Electrical impedance tomography

Electrical Impedance Tomography (EIT), is a medical imaging technique in which an image of the conductivity or permittivity of part of the body is inferred from surface electrical measurements. Typically conducting electrodes are attached to the skin of the subject and small alternating currents applied to some or all of the electrodes. The resulting electrical potentials are measured, and the process repeated for numerous different configurations of applied current.

Proposed applications include monitoring of lung function, detection of cancer in the skin and breast and location of epileptic foci. All applications are currently considered experimental. For a detailed review of medical applications see ^[1]

In geophysics a similar technique (called electrical resistivity tomography) is used using electrodes on the surface of the earth or in bore holes to locate resistivity anomalies, and in industrial process monitoring the arrays of electrodes are used for example to monitor mixtures of conductive fluids in vessels or pipes. The method is used in industrial process imaging^[2] for imaging conductive fluids. In that context the technique is usually called Electrical resistance tomography (note the slight contrast to the name used in geophysics). Metal electrodes are generally in direct contact with the fluid but electronics and reconstruction techniques are broadly similar the the medical case.

The credit for the invention of EIT as a medical imaging technique is usually attributed to John G. Webster in around 1978^[3], although the first practical realisation of a medical EIT system was due to David C. Barber and Brian H. Brown ^[4]. In geophysics the idea dates from the 1930s.

Mathematically the problem of recovering the 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^[5], and in the mathematical literature of inverse problems it is often referred to as the "Calderón Problem". There is extensive mathematical research on the problem of uniqueness of solution and numerical algorithms for this problem^[6].

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Details

In biological tissue the electrical conductivity and permittivity varies between tissue types as well as depending on temperature and physiological factors. For example lungs become less conductive as the alveoli become filled with air. In EIT adhesive electrides applied to the skin and an electric current, typically a few milli-Amperes of alternating current at a frequency of 10-100 hKz, is appled across two or more electrodes. Other electtrodes 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 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 times is left-multiplied by the regularized inverse to produce an approximate difference between the permitivity 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.

Examples

The above images are from the EIT group at Oxford Brookes University and depict an early attempt at three dimensional EIT imaging of the chest using the OXBACT3 EIT system. The reconstructed image is a time average and shows lungs as low conductivity regions. Although an accurate chest shape was used only a 2D reconstruction algorithm was used resulting in a distorted image. The results of a similar chest study were published in ^[7].

Commercial systems

Although medical EIT systems are not widely used several medical equipment manufactures now supply commercial versions of systems developed by university research groups. The first such system is produced by Maltron International [2] who distribute a Sheffield Mark 3.5 system. Other manufactures include Dräger Medical, Viasys Health Care, a respirotory monitoring company who distribute Goe MF II system that was developed at the University of Goettingen. Sim-Tecknika [3] who manufacture systems based on designs by the Research Institute of Radiotechnology and Electronics of the Russian Academy of Science, in Moscow, aimed especially at breast cancer detection. Such systems typically comply with medical safety legislation and are being used by research groups in hospitals, notably in intesnive care for monitoring ventilation.

References

1. ^ Holder D.S., Electrical Impedance Tomography: Methods, History and Applications, Institute of Physics, 2004. ISBN 0-7503-0952-0.
2. ^ MS Beck and R Williams, Process Tomography: Principles, Techniques and Applications, Butterworth-Heinemann (July 19, 1995),ISBN 0750607440
3. ^ Henderson R.P. and Webster J.G. (1978) An Impedance Camera for Spatially Specific Measurements of the Thorax. IEEE Trans. Biomed. Eng. 25: 250-254.
4. ^ Barber D.C. and Brown B.H. (1984) Applied Potential Tomography (Review Article). J. Phys. E:Sci. Instrum 17: 723 - 733.
5. ^ 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 CALDERON, Alberto P. On an inverse boundary value problem. Mat. apl. comput., 2006, vol.25, no.2-3, p.133-138. ISSN 0101-820 [1]
6. ^ 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
7. ^ N. Kerrouche, CN McLeod, WRB Lionheart, Time series of EIT chest images using singular value decomposition and Fourier transform, Physiol. Meas. 22 No 1, 2001 147-157