Modeling an angiogenesis treatment after a myocardial infarction

Abstract

A serious complication that patients face after a heart attack is the formation of scar tissue at the damaged part of the heart. This scar leads to stiffening of the damaging region, and thereby it requires more perfomance of the heart muscle, which leads to fatigue and hence to failure and thereby causing immediate death of the patient. To circumvent scar tissue formation, stem cells are injected which trigger the angiogenetic response, leading to fewer invading fibroblast which produce scar tissue in the form of an excess on extra cellular matrix. The goal of this research is to learn more about the number of stem cells that has to be injected into the wound of the heart after a heart attack, aiming to avoid the formation of scar tissue. We develope a model for angiogenesis under the injection of stem cells onto the damaged part of the heart after an infarction. The model is based on reaction-transport equations with a certain degree of hyperbolicity due to chemotaxis as an important mechanism for cell migration. Using the method of characteristics, we will be able to quickly estimate the efficiency of treatment with respect to biological parameters like the number of stem cells injected. The method, which is based on a “snail trail” formalism, was originally set up in one dimension. One of the challenges in this research is to construct a more-dimensional counterpart of the equations. Furthermore, we implemente finite element and discontinuous Galerkin techniques to solve the system of partial differential equations.