Brain Topography, Volume 5, Number 2, 1992
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Electrical Impedance Tomography (Eli) of Brain Function D.S. Holder*
Summary: Electrical impedance tomography (EIT) is a recently developed technique which enables the internal impedance of an object to be imaged non-invasively. Images are at present reconstructed from measurements made at 51 kHz with a ring of sixteen electrodes placed around the subject. A minimum data set is acquired in 40 msec, and an image can be reconstructed in about 5 sec. The technique is rapid, safe, portable and inexpensive, and so is ideal for non-invasive continuous imaging at the bedside. It cannot be used at present to image changes in the brain with scalp electrodes, as the relative resistance of the skull is too great. It should be possible to use it in the near future with a ring of subdural electrodes to produce images of brain regions undergoing anoxic depolarization in conditions such as epilepsy or stroke. It may be possible to use it in the future to image impedance changes related either to blood flow or depolarization during functional activity. Images of depolarization could be produced with a temporal resolution of milliseconds and would form a substantial advance in neuroscience methodology. Keywords: Impedance; Electrical impedance tomography; Neuroimaging; Neurophysiology; Cerebral function; Epilepsy.
Introduction to Electrical Impedance Tomography (EIT) By Ohm's law, the resistance of an object can be calculated if the voltage across it and the current passed are known. In principle, this could be done with just two electrodes, but the measured resistance then includes that of the electrode-tissue interfaces as well as the subject. M e a s u r e m e n t is b e s t p e r f o r m e d w i t h four electrodes, which avoids this problem (figure 1). Inpractice, alternating current at above 10 kHz is used for most biological measurement, because there is less risk of exciting nerves, and electrode problems are reduced. With alternating current, both resistances and capacitances influence the passage of current. The two components resistive and capacitative - may be separated electronically. "Impedance" refers to their combined effect in impeding the flow of current. In practice, at the frequencies used in EIT, resistive effects are paramount, and impedance may be approximated to resistance. The term "impedance" will be used synonymously with "resistance" below. When current is applied in this w a y to a conducting
*Departments of Physiology, University College and Clinical Neurophysiology, The Maudsley Hospital, London, UK. Accepted for publication: July 13, 1992. Corrrespondence and reprint requests should be addressed to D.S. Holder, Department of Physiology, University College, London, WCIE 6BT, UK. Copyright © 1992 Human Sciences Press, Inc.
subject, it flows in three dimensions. Most will flow directly between the electrodes, but some will travel by more circuitous routes. In fact, some current will flow in a graded w a y in all parts of the subject, but the majority may be thought of as flowing in a spindle or banana shaped volume (figure 1). The principle of EIT is that a large number of such impedance measurements are made from electrodes placed on the boundary of an object. Each measurement represents the impedance of a banana or spindle shaped volume of tissue, weighted according to the distribution of current flow. These canbe reconstructed into an image by computer. There is a fundamental difference to attempted imaging of endogenously produced electric or magnetic fields. It is mathematically impossible to produce unique reconstructions of the multiple unknown sources which occur in EEG or MEG. Hypothetical source localization is possible if certain assumptions are made about the number and nature of the sources, but it is not usually possible to justify these in any particular case. In contrast, in EIT the position and nature of the current source is known, so reconstruction is in principle unique, although it may be difficult in practice. At present, images are two-dimensional i.e., they are made as if all current flowed in the plane of the electrodes, so that the image represents impedance changes in the electrode plane only. As current flows in 3-D, this is an over-simplification (see below). Whilst there are many ways of achieving this in theory, the following description refers to the only device which is commercially available for clinical use - the "Sheffield
88
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Figure 1. a) Ohm's law. In the simplest case, an unknown resistance may be measured by applying a known voltage from a battery. The resulting current flows in inverse proportion to the resistance, b) Biological impedance measurement. A constant current is applied to the unknown subject via two electrodes. Current flows in three dimensions (shown here diagrammatically only as two). The impedance can be calculated because it is proportional to the voltage measured from two other electrodes. This"four electrode'" method minimizes artefacts due to variations in the impedances of the electrodes themselves: A constant current is applied irrespective of the current electrode impedances, and the impedance of the voltage measuring electrodes becomes negligible in comparison to the much larger input impedance of modern voltage measuring circuits.
