Effect of electrical stimulation on biological cells by capacitive coupling – an efficient numerical study considering model uncertainties

Electrical stimulation of biological samples such as tissues and cell cultures attracts growing attention due to its capability of enhancing cell activity, proliferation and differentiation. Eventually, profound knowledge of the underlying mechanisms paves the way for innovative therapeutic devices. Capacitive coupling is one option of delivering electric fields to biological samples and has advantages with regard to biocompatibility. However, the mechanism of interaction is not well understood. Experimental findings could be related to voltage-gated channels, which are triggered by changes of the transmembrane potential (TMP). Numerical simulations by the Finite Element method (FEM) provide a possibility to estimate the TMP. For realistic simulations of in vitro electric stimulation experiments, a bridge from the mesoscopic level down to the cellular level has to be found. A special challenge poses the ratio between the cell membrane (a few nm) and the general setup (some cm). Hence, a full discretization of the cell membrane becomes prohibitively expensive for 3D simulations. We suggest using an approximate FE method that makes 3D multi-scale simulations possible. Starting from an established 2D model, the chosen method is characterized and applied to realistic in vitro situations. A to date not investigated parameter dependency is included and tackled by means of Uncertainty Quantification (UQ) techniques. It reveals a strong, frequency-dependent influence of uncertain parameters on the modeling result.