Modelling Blood Vessels: A Deterministic Method With Fractal Structure Based On Physiological Rules

A model which recreates the normal process of blood vessel formation has been developed. The model is a deterministic iterative process derived from biological rules of angiogenesis: as tissues grow, cells which exceed a critical distance from existing blood vessels force the spawning of new vessels from those nearby. The resulting vascular trees (VT) closely approximate real vascular patterns. Features of real vessels, such as branching patterns, watersheds and territories, collaterals and anastamoses, and a distinction between central and peripheral organization are recapitulated. Mathematically, the structures are fractal. Other fractal trees used to model the circulation are simple geometric constructs. Unlike these, the VT model uses a natural set of rules to create networks which are topologically correct. This model can be used whenever an accurate equivalent of the circulation is needed for bioengineering and physiological studies.