A time-dependent numerical model of transmembrane voltage inducement and electroporation of irregularly shaped cells

We describe a finite-element model of a realistic irregularly shaped biological cell in an external electric field that allows the calculation of time-dependent changes of the induced transmembrane voltage (Delta Psi) and simulation of cell membrane electroporation. The model was first tested by comparing its results to the time-dependent analytical solution for Delta Psi on a nonporated spherical cell, and a good agreement was obtained. To simulate electroporation, the model was extended by introducing a variable membrane conductivity. In the regions exposed to a sufficiently high Delta Psi, the membrane conductivity rapidly increased with time, leading to a modified spatial distribution of Delta Psi. We show that steady-state models are insufficient for accurate description of Delta Psi, as well as determination of electroporated regions of the membrane, and time-dependent models should be used instead. Our modeling approach also allows direct comparison of calculations and experiments. As an example, we show that calculated regions of electroporation correspond to the regions of molecular transport observed experimentally on the same cell from which the model was constructed. Both the time-dependent model of Delta Psi and the model of electroporation can be exploited further to study the behavior of more complicated cell systems, including those with cell-to-cell interactions.