Modeling of Irreversible Electroporation for Ventricular Tachycardia – MIRE4VTach

For people with ventricular tachycardia, the electrical wave traveling through the heart is chaotic and this affects the heart's pumping function. One of the major treatments of this arrhythmia is catheter ablation which consists in destroying small areas of heart tissue to isolate or destroy the cause of the rapid and irregular heartbeats. In this project, we focus on the study of a novel and non-thermal ablation technique: irreversible electroporation ablation occuring when biological tissues are subjected to very intense electric pulses. Despite very encouraging results, some difficulties still occur to use this approach in the clinical routine due to its technical complexity. The objective of this project is to provide new mathematical models of electroporation ablation for ventricular tachycardia and numerical criteria for treatment assessment from clinical data. Motivated by deep clinical applications, MIRE4VTach addresses several mathematical challenges in both PDE and numerical methods areas. Specifically, a well-designed and rigorous asymptotic analysis will be set up to describe the transmission of molecules across the cell membrane in order to model the phenomenon at the cell scale. Another theoretical challenge resides in the development of data assimilation strategies allowing to integrate very numerous measurements as medical images or signal data. This mathematical point is fundametal to compute the distribution of the electric field for a given patient. And last but not least, the homogenization of a microscopic problem - in order to derive a electrophysiological model at the tissue scale after the electroporation process - is also a hard task for a rigorous convergence result.