| Electrical Impedance Tomography |
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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 Holder D.S., Electrical Impedance Tomography: Methods, History and Applications, Institute of Physics, 2004. ISBN 0-7503-0952-0. 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 credit for the invention of EIT as a medical imaging technique is usually attributed to and Brian H. Brown Barber D.C. and Brown B.H. (1984) Applied Potential Tomography (Review Article). J. Phys. E:Sci. Instrum 17: 723 - 733.. 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 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 . The paper has been reprinted as CALDERON, Alberto P. On an inverse boundary value problem. Mat. apl. comput., 2006, vol.25, no.2-3, p.133-138. ISSN 0101-820 [http://www.scielo.br/scielo.php?script=sci_abstract&pid=S0101-82052006000200002&lng=en&nrm=iso&tlng=en] , 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 problemUhlmann 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. 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 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. REFERENCES EXTERNAL LINKS
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