Impedance spectroscopy of human erythrocytes: system calibration and nonlinear modeling.

We present in detail our impedance measurement method, the cell embodding technique, for human erythrocytes, and an accurate calibration procedure for a true four-electrode impedance measurement system. This technique with the calibration procedure gives reliable impedance measurements over a wide frequency range--1 Hz to 10 MHz. To achieve high sensitivity in this frequency range, we embed the cells in the pores of a Nuclepore filter. The calibration procedure assumes that the measurement system is linear, and requires measurement of three reference impedances. The reliability of this procedure is demonstrated with various RC circuits, and application of it to the bio-impedancae measurement system eliminates a quasi-dispersion in the high-frequency range, and increases the bandwidth at both the low- and high-frequency ends of the range by about a decade. We model the impedance of the cells embedded within the filter with an equivalent circuit that is consistent with the geometry and interfaces present. The experimental data are fitted to this model by means of a complex nonlinear least squares (CNLS) fit, which simultaneously fits the real and imaginary parts of the impedance with the Levenberg-Marquardt algorithm. The impedance spectra of human erythrocytes are found to display constant-phase-angle (CPA) characteristics. A CPA element is an impedance of the form Z = A/(jw) alpha, where A is a constant, j = square root -1, omega is angular frequency, and 0 < alpha < 1, and has been used to describe the ac response of the interface between the cell surface and the external electrolyte solution. Such a CPA element may be related to fractal character of the interface.