## The ECIS™ Model

We can apply a mathematical model of the impedance changes due to the presence of a cell layer, where the impedance data can be used to calculate cell morphological parameters including the barrier function of the cell layer, the spacing between the ventral side of the cell and the substratum, and the cell membrane capacitance. If you wish to study this approach in detail, we suggest you consult the PNAS paper [Giaever and Keese, PNAS 88, 7896 (1991) ] where the model is developed and the equations that describe it solved. In this paper the validity of the model is also confirmed by comparing calculated values of resistance and capacitance of cell-covered electrodes with those measured using ECIS over a three magnitudes of AC frequency (100 to 100,000 Hz). A brief description of that model and its use is described below; we hope this will give you an understanding of some of the key points.

To employ the model to refine ECIS data, the resistance and capacitance of the cell free electrode is measured at several different AC frequencies. In the model cells are represented as disk shaped objects having insulating membrane surfaces and filled with conducting electrolyte. Cells modeled as disks

Since the focal adhesion plaques of cells represent a very small fraction of the total ventral surface of the spread cell, we treat the cells as hovering a small distance above the electrode which serves as their substratum. In calculating how the impedance changes due to this cell coverage, we assume that the resistance and capacitance of the gold surface itself does not change but that the measured capacitance and resistance change because the cells alter the path of the current flow. The main source of the impedance change can be attributed to the fact that some current must flow through the narrow spaces between the ventral surface of the cells and the electrode, and that current flows out through the narrow spaces between the cells (barrier resistance). AC current can pass directly through the cells since their insulating membranes serve as capacitors themselves. The model determines three parameters by fitting the theory to the experimental curves.

1. One is the barrier resistance, Rb, which can range from 0 to approximately 100ohm-squared or more. This is an important parameter for studies of endothelial and epithelial cells.
2. The next parameter is called alpha, is a measure of the constraint on current flow beneath the cells. It is related to the radius of the cell and its average height above the substratum. ECIS provides perhaps the most sensitive means available to study changes in this region beneath the cells.
3. Finally, using measurements of the cell-covered electrode at different frequencies, it is possible to determine the average capacitance of the cell plasma membranes, Cm.  The measured impedance can be broken down into three parameters
1. Rb, the barrier function of the cell layer
2. Alpha, a term associated with the constricted current flow beneath the cell
3. Cm, the membrane capacitance

[Giaever, I. and Keese, C.R., PNAS 81, 3761 (1991)]