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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 [1]

The credit for the invention of EIT as a medical imaging technique is usually attributed to John G. Webster in around 1978[2], although the first practical realisation of a medical EIT system was due to David C. Barber and Brian H. Brown [3]. 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[4], 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[5].

## ExamplesEdit

 Electrodes on chest Wires attached Resulting image

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 [6].

## ReferencesEdit

1. Holder D.S., Electrical Impedance Tomography: Methods, History and Applications, Institute of Physics, 2004. ISBN 0-7503-0952-0.
2. Henderson R.P. and Webster J.G. (1978) An Impedance Camera for Spatially Specific Measurements of the Thorax. IEEE Trans. Biomed. Eng. 25: 250-254.
3. Barber D.C. and Brown B.H. (1984) Applied Potential Tomography (Review Article). J. Phys. E:Sci. Instrum 17: 723 - 733.
4. Calderón A.P. (1980) On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Rio de Janeiro. Scanned copy of paper
5. Uhlmann G. (1999) Developments in inverse problems since Calderón's foundational paper, Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderón, (editors ME Christ and CE Kenig), University of Chicago Press, ISBN 0-226-10455-9
6. N. Kerrouche, CN McLeod, WRB Lionheart, Time series of EIT chest images using singular value decomposition and Fourier transform, Physiol. Meas. 22 No 1, 2001 147-157