Theory
In biological tissue the electrical conductivity and permittivity varies between tissue types likewise depending on temperature and physiological factors. For example lungs are less conductive when the alveoli is 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.
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 to electrolytic 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 a variant of Levenburg–Marquart method) to fit the measured data. This is more challenging as it requires an accurate body shape and the exact position of the electrodes. Much of the fundamental work underpinning Electrical Impedance was published in 1992, from the Glenfield Hospital Project.
The open source project EIDORS provides a suite of programs (written in Matlab / Octave) for data reconstruction and display under the GNU GPL license.
Read more about this topic: Electrical Impedance Tomography
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