Ablation, percolation, and afterdepolarization.

Ablation is an effective treatment for cardiac arrhythmias, and its primary goal is to remove excitability from cells to break pathological reentrant circuits or focal activities and thereby prevent recurrent arrhythmias. Ablation prevents excitation by destroying cells in targeted regions. However, if ablation does not eliminate sufficient cells, waves of action potentials (APs) may continue to propagate, and ablation may fail to suppress arrhythmias. In this study, we develop a theoretical approach that predicts the minimum number of ablated cells to break reentrant circuits and suppress the initiation and propagation of focal activities. Ablation creates a mixture of excitable and nonexcitable cells. As the fraction of excitable cells increases, the probability of AP wave propagation increases, since an AP can only propagate when an excitable cell excites another excitable cell. When this fraction exceeds the "percolation threshold," as defined in percolation theory, AP waves always propagate successfully, regardless of the size of the ablated area. Therefore, for reentrant arrhythmias, the fraction of excitable cells in the ablation area must be below the percolation threshold to block AP waves. For focal arrhythmias, delayed afterdepolarizations (DADs) can trigger premature ventricular contractions (PVCs) when DADs overcome the source-sink mismatch. Ablation of excitable cells also reduces the functional electrical sink, making it easier to initiate triggered activities. However, if the fraction of excitable cells in the ablation area is below the percolation threshold, triggered activities also cannot propagate. On the other hand, when the fraction of excitable cells is high, even though AP waves can propagate more easily, the initiation of PVCs becomes more difficult due to the source-sink mismatch. The propensity for PVCs reaches its maximum at the percolation threshold. These scenarios can also apply to other pathological conditions, such as myocardial ischemia and infarction, where excitable myocytes are interspersed with nonexcitable tissue.