We proposed a mathematical model for the microdynamics of cultured cells measured with ECIS (Electrical Cell-substrate Impedance Sensing) system that can separately evaluate cell-to-cell and cell-to-substrate gaps. Our mathematical model is composed of culture medium impedance between cells (Zsol), cell impedance (Zc), and polarization impedance of the electrode (Zp). Zsol consists of the resistance between cells (Rsol) and the capacitance between cells (Csol) of the culture medium. In particular, Rsol is the resistance component related to the cell-to-cell distance (A). Zc consists of capacitance of the cell membrane (Cc) and resistance of the cell membrane (Rc). Zp depends on the cell-to-substrate distance (h) because of the shielding effect of cells to the electrode. The shielding effect is defined as shielding coefficient (Sk). We examined the changes in the impedance of the electrode without or with cells in various conditions. The electrical characteristics of the electrode with or without cells agreed well with those measured in ECIS system. It was found that whether A or h caused the changes in the impedance could be determined based on the changes in the total resistance and reactance (capacitance); A mainly affects the total resistance value, and h mainly affects total capacitance value. Therefore, we can simply estimate the changes in cell-to-cell and cell-to-substrate gaps with measured total resistance and reactance (capacitance). Based on these results, when the cultured endothelial cells (HUVEC) were stimulated with estrogen for 40 hours, it was proved that the cell-to-cell distances decreased, even though the cell-to-electrode distances slightly increased. This result suggests that the barrier function of endothelium is fortified by estrogen.
EVALUATION OF MICROMOTION OF VASCULAR ENDOTHELIAL CELLS IN ELECTRICAL CELL-SUBSTRATE IMPEDANCE SENSING (ECIS) METHOD USING A MATHEMATICAL MODEL
