Modeling postshock evolution of large electropores

The Smoluchowski equation (SE), which describes the evolution of pores created by electric shocks, cannot be applied to modeling large and long-lived pores for two reasons: (1) it does not predict pores of radius above 20 nm without also predicting membrane rupture; (2) it does not predict postshock growth of pores. This study proposes a model in which pores are coupled by membrane tension, resulting in a nonlinear generalization of SE. The predictions of the model are explored using examples of homogeneous (all pore radii r are equal) and heterogeneous $(0\mathrm{}<~r<~r_{\max })$ distributions of pores. Pores in a homogeneous population either shrink to zero or assume a stable radius corresponding to the minimum of the bilayer energy. For a heterogeneous population, such a stable radius does not exist. All pores, except $r_{\max },$ shrink to zero and $r_{\max }$ grows to infinity. However, the unbounded growth of $r_{\max }$ is not physical because the number of pores per cell decreases in time and the continuum model loses validity. When the continuum formulation is replaced by the discrete one, the model predicts the coarsening process: all pores, except $r_{\max },$ shrink to zero and $r_{\max }$ assumes a stable radius. Thus, the model with tension-coupled pores does not predict membrane rupture and the predicted postshock growth of pores is consistent with experimental evidence.