Finite Element evaluation of the electric field distribution in a cell-aggregates

Electroporation of cells is obtained by applying pulsed electric fields generated by a sequence of voltage pulses. In the past, the influence of the electrical characteristics of the medium and cell density was studied experimentally and with Finite Element simulation. In particular, the simulation of inhomogeneities in terms of electric conductivity in the treatment area showed that the electric field dis- tribution around the cells is modified with respect to the use of a homogeneous media. Moreover, cell aggregation evidenced a local modification of the electric field and transmembrane potential. In par- ticular, accurate simulations of the extracellular en- vironment have been demonstrated to predict more accurately the electric field around the cell mem- brane. Moreover, the electric field distribution is correlated also to cell permeabilization. This paper evaluates numerically the electroporation of cells considering aggregates of 9 or 25 cells. The cells are modelized as circles, with a given diameter, surrounded by a membrane with a thickness of 7 nm. The electroporation effect was simulated mod- elling the membrane layer with the Smoluchowski equation that estimates the number of pores as a function of the electric field intensity. The 2D geometry of the Finite Element Model in- cludes a square with a side of 1 mm where the circles that represent the cells are in the center of this area. The time varying electric field is applied by a rectangular voltage to two parallel faces that represent the electrodes. The pulse is 100 μs long and it is characterized by a 10 μs rise/fall time. The amplitude of the voltage is set to 100 V that is equi- valent to 1000 V/cm in the center of the pulse in homogeneous conditions. A conduction problem and an electromagnetic time transient problem was solved using COMSOL software. By using the numerical model, it is possible to es- timate the intensity of the electric field and trans- membrane potential in the examined region with cells. The effect of cell aggregates on electric field distribution and transmembrane potential values is compared to the effect obtained in the case of a single cell. Moreover, the transmembrane potential and electric field distribution with and without the Smoluchowski equation in cell membrane is evalu- ated. Simulation results will be validated with a set of experiments with cells in adhesion.