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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 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. All applications are currently considered experimental. (For a detailed review of medical applications, see the first reference.)
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 the medical case.
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 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 Calder, and in the mathematical literature of inverse problems it is often referred to as "Calder's Inverse Problem" or the "Calder Problem". There is extensive mathematical research on the problem of uniqueness of solution and numerical algorithms for this problem.
Contents
1 Details
2 Examples
3 Commercial systems
4 References
5 External links
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Details
In biological tissue the electrical conductivity and permittivity varies between tissue types as well as depending on temperature and physiological factors. For example lungs become less conductive as the alveoli become filled with air. In EIT adhesive electrodes applied to the skin and an electric current, typically a few milli-Amperes of alternating current at a frequency of 10-100 kHz, is applied across two or more electrodes. Other electrodes are used to measure the resulting voltage. This is repeated for numerous "stimulation patterns", such as successive pairs of adjacent electrodes.

A cross section of a chest showing a current being applied across two electrodes resulting in current stream lines and equi-potential lines
The currents used are relatively small, and certainly below the threshold at which they would cause stimulation of nerves. The frequency of the alternating current is sufficiently high not to give rise toelectrolytic effects in the body and the Ohmic power dissipated is sufficiently small and diffused over the body to be easily handled by the body's thermoregulatory system.
The current is applied using current sources, either a single current source switched between electrodes using a multiplexor or a system of Voltage-to-current converters, one for each electrode, each controlled by a digital to analog converter. The measurements again may be taken either by a single voltage measurement circuit multiplexed over the electrodes or a separate circuit for each electrode. Earlier systems typically used an analog demodulation circuit to convert the alternating voltage to a direct current level then an analog to digital converter. Many recent systems convert the alternating signal directly, the demodulation then being performed digitally. Many EIT systems are capable of working at several frequencies and can measure both the magnitude and phase of the voltage.
The voltages measured are then passed to a computer to perform the reconstruction and display of the image. If images are required in real time a typical approach is the application of some form of regularized inverse of a linearization of the forward problem. In most practical systems used in a medical setting a 'difference image' is formed. That is, the differences in voltage between two time points is left-multiplied by the regularized inverse to produce an approximate difference between the permittivity and conductivity images. Another approach is to construct a finite element model of the body and adjust the conductivities (for example using...(and so on)

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