Improved numerical approach for electrical modeling of biological cell clusters

Abstract

This article presents an efficient numerical approach to simulate the process of polarization and ion conduction in membranes of biological cells subjected to intense electric fields. The proposed method uses Coulomb's law to calculate the electric field on the surface of the cell membrane and the continuity equation for calculating the difference in electric potential between the faces of the membrane. The behavior of the membrane conductance is described by a model of electroporation proposed in literature. This method provides results that agree well with the analytical model of polarization of an isolated cell suspended in electrolytic solution and also provides results for the conductance of the membrane during electroporation of cells in concentrated suspensions that agree with experimental results already published.

A Microdosimetric Study of Electropulsation on Multiple Realistically Shaped Cells: Effect of Neighbours

“…A second important consideration is that when in vitro, or even in vivo experiments are carried out, the presence of multiple cells cannot be disregarded; some studies show the importance of considering models with cluster of cells (Susil et al 1998;Esser et al 2007Esser et al , 2009Weaver 2003, 2006;Joshi et al 2008;Kotnik et al 2010;Mezeme et al 2012;Pavlin et al 2002;Pucihar et al 2007;Ramos 2010;Gowrishankar et al 2013;Towhidi et al 2008). The TMP in a cell suspension depends on the cell density (Susil et al 1998;Pavlin et al 2002;Pucihar et al 2007;Mezeme et al 2012) and organisation (Susil et al 1998;Pavlin et al 2002).…”

Sinusoidal Signal Analysis of Electroporation in Biological Cells

“…The models are usually developed for isolated spherical or spheroidal cells using proposed membrane conductance distributions [1], [20] and are obtained from the static solution to Laplace's equation using the simplest possible structure of a cell with a nonconductive thin membrane filled internally by a homogeneous medium. More complex situations in which the interaction between cells is not neglected or in which the membrane conductance is calculated based on dynamic models of electroporation can be solved by numerical methods [21], [22]. The methods already proposed [23]- [25], however, do not offer direct mathematical expressions to calculate the membrane conductance as a function of measurable parameters of the process.…”

Electroporation of Kluyveromyces marxianus and -D-galactosidase Extraction

“…The pulse length has increasing influence on membrane conductance as the applied field increases, but shows saturation for field of 400 kV/m and time length higher than 2 ms. The proposed models of pore creation in electroporation are based on the Boltzmann statistical distribution that depends on the energy stored in the pores of the membrane (Glaser et al, 1988;Krassowska & Neu, 1999;Ramos, 2010). So these models have terms that depend exponentially on the squared transmembrane potential.…”

“…Models are developed for isolated spherical or spheroidal cells using proposed membrane conductance distributions (Kinosita & Tsong, 1979;Pavlin & Miklavcic, 2003) and are obtained from the static solution to Laplace's equation using the simplest possible structure of a cell with a nonconductive thin membrane filled internally by a homogeneous medium. More complex situations in which the interaction between cells is not neglected or when the membrane conductance is calculated based on dynamic models of electroporation can be solved by numerical methods (Neu & Krassowska, 1999;Ramos et al, 2004;Ramos, 2010).…”