DOI: 0812.0157Nov 30, 2008Paper

Distributed self-regulation of living tissue. Effects of nonideality

ArXiv
Wassily LubashevskyReinhard Mahnke

Abstract

Self-regulation of living tissue as an example of self-organization phenomena in active fractal systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any governing center and, thereby, their self-regulation is based on a cooperative interaction of all the elements. The paper develops a mathematical theory of a vascular network response to local effects on scales of individual units of peripheral circulation. First, it formulates a model for the self-processing of information about the cellular tissue state and cooperative interaction of blood vessels governing redistribution of blood flow over the vascular network. Mass conservation (conservation of blood flow as well as transported biochemical compounds) plays the key role in implementing these processes. The vascular network is considered to be of the tree form and the blood vessels are assumed to respond individually to an activator in blood flowing though them. Second, the constructed governing equations are analyzed numerically. It is shown that at the first approximation the blood perfusion rate depends locally on the activator concentration in the cellular tissue, which is due to t...Continue Reading

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