MATHEMATICAL-MODELING, SIMULATION AND PREDICTION OF TUMOR-INDUCED ANGIOGENESIS

Angiogenesis, the formation of blood vessels from a pre-existing vascu lature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and dev elop, driven by endothelial cell migration and proliferation, and orga nise themselves into a dendritic structure. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of soli d tumours. In this paper we present a novel mathematical model which d escribes the formation of the capillary sprout network in response to chemical stimuli (tumour angiogenesis factors, TAF) supplied by a soli d tumour. The model also takes into account endothelial cell-extracell ular matrix interactions via the inclusion of fibronectin in the model . The model consists of a system of nonlinear partial differential equ ations describing the response in space and time of endothelial cells to the TAF and the fibronectin (migration, proliferation, anastomosis, branching). Using the discretized system of partial differential equa tions, we use a deterministic cellular automata (DCA) model. which ena bles us to track individual endothelial cells and incorporate branchin g explicity into the model. Numerical simulations are presented which are in very good qualitative agreement with experimental observations. Certain experiments are suggested which could be used to test the hyp otheses of the model and various extensions and developments of the mo del with particular applications to anti-angiogenesis strategies are d iscussed.