Cardiac arrhythmias are irregularities in the normal rhythm of the heart, caused by anomalies in the electrical activity of the myocardium. Among the many ablation strategies used to isolate these pathologies, Pulsed electric Field Ablation (PFA) has emerged as a novel non-thermal technique, ensuring the precise targeting of the abnormal tissue and the preservation of the tissue scaffold. This work is aimed at proposing a mathematical model to study the long-term effects of PFA on the cardiac tissue, regarding two different pathologies: Atrial Fibrillation (AF) and Ventricular Tachycardia (VT). To describe the electrical activity of the heart we start from the bidomain model - a standard model describing the electrophysiology of the heart - and we modify it depending on the pathology of interest. In the context of AF, we introduce inside the ablated area a small parameter ε - proportional to the thickness of the region - that also rescales the intra-cellular conductivity. We analyze the static version of the modified bidomain system in the semi-linear context, and we perform a formal asymptotic analysis to determine the approximate transmission conditions at the interface between the ablated area and the healthy region, as ε approaches zero. The asymptotic expansion at any order is proven and numerically validated. We also propose numerical simulations in a dynamic context. By considering a synthetic geometry of a left atrium, we simulate the isolation of a pulmonary vein from which AF is supposed to trigger. Results are compared with another technique, radio-frequency ablation (RFA), known to burn cardiac tissue through heat transfer and then to destroy the tissue scaffold. Our objective is to numerically predict the success or failure of the two ablation procedures. Then, we validate our approaches in a real heart data, in the context of VT. The arrhythmia was induced in different sheep and then a PFA procedure was performed to treat the induced VT. Simulations are performed to reproduce VT in a sheep ventricle geometry. Simulations of PFA are compared with RFA to numerically predict the success or failure of the two ablation procedures. Numerical results are also validated through the activation endocardium map built before the PFA intervention. This work provides a first numerical study of the mathematical descriptions of PFA in both AF and VT context, opening perspectives towards clinical applications.