## Impedance Measurement

ECIS measurements are made using an AC signal, where the current oscillates in a sinusoidal manner from as low as a few hundred to nearly 100,000 Hz in different measurements. Using AC instead of DC signals to monitor the cells upon electrodes has two important consequences. First, an AC source is used such that the electrolytes in the culture media are not deposited upon the electrode causing the properties of the electrodes to change or polarize. The use of an AC signal also offers another very significant advantage that is briefly described below.

Thus far, we have only referred to impedance, the AC equivalent to resistance, and this is often the only parameter one may wish to follow to study many aspects of cell behavior. If one were to apply the AC current (I) to the electrode system and measure the resulting voltage (V) across the electrodes, the impedance (Z) is simply given by the AC equivalent of Ohm's law:

Z=V/I

The ECIS Zθ instrument, however, is capable of monitoring both the voltage and the phase of the voltage relative to the current. Combining these parameters, the impedance can be broken down into two parts -- one due to pure resistance and the other to the reactance of the system. The reactive part (X_{c}) in this case is due to the capacitance (C) associated with the metal surfaces in the tissue culture medium (the electrolyte).

We have elected to represent the signal received from the ECIS electrodes as a simple resistor and capacitor in series.

For this simple RC circuit, the impedances of each of the circuit elements are given by:

R=V(in phase)/I

Xc=V(out of phase)/I

and the total impedance is given by,

Z= (R^{2} + X_{c}^{2}) 0.5

Xc (the capacitive reactance in ohms) depends upon the AC frequency (f) is given by:

Xc =1/(2Π f C)

Since we know the frequency, we can obtain the capacitance (C) from this term.

With this information, it is possible to state more regarding the cells than simply the time changes in impedance. We, of course, can now report changes over time in the pure resistive (R) as well as the capacitive portions (C) of the impedance, and these are very useful. We shall also see that these data can be further refined using a model that gives back information on the barrier function of cell layers, the spacing beneath the cell and its substratum, and the capacitance of the cell's plasma membranes.

### AC Phase measurements

The ECIS Zθ applies an approximately constant current through the ECIS electrodes of about 1 microampere or less. This current results in a voltage across the electrodes that varies in a sinusoidal fashion at the same frequency as the applied current.

Were this simply a measurement of a pure resistance, the two sine waves, that of the voltage and of the current, would be exactly in phase -- the waveforms would have different values, but would coincide exactly.

Were this a measurement of a pure capacitance, the two sine waves would be said to be 90 degrees (one quarter wavelength) out-of-phase -- the voltage lagging the current. In this case, when the current is at its peak, the voltage is zero and when the current is at zero, the voltage is at a peak. We refer to the voltage in this case as the out-of-phase voltage.

In the actual ECIS measurement, since we have both resistance and capacitance, the voltage and current are somewhere in between these two situations. The ECIS instrumentation in the ECIS Zθ model measures this phase difference and breaks this voltage down into two pure in and out-of-phase components that together -add up to the actual signal. These are the voltages used in finally calculating the resistance and capacitance of the ECIS electrodes.