Four-electrode techniques

Four-electrode technique for conductivity measurements — Figure. 

FIGURE 21.5 A schematic diagram of the four-electrode technique for measuring tissue conductivities. Current, I, is passed through the outer two electrodes, and the potential, V, is measured between the inner two. The interelectrode distance is s. 

Figure 3.15 shows admittance Wessel plots obtained with four-electrode technique (Grimnes and Martinsen, 2010). The left part of Figure 3.15 is two calf spectra with electrode axis parallel (black) and perpendicular (gray) to the direction of the muscle fibers. Notice how the gray circular arc apparently approaches zero real admittance values at low frequencies. 

Without the skin and with the living body tissue considered purely resistive, the resistance, R, of a body segment is determined by the mean resistivity, p mean length, L and mean cross-sectional area. A, according to R = pL/A. The resistance can be measured by a four-electrode technique (Freiberger, 1933 Grimnes, 1983a). 

Figure 4.26 Body segment resistance distribution (no skin contribution, no current constriction). Values presented are as found with a four-electrode technique 500 Q is a one-finger contribution. Linear values according to Eq. 2.2 are not very dependent on current density levels.

It was a long way to go before the genesis of the surface potential differences caused by action potentials deep in the thorax was understood. It was the work of Einthoven and the lead concept that paved the way. It was Burger and van Milaan who introduced the lead vector, making it possible to find the direction to go. Richard McFee replaced the lead vector by the lead field, defined as the electric field set up in the body by a unit current applied to the pick up electrode pair. Otto Schmitt reintroduced the old Helmholtz concept about reciprocity and introduced the concept of transfer impedance already known from the use of four-electrode technique. And it was David Geselowitz who finally put it in the elegant mathematical form. A certain similarity with the Faraday—Maxwell intellectual process runs in our minds. 

Schwan, H.P., Ferris, C.D., 1968. Four-electrode techniques for impedance measurement with high resolution. Rev. Sci. Instrum. 39 (4), 481—485. 

In addition to passive impedance measurements, four-electrode techniques find application in active plethysmography as well. 

The measurement of effective conductivities is complicated by the traditionally used electrode geometry. Typically, one uses a four-electrode technique [ Steendijk et al., 1993], in which two electrodes inject current and two others measure the potential (Figure 21.5). Gielen et al. [1984] used this method to measure the electrical properties of skeletal muscle and found that the effective conductivity depended on the interelectrode distance. Roth [1989] reanalyzed Gielen et al. s data using the spatial frequency dependent model and found agreement with some of the more unexpected features or their data (Figure 21.6). Table 21.1 contains typical values of skeletal muscle effective conductivities and microscopic tissue parameters. Table 21.2 Hsts nerve effective conductivities. 

Four-electrode technique for conductivity measurements — Figure. One possible electrode arrangement for the four-probe conductivity measurements, used often in sohd-state electrochemistry... 

The electrical conductivity of low-resistance polymers and polymer composites can be determined by two four-electrode techniques the standard method for testing bar-shape specimens of semiconductors and conductors and the four-point probe method developed for nondestructive testing of sheets and thin films. In both methods two external probes (electrodes) are used as the cunent electrodes and the two inner probes are used to measiue the voltage drop. Using four probes eliminates possible erroneous results due to the probe resistance and the contact resistance between the electrode and the tested material. Hiis method also allows the elimination of the influence of the barriers at the electrode/material contact on the temperature dependence of the conductivity. 

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