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Electrical Impedance Tomography (EIT) is a non-invasive medical imaging technique in which an image of the conductivity or permittivity of part of the body is inferred from surface electrode measurements. Electrical conductivity depends on free ion content and differs considerably between various biological tissues (absolute EIT) or different functional states of one and the same tissue or organ (relative or functional 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). 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.〔Brown B.H. (2003) "Electrical Impedance Tomography (EIT) – A Review". ''J. Med. Eng. Technol.'' 27(3): 97–108.〕〔Cheney M., Isaacson D. and Newell J. C. (1999) "Electrical impedance tomography". "SIAM review" 41(1): 85–101.〕 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).〔Bodenstein M., David M., Markstaller K. (2009) "Principles of electrical impedance tomography and its clinical application". ''Crit. Care Med." 37(2): 713–724.〕 However, in contrast to linear x-rays used in Computed Tomography, electric currents travel three dimensionally along the path of least resistivity. This means, that a part of the electric current leaves the transverse plane with blood flow 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,〔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 problem of uniqueness of solution 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, ISBN 0-226-10455-9〕 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 inhomogeneities 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 relative or functional EIT (f-EIT).〔 Functional EIT (f-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 in functional EIT.〔〔〔Costa E.L., Lima R.G., Amato M.B. (2009) "Electrical impedance tomography". ''Curr. Opon. Crit. Care'' 15(1): 18–24.〕 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. ISBN 0-7503-0952-0.〕 imaging of brain activity. as well as a diagnostic tool for impaired gastric emptying.〔〔〔Trokhanova O.V., Chijova Y.A., Okhapkin M.B. et al. (2013) "Possibilities of electrical impedance tomography in gynecology". ''J. Phys. Conference Series" 434, 012038.〕 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. 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.〔Barber D.C, Brown B.H. and Freeston I.L. (1983) "Imaging Spatial distributions of resistivity using Applied Potential Tomography". ''Electronics Letters'', 19, 93–95.〕 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.〔M.S. Beck and R. Williams, ''Process Tomography: Principles, Techniques and Applications, Butterworth–Heinemann'' (July 19, 1995), ISBN 0-7506-0744-0〕 Setup and reconstruction techniques are comparable to EIT. In geophysics, the idea dates from the 1930s. ==Theory== As previously mentioned, electrical conductivity and permittivity varies between biological tissue types and depends 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 isolating 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 milli-Amperes 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.〔〔〔〔〔Holder David S.: ''Electrical Impedance Tomography. Methods, History and Applications'', Institute of Physics: Bristol und Philadelphia 2005, ''Part 1 Algorithms''〕〔Lionheart W.R.B. (2004) "EIT reconstruction algorithms: pitfalls, challenges and recent developments" (Review Article). ''Physiol. Meas.'' 25: 125–143.〕 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〔Cook, R. D., Saulnier, G., Gisser, D. G., Goble, J. C., Newell, J. C., & Isaacson, D. (1994). ACT3: A high-speed, high-precision electrical impedance tomograph. Biomedical Engineering, IEEE Transactions on, 41(8), 713–722.〕) it is possible to adaptively determine optimal current patterns.〔Gisser, D. G., Isaacson, D., & Newell, J. C. (1990). Electric current computed tomography and eigenvalues. SIAM Journal on Applied Mathematics, 50(6), 1623–1634.〕 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.〔Dodd M. and Mueller J. L. (2014) "A Real-time D-bar Algorithm for 2-D Electrical Impedance Tomography Data" arXiv:1404.5978〕 Most practical systems used in the medical surrounding 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 in the 1980s and 1990s.〔〔Cheney, M., & Isaacson, D. (1995). Issues in electrical impedance imaging. Computing in Science and Engineering, 2(4), 53–62.〕〔〔〔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.〕 See also the work published in 1992 from the Glenfield Hospital Project (reference missing). 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 (figure 1), 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 given size can be distinguished.〔〔Alessandrini, G. (1988). Stable determination of conductivity by boundary measurements. Applicable Analysis, 27(1–3), 153–172.〕 This explains the necessity of highly sophisticated mathematical algorithms that will account for the inverse problem and its ill-posedness. Further difficulties in absolute EIT arise from inter- and intraindividual differences of electrode conductivity associated with distorted image reconstruction and artifacts. It is also important to bear in mind, that the body part of interest is rarely precisely rotund and that interindividual anatomy varies, e.g. thorax shape, affecting individual electrode spacing.〔Boyle A., Adler A. (2011) "The impact of electrode area, contact impedance and boundary shape on EIT images." ''Physiol. Meas.'' 32(7): 745–54.〕 ''A priori'' data accounting for age-, height- and gender-typical anatomy can reduce proneness to artifacts and image distortion.〔Ferrario D., Grychtol B., Adler A., Solà J., Böhm S.H., Bodenstein M. (2012) "Toward morphological thoracic EIT: major signal sources correspond to respective organ locations in CT." ''IEEE Trans. Biomed. Eng.'' 59(11): 3000–8.〕 Improving the signal-to-noise ratio, e.g. by using active surface electrodes, further reduces imaging errors.〔Rigaud B., Shi Y., Chauveau N., Morucci J.P. (1993) "Experimental acquisition system for impedance tomography with active electrode approach." ''Med. Biol. Eng. Comput.'' 31(6): 593–9.〕〔Gaggero P.O., Adler A., Brunner J., Seitz P. (2012) "Electrical impedance tomography system based on active electrodes." ''Physiol. Meas.'' 33(5): 831–47.〕 Some of the latest EIT systems with active electrodes monitor electrode performance through an extra channel and are able to compensate for insufficient skin contact by removing them from the measurements. Functional EIT bypasses most of these issues by recording measurements in the same individual between two or more physiological states associated with linear conductivity changes. One of the best examples for this approach is lung tissue during breathing due to linear conductivity changes between inspiration and expiration which are caused by varying contents of isolating air during each breath cycle.〔 This permits digital subtraction of recorded measurements obtained during the breath cycle and results in functional images of lung ventilation. One major advantage is that relative changes of conductivity remain comparable between measurements even if one of the recording electrodes is less conductive than the others, thereby preventing most artifacts and image distortions.〔 However, incorporating ''a priori'' data sets or meshs in functional EIT is still useful in order to project functional images onto the most likely organ morphology, which depends on weight, height, gender, and other individual factors.〔 The open source project EIDORS provides a suite of programs (written in Matlab / Octave) for data reconstruction and display under the GNU GPL license. The direct nonlinear D-bar method〔Mueller J L and Siltanen S (2012), Linear and Nonlinear Inverse Problems with Practical Applications. SIAM.〕 for nonlinear EIT reconstruction is available in Matlab code at (). The (Open Innovation EIT Research Initiative ) is aimed at advancing the development of electrical impedance tomography (EIT) in general and to ultimately accelerate its clinical adoption. A plug-and-play (EIT hardware and software package ) is available through (Swisstom ) and can be acquired at net cost price. Image reconstruction and processing of raw data obtained with this set can be carried out without any limitations by the software tools provided through EIDORS. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「electrical impedance tomography」の詳細全文を読む スポンサード リンク
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