A Time-Dependent Numerical Model of Transmembrane Voltage Inducement and Electroporation of Irregularly Shaped Cells

Abstract

Abstract-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 (∆Ψ) and simulation of cell membrane electroporation. The model was first tested by comparing its results to the time-dependent analytical solution for ∆Ψ 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 ∆Ψ, the membrane conductivity rapidly increased with time, leading to a modified spatial distribution of ∆Ψ. We show that steady-state models are insufficient for accurate description of ∆Ψ, 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 ∆Ψ 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.

Comparison between direct and reverse electroporation of cells in situ: a simulation study

“…2006; Pucihar et al. 2009). The simulation result for this model was compared with the available analytical solution.…”

“…2006; Pucihar et al. 2009). Electric potential of intracellular and extracellular media was calculated using equation (A1).…”

“…2013)Cell membrane relative permittivity ε m 5(Pucihar et al. 2009)Cytoplasmic electric conductivity0.3 S m −1 (Pucihar et al. 2009; Towhidi and Miklavcic 2010; Rems et al.…”

“…2013)Cytoplasmic relative permittivity80(Pucihar et al. 2009)Nucleus radius4 × 10 −6  m(Rems et al. 2013)Nucleus membrane thickness10 × 10 −9  m(Rems et al.…”

Modeling electroporation of the non-treated and vacuum impregnated heterogeneous tissue of spinach leaves

“…The vertical sides of the model were modeled as electrically insulated. Mathematical equations describing electroporation of the cell membrane were taken from DeBruin and Krassowska (1999) and the method for calculating the induced transmembrane voltage was adopted from Pucihar, Miklavcic, and Kotnik (2009). Electric potential V was calculated by…”