Nonlinear Dispersive Cell Model for Microdosimetry of Nanosecond Pulsed Electric Fields

Abstract

For nanosecond pulsed electric fields (nsPEFs) based application, the underlying transmembrane potential (TMP) distribution of the plasma membrane is influenced by electroporation (EP) of the plasma membrane and dispersion (DP) of all cell compartments and is important for predicting the bioelectric effects. In this study, we analysed temporal and spatial distribution of TMP induced by nsPEFs of various durations (3 ns, 5 ns unipolar, 5 ns bipolar, and 10 ns) with the consideration of both DP and EP. Based on the double-shelled dielectric spherical cell model, we used second-order Debye equation to characterize the dielectric relaxation of plasma membrane and nuclear membrane in the frequency domain and transformed the Debye equation into the time domain with the introduction of polarization vector, then we obtained the time course of TMP by solving the combination of Laplace equation and time-domain Debye equation. Next, we used the asymptotic version of the smoluchowski equation to characterize electroporation of plasma membrane and added it to our model to achieve the temporal and spatial distribution of TMP and pore density. Much faster and more pronounced increased in TMP can be found with the consideration of dielectric relaxation of plasma membrane and nuclear membrane, and much larger electroporated area of at least half of the plasma membrane was obtained with the consideration of both DP and EP. Through the simulation it is clearer to understand the relationship.