Justification of Point Electrode Models in Electrical Impedance Tomography

Abstract

The most accurate model for real-life electrical impedance tomography is the complete electrode model, which takes into account electrode shapes and (usually unknown) contact impedances at electrode-object interfaces. When the electrodes are small, however, it is tempting to formally replace them by point sources. This simplifies the model considerably and completely eliminates the effect of contact impedance. In this work we rigorously justify such a point electrode model for the important case of having difference measurements ("relative data") as data for the reconstruction problem. We do this by deriving the asymptotic limit of the complete model for vanishing electrode size. This is supplemented by an analogous result for the case that the distance between two adjacent electrodes also tends to zero, thus providing a physical interpretation and justification of the so-called backscattering data introduced by two of the authors.

Electrical Impedance Tomography

“…The trace on the boundary cannot be evaluated at a point, so point measurements of voltage are undefined. However it can be shown that if the conductivity is changed only in the compliment of a neighborhood of @ the resulting voltage difference at the boundary can be evaluated at points [52].…”

Remote Real Time Monitoring for Underground Contamination in Mongolia Using Electrical Impedance Tomography

“…In practice, the voltage data measured on each current-carrying electrode are excluded to avoid the contact impedance problem. Moreover, the use of difference data in the methods proposed here averts the influences of contact impedance as well as singularities caused by point electrodes [6].…”

Convex source support in three dimensions

“…[14]): Constant flux of current is maintained between two electrodes at fixed locations y + and y − . Meanwhile, the third electrode, which is moved along ∂D and not used for current injection, measures the boundary potential.…”