Electrical Impedance Tomography

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. Until recently, all applications have been considered experimental. However in 2011 the first commercial EIT device for lung function monitoring in intensive care patients was introduced.

The invention of EIT as a medical imaging technique is usually attributed to John G. Webster and a publication in 1978, although the first practical realisation of a medical EIT system was detailed in 1984 due to the work of David C. Barber and Brian H. Brown.

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 Calderón, and in the mathematical literature of inverse problems it is often referred to as "Calderón's Inverse Problem" or the "Calderón Problem". There is extensive mathematical research on the problem of uniqueness of solution and numerical algorithms for this problem.

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 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 to the medical case. In geophysics, the idea dates from the 1930s.