Fractal Physiology

This volume delineates the use of fractal patterns and measures of fractal dimensions in describing and understanding general aspects of biology, particularly human physiology. After describing the ubiquitous nature of fractal phenomena, the authors give examples of the properties of fractals in space and time. Proceeding from mathematical definitions, they develop detailed practical methods for assessing the fractal characteristics of wave forms varying with time, tissue density variation, and surface irregularities. Most importantly, the authors show how fractal variation defines internal spatial or temporal correlations within the fractal system or object. Simple, recursively applied rules can give rise to complex biological structures by a variety of methods. This suggests that genetic rules govern the general structuring of an organism, while rules implied by interactions at the biochemical, cellular, and tissue levels govern ontogenic development and therefore play the major role in the growth of an organism. Chaos, or non-linear dynamics, is introduced as a stimulating way to examine biological behavior at the cellular and whole animal levels, even though proof of the chaotic nature of normal physiologic events is as yet meager. The later chapters give sets of examples of structural and behavioral fractal phenomena in nerve and muscle, in the cardiovascular and respiratory systems and in growth processes. Why molecular interactions and complex systems give rise to fractals is explored and related to the ideas of emergent properties of systems operating at high levels of complexity.

Klappentext

I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.

Inhalt

I Overview.- 1. Introduction: Fractals Really Are Everywhere.- II Properties of Fractals and Chaos.- 2. Properties of Fractal Phenomena in Space and Time.- 3. The Fractal Dimension: Self-Similar and Self-Affine Scaling.- 4. Fractal Measures of Heterogeneity and Correlation.- 5. Generating Fractals.- 6. Properties of Chaotic Phenomena.- 7. From Time to Topology: Is a Process Driven by Chance or Necessity?.- III Physiological Applications.- 8. Ion Channel Kinetics: A Fractal Time Sequence of Conformational States.- 9. Fractals in Nerve and Muscle.- 10. Intraorgan Flow Heterogeneities.- 11. Fractal Growth.- 12. Mechanisms That Produce Fractals.- 13. Chaos? in Physiological Systems.- Works Cited.