Distributed self-regulation of living tissue. Effects of nonideality

TL;DR

This paper develops a mathematical model of vascular self-regulation in living tissue, highlighting how blood flow redistribution responds to local tissue effects through cooperative vessel interactions and hierarchical network structure.

Contribution

It introduces a novel mathematical framework for understanding self-regulation in vascular networks, emphasizing the role of nonlocal effects and hierarchical organization.

Findings

Blood perfusion rate depends locally on activator concentration.

Distinction between vessel-level and network-level reaction thresholds.

Nonlocal dependence of blood flow on activator concentration changes with levels.

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 the hierarchical structure of the vascular network. Then the distinction between the reaction threshold of individual vessels and that of the vascular network as a whole is demonstrated. In addition, the nonlocal component of the dependence of the blood perfusion rate on the activator concentration is found to change its form as the activator concentration increases.