Estudo numérico sobre o fenômeno de eletroporação em células isoladas

Abstract

A cell subjected to sufficiently intense electric fields of short duration displays the formation of pores, transient aqueous pathways, in its membrane. The phenomenon can be reversible, with the closure of the pores, or irreversible resulting in cell death. Both versions of the phenomenon have various applications in medicine and biology. The main goals of this thesis are to study and compare different approaches for the calculation of the electroporation current through a numeric model of electroporation in single cells subjected to microssecond electric pulses. Three main results are planned for each approach: the number of pores, the pore radii, and the transmembrane potential difference, including their respective spatial distributions and time evolutions. From a review of the literature the main equations that describe the phenomeon were determined, i.e. the Smoluchowski equation that calculates the pore density and the Laplace equation that describes the electric potential. A complete bidimensional numeric simulation model for the cell electroporation was implemented, based in an asymptotic aproximation of the Smoluchowski equation for the calculation of the number of pores and their radii and a finite difference aproximation for the Laplace equation for the potential calculation. It is assumed that the cell is spheric, with an uniform membrane and the relevant media - external medium, cytoplasm and cell membrane - homogenous. The cell is assumed isolated and subjected to an electric pulse between two paralel plates. From those assumptions and the known characteristics of the phenomenon, aproximations for the relevant equations were developed in order to simplify their numerical implementation. Due to the simplicity of the geometry the finite differences in time domain method was chosen as it allows easy modeling of the temporal characteristics of the problem. Finite difference aproximations of the equations were developed and solved for the coupled system. This simulation was validated with results qualitatively and quantitatively consistent with the literature. Using this simulation the electroporation current modeling was studied, comparing two models broadly used in literature and analysing the possible impact in applications. Meaningful differences in the results were found, and the ion flux model is recommended, specially for short simulations in which the pores do not grow to large sizes.