Section: New Results

Cardiac Electrophysiology at the Microscopic Scale

We focused on establishing a microscopic model for cardiac electrophysiology simulations and proving the existence of a solution. We started with writing a mathematical proof allowing from well known physical equations and properties of the cardiac tissue to establish the model. Then, we worked on a variational formulation of the problem, and describing a weak solution of it. The idea is to compute energy estimates and to bound them so that we can extract a convergent sequence of functions in the appropriate Sobolev space. With my PhD advisor, we started to write an article about these two proofs. We also worked on CEPS code to implement some functionalities that will fit my requirements in a near future regarding the simulations we have to design. The main difficulty we identified is, provided we get a well defined geometry and mesh of cardiac cells, to implement the ionic flux between cells. First simulation of a simple "two-cells communication" problem will probably, if the results meet experimental observations, lead to another article. We also attended Imaged Based Biomedical Modelling 2015, a summer course organized by SCI institute (University of Utah), which was designed to give attendees guidelines about vizualisation and modelling, especially on cardio electrophysiology.