Electrical impedance tomography
Electrical Impedance Tomograpy (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 numerious 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.
In geophysics a similar technique is used using electrodes on the surface of the earth or in bore holes to locate resistivity annomolies, and in industrial process monitoring the arrays of electrodes are used for example to monitor mixtures of conductive fluids in vessels or pipes.
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 refered to as the "Calderón Problem". There is extensive mathematical research on the problem of uniqueness of solution and numerial algorithms for this problem.
References
- 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.
- Barber D.C. and Brown B.H. (1984) Applied Potential Tomography (Review Article). J. Phys. E:Sci. Instrum 17: 723 - 733.
- Calderón A.P. (1980) On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Rio de Janeiro.
- 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: 0226104559
