A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes

Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods

Book chapter (2018)

Authors

F.J. Vermolen Numerical Analysis - EEMCS
L.Y.D. Crapts External organisation
J.K. Ryan University of East Anglia
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Chemotaxis Discontinuous Galerkin method Stem cells Fibrosis Myocardial infarction Snail trail model
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.