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 are applied to some or all of the electrodes. The resulting electrical potentials are measured, and the process may be repeated for numerous different configurations of applied current.
Proposed applications include monitoring of lung function, detection of cancer in the skin and breast, location of epileptic foci and imaging of brain activity. Until recently, all applications have been considered experimental. However in 2011 the first commercial EIT device for lung function monitoring in intensive care patients was introduced.
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 realisation of a medical EIT system was detailed in 1984 due to the work of David C. Barber and Brian H. Brown.
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.
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 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 to the medical case. In geophysics, the idea dates from the 1930s.
In biological tissue the electrical conductivity and permittivity varies between tissue types likewise depending on temperature and physiological factors. For example lungs are less conductive when the alveoli is filled with air. In EIT adhesive electrodes applied to the skin and an electric current, typically a few milli-Amperes of alternating current at a frequency of 10–100 kHz, is applied across two or more electrodes. Other electrodes 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 to 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 time points is left-multiplied by the regularized inverse to produce an approximate difference between the 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 published in 1992, from the Glenfield Hospital Project.
Lung imaging 
EIT is useful for monitoring patient lungs because the air has a large conductivity contrast to the other tissues in the thorax. The most promising clinical application of lung EIT measurements is for Lung function monitoring of patients being treated with Mechanical ventilation. Such ventilation can often result in Ventilator-associated lung injury. EIT can resolve the changes in the distribution of lung volumes between dependent and non-dependent lung regions as ventilator parameters are changed. Thus, EIT measurements may be used to control the specific ventilator settings to maintain lung protective ventilation for each patient.
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 have been published.
Most EIT studies have focused on regional lung function monitoring using the information determined by functional EIT (f-EIT). However absolute EIT (a-EIT) also has the potential to become a clinically useful tool for Lung imaging, as this approach would allow one to directly distinguish between lung conditions which result from regions with lower resistivity (e.g. hemothorax, pleural effusion, atelectasis and lung edema) and those with higher resistivity (e.g. pneumothorax, emphysema).
The reconstruction of absolute impedance images requires that the exact dimensions, the shape of the body and the precise location of the electrodes, be taken into account, as simplified assumptions would lead to major reconstruction artifacts. While initial studies assessing aspects of a-EIT have already been published, as of today this area of research has not yet reached the level of maturity which would make it suitable for clinical use. In contrast, functional EIT determines relative impedance changes that may be caused by either ventilation or changes of end-expiratory lung volume. These relative changes are referred to a baseline level, which is typically defined by the intra-thoracic impedance distribution at the end of expiration. Functional EIT images can be generated continuously, directly at the bedside. These attributes make regional lung function monitoring particularly useful whenever there is a need to improve oxygenation or CO2 elimination and when therapy changes are intended to achieve a more homogenous gas distribution in mechanically ventilated patients. EIT lung function imaging can resolve the changes in the regional distribution of lung volumes between e.g. dependent and non-dependent lung regions as ventilator parameters are changed. Thus, EIT measurements may be used to control the specific ventilator settings to maintain lung protective ventilation for each patient.
Breast imaging 
EIT is being investigated in the field of breast imaging as an alternative/complementary technique to mammography and magnetic resonance imaging (MRI) for breast cancer detection. The low specificity of mammography  and of MRI  result in a relatively high rate of false positive screenings, with high distress for the patient and cost for the healthcare structure. These shortcomings and concerns related to the use of ionizing radiation, for mammography, and with the nephrotoxicity of Gadolinium, the contrast agent used in breast MRI, make the development of alternative techniques highly desirable.
Literature shows that the electrical properties differ between normal and malignant breast tissues, setting the stage for cancer detection through determination of electrical properties.
A successful commercial development of non-tomographic electrical impedance imaging is the T-Scan device  which has been demonstrated to improve sensitivity and speciﬁcity when used as an adjunct to screening mammography. A report to the United States Food and Drug Administration (FDA) describes a study involving 504 subjects where the sensitivity of mammography was 82%, 62% for the T-Scan alone, and 88% for the two combined. The speciﬁcity was 39% for mammography, 47% for the T-Scan alone, and 51% for the two combined.
Several research groups are across the world are actively developing the technique.
Brain imaging 
EIT has been suggested as a basis for brain imaging to enable the detection and monitoring of cerebral ischemia and haemorrhage, epileptic foci localization, together with research into normal brain function and neuronal activity.
In this use EIT depends upon applying low frequency currents above the skull that are around <100 Hz since during neuronal rest at this frequency these currents remain in the extracellular space unable enter into the intracellular space within neurons. However when a neuron makes an action potential or depolarization, the resistance of its membrane preventing this reduces by a factor of 80. When this happens across large numbers of neurons a resistivity change is made of about 0.06–1.7%. This resistivity change provides a means of detecting coherent neuronal activity across large numbers of neurons and so the tomographic imaging of neural activity in the brain.
Unfortunately while such changes are detectable "they are just too small to support reliable production of images." The prospects of using this technique for imaging will depend upon improved signal processing or recording.
A study reported in June 2011 that Functional Electrical Impedance Tomography by Evoke Response (fEITER) has been used to image changes in brain activity after injection of an anaesthetic. One of the benefits of the technique is that the equipment required is small enough and easy enough to transport so that it can be used in operating theatres.
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  who distribute a Sheffield Mark 3.5 system. Other manufactures include Dräger Medical, CareFusion, a respiratory monitoring company who distribute Goe MF II system that was developed at the University of Göttingen. Impedance Medical Technologies  who manufacture systems based on designs by the Research Institute of Radioengineering 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 intensive care for monitoring ventilation. An EIT device for lung function monitoring that is designed for everyday clinical use in the critical care environment has been made available by Dräger Medical in 2011 
See also 
- Electrical resistivity tomography
- Electrical capacitance tomography
- Respiratory monitoring
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- EIDORS - Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software at Sourceforge
- Shocking truth about what your brain does when you're asleep YouTube video of brain activity imaged with fEITER