electrical impedance tomography electrical impedance tomography electrical impedance tomography (eit) is a noninvasive type of medical imaging in which the electrical conductivity, permittivity, and impedance of a part of the body is inferred from surface electrode measurements and used to form a tomographic image of that part. electrical conductivity varies considerably among various biological tissues (absolute eit) or the movement of fluids and gases within tissues (difference eit). the majority of eit systems apply small alternating currents at a single frequency, however, some eit systems use multiple frequencies to better differentiate between normal and suspected abnormal tissue within the same organ (multifrequency-eit or electrical impedance spectroscopy). electrical impedance tomographyfigure 1: a cross section of a human thorax from an x-ray ct showing current stream lines and equi-potentials from drive electrodes. note how lines are bent by the change in conductivity between different organs.purposemeasurements are used to form a tomographic image of a part of human body typically, conducting surface electrodes are attached to the skin around the body part being examined. small alternating currents will be applied to some or all of the electrodes, the resulting equi-potentials being recorded from the other electrodes (figures 1 and 2). this process will then be repeated for numerous different electrode configurations and finally result in a two-dimensional tomogram according to the image reconstruction algorithms incorporated. since free ion content determines tissue and fluid conductivity, muscle and blood will conduct the applied currents better than fat, bone or lung tissue. this property can be used to reconstruct static images by morphological or absolute eit (a-eit). however, in contrast to linear x-rays used in computed tomography, electric currents travel three dimensionally along all the paths simultaneously, weighted by their conductivity (thus primarily along the path of least resistivity, but not exclusively). this means, that a part of the electric current leaves the transverse plane and results in an impedance transfer. this and other factors are the reason why image reconstruction in absolute eit is so hard, since there is usually more than just one solution for image reconstruction of a three-dimensional area projected onto a two-dimensional plane. 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 calderón, and in the mathematical literature of inverse problems it is often referred to as "calderón's inverse problem" or the "calderón problem". there is extensive mathematical research on the problem of uniqueness of solution and numerical algorithms for this problem. compared to the tissue conductivities of most other soft tissues within the human thorax, lung tissue conductivity is approximately five-fold lower, resulting in high absolute contrast. this characteristic may partially explain the amount of research conducted in eit lung imaging. furthermore, lung conductivity fluctuates intensely during the breath cycle which accounts for the immense interest of the research community to use eit as a bedside method to visualize inhomogeneity of lung ventilation in mechanically ventilated patients. eit measurements between two or more physiological states, e.g. between inspiration and expiration, are therefore referred to as time difference eit (td-eit). time difference eit (td-eit) has one major advantage over absolute eit (a-eit): inaccuracies resulting from interindividual anatomy, insufficient skin contact of surface electrodes or impedance transfer can be dismissed because most artifacts will eliminate themselves due to simple image subtraction in f-eit. this is most likely the reason why, as of today, the greatest progress of eit research has been achieved with difference eit. further eit applications proposed include detection/location of cancer in skin, breast, or cervix, localization of epileptic foci, imaging of brain activity. as well as a diagnostic tool for impaired gastric emptying. attempts to detect or localize tissue pathology within normal tissue usually rely on multifrequency eit (mf-eit), also termed electrical impedance spectroscopy (eis) and are based on differences in conductance patterns at varying frequencies. history the invention of eit as a medical imaging technique is usually attributed to john g. webster and a publication in 1978, although the first practical realization of a medical eit system was detailed in 1984 due to the work of david c. barber and brian h. brown. together, brown and barber published the first electrical impedance tomogram in 1983, visualizing the cross section of a human forearm by absolute eit. even though there has been substantial progress in the meantime, most a-eit applications are still considered experimental. however, two commercial f-eit devices for monitoring lung function in intensive care patients have been introduced just recently. a technique similar to eit is used in geophysics and industrial process monitoring – electrical resistivity tomography. in analogy to eit, surface electrodes are being placed on the earth, within bore holes, or within a vessel or pipe in order to locate resistivity anomalies or monitor mixtures of conductive fluids. setup and reconstruction techniques are comparable to eit. in geophysics, the idea dates from the 1930s. electrical resistivity tomography has also been proposed for mapping the electrical properties of substrates and thin films for electronic applications. theory in this prototype, the electrodes are attached around a grapefruit which represents a child's head. liquid is injected into the grapefruit to mimic brain haemorrhage. electrical conductivity and permittivity vary among biological tissue types and depend on their free ion content. further factors affecting conductivity include temperature and other physiological factors, e.g. the respiratory cycle between in- and expiration when lung tissue becomes more conductive due to lower content of insulating air within its alveoli. after positioning surface electrodes through adhesive electrodes, an electrode belt or a conductive electrode vest around the body part of interest, alternating currents of typically a few milliamperes at a frequency of 10–100 khz will be applied across two or more drive electrodes. the remaining electrodes will be used to measure the resulting voltage. the procedure will then be repeated for numerous "stimulation patterns", e.g. successive pairs of adjacent electrodes until an entire circle has been completed and image reconstruction can be carried out and displayed by a digital workstation that incorporates complex mathematical algorithms and a priori data. the current itself is applied using current sources, either a single current source switched between electrodes using a multiplexer 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 eit systems still used an analog demodulation circuit to convert the alternating voltage to a direct current level before running it through an analog-to-digital converter. newer systems convert the alternating signal directly before performing digital demodulation. depending on indication, some eit systems are capable of working at multiple frequencies and measuring both magnitude and phase of the voltage. voltages measured are passed on to a computer to perform image reconstruction and display. the choice of current (or voltage) patterns affects the signal-to-noise ratio significantly. with devices capable of feeding currents from all electrodes simultaneously (such as act3) it is possible to adaptively determine optimal current patterns. if images are to be displayed in real time a typical approach is the application of some form of regularized inverse of a linearization of the forward problem or a fast version of a direct reconstruction method such as the d-bar method. most practical systems used in the medical environment generate a 'difference image', i.e. differences in voltage between two time points are left-multiplied by the regularized inverse to calculate an approximate difference between 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 done at rensselaer polytechnic institute starting in the 1980s.