Illustrative example of my research: Cardiac Ablation by Electroporation

Context & objective

  • Isolation of reentry areas at the origin of atrial fibrillation by destroying small areas of the heart
  • Novel non-thermal ablation technique: Pulsed electric Field Ablation (PFA) which takes advantage of irreversible electroporation
  • In the context of atrial fibrillation, explain the higher recurrence rate after radiofrequency ablation (RFA) compared to PFA

    • Strategy & Modeling

  • Strategy: Build a cardiac electrophysiological model of a cardiac domain containing a region ablated by PFA (& by RFA) and make numerical comparisons.
  • We start from the bidomain model and we make modeling hypothesis inside the ablated region
  • It leads to the introduction of a small parameter

    • Mathematical Analysis

  • Existence & Uniqueness: under conditions on the ionic term
  • Asymptotic Analysis: Ansatz, Problem at order p (inside and outside the membrane), Convergence proof with convergence order

    • Numerical Simulation

  • Numerical resolution: Finite Element Method, BDF 2, FreeFEM++
  • Non-overlapping Schwarz-type algorithm: Penalty parameter chosen very carefully through a mathematical study
  • Mesh, fibers and codes are available here: https://gitlab.inria.fr/snatipol/af-pfa-rfa
  • Kedem–Katchalsky transmission condition for RFA with different values of the permeability coefficient

    • Corresponding articles

  • S. Nati Poltri, G. Caluori, P. Jaïs, A. Collin, C. Poignard. Electrocardiology modeling after catheter ablations for atrial fibrillation. Proc. of FIMH, 2023.
  • A. Collin, S. Nati Poltri, C. Poignard. Electrocardiology modeling after pulsed field ablation relying on asymptotic analysis, 2024 (to submit).

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