Biophysical implications of Maxwell stress in electric field stimulated cellular microenvironment on biomaterial substrates

Abstract

A number of experimental studies have established the critical role of electric field stimulation on cell functionality modulation of various cell types on a wide range of biomaterial platforms in vitro. In particular, cell fate processes, morphological changes and electroporation are significantly modulated over a narrow range of electric field stimulation conditions. Although a few studies using electrical network theory, first principle simulations and electrohydrodynamic models are reported in the literature, the present study establishes a theoretical foundation to a new perspective that bioelectric stress can significantly influence cell morphological changes/electroporation and in a broader sense, the cell response to electric field on biomaterial substrates. A single cell is modelled as a spherical membrane separating the culture medium and the cytoplasm having different dielectric properties. The analytical solutions to the Laplace equation and Poisson equation for the system are adopted to quantitatively capture the potential distribution in the cellular microenvironment for different cases. These include a cell on a conducting substrate, on an insulating substrate and a cell with surface charge density, in electric field stimulated cellular microenvironment. The biophysical significance of the normal stress distribution has been discussed in terms of the variation in the cellular deformation, depending on the frequency of the electric field and substrate conductivity. A significant difference has been observed in the deformation behavior at higher frequencies (>109 Hz) compared to low frequency and DC electric fields. This theoretical study therefore unravels the significance of substrate conductivity in synergy with electric field parameters to modulate cell response. In addition, the tangential component of the Maxwell stress tensor (shear stress), a measure of the stretching force on the membrane, has been used to obtain estimates of the critical electric field required for membrane rupture. It has been predicted that a cell with surface charge density requires electric fields of the order of 10 kV/mm in order to undergo membrane rupture, which is in line with the experimental observations reported in the literature. Taken together, the presented analysis is expected to provide guidelines to develop next generation biomaterials and biomedical devices for regenerative medicine and cancer treatments.