Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis

摘要: Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The then grow and develop, driven initially by endothelial-cell migration, organize themselves into dendritic structure. Subsequent cell proliferation near sprout tip permits further extension ultimately completes process. Angiogenesis occurs during embryogenesis, wound healing, arthritis growth solid tumors. In this paper we present both continuous discrete mathematical models which describe network stimuli (tumor angiogenic factors, TAF) tumor. also take account essential endothelial cell-extracellular matrix interactions via inclusion macromolecule fibronectin. model consists system nonlinear partial differential equations describing initial migratory cells TAF Numerical simulations system, using parameter values based on experimental data, presented compared qualitatively with vivo experiments. We use discretized form develop biased random-walk enables us track individual at tips incorporate anastomosis, mitosis branching explicitly model. theoretical networks generated computer morphology observed