Electroporation Modelling of Irregular Nucleated Cells Including Pore Radius Dynamics

When high-amplitude, short-duration electric pulses are applied to cells the permeability of their membranes is increased. From the biological point of view, the phenomenon is quite well understood, however, it is important to develop accurate numerical models to investigate the electroporation effectiveness in terms of electrical, geometrical and physical parameters. To this aim, in this paper, we illustrate a spatio-temporal, non-linear, and dispersive multiphysics approach to study the electroporation in irregularly nucleated shaped cells. The model couples the Maxwell equations with the partial differential equation describing the creation and closure of pores as well as the evolution of the pore size. The dispersive properties of biological media and the irregular geometries of the membranes have been described using the multi-relaxation Debye-based relationship and the Gielis superformula, respectively. Numerical simulations highlight the importance to include in the model the spatial and temporal evolution of the pore radius. In fact, the obtained numerical results show significant discrepancies between our model and the one in which the pore radius dynamics is negligible.