A discontinuous Galerkin model for the simulation of chemotaxis processes: application to stem cell injection after a myocardial infarction

Fred Vermolen, Linda Crapts, Jennifer Ryan

Research output: Chapter in Book/Report/Conference proceedingChapter

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-. This growth factor attracts the endothelial cells that migrate towards the stem cells as a result of chemotaxis. The description of the formation of a vascular network is characterised 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. The paper presents a Discontinuous Galerkin method on quadrilateral meshes to solve the system of partial differential equations in two spatial dimensions.
Original languageEnglish
Title of host publicationNumerical Methods and Advanced Simulation in Biomechanics and Biological Processes
EditorsMiguel Cerrolaza, Sandra Shefelbine, Diego Garzón-Alvarado
PublisherAcademic Press
Pages95-115
Edition1
ISBN (Print)9780128117187, 9780128117194
Publication statusPublished - 5 Oct 2017

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