Nonlinear behaviors of capillary formation in a deterministic angiogenesis model

by Shuyu Suna, Mary F. Wheelera, Mandri Obeyesekereb, Charles Patrick Jr.b
Year: 2005

Bibliography

S. Sun, M. F. Wheeler, M. Obeyesekere and C. W. Patrick Jr., “Nonlinear behaviors of capillary formation in a deterministic angiogenesis model”, Nonlinear Analysis, 63(5-7), e2237-e2246, 2005.

Abstract

In this paper, we consider a deterministic approach for modeling angiogenesis. The model equations form a nonlinear coupled system of partial and ordinary differential equations. We propose an efficient, accurate and locally conservative numerical method to solve the nonlinear system. Computational results indicate that the model generates the overall dendritic structure and pattern of the capillary network morphologically similar to those observed in vivo. The influence of the capillary network and the growth factor distribution on each other and their interaction are investigated using numerical simulations.

Keywords

Angiogenesis Capillary network Growth factors