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

TL;DR

This paper presents a scalable, parallel numerical framework using Voronoi and Octree grids for detailed mesoscale simulations of cell aggregate electropermeabilization, capturing experimental phenomena and enabling tissue-level studies.

Contribution

It introduces a novel parallel Voronoi-based numerical approach with VIM for mesoscale electropermeabilization simulations, capable of handling large, heterogeneous cell aggregates.

Findings

Successfully replicates shadowing effects observed in experiments.

Accurately models impedance evolution over time.

Demonstrates scalability with over 27,000 cells in a large volume.

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.