Nonlinear dispersive cell model for microdosimetry of nanosecond pulsed electric fields

For applications based on nanosecond pulsed electric fields (nsPEFs), the underlying transmembrane potential (TMP) distribution on the plasma membrane is influenced by electroporation (EP) of the plasma membrane and dielectric dispersion (DP) of all cell compartments which is important for predicting the bioelectric effects. In this study, the temporal and spatial distribution of TMP on the plasma membrane induced by nsPEFs of various pulse durations (3 ns, 5 ns unipolar, 5 ns bipolar, and 10 ns) is investigated with the inclusion of both DP and EP. Based on the double-shelled dielectric spherical cell model, the Debye equation describing DP is transformed into the time-domain form with the introduction of polarization vector, and then we obtain the time course of TMP by solving the combination of Laplace equation and time-domain Debye equation. Next, the asymptotic version of the Smoluchowski equation is included to characterize the EP of plasma membrane in order to observe more profound electroporation effects with larger pore density and electroporated areas in consideration of both DP and EP. Through the simulation, it is clearer to understand the relationship between the applied nsPEFs and the induced bioelectric effects.