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 types of biological tissues or due to the movement of fluids and gases within tissues. 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. 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 td-EIT. This is most likely the reason why, as of today, the greatest progress of EIT research has been achieved with time 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.