Herman P. Schwan

ELECTRODE POLARIZATION IMPEDANCE AND MEASUREMENTS IN BIOLOGICAL MATERIALS

Consideration attention has been devoted to the direct current (DC) characteristics of metal electrodes and comparatively little work is concerned with their transient and alternating current (AC) steady state performance. This is surprising since most of the biological work necessitating electrodes either is concerned with the registration of time-dependent signals or with the application of transients or alternating currents and potentials. It is naive to assume that an electrode which has excellent DC-characteristics-i.e., is “nonpolarizab1e”-is also suitable for studies with transients or alternating currents. Indeed, many electrodes which are known for their low DC-polarizability have a high polarization impedance and electrodes of excellent AC-characteristics are often inadequate for DC-purposes. For example, the platinum electrode which is so suitable for AC-work is a very poor performer for DC-studies. As far as we know, only one attempt to develop an electrode which combines good DC-performance with low AC-polarization impedance has been conducted in recent years.’ Transient aspects have been studied recently by Weinman and Mahler.2 This article will be concerned with the behavior of metal electrodes which is evoked by the passage of alternating currents. The presence of alternating current electrode polarization can be a major nuisance in biological impedance work. The relative magnitude of the electrode impedance contributing to the total sample impedance of interest is particularly pronounced at low frequencies and for more conducting materials. Even though the elements of AC-electrode polarization have been known for quite some time, recognition of the disturbing presence of electrode impedances and appropriate corrections are frequently neglected and effects due to the electrodes erroneously ascribed to the sample under study. Indeed, a significant fraction of all biological impedance work is subject to inquiry on this account. We shall (1) very briefly review some of the fundamental properties of AC-electrode polarization impedances, (2) discuss in greater detail the limits of linearity of electrode behavior and its implications in microelectrode work, and ( 3 ) describe a variety of techniques, in part known for some time and in part new, which are useful for the correction or elimination of electrode-induced errors in biological impedance work.

THE CONDUCTIVITY OF LIVING TISSUES

Studies of the potential distribution on the surface of the human body have shown that the electrical activity of the heart can be represented by a fixedlocation, rotating dipole of time-dependent magnitude as summarized in Frank’s preceding paper. The location of this dipole can be expected to coincide in space only with the electrical center of the heart when variation of resistivity of the tissues surrounding the heart is small. Therefore, investigation of the homogeneity of the electrical properties of tissue is indicated. Furthermore, it is desirable to determine whether the capacitance of tissue components is sufficiently small throughout the cardiac frequency spectrum to justify neglect of capacitive-current components in any theory of the ECG. If the capacitance of tissue were found to be excessive, the electrical phase angle of the transfer impedance, which is defined by heart dipole current and surface body potential, would be sufficiently large and variable with frequency to affect the shape of the ECG. In this case surface potentials would depend, not only on heart activity and purely geometrical factors, but also on electrical impedances of the various tissue complexes involved. These facts, aside from our general interest in tissue impedance, stimulated our investigations of tissue impedance in situ a t low frequencies. We have discussed our data and associated technical problems in detail We shall therefore summarize here the results only to an extent sufficient to answer the questions formulated above. We restrict ourselves to values measured in silu in living dogs with current levels that are small enough to avoid excitation; that is, we report data that characterize the passive electrical characteristics of tissue as existent for the currents generated by the heart. The frequency dependence of the resistivity of liver is demonstrated in FIGURE 1. The curve is characteristic for all samples of muscular, liver, and lung tissue, while the frequency dependence of fatty tissue, shown also in the figure, is somewhat smoother. TABLE 1 gives the specific-resistance data of various tissues, averaging hundreds of values, a t 10, 100, and 1000 cps. The data show that the resistances of the major types of tissue surrounding the heart are nearly identical. Lung tissue has a value that is perhaps about 20 per cent higher than muscle, liver, and heart muscle. This is not necessarily significant, however, in view of comparable standard-deviation values that characterize variation from one sample to a n ~ t h e r . ~ The resistance values are higher than those previously stated by They agree much better with theoretical expectation, which is based on the amount of cellular volume concentration and air and blood content in areas such as the lung.6 An exception is fatty material, whose resistivity is substantially larger than that of

Cellular membrane potentials induced by alternating fields

Membrane potentials induced by external alternating fields are usually derived assuming that the membrane is insulating, that the cell has no surface conductance, and that the potentials are everywhere solutions of the Laplace equation. This traditional approach is reexamined taking into account membrane conductance, surface admittance, and space charge effects. We find that whenever the conductivity of the medium outside the cell is low, large corrections are needed. Thus, in most of the cases where cells are manipulated by external fields (pore formation, cell fusion, cell rotation, dielectrophoresis) the field applied to the cell membrane is significantly reduced, sometimes practically abolished. This could have a strong bearing on present theories of pore formation, and of the influence of weak electric fields on membranes.

