A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods

F.J. Vermolen, L.Y.D. Crapts, J.K. Ryan

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientificpeer-review

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.

Original languageEnglish
Title of host publicationNumerical Methods and Advanced Simulation in Biomechanics and Biological Processes
EditorsMiguel Cerrolaza, Sandra Shefelbine, Diego Garzón-Alvarado
PublisherElsevier
Pages95-115
Number of pages21
ISBN (Electronic)9780128117194
ISBN (Print)9780128117187
DOIs
Publication statusPublished - 2018

Keywords

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

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    Vermolen, F. J., Crapts, L. Y. D., & Ryan, J. K. (2018). A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin methods. In M. Cerrolaza, S. Shefelbine, & D. Garzón-Alvarado (Eds.), Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes (pp. 95-115). Elsevier. https://doi.org/10.1016/B978-0-12-811718-7.00006-X