A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes

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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)

Author(s)

F.J. Vermolen (TU Delft - Electrical Engineering, Mathematics and Computer Science)

L.Y.D. Crapts (External organisation)

J.K. Ryan (University of East Anglia)

Research Group

Numerical Analysis

Chemotaxis Discontinuous Galerkin method Stem cells Fibrosis Myocardial infarction Snail trail model

DOI related publication

https://doi.org/10.1016/B978-0-12-811718-7.00006-X Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:9dad54b3-64a9-4f66-83ea-327e2b6a39ea

More Info

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Publication Year

2018

Language

English

Research Group

Numerical Analysis

Bibliographical Note

Chapter 6

Pages (from-to)

95-115

Publisher

Elsevier

ISBN (print)

9780128117187

ISBN (electronic)

9780128117194

Downloads counter

140

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.