title: Hybrid modeling of tumor-induced angiogenesis.
abstract: When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the family of interacting underlying fields. To reduce this complexity, we take advantage of the system intrinsic multiscale structure: we describe the stochastic dynamics of the cells at the vessel tip at their natural mesoscale, whereas we describe the deterministic dynamics of the underlying fields at a larger macroscale. Here, we set up a conceptual stochastic model including branching, elongation, and anastomosis of vessels and derive a mean field approximation for their densities. This leads to a deterministic integropartial differential system that describes the formation of the stochastic vessel network. We discuss the proper capillary injecting boundary conditions and include the results of relevant numerical simulations.
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
authors.affiliation: G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain and 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: M
authors.initials: M
authors.lastname: Alvaro
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
mesh_terms: D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply*; D009389:Neovascularization, Pathologic