A Parallel Voronoi-Based Approach for Mesoscale Simulations of Cell Aggregate Electropermeabilization.

We introduce an approach for simulating mesoscale electropermeabilization of a cluster of cells. We employ a forest of Octree grids along with a Voronoi mesh in a parallel environment and in the context of the level-set method that exhibits excellent scalability. We exploit the electric interactions between the cells through a nonlinear partial differential equation 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 $31\,000$ well-resolved cells with a heterogenous mix of morphologies that are randomly distributed throughout the domain. We follow the dynamical evolution of more than $228\,000\,000$ nodes through timescales that enable the unprecedented numerical studies of the electropermeabilization effects in the cluster-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 and exploiting the effect of cluster environment on the efficiency of electropermeabilization.