CELL ELECTROPERMEABILIZATION MODELING VIA MULTIPLE TRACES FORMULATION AND TIME SEMI-IMPLICIT MULTISTEP COUPLING

Journal article, 2024

We simulate the electrical response of multiple disjoint biological three-dimensional
cells undergoing an electropermeabilization process. Instead of solving the boundary value problem in
the unbounded volume, we reduce it to a system of boundary integrals equations-the local multiple
traces formulation-coupled with nonlinear dynamics on the cell membranes. Though in time the
model is highly nonlinear and poorly regular, the smooth geometry allows for boundary unknowns
to be spatially approximated by spherical harmonics. This leads to spectral convergence rates in
space. In time, we use a multistep semi-implicit scheme. To ensure stability, the time step needs
to be bounded by the smallest characteristic time of the system. Numerical results are provided to
validate our claims, and future enhancements are pointed out.