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 integro-partial 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.

arXiv comment12 pages, 5 figures

References in corpus (2)

• On the approximation of mean densities of random closed sets
• Self-sustained current oscillations in the kinetic theory of semiconductor superlattices

Cited by in corpus (8)

• Stochastic Model of Tumor-induced Angiogenesis: Ensemble Averages and Deterministic Equations
• Soliton-like attractor for blood vessel tip density in angiogenesis
• Constructing solutions for a kinetic model of angiogenesis in annular domains
• Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis
• Well posedness of an angiogenesis related integrodifferential diffusion model
• Two dimensional soliton in tumor induced angiogenesis
• Soliton approximation in continuum models of leader-follower behavior
• Integrodifference master equation describing actively growing blood vessels in angiogenesis