ED Mathématiques et Informatique
Multiscale mathematical modeling of pulsed field cardiac ablation
by Simon BIHOREAU (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 10h00 - Salle de Conférences Institut de Mathématiques de Bordeaux IMB, Bâtiment A33, 33400 Talence
in front of the jury composed of
- Michael LEGUEBE - Chargé de recherche - Université de Bordeaux - Directeur de these
- François ALOUGES - Professeur des universités - ENS Paris-Saclay - Rapporteur
- Luca GERARDO-GIORDA - Professeur des universités - Johannes Kepler University - Rapporteur
- Céline GRANDMONT - Directrice de recherche - Inria Paris - Examinateur
- Lisl WEYNANS - Professeure des universités - Université de Bordeaux - Examinateur
- Annabelle COLLIN - Professeure des universités - Nantes Université - CoDirecteur de these
Cardiac ablation is a key procedure in the treatment of arrythmias, one of the leading causes of death worldwide. The goal is to kill cardiac cells in a small targeted pathological area using a catheter inserted into the heart chambers. For decades, radiofrequency ablation (RFA), based on thermal injury, has been the clinical standard. However, in recent years, a new method of ablation — already established in tumor ablation — has emerged. This technique relies on irreversible electroporation, a micro-biological phenomenon in which the cell membrane is disrupted under the influence of a strong electric field, leading to cellular death. Modeling this technique, known as PFA (Pulsed Field Ablation), is crucial for understanding how the microscopic effect of electroporation translates to the macroscopic - or tissue - scale and for providing better guidance to clinicians during procedures. In tumor ablation, the macroscopic electroporation effect is often modeled using a simple Poisson equation with a nonlinear conductivity. However, we believe that a more physiologically accurate model can be derived and may offer deeper insights, particularly for cardiac tissue, which exhibits strong heterogeneity and anisotropy. In this PhD thesis, we perform the periodic homogenization of a nonlinear bidomain microscopic model, in which electroporation is represented as a nonlinear increase in cell-membrane conductance relative to the transmembrane voltage - the difference between intra- and extracellular electric potentials. The full two-scale expansion is derived and rigorously justified under periodic boundary conditions. Based on the first two terms (orders 0 and 1) of the two-scale expansion, we propose a practical macroscopic model, along with meaningful macroscopic quantities for identifying the effectively ablated region, including an effective membrane conductance. The model is numerically implemented using FreeFem++, a finite element library. We numerically explore the link between microscopic and macroscopic quantities — mainly expressed through a nonlinear algebraic equation — which leads us to propose a computational acceleration of the model. Moreover, a basic sensitivity analysis is performed on the model parameters, including the shape of the nonlinearity and the geometry of cells - defining the fiber orientation. Finally, we apply the proposed model to clinically relevant scenarios. We first compare the simulated lesions shape with experimental data, revealing the importance of fiber direction within cardiac tissue and of pulse repetition. Concerning the last point, we propose a modification of our model - consistent with the homogenization it is derived from - to account for tissue conductivity memory effect between repeated pulses. We then apply our model to experimental data obtained through our collaboration with IHU Liryc, where ventricular tachycardia was induced and treated using PFA in different sheep. Numerical simulations provide insight into the occurrence of lethal atrioventricular blocks observed during the experiments, suggesting that clinical intuition developed for RFA may not directly translate to PFA in highly heterogeneous cardiac regions. Finally, we propose a complete numerical workflow to compare model predictions with experimental lesions reconstructed in realistic cardiac geometries, and we present a first qualitative comparison.