Geometric effects on resistivity measurements with four-electrode probes in isotropic and anisotropic tissues

Abstract

We studied via computer simulation the effects of electrode diameter, electrode length, interelectrode spacing, and tissue size on the accuracy of measured tissue resistivities and anisotropy ratios obtained with the widely used four-electrode technique. Such measurements commonly assume an ideal situation in which the four electrodes are infinitesimally small and the tissue is semi-infinite. Our study shows that these geometric factors can significantly affect measured resistivities, particularly for anisotropic tissues. The measured anisotropy ratio is decreased by either 1) increasing the electrode diameter or length relative to the interelectrode spacing of the probe or 2) decreasing tissue size. We have provided an equation for estimating errors in the measured anisotropy ratio from the parameters of electrode and tissue geometries. The simulation findings are supported by our in vitro experimental results.

Possible Four-Electrode Configurations for Measuring Cardiac Tissue Fiber Rotation

“…The method presented here for finding fiber rotation is based on the four-electrode technique. Although the effect of electrode size and spacing, on resistivity measurements in skeletal muscle, has been studied by Wang et al [17], few measurements [8]- [10] of conductivities in cardiac tissue have actually been made using the four-electrode technique, due to the difficulties associated with electrodes and electrode spacings of micrometre order. However, considerable recent interest has been shown in this field [11], [12], [18] and a number of studies, which demonstrate the feasibility of making various types of cardiac measurements using small electrodes with close spacings, have been conducted.…”

A New Geometric Factor for In Situ Resistivity Measurement Using Four Slender Cylindrical Electrodes

“…The wide variation in the reported resistivities have been viewed from a measurement theoretical viewpoint and attributed to one or more of the following factors [13]: 1) errors in the measurement setup and the method applied to calculate the resistivity from the actual measured data; 2) differences in the tissue preparation and conditioning; 3) inter-individual differences in the (patho-) physiological state of tissue samples. Studies based on computer simulation and experimental results have shown that in situations whereby slender cylindrical electrodes are used and is not small in comparison to , the measured tissue resistivity, which are obtained using in (1) are affected by the geometry of the four-electrode probes [3]. A physical model consisting of air, a saline solution layer and an agar layer has also been used to demonstrate the dependence of apparent resistance of four-electrode probes on insertion depth [5].…”

“…All the electrodes are immersed in a homogeneous, isotropic, and semi-infinite medium, and the four electrodes are modeled as points. In the circumstances, the resistivity of the medium is obtained from the following well-known expression [1], [3], [12] (1)…”

Resistivity Measurement of a Small-Volume Sample Using Two Planar Disc Electrodes and a New Geometric Factor

“…However, the application of the fourelectrode method for biological measurement [5] is known to be affected by sample size [5] and electrode geometry [6]. On the other hand, the two-electrode method is strongly affected by electrode polarization, although it does have the advantage of enabling the usage of a smaller electrochemical sensor [7].…”