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 applied to some or all of the electrodes. The resulting electrical potentials are measured, and the process 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 credit for the invention of EIT as a medical imaging technique is usually attributed to John G. Webster in around 1978, although the first practical realisation of a medical EIT system was due to David C. Barber and Brian H. Brown . In geophysics the idea dates from the 1930s.

Mathematically the problem of recovering the 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 the "Calderón Problem". There is extensive mathematical research on the problem of uniqueness of solution and numerial algorithms for this problem.

Examples
The above images are from the EIT group at Oxford Brookes University and depict an early attempt at three dimensional EIT imaging of the chest using the OXBACT3 EIT system. The reconstructed image is a time average and shows lungs as low conductivity regions. Although an accurate chest shape was used only a 2D reconstruction algorithm was used resulting in a distorted image. The results of a similar chest study were published in.