title: Minimal model for tumor angiogenesis.
abstract: In this work, we show a mathematical model for the angiogenesis by endothelial cells. We present the model at the level of partial differential equations, describing the spatiotemporal evolution of the cell population, the extracellular matrix macromolecules, the proteases, the tumor angiogenic factors, and the possible presence of inhibitors. We mainly focus, however, on a complementary, more physiologically realistic, hybrid approach in which the cells are treated as individual particles. We examine the model numerically in two-dimensional settings, discussing its comparison with experimental results.
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: N
authors.initials: N
authors.lastname: Whitaker
authors.forename: D J
authors.initials: DJ
authors.lastname: Good
authors.forename: G J
authors.initials: GJ
authors.lastname: Herring
mesh_terms: D020533:Angiogenesis Inhibitors / Q000502:physiology; D042501:Angiogenic Proteins / Q000502:physiology; D000818:Animals; D042783:Endothelial Cells / Q000473:pathology; D004730:Endothelium, Vascular / Q000473:pathology; D016326:Extracellular Matrix Proteins / Q000502:physiology; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply*; D009389:Neovascularization, Pathologic / Q000188:drug therapy / Q000473:pathology*; D010447:Peptide Hydrolases / Q000502:physiology
chemical_list: D020533:Angiogenesis Inhibitors; D042501:Angiogenic Proteins; D016326:Extracellular Matrix Proteins; D010447:Peptide Hydrolases