EIT system" (Barber and Seagar 1987; Brown and Seagar 1987). Sixteen electrodes are equally spaced around the subject. A current of 5 mA or less at 51 kHz is passed between two adjacent electrodes, and the resistive component of the potential difference is then recorded in turn from each of the thirteen adjacent pairs of other available electrodes. The system is controlled by an IBM compatible microcomputer with an Inte180186 processor. A minimum data set may be collected in 40 msec. Multiple sets of data-usually over a few seconds - may be averaged in order to reduce noise. The algorithm is illustrated in Figure 2. It is not theoretically optimum, but is rapid and practicable. In particular, it is relatively robust in situations, such as in clinical subjects, where electrode placement is not exact. One image can be reconstructed in about 5 sec. About thirty of these Sheffield EIT systems have been constructed and are being assessed worldwide. The system is not in routine clinical use for any purpose, but is used in clinical research for monitoring gastric emptying. Preliminary examples of EIT images of the thoracic impedance gated to the ECG or respiration, and the upper arm d u r i n g fracture healing have been published (Webster 1990; Holder (in press)). Preliminary images of intraventricular haemorrhage in the neonate (Murphy et al. 1987), or ECG gated changes in the adult head (McArdle et al. 1989) have been published, but are single examples and their relationship to underlying tissue properties was not established.
The Sheffield EIT system is a prototype device and has several specific limitations as a result of its design: 1) Spatial resolution. The spatial resolution (defined as the distance apart two objects need to be to be separated by an impedance value of 1/e of the peak changes) for a point impedance disturbance in a tank of saline might be expected to be roughly 20% of the tank diameter at the centre or 10-16% near the edge (Eyuboglu et al. 1989; Holder 1992a). 2) Off-plane impedance changes. Impedance changes out of the plane of the electrodes would be expected to produce changes in the image, as current spreads in all directions. Eyuboglu et al. (1989) found that impedance changes from a progressively smaller central area were represented in the image, as an impedance disturbance progressively moved off-plane. Therefore an impedance change which was actually the full diameter of the electrode array, but off-plane, would appear in the image as a central impedance disturbance. 3) Distortion due to assumption of initial constant resistivity. Any inhomogeneity in the baseline resistivity of the subject will produce greater inaccuracy, as the program used assumes homogeneous resistivity in calculating the equipotential lines on which back projection is based. 4) Imaging of impedance differences only. The imaging procedure has been designed to image only the difference between a specified reference image and subsequent images. 5) Assumption of a circular electrode array. It is assumed that the electrodes are equally spaced and form a circle. Any deviation from this will
Impedance Imaging of Brain Function
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9 Figure 2. The reconstruction algorithm, a) Data collection procedure, b) It is assumed that the object has an initially constant resistivity. The current applied to an adjacent electrode pair is equivalent to a dipole, and p r o d u c e s t h e illustrated lines of isopotential. (These are calculated in advance and included in the algorithm). The empirical principle of the algorithm is that a small resistance c h a n g e within such a sector produces a proportional c h a n g e in the potential difference between the electrodes on the boundary of the sector enclosing the change. The boundaries of the sector are taken to be the isopotential lines which end on the electrodes. This is illustrated for a circular resistance change in the sector ending at electrodes 6 and 7 when current was applied to electrodes 16 and 1. c) Reconstruction is performed by back-projecting e a c h c h a n g e in PD along its corresponding sector, and then adding all the resulting changes. This produces a blurred reconstructed image, which is improved by weighting the contribution of each pixel, and with the use of an empirical de-blurring filtering function. This is illustrated for the object in (b). Each sector containing altered resistance is b o u n d e d by a heavy line.
result in a distortion in the image. These limitations pose problems for current research with the Sheffield EIT system, but there are good grounds for anticipating substantial technical improvements in the future. Major areas of development at present include: 1) I m p r o v e d data acquisition. Use of 128 electrodes could in theory produce a spatial resolution of 1% of the diameter of the electrode array (Barber and Brown 1984). Preliminary results with 32 electrode systems have been reported (Fuks et al. 1991). Alternative current drive arrangements should give better signal-tonoise ratios in the centre of the image, and absolute images may become possible (see Webster 1990). 2) Improved reconstruction algorithms. The Sheffield system only uses one iteration. Superior iterative algorithms have been proposed. These require greater computing power and time, but rapid reconstruction should become possible, especially with the use of parallel computers
(Paulson et al. 1990;see Webster 1990). Other areas under development include imaging at multiple frequencies (Griffiths and Zhang 1989; Riu et al. (in press); Wang et al. 1992) and in three dimensions (Goble and Isaacson 1990). At the present time, EIT cannot therefore compete with most other brain imaging methods in terms of spatial resolution. It does, however, have the following potential advantages: 1) It is non-invasive. Currents used (less than 100 ~A peak-to-peak at 51 kHz on the brain) are safer than limits required by British Standards and do not damage or excite tissue. 2) The equipment is portable. The Sheffield system comprises a multiplexer about the size of a video recorder, attached to a microcomputer. It can be placed at the bedside or on a laboratory bench. The electronics can be made smaller if needed (Brown et al. 1990). 3) The system costs about £15,000 sterling at present. It is therefore far less expen-
90 sive than other imaging devices such as X-ray computer tomography or Positron Emission Tomography (PET). 4) The temporal resolution is 40 msec (25 frames may be collected per second). Temporal resolution of a few tens of microseconds could be produced by averaging after repeated stimuli; individual potential measurements could be saved in separate m e m o r y bins and combined subsequently. 5) Small impedance changes of less than 1% can be reliably discriminated (Holder 1992a). 6) Impedance changes in a characteristic w a y in certain physiological conditions. EIT could therefore provide a uniquely practical imaging method in a clinical or research situation where continuous images are required over a protracted period.
