Thin-layer approximation for the multi-physics and multiscale simulation of cell membrane electrodeformation

Multi-physics simulation techniques provide a platform that is used to gain insights into complex biological problems with multiple length scales such as cell electrodeformation (ED) and electropermeabilization (EP). However, owing to the large degrees of freedom required to compute the electromechanical properties at very different length scales (membrane thickness, cell size, and customized tissue scaffold) finite element (FE) simulations can be computationally very expensive. Here, we report on a general method of analysis by which we can systematically simulate multiscale ED under direct-current electric fields. In the context of electromechanical continuum behavior, the key novelty of our work is the introduction of a specific Dirichlet boundary condition, i.e. thin-layer approximation (TLA), to represent the capacitive elastic cell membrane. To test the robustness of this newly proposed procedure, Maxwell stress tensor (MST) and cell displacement arising from ED forces obtained with the TLA are compared with a model using a physical thickness of the cell membrane. Furthermore, we present our results in terms of benchmark points for vesicle deformation induced by an electric field excitation and we confirm our approximate results are relevant to predict the aspect ratio characterizing the ellipsoidal deformation of an initially spherical vesicle.