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 language | English |
|---|---|
| Title of host publication | Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes |
| Editors | Miguel Cerrolaza, Sandra Shefelbine, Diego Garzón-Alvarado |
| Publisher | Academic Press |
| Chapter | 6 |
| Pages | 95-115 |
| Number of pages | 21 |
| Edition | 1 |
| ISBN (Print) | 9780128117187, 9780128117194 |
| Publication status | Published - 5 Oct 2017 |