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.
|Title of host publication||Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes|
|Editors||Miguel Cerrolaza, Sandra Shefelbine, Diego Garzón-Alvarado|
|ISBN (Print)||9780128117187, 9780128117194|
|Publication status||Published - 5 Oct 2017|