Non-linear time domain model of electropermeabilization: Effect of extracellular conductivity and applied electric field parameters

Abstract

This paper describes simulation results obtained from a previously reported numerical model for a single cell exposed to an arbitrary waveform electric field pulse. This paper concentrates on how the efficiency of electroporation related applications can be significantly improved by appropriately adjusting the parameters of applied electric field and conductivity of the external medium, σe. Emphasis is given here on the normalization of the degree of electroporation for a range of cell radii. The simulated results indicate that it may be difficult for cells of substantially different sizes to be close to uniformly electroporated if surrounded by media with a conductivity higher than around 5*10⁻³ S/m for 100 kHz bipolar pulses, or 0.2 S/m for 1 MHz bipolar pulses. To achieve as normalized as possible electroporation for the radii/size variation required in any particular application, using a lower σe would be preferable. There is, however, a limit to how low the external conductivity can be made, as the applied electric field amplitude must stay within practical limits. Considering 3*10¹³ pores/m² as a nominal pore density N for approximately optimum electroporation, σe could be as low as 0.08 S/m for a 7.5 µm cell radius with a peak electric field of 1.2*10⁵V/m (depending on the pulse shape and frequency). For a 15 µm cell radius, σe could be as low as 0.05 S/m (depending on the pulse shape and frequency). It is seen that the relative difference of N between the two cell sizes investigated is consistently lower for a bipolar sine wave electric field compared to a bipolar square wave electric field, even though the square wave electric field peak amplitude is always lower for an equivalent N.