A parallel Voronoi-based approach for mesoscale simulations of cell aggregate electropermeabilization

Abstract

We introduce a numerical framework that enables unprecedented direct numerical studies of the electropermeabilization effects of a cell aggregate at the meso-scale. Our simulations qualitatively replicate the shadowing effect observed in experiments and reproduce the time evolution of the impedance of the cell sample in agreement with the trends observed in experiments. This approach sets the scene for performing homogenization studies for understanding the effect of tissue environment on the efficiency of electropermeabilization. We employ a forest of Octree grids along with a Voronoi mesh in a parallel environment that exhibits excellent scalability. We exploit the electric interactions between the cells through a nonlinear phenomenological model that is generalized to account for the permeability of the cell membranes. We use the Voronoi Interface Method (VIM) to accurately capture the sharp jump in the electric potential on the cell boundaries. The case study simulation covers a volume of (1 mm) 3 with more than 27, 000 well-resolved cells with a heterogeneous mix of morphologies that are randomly distributed throughout a spheroid region.

$In~Silico$ Electrical Modeling of Cell Aggregates

“…These two approaches have to be complemented with a purely numerical approach, which consists in solving the cell scale PDE (7) in a large number of cells. A first impressive result has been obtained by Mistani et al in the context of electroporation [11], where the time-dependent nonlinear model of Leguèbe et al [10] has been simulated on 30 thousands of cells.…”

“…new homogenized formula of tissue impedance is proposed, generalizing the so-called Maxwell-Garnett formula to cells with any geometrical configurations and without any dilution assumption. The paper proposes thus a complementing approach to the full numerical approach previously proposed in [8], [11]. It is worth noting that this study is restricted to the linear regime.…”

Numerical Simulations as Means for Tailoring Electrically Conductive Hydrogels towards Cartilage Tissue Engineering by Electrical Stimulation

“…Our results indicate that there is no crucial difference of the stimulation with respect to the cell location inside the hydrogel and the cell morphology. Nevertheless, for future research, we aim at developing more realistic models with many cells as recently presented for a different use case [ 57 ]. However, our study contributes to the design of future UQ studies for such complex and numerically expensive models.…”

Effect of electrical stimulation on biological cells by capacitive coupling – an efficient numerical study considering model uncertainties

“…Nevertheless, similar models are commonly used across different communities [17], [23], [24], [51]. More sophisticated models including many cells require large highperformance-computing facilities [52]. For types of tissue such as cartilage, where the volume fraction of the cells is small such that the distance between the cells is rather large [53], [54], models including few or only one cell might be sufficient.…”