Is local metabolism the basis of the fractal vascular structure in the heart?

Abstract

The distribution of blood flow in the heart muscle is very heterogeneous and shows a self-similar fractal pattern, extending to small spatial scales. It is very likely that local oxygen consumption is more or less proportional to local blood flow and that local aerobic metabolism also is very heterogeneous. It is not yet clear whether local metabolism is heterogeneous in origin and the distribution of flow has secondarily adapted to metabolism, or, the other way around, whether flow is primarily heterogeneous because of the irregular structure of the coronary tree and flow has adapted to metabolism. Little is known yet about the developmental and adaptive mechanisms which bring about mutual adjustment between vascular growth and local metabolic demand, and genes and growth factors involved in shaping the structure of the coronary tree have only begun to be identified. Fractal and nonlinear dynamic mathematical models generate complex heterogeneous structures from simple nonlinear deterministic rules which are recursively applied. Such nonlinear models may thus help to explain the generation of large vascular trees regulated by synergy of a limited number of genes and signaling molecules. This may explain the relative regularity of space filling of the vascular tree and the asymmetry of branching and flow distribution in the tree.