Asymptotic Analysis of the Static Bidomain Model for Pulsed Field Cardiac Ablation
Résumé
Cardiac arrhythmias are caused by faulty electrical signals in the heart, which lead to chaotic wave propagation and impaired cardiac function. This work focuses on a non‐thermal ablation technique based on electroporation (EP), a promising method for treating arrhythmias, called pulsed field ablation (PFA). Assuming that the thickness of the electroporated region is small compared to the whole domain and that the intracellular conductivity within the EP region scales with a factor proportional to the square of the thickness parameter, we derive an electrophysiological model of a cardiac domain containing a region ablated by PFA. We then provide a formal asymptotic analysis at any order by considering an asymptotic expansion of the intracellular and extracellular potentials both outside and inside the EP domain in a static nonlinear context. This allows us to derive transmission conditions at the interface at any order. Moreover, we give a proof of the asymptotic expansion by deriving estimates of the H 1 ‐ and L 2 ‐norms of the errors of an expansion with a given number of terms. The asymptotic expansion has been validated by numerical convergence tests.
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