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 are applied to some or all of the electrodes, the resulting equipotentials being recorded from the other electrodes. 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 used.
Since free-ion content determines tissue and fluid conductivity, muscle and blood will conduct applied currents better than fat, bone, or lung tissue. This property can be used to construct images. 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 highest conductivity, but not exclusively). Image construction can be difficult because there is usually more than one solution for 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 was posed by 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 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 uniqueness of solutions and numerical algorithms for this problem.Uhlmann 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,
Compared to the 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 during the breath cycle which accounts for the 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).
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.
Further EIT applications proposed include detection/location of cancer in skin, breast, or cervix, localization of epileptic foci,Holder D.S., Electrical Impedance Tomography: Methods, History and Applications, Institute of Physics, 2004. . 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 the 1984 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 since this, most a-EIT applications are still considered experimental, though there are commercial systems available.
Electrical resistivity tomography, a technique similar to EIT is used in geophysics and industrial process monitoring. 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.M.S. Beck and R. Williams, Process Tomography: Principles, Techniques and Applications, Butterworth–Heinemann (July 19, 1995), 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
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 adhesive surface 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 electrodes. The remaining electrodes will be used to measure the resulting voltage. The procedure will then be repeated for numerous stimulation patterns, i.e., 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. Image reconstruction incorporates complex mathematical algorithms and a priori data.Holder David S.: Electrical Impedance Tomography. Methods, History and Applications, Institute of Physics: Bristol und Philadelphia 2005, Part 1 Algorithms
The current itself is applied using 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 may be taken either by a single voltage measurement circuit multiplexed over the electrodes or a separate circuit for each electrode. Earlier EIT systems 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 to digital before performing digital demodulation. Some EIT systems are capable of working at multiple frequencies and measuring both magnitude and phase of the electrode voltages. 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.
The achievable frame rate is set by the time needed to collect a complete set of boundary measurements. Where the excitation is routed sequentially between electrode pairs, an approach known as time-division multiplexing, fast 16-electrode instruments are typically limited to a few hundred frames per second. An alternative, first proposed for biomedical EIT, is to drive several excitations simultaneously, each at a distinct frequency, and to separate the superimposed responses by Fourier analysis, a scheme known as frequency-division multiplexing. Because the excitation is then continuous rather than switched, the transients arising from electrode–electrolyte contact impedance are suppressed, removing the dead time otherwise needed for the signal to settle. An implementation of this principle on a field-programmable gate array has been reported to image a 16-electrode sensor at up to 3,906 frames per second, with a signal-to-noise ratio of 55.6–69.1 dB across the 3.9–468.7 kHz band. Frame rates in this range are chiefly of interest in industrial process tomography, where multiphase flow structures evolve far faster than the physiological signals targeted in medical EIT.
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 Levenberg–Marquardt algorithm) to fit the measured data. This is more challenging as it requires accurate knowledge of body shape and the position of the electrodes.
Much of the fundamental work underpinning Electrical Impedance was done at Rensselaer Polytechnic Institute starting in the 1980s.Cheng, K. S., Isaacson, D., Newell, J. C., & Gisser, D. G. (1989). Electrode models for electric current computed tomography. Biomedical Engineering, IEEE Transactions on, 36(9), 918–24.Somersalo, E., Cheney, M., & Isaacson, D. (1992). Existence and uniqueness for electrode models for electric current computed tomography. SIAM Journal on Applied Mathematics, 52(4), 1023–1040.Cheney, M., & Isaacson, D. (1992). Distinguishability in impedance imaging. Biomedical Engineering, IEEE Transactions on, 39(8), 852–860.
Absolute EIT approaches are targeted at digital reconstruction of static images, i.e., two-dimensional representations of the anatomy within the body part of interest. As mentioned above and unlike linear x-rays in computed tomography, electric currents travel three-dimensionally along the path of least resistivity, which results in partial loss of the electric current applied (impedance transfer, e.g., due to blood flow through the transverse plane). This is one of the reasons why image reconstruction in absolute EIT is so complex, since there is usually more than just one solution for image reconstruction of a three-dimensional area projected onto a two-dimensional plane. Another difficulty is that, given the number of electrodes and the measurement precision at each electrode, only objects bigger than a defined size can be distinguished.Alessandrini, G. (1988). Stable determination of conductivity by boundary measurements. Applicable Analysis, 27(1–3), 153–172.