Non-linear time domain model of electropermeabilization: Response of a single cell to an arbitrary applied electric field

Background: Electroporation is now a common tool in biotechnology and is used in a number of medical treatments. Until recently, the development of theoretical models of electroporation has lagged behind the experimental research. In order to optimize the efficiency of electroporation, it is important to consider as many biological and physical aspects as possible and it is a necessity that a variety of electric pulse parameters be tried. Thus a comprehensive model which can predict electropermeabilization as a result of any form of applied electric field and other important electroporation parameters is necessary. Results: A numerical model for a single cell electroporated by application of arbitrary external electric field pulses has been developed. The model is used to compare the transmembrane potential Vm, and pore density N, developed in response to the pulses. Vm and N are calculated via a piece-wise step response method that enables solutions to be obtained for any practical applied electric field waveform. Pore density is shown to increase so long as a threshold Vm is maintained by the electric field, and effectively clamps Vm to just over 1 V while N is increasing. Short unipolar pulses are also shown to create asymmetrical N between the two cell polar regions, whereas bipolar pulses result in a symmetrical N. Conclusions: The model presented here helps predict dynamic non-linear results of electropermeabilization, given any form of applied electric field and other important electroporation system parameters. This model can be used as a tool for the determination of starting parameters in biological applications.