A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes

Abstract

We present a mathematical formalism for the simulation of angiogenesis treatment in the heart after a myocardial infarction. The formalism treats the injection of stem cells at the surface of the heart, which then, release growth factor TG-β. This growth factor attracts the endothelial cells that migrate toward the stem cells as a result of chemotaxis. The description of the formation of a vascular network is characterized by taking into account the vessel tips as well as their sprouts. The method is based on a Keller-Segel formalism for chemotaxis for the vessel tips, combined with a "snail trail" mechanism to simulate the migration of the sprouts. This chapter presents a discontinuous Galerkin method on quadrilateral meshes to solve the system of partial differential equations in two spatial dimensions.