Modeling and numerical simulations of irreversible electroporation for cardiac ablation  (Annabelle Collin)

In healthy hearts, the propagation of electrical waves follows a predictable pattern, whereas in people suffering from arrhythmia, the electrical waves can become chaotic and affect the heart's pumping function. The main treatment is catheter ablation, during which small areas of heart tissue are destroyed to isolate the cause of the irregular heartbeats. Most catheter ablations are performed thermally through the application of a radiofrequency electromagnetic field (RFA), but in this work, we focus on the study of a non-thermal ablation technique: pulsed electric field ablation (PFA), which utilizes irreversible electroporation, a complex cell death phenomenon that occurs when biological tissue is exposed to very intense electrical pulses. This technique has been used in oncology for more than a decade, but in cardiology it is still in its infancy due to the technical complexity of this novel approach. Mathematical models and numerical strategies could improve the understanding of PFA on the cardiac signal. In this talk, I will introduce the various mathematical challenges that we would like to address. Second, I will present a bidomain model incorporating a nonlinear transport term derived thanks to a two-scale approach that can account for the different time and length scales between cardiac electrophysiology and electroporation. Numerical simulations with industrial catheter geometries will also be presented, showing first interesting results for the determination of the electroporated area. Third, I will present a cardiac electrophysiological model of a cardiac domain containing a region ablated by PFA. Considering modeling assumptions and performing a rigorous asymptotic analysis, we determine the transmission conditions at the interface between the two regions. Numerical simulations performed thanks to well-designed Schwarz algorithms will be presented in the context of atrial fibrillation. A numerical comparison between PFA and RFA will allow to propose a numerical explanation for the higher rate of fibrillation recurrence after RFA compared to PFA