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Effective Conductivity of a Suspension of Permeabilized Cells: A Theoretical Analysis

Mojca Pavlin and Damijan Miklavi

University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia

Correspondence: Address reprint requests to Mojca Pavlin, M.Sc., University of Ljubljana, Faculty of Electrical Engineering, Traka 25, SI-1000 Ljubljana, Slovenia. Tel.: 386-1-476-8768; Fax: 386-1-426-4658; E-mail: mojca{at}svarun.fe.uni-lj.si.

During the electroporation cell membrane undergoes structural changes, which increase the membrane conductivity and consequently lead to a change in effective conductivity of a cell suspension. To correlate microscopic membrane changes to macroscopic changes in conductivity of a suspension, we analyzed the effective conductivity theoretically, using two different approaches: numerically, using the finite elements method; and analytically, by using the equivalence principle. We derived the equation, which connects membrane conductivity with effective conductivity of the cell suspension. The changes in effective conductivity were analyzed for different parameters: cell volume fraction, membrane and medium conductivity, critical transmembrane potential, and cell orientation. In our analysis we used a tensor form of the effective conductivity, thus taking into account the anisotropic nature of the cell electropermeabilization and rotation of the cells. To determine the effect of cell rotation, as questioned by some authors, the difference between conductivity of a cell suspension with normally distributed orientations and parallel orientation was also calculated, and determined to be <10%. The presented theory provides a theoretical basis for the analysis of measurements of the effective conductivity during electroporation.

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