A Voronoi Interface approach to cell aggregate electropermeabilization

Arthur Guittet (1, 2) , Clair Poignard (3, 4) , Frederic Gibou (1, 2)

1 UC Santa Barbara - University of California [Santa Barbara]
2 Department of Mechanical Engineering [Santa Barbara]
3 IMB - Institut de Mathématiques de Bordeaux
4 MONC - Modélisation Mathématique pour l'Oncologie

We present a Voronoi Interface approach to the study of cell electropermeabilization. We consider the nonlinear electropermeabilization model of Poignard et al. [20], which takes into account the jump in the voltage potential across cells' membrane. The jump condition is imposed in a sharp manner, using the Voronoi Interface Method of Guittet et al. [14], while adaptive Quad-/Oc-tree grids are employed to automatically refine near the cells boundary for increased accuracy. Numerical results are provided to illustrate the accuracy of the methods. We also carry out simulations in three spatial dimensions to investigate the influence of shadowing and of the cells shape on the degree of permeabilization.

Mots clés: Quad/Oc-tree; Voronoi; Level-Set method; 92C37; 2000 MSC: 65M08; 65M12; Sharp methods; Finite Volume method; Cell modelling

Domaines: Equations aux dérivées partielles [math.AP]

Arthur Guittet, Clair Poignard, Frederic Gibou. A Voronoi Interface approach to cell aggregate electropermeabilization. Journal of Computational Physics, 2017, 332, pp.143 - 159. ⟨10.1016/j.jcp.2016.11.048⟩. ⟨hal-01483521⟩