Distributed mechanism of living tissue self-regulation as a self-organization phenomenon in active fractal media

Abstract

The living tissue self-regulation is considered as an example of the general problem of adapting and self-sustaining of active fractal systems of biological, ecological, and social nature. A distinctive feature of such systems is the absence of a unified governing center. Their self-regulation is based on cooperative distributed interaction between all elements. A mathematical description of the response of the vascular network in individual organs to local effects is developed. A model for self-processing of information about the state of cellular tissue and cooperative interaction of blood vessels under distributed control of blood circulation in the vascular network is formulated. The law of conservation of, in particular, blood and transported chemical compounds at the nodes of the vascular network plays a key role in the description of these processes. The arterial and venous beds are assumed to be of the tree form. The vascular network behavior is described in terms of the individual response of blood vessels to the concentration of activator in blood flowing through them. The equations obtained are solved numerically. First, it is shown in the first approximation that the blood perfusion rate is a local function of the activator concentration in the cellular tissue, which is due to the hierarchical structure of the vascular network. Second, a fundamental difference is found between the threshold of individual vessel response to the concentration of activator in blood and the threshold response of the vascular network as a whole to the presence of activator in the cellular tissue. Third, it is shown that the blood perfusion rate can be essentially nonuniform in space. Fourth, the nonlocal dependence of perfusion rate on activator concentration is found to change its form with increasing activator concentration.