Electrical impedance tomography (EIT) is a medical imaging technique in which an image of the conductivity or permittivity of part of the body is inferred from surface electrical measurements. Typically, conducting electrodes are attached to the skin of the subject and small alternating currents are applied to some or all of the electrodes. The resulting electrical potentials are measured, and the process may be repeated for numerous different configurations of applied current.
Proposed applications include monitoring of lung function, detection of cancer in the skin and breast and location of epileptic foci. All applications are currently considered experimental. (For a detailed review of medical applications, see the first reference.[1])
In geophysics a similar technique (called electrical resistivity tomography) is used using electrodes on the surface of the earth or in bore holes to locate resistivity anomalies, and in industrial process monitoring the arrays of electrodes are used for example to monitor mixtures of conductive fluids in vessels or pipes. The method is used in industrial process imaging[2] for imaging conductive fluids. In that context the technique is usually called electrical resistance tomography (note the slight contrast to the name used in geophysics). Metal electrodes are generally in direct contact with the fluid but electronics and reconstruction techniques are broadly similar the medical case.
The credit for the invention of EIT as a medical imaging technique is usually attributed to John G. Webster in around 1978,[3] although the first practical realisation of a medical EIT system was due to David C. Barber and Brian H. Brown.[4] In geophysics, the idea dates from the 1930s.
Mathematically, the problem of recovering conductivity from surface measurements of current and potential is a non-linear inverse problem and is severely ill-posed. The mathematical formulation of the problem is due to Alberto Calder?n,[5] and in the mathematical literature of inverse problems it is often referred to as "Calder?n's Inverse Problem" or the "Calder?n Problem". There is extensive mathematical research on the problem of uniqueness of solution and numerical algorithms for this problem.[6]
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