischemia on high-frequency QRS potentials. Circ. Res. 68:1751-1760, 1991.
10. PESKIN, C. S., and MCQUEEN, D. M. Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets. Am. J. Physiol. 266 (Heart Circ Physiol 35):H319-328, 1994.
11. SHLESINGER, M. F. Fractal time and 1/f noise in complex systems. Ann. NY Acad. Sci. 504:214-228, 1987.
12. PENG, C.-K.; MIETUS, J.; HAUSDORFF, J. M.; et al. Long-range anti-correlations and non-Gaussian behavior of the heartbeat. Phys. Rev. Lett. 70:1343-1346, 1993.
13. PENG, C.-K.; BULDYREV, S. V.; HAUSDORFF, J. M.; et al. Fractal landscapes in physiology and medicine: Long-range correlations in DNA sequences and heart rate intervals. In Fractals in Biology and Medicine, edited by G. A. LOSA, et al. Basel: Birkhauser-Verlag, 1994. 55-65.
14. STANLEY, H. E.; BULDYREV, S. V.; GOLDBERGER, A. L. et al. Statistical mechanics in biology: How ubiquitous are long-range correlations? Physica A. 205:214-253, 1994.
15. KOBAYASHI, M., and MUSHA, T. 1/f fluctuation of heartbeat period. IEEE Trans. Biomed. Eng. 29:456-457, 1982.
16. SZETP, H.; CHEN, P. Y.; DECENA, J. A.; et al. Fractal properties of fetal breathing dynamics. Am. J. Physiol. 263 (Regulatory Interactive Comp. Physiol. 32):R141-147, 1992.
17. MARSH, D. J.; OSBORN, J. L.; and COWLEY, A. W. 1/f fluctuations in arterial pressure and regulation of renal blood flow in dogs. Am. J. Physiol. 258: F1394-1400, 1990.
18. HAUSDORFF, J. M.; PENG, C.-K.; LADIN, Z.; et al. Is walking a random walk? Evidence for long-range correlations in the stride interval of human gait. J. Appl. Physiol. 78:349-358, 1995.
19. HAUSDORFF, J. M.; PURDON, P. L.; PENG, C.-K.; et al. Fractal dynamics of human gait: Stability of long-range correlations in stride interval fluctuations. J. Appl. Physiol. 80:1448-1457, 1996.
20. HAUSDORFF, J. M.; MITCHELL, S. L.; FIRTION, R.; et al. Altered fractal dynamics of gait: Reduced stride interval correlations with aging and Huntington's disease. J. Appl. Physiol. 82:262-269, 1997.
21. GOLDBERGER, A. L.; KOBALTER, K.; and BHARGAVA, V. 1/f-like scaling in normal neutrophil dynamics: Implications for hematologic monitoring. IEEE Trans. Biomed. Eng. 33:874-876, 1986.
22. IVANOV, P. C.; ROSENBLUM, M.; PENG, C.-K.; et al. Scaling behavior of heartbeat intervals obtained by wavelet-based time series analysis. Nature 383:323-327, 1996.
23. PENG, C.-K.; HAVLIN, S.; STANLEY, H. E.; and GOLDBERGER, A. L. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. CHAOS 5:82-87, 1995.
24. GOLDBERGER, A. L.; FINDLEY, L.; BLACKBURN, M. J.; and MANDELL, A. J. Nonlinear dynamics of heart failure: Implications of long-wavelength cardiopulmonary oscillations. Am. Heart J. 107:612-615, 1984.
25. KAPLAN, D. T.; FURMAN, M. I.; PINCUS, S. M.; et al. Aging and the complexity of cardiovascular dynamics. Biophys. J. 59:945-949, 1991.
26. LIPSITZ, L. A., and GOLDBERGER, A. L. Loss of "complexity" and aging: Potential applications of fractals and chaos theory to senescence. JAMA 267: 1806-1809, 1992.
27. GOLDBERGER, A. L. Applications of chaos to physiology and medicine. In Applied Chaos, edited by J. H. KIM and J. STRINGER. New York: John Wiley, 1992. 321-329.
28. CHEYNE, J. A case of apoplexy in which the fleshy part of the heart was converted into fat. Dublin Hosp. Rep. 2:216-223, 1818.
29. SAUL, J. P.; ARAI, Y.; BERGER, R. D.; et al. Assessment of autonomic regulation in chronic congestive heart failure by heart rate spectral analysis. Am. J. Cardiol. 61:1292-1299, 1988.
30. REIMANN, H. A. Periodic disease: A probable syndrome including periodic fever, benign paroxysmal peritonitis, cyclic neutropenia and intermittent arthralgia. JAMA 136:239-244, 1948.
31. REIMANN, H. A. Periodic Diseases. Philadelphia: F. A. Davis, 1963.
32. GLASS, L., and MACKEY, M. C. Pathological conditions resulting from instabilities in physiological control systems. Ann. NY Acad. Sci. 316:214-235, 1979.
33. MACKEY, M. C., and GLASS, L. Oscillation and chaos in physiologic control systems. Science 197:287-289, 1979.
34. MILTON, J., and BLACK, D. Dynamic diseases in neurology and psychiatry. CHAOS 5:8-13, 1995.
35. GOLDBERGER, A. L., and RIGNEY, D. R. Sudden death is not chaos. In Dynamic Patterns in Complex Systems, edited by J. A. S. KELSO, A. J. MANDELL, and M. F. SHLESINGER. Teaneck, NJ: World Scientific Publishers, 1988. 248-264.
36. GOLDBERGER, A. L., and RIGNEY, D. R. Nonlinear dynamics at the bedside. In Theory of Heart, edited by L. GLASS, P. HUNTER, and A. MCCULLOCH. New York: Springer, 1991. 583-605.
37. KATZ, M.; MEIZNER, I.; SHANI, N.; and INSLER, V. Clinical significance of sinusoidal fetal heart rate pattern. Br. J. Obstet. Gynaecol. 90:832-836, 1983.
38. GOLDBERGER, A. L.; RIGNEY, D. R.; MIETUS, J.; et al. Nonlinear dynamics in sudden cardiac death syndrome: Heartrate oscillations and bifurcations. Experientia 44:983-987, 1988.
39. LIPSITZ, L. A.; HASHIMOTO, F.; LUBOWSKY, L. P.; et al. Heart rate and respiratory rhythm dynamics on ascent to high altitude. Br. Heart J. 74:390-396, 1995.
40. PARKINSON, J. An Essay on the Shaking Palsy. London: Sherwood, Neeley and Jones, 1817.
41. KITA, Y.; ISHISE, J.; YOSHITA, Y.; et al. Power spectral analysis of heart rate and arterial blood pressure oscillations in brain-dead patients. J. Auton. Nerv. Syst. 44:101-107, 1993.
42. SUGIHARA, G.; ALLEN, W.; SOBEL, D.; and ALAN, K. D. Nonlinear control of heart rate variability in human infants. Proc. Natl. Acad. Sci. USA 93:2608-2613, 1996.