title: Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations.
abstract: A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing one to extract a deterministic integro-partial-differential description of the vessel tip density [Phys. Rev. E 90, 062716 (2014)]. Here we solve the stochastic model, show that ensemble averages over many realizations correspond to the deterministic equations, and fit the anastomosis rate coefficient so that the total number of vessel tips evolves similarly in the deterministic and ensemble-averaged stochastic descriptions.
authors.affiliation: G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
authors.forename: F
authors.initials: F
authors.lastname: Terragni
authors.affiliation: G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Carretero
authors.affiliation: ADAMSS, Universitá degli Studi di Milano, 20133 Milano, Italy.
authors.forename: V
authors.initials: V
authors.lastname: Capasso
authors.affiliation: G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
authors.forename: L L
authors.initials: LL
authors.lastname: Bonilla
mesh_terms: D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply*; D009389:Neovascularization, Pathologic; D013269:Stochastic Processes