Chaos? in Physiological Systems

Abstract

Over the last two decades chaotic dynamical systems analysis has become a standard tool for systems analysis in the hydrodynamics of turbulence, in mechanical systems, and in electrical signals. The label “chaotic” referes to the lack of predictability of the weather and other complex systems. We can use “chaos” theory to enhance our understanding of cardiovascular pressures, flows, heart rates, and tracer exchanges. “Chaos” is the descriptor applied to the state of a system that is unpredictable, even though bounded. Poincaré (1880) observed that some simple differential equations resulted in unpredictable behavior. But, as brought forcefully to our attention in modern times by Lorenz (1963), the unpredictability is not necessarily equivalent to randomicity. There is no reason to think that biological systems must be chaotic, and Glass and Malta (1990) argue that biochemical systems are in general not chaotic, so in this essay the focus is on the idea that consideration of chaotic and fractal aspects of systems augments our power to examine and interpret data, and perhaps to characterize the system.

In physics it is our habit to try to approach the explanation of a physical process by splitting this process into elements. We regard all complicated processes as combinations of simple elementary processes ... that is, we think of the wholes before us as the sum of their parts. But this procedure presupposes that the splitting of the whole does not affect the character of the whole ... Now, when we deal with the irreversible processes in this fashion the irreversibility is simply lost. One cannot understand such processes on the assumption that all properties of the whole may be approached by a study of its parts.

Max Planck (1915)