Specific Resistance of Body Tissues

The resistive properties of various tissues surrounding the heart were investigated in a number of living dogs. Alternating currents of a frequency varying between 10 and 10,000 c.p.s. have been used for this purpose. Technical problems associated with such measurements are analyzed. The results show that the resistive properties of most tissues are comparable and that the resistivity decreases slowly as the frequency increases.

Linear and nonlinear electrode polarization and biological materials

Electrode polarization is a major nuisance while determining dielectric properties of cell and particle suspensions and tissues, particularly at low frequencies. Understanding of these interfacial phenomena and appropriate modelling are essential in order to correct for its distortion of the dielectric properties of the sample of interest. I survey the following topics, concentrating on contributions from our laboratory:Linear properties of electrode polarization and relevant modelsEffects of electrode polarization on sample impedanceEffects of sample on polarization impedanceTechniques of correctionExtension of linear to nonlinear modelsHarmonics generated in the nonlinear range.

Alternating current electrode polarization

SummaryThis article summarizes principles of alternating current electrode polarization. The importance of alternating current electrode polarization in biological impedance studies is discussed. The following topics are treated in detail: Definition of Electrode Polarization Impedance; Linearity and Superpositioning Principle; Frequency Dependence of Electrode Impedance; Preparation of Electrodes (Optimal current density for platinum black application, Stability of electrode impedance, Cell design for platinization purposes, Aging and cleaning of electrodes); Effect of Electrode Polarization on Biological Impedances; Effects of Biological Matter on Electrode Polarization; Techniques to Correct for Electrode Polarization (Electrode distance variation technique, Large electrode distance, Graphical technique, Substitution technique, Frequency variation technique, Four-electrode technique); Transient Response of Electrodes; Microelectrodes.

Four‐Electrode Null Techniques for Impedance Measurement with High Resolution

At low frequencies, the normally difficult measurement of the dielectric properties of conducting materials is severely compromised by electrode polarization. This problem at the electrode‐sample interface arises from the modulation of the normal dc boundary potential by the passage of alternating current. A solution, permitting a conductance resolution of 1:105 for frequencies between 10 cps and 1 kc, is to use a second noncurrent‐carrying pair of electrodes to measure the voltage across the sample and to employ a null technique for obtaining the required precision. Several four‐electrode null techniques are proposed, each having certain relative merits. In all cases the resolution in capacitance is shown to be governed by a combination of the resolution in conductance, the sample properties, and the frequency of the measurement.

Hot Spots Generated in Conducting Spheres by Electromagnetic Waves and Biological Implications

The distribution of the heating potential generated by an incident electromagnetic plane wave on a conducting sphere simulating the human head was investigated. It was found that for a sphere of 10-cm radius having the same electrical characteristics as those of biological tissues, no hot spots are generated inside. While at lower frequencies the heating is relatively uniform with some polarization effects, for frequencies above 1000 MHz only skin heating takes place. For a sphere of the same size but of conductivity ?= 10 mmho/cm (which for f>1000 is lower than that of biological tissues) hot spots occur inside for f>1000 MHz. Intense hot spots also occur inside spheres of radius 5 cm having the same electrical characteristics as those of biological tissues in the frequency region of 250 MHz

Linear and nonlinear properties of platinum electrode polarisation. Part 1: frequency dependence at very low frequencies

The polarisation impedance of the platinum electrode was measured in physiological saline (0·9% NaCl) over six decades of frequencies down to 1 mHz. The applicability, of Fricke’s phase angle rule was verified down to 10 mHz. The resistive shunt which emerges at lower frequencies was shown to be equivalent to the direct current (d.c.) impedance of the interface. A Cole-Cole (1941) type of relaxation model is proposed to describe the interface behaviour over all frequency ranges. Nonlinear polarisation measurments have demonstrated the validity of Schwan’s limit law of linearity at very low frequencies.

ELECTRICAL PROPERTIES OF BOUND WATER

Water bound to the surface of macromolecules is indicated whenever the physical properties of a macromolecular suspension cannot be readily accounted for by the properties of the suspending medium and those of the macromolecules. I shall report here some of the electrical properties of macromolecular suspensions observed a t very high frequencies and whatever this may imply for the electrical properties of bound water. Essentially macroscopic and valid concepts will be applied in order to reduce experimental dielectric data to those of bound water. No detailed molecular interpretation will be attempted. The dielectric properties of protein in electrolytes have been extensively investigated during the 1940s throughout the radio frequency range, primarily by Oncley and his associates (Oncley, 1942, 1943). Experimental data could be understood in terms of a sum of two Debye type relaxation mechanisms.