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 language | English |
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Title of host publication | Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes |
Editors | Miguel Cerrolaza, Sandra Shefelbine, Diego Garzón-Alvarado |
Publisher | Elsevier |
Pages | 95-115 |
Number of pages | 21 |
ISBN (Electronic) | 9780128117194 |
ISBN (Print) | 9780128117187 |
DOIs | |
Publication status | Published - 2018 |
Bibliographical note
Chapter 6Keywords
- Chemotaxis
- Discontinuous Galerkin method
- Fibrosis
- Myocardial infarction
- Snail trail model
- Stem cells