Laplace Plane Analysis of Skin Impedance: A Preliminary Investigation

Abstract

The impedance and phase angle of skin as functions of frequency were determined by Laplace plane analysis of the time domain current resulting from an external voltage perturbation. Bode plots of these functions established a passive equivalent circuit model for skin impedance which is valid over a wide range of frequencies. Typical values for the model circuit elements are given for ten human subjects.The electrical properties of any biological tissue depend on its intrinsic structure and, for in vivo studies, on the functional state of the organism. For the case of human skin, the impedance can vary with the thickness and moisture content of the stratum corneum, the concentration and activity of sweat glands, localized injury, the age of the subject, and environmental factors such as temperature and humidity. Seasonal and diurnal variations have been measured: For example, the d-c resistance of skin tends to increase during sleep. Short-term fluctuations are the basis for various monitoring techniques, including the electrocardiogram, electroencephalogram, and impedance plethysmography. Changes in impedance are also associated with the psychological state of the subject (1).Studies of the a-c impedance of biological systems, including human skin, have generally involved direct measurement of the impedance and phase angle as functions of the frequency of the applied voltage or current (2-5). Any such measurement over a wide range of frequencies tends to be cumbersome and time-consuming. Measurements with an impedance bridge have the additional disadvantage that some a priori assumptions must be made regarding an equivalent circuit for the skin impedance. Other reports have presented approximation methods for deriving the equivalent circuit components from the current response to a square voltage pulse input (6, 7). Burton (8) applied Bode analysis to measurements of the skin impedance and phase angle. By means of this method a passive equivalent circuit can be synthesized for any electrical "black box" from plots of its impedance and phase angle vs. frequency. The only assumption required is that the system consists solely of passive linear lumped circuit elements (8,9). Even though the resulting model is not necessarily unique (8), it must represent the system accurately in the frequency range studied.By extending this technique one step further, the entire frequency spectrum of any system can be computed by applying a Laplace transformation to the current response to an arbitrary voltage perturbation, thus eliminating the tedious process of point-by-point measurement of the impedance and phase angle. MethodIn order to obtain the impedance of a system as a function of frequency, the input voltage perturbation V(t) and the resulting current l(t) must be converted from the time domain (t) to the complex frequency domain (s). This may be accomplished by means of a Laplace transformation. The transform F(s) of a time domain function f(t)is defined as Key words: transient analysis, skin equivalent circuit, galvanic ...