## Luis Bonilla (09/07/15)

Math Colloquium

### Speaker: Luis L. Bonilla, Universidad Carlos III de Madrid

Title: Hybrid modeling of tumor induced angiogenesis

Location: VR-II, 158.

Time: Thursday, July 9, at 13:30-14:30.

### Abstract:

Angiogenesis is the formation of blood vessels induced by a deficit of oxygen in tissues. It is a basic process in wound repair, formation of vessel networks during growth. diseases of inflammatory character, cancer, etc. 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 elds. To reduce this complexity, we take advantage of the system intrinsic multiscale structure: we describe the stochastic cell dynamics at their natural microscale, whereas we describe the deterministic dynamics of the underlying fields at a larger macroscale. We set up a conceptual stochastic model including branching, elongation, and anastomosis of vessels and derive a mean eld approximation for their densities. This leads to a deterministic integro-partial differential system that describes the formation of the stochastic vessel network. We discuss the proper capillary injecting boundary conditions and the results of relevant numerical simulations.