The Possible use of EIT to Image Impedance Changes in the Brain During Functional Activity At present, there are excellent ways of imaging structural abnormalities in the brain by X-ray CT or MRI. EIT may prove to have clinical utility as a practical monitoring method for early diagnosis in conditions such as intraventricular haemorrhage in the neonate (Murphy et al. 1987), but its relatively poor spatial resolution makes it unlikely that it will ever replace existing methods for routine high-resolution structural diagnosis. Changes related to blood flow may already be imaged by Positron Emission Tomography or Single Photon Emission Computed Tomography. These have a temporal resolution of tens of seconds or more and a spatial resolution of several millimeters, and are large, expensive and immovable. At present, the use of EIT for this purpose remains to be established, but its portability and superior temporal resolution m a y permit it to become a useful alternative imaging method. In other situations, its superior temporal resolution may render it qualitatively superior to PET or SPECT. The immediate application of EIT with the Sheffield system for imaging in the adult head will be restricted due to its technical limitations. It would, of course, be convenient to image with scalp electrodes. Unfortunately, because of the assumption of uniform initial resistivity, spatial resolution of brain changes is degraded unacceptably (Holder 1992a). The spatial resolution of the Sheffield system is about 20% for distinguishing two discrete disturbances, but it can localize the centre of a single disturbance with an accuracy of 5% of the electrode array diameter in a saline tank (Holder 1992a). With the Sheffield system, it should therefore be possible to produce reasonable images in the laboratory or in patients if electrodes can be positioned on the brain. Imaging with scalp electrodes should become possible in the future, w h e n c u r r e n t drive arrangements and
Holder
reconstruction algorithms are improved.
Impedance changes due to cell swelling during stroke, spreading depression or epilepsy When cerebral grey matter outruns its energy supply, a characteristic sequence of events takes place. This is termed "anoxic depolarization", because it occurs during pure hypoxia, but the term has been extended to include the similar events which occur in ischaemia, spreading depression or epilepsy. These events have been most studied in the cerebral cortex, but also occur in other areas of grey matter in the brain. When measured in the cerebral cortex, the characteristic event is that spontaneous electrical activity ceases and a sustained negative shift of tens of millivolts is recorded with an electrode on the cortical surface. These events are accompanied by a substantial m o v e m e n t of ions and water, as ionic homeostasis fails. Water follows sodium and chloride into cells, so that the extracellular space shrinks by about 50% (Hansen and Olsen 1980).. At frequencies up to 100 kHz, the great majority of current applied to the brain passes through the extracellular fluid. This component of current will be resistive and so is measured by the Sheffield EIT system, which measures the in-phase component of the impedance. During anoxic depolarization, the impedance of grey matter in brain therefore increases, because the extracellular space shrinks. (Changes in temperature, the impedance of neuronal membranes, and blood volume may also contribute, but the effect due to cell swelling is greatly predominant.) Large impedance increases of about 20 - 100% occur during cerebral ischaemia in species such as the rat (Holder, 1992b), cat (Hossman 1971) and m o n k e y (Gamache et al. 1975). Spreading depression is a phenomenon which can be elicited in the grey matter of experimental animals by applying potassium chloride solution or mechanical trauma. Intense activity of depolarized cells occurs, so that potassium and excitatory amino-acids pass into the extracellular space. These then excite neighbouring cells by diffusion. In this way a concentric "ripple" of activity moves out from the site of initial disturbance like a ripple in a pond. It moves at about 3mm per rain, and has been postulated to be the cause of the migraine aura in humans (Pearce 1985). Impedance increases of about 40% occur in various species (Holder 1992c; Bures et al. 1974). During epilepsy induced in experimental animals, reversible cortical impedance increases of 5 - 20% have been observed during measurement at I kHz with a two electrode system in the rabbit or cat (Van Harreveld and Schad6 1962). The changes had a duration similar to the period of epileptic EEG activity and were due to anoxic depolarization