$In~Silico$ Electrical Modeling of Cell Aggregates

This article deals with two different approaches to model the cell aggregates submitted to an electric stimulation, namely, the equivalent circuit approach and the theoretical homogenization. For each approach, the effective impedance of the cell aggregate is given, enabling a comparison between the different models. Regarding the circuit approach, a variability in the electric parameters of the circuit in series is known to provide anomalous relaxation similar to a constant phase element model. For lognormal distribution of the parameters, a new link between the effective impedance and both arithmetic and geometric means is given. The second approach deals with the theoretical—but periodic—homogenization approach. The idea is to consider the sample as a periodic aggregate composed of a large number of cells. In each cell, the electric potential is governed by the electroquasi-static model. The formal two-scale analysis leads to the so-called bidomain model, enabling a novel definition of the tissue impedance, generalizing the Maxwell–Garnett formula to cells with any geometrical configuration and without any dilution assumption. Interestingly, the microscale cell organization is shown to affect the effective impedance of the sample, linking the cell and the tissue properties.