Cut finite element discretizations of cell-by-cell EMI electrophysiology models (Q6585307)

This paper presents a novel approach for solving the extracellular-membrane-intracellular (EMI) model in electrophysiology, particularly addressing the challenge of complex cellular geometries in brain tissue modeling. Traditionally, high-quality mesh generation for these geometries poses significant computational burdens, motivating the authors to propose a cut finite element method (CutFEM) that permits non-conforming meshes.\N\NThe authors develop two CutFEM formulations: a single-dimensional approach where intra- and extracellular potentials are primary unknowns, and a multi-dimensional formulation incorporating electrical current as an unknown, leading to a saddle-point problem.\N\NThe work introduces a new discretization technique for the membrane-bound ODEs on the unaligned interface, further streamlining simulation workflows. Extensive numerical experiments confirm the stability and efficiency of the proposed methods, demonstrating CutFEM's applicability to high-resolution brain cell simulations with complex morphologies.