Numerical study of the electrical conductivity and polarization in a suspension of spherical cells

The Effective Conductivity and the Induced Transmembrane Potential in Dense Cell System Exposed to DC and AC Electric Fields

“…5. The numerically calculated decrease in the induced TMP is in agreement with other experimental [39] and numerical [24], [27] studies on dense cell systems.…”

“…This requires solving Laplace equation for a system of many interacting particles (cells) which, however, cannot be obtained analytically [18]- [20]. In the last few years, it was shown that numerical methods can be successfully applied to obtain the induced TMP in complex cell systems such as suspensions, aggregates, and tissue [21]- [27]. On the other hand, for calculation of the effective conductivity, it was shown by several studies [10], [18], [19], [28] that approximate effective medium theory (EMT) equations can be effectively used to interpret experimental data.…”

Improved numerical approach for electrical modeling of biological cell clusters

“…Pavlin et al [19] obtained by finite element modeling that a reduction of about 17% can occur with a volume fraction of 0.5 compared to the potential on the pole of a single cell. Similarly, Ramos et al [21] obtained by finite difference modeling that the potential on the pole of the cell decreases linearly with increasing volume fraction, showing a reduction of about 19% with p = 0.5. Thus, the threshold field to produce electroporation increases with increasing concentration of cells in suspension.…”

“…Secondary effects from ion channels and resting potential were not taken into account in this study, since this has been a common practice in other articles [10,20,21] because they have little effect on the potential and membrane conductance under intense applied fields. However, they could easily be included by modifying the conduction current term across the membrane as given by Eqs.…”

“…In the first step one can use traditional numerical methods such as finite elements or finite difference methods. These approaches have been used by some authors [9,18,21], but since they use discretization volume, they require a very large computational effort when using large number of cells. Furthermore, there is an additional problem in the fact that the cell membrane is extremely thin in relation to the cell radius, making it difficult to build a discretization mesh which allows a precise calculation of the electric field inside the membrane.…”