The VT model: a deterministic model of angiogenesis and biofractals based on physiological rules

Abstract

A vascular tree (VT) model is developed that recreates vascular embryology and anatomy. It is a nonlinear deterministic process defined via topology and set theory. The accuracy of the model is due to its foundations in natural physiology. Real and VT angiogenesis are closed-loop control systems, with vessels growing reactively in response to inputs generated by tissue growth. This system creates efficient distribution networks. Critical mathematical features of real vessels, such as density and r-net concepts, are reproduced. VT structures, like real vessels, are fractal, and the VT model explains how a fractal anatomy can arise from a nonlinear physiology. It is argued that the VT model is a suitable analog of the circulation for bioengineering or physiological studies, and it may be a generalized model for the study of biofractals.<>