Abstract
Application of chaos theory to medicine has yielded intriguing and controversial results. In this paper, a continuous conjecture for the solution of the Poincaré equation suggests that chaos provides a framework for the measurement of disorder within a system. However, as demonstrated by the behavior of the continuous versus the discrete approach to chaos, the general use of the term chaos must be used with care. The theoretical results are illustrated in two medical applications dealing with hemodynamic flow and congestive heart failure.
This work was supported in part by a grant from University of California Valley Medical Education Foundation.
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References
Poincaré. H., Memoire sur les courbes definies par les equations differentielles, J. Math. Pures et Appliq., 4th Ser., 1, 1885, 167–244.
Gleick, J., Chaos, Making a New Science, Penguin Books, New York, 1987.
Cohen, M.E., Hudson, D.L., Anderson, M.F., A conjectured continuous approach to chaotic modeling, Nonlinear Theory and Its Applications, 1993, 783–786.
Tsonis, P.A. Tsonis, A.A., Chaos: principles and implications in biology, Computer Applications in the Biosciences, 5 (1), 1989, 27–32.
Goldberger, A.L., West, B.J., Fractals in physiology and medicine, Yale Journal of Biology and Medicine, 60, 1987, 421–435.
Goldberger, A.L., Cardiac chaos, Science, 243 (2987), 1989, 1419.
Cohen, M.E., Hudson, D.L., Computational Aspects of Chaos Theory, ISCA, 1994, 89–93.
Cohen, M.E., Hudson, D.L., Anderson, M.F., The effect of vasoactive drugs on the chaotic nature of blood flow, MEDINFO, K.C. Lun, et al., Eds., North Holland, 1992, 931–936.
Szego, G., Orthogonal Polynomials, American Math. Soc. Colloquium Publications, XXIII, 1939, 59.
Burton, R.L., Faires, J.D., Reynolds, A.C., Numerical Analysis, Prindle, Weber, and Schmidt, Boston, 1978.
Cohen, M.E., Hudson, D.L., Moazamipour, H., Anderson, M.F., Chaotic blood flow analysis in an animal model, Computer Applications in Medical Care, 1990, 14, 323–327.
Cohen, M.E., Hudson, D.L., Anderson, M.F., Vazquez, C., Blood flow data exhibit chaotic properties, Int. J. of Microcomputer Applications, 12 (3), 1993, 82–87.
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© 1995 Springer-Verlag Berlin Heidelberg
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Cohen, M.E., Hudson, D.L., Anderson, M.F., Deedwania, P.C. (1995). Implications of a continuous approach to chaotic modeling. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035980
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DOI: https://doi.org/10.1007/BFb0035980
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