Evaluation of the Current in the Cell Membrane for Numerical Simulations of Electroporation

Abstract

This study presents a rigorous numerical analysis of the current in the cell membrane, subjected to a uniform electric field, and its impact in the pore formation. The numerical model considers a single cell composed of uniform membrane and cytoplasm, in a suspension medium. The current in the cell membrane is calculated using two different approaches. The first uses a lumped parameters approach based on the geometry of the pore, while the second describes the flow of ions through the pore considering the interaction with the pore walls as an energy barrier. The formation and growth of the pores is solved using an asymptotic approximation of the Smoluchowski’s equation. The electrical potential induced in the cell membrane, which is coupled with the current in the membrane, is resolved in spherical coordinates using the finite difference method. The two approaches have qualitatively similar results but significant quantitative differences in the number and radii of pores. The ionic flow approach has resulted in the formation of fewer pores and reduced pore growth. Approximately 38,000 fewer pores are created, a 21% difference, and the largest pores are approximately 8nm smaller, a 24% difference. Thus, this approach results in a less conductive membrane and smaller electroporated area.