Fractal Physiology (review)

becomes a debatable issue" (p.260). But the conditions for such fully informed judgment surely are impossible for many or most humans to meet. It would be interesting to find out if the thousands of persons who read this book face the deaths of others or participate in their own dying differently. One hopes that they will; one even hopes that for oneself. James M. Gustafson Humanities and Comparative Studies Emory University Box 73, Administration Building Atlanta, Georgia 30322 Fractal Physiology. By Bassingthwaighte, R. B., J. B. Liebovitch, and B. J. West. New York: Oxford Univ. Press, 1994. Pp. 364. $55.00. What are fractals, and what does a seemingly esoteric branch of nonlinear mathematics ("chaos theory") have to do with basic problems in physiology and medicine, ranging from the ion-channel kinetics to integrative neural structure and function? Such questions are addressed in this highly readable and engaging monograph by Bassingthwaighte, Liebovitch, and West. The termfractal, as coined by mathematician Benoit Mandelbrot, describes a ubiquitous class of objects that do not have a characteristic (single) scale of length. Such forms are self-similar, or, more technically, self-affme. If you magnify a fractal image—consider the roots or branches of a tree—you find it is composed of subunits which are similar but usually not identical to the larger scale form. Closer examination of these subunits, in turn, reveals that they are composed of self-similar sub-subunits. For an idealized (e.g., computergenerated ) fractal, this internal look-alike property of self-similarity or scaleinvariance goes on indefinitely. For "real world" fractals, the self-similarity is more limited. Indeed quantifying over what range such fractal scaling exists is one of the many important topics covered in this text. Fractal geometry appears to be widespread in human biology. Self-similar anatomic structures include the tracheo-bronchial tree, the vascular network, arborizing dendrites on neurons, and the multiple enfoldings of the bowel and brain. What physiological functions are subserved by such iterated architectures? Fractal anatomies may facilitate a variety of adaptive mechanisms, particularly those associated with amplification of surface area for gas exchange and nutrient absorption, as in the lung and bowel, and with information processing and exchange, as in the nervous system. Their intrinsic redundancy makes fractals resistant to injury. Perturbation of a structure (or process) with multiple scales is less likely to cause it to completely break down than a comparable insult to a less robust one. A more subtle but equally important application of fractals is to physiologic function (dynamics). The fractal concept applies not just to static geometric objects but also to a wide class of complex processes that lack a characteristic scale of time. Such fractal processes produce a complex type ofoutput associated Perspectives in Biology and Medicine, 39, 1 ¦ Autumn 1995 141 with statistically self-similar fluctuations across multiple scales of time. Of interest is recent evidence suggesting that a variety of neuro-regulatory processes appear to possess this scale-free property, including the mechanisms responsible for controlling fluctuations in our heartbeat and blood pressure. This capacity to generate a broadband type of output may make such scale-free systems more plastic and responsive to an inherently unpredictable and capricious environment . Fractal Physiology provides a readable and detailed introduction to the anatomic and dynamical aspects of fractals in biomedicine. Part I gives a brief but systematic overview. Part II describes specific properties of fractals, including different mechanisms for generating fractals involving either deterministic processes (i.e., chaos) or stochastic mechanisms, such as diffusion limited aggregation (DLA). Part III focuses on specific physiologic applications, with an emphasis on ion-channel kinetics, neural excitation, and heterogeneous blood flow, as well as fractal growth mechanisms. The book concludes with an informative and balanced discussion of the controversial topic of deterministic chaos in physiology . These topics should find an enthusiastic audience among biomedical researchers and clinicians wishing a rigorous yet friendly introduction to highly technical (and often misconstrued) concepts, as well as among physicists and applied mathematicians in search of physiologic grist for their nonlinear mills. The nexus of biology and nonlinear dynamics is rapidly emerging as one of the most exciting frontiers in modern science. This book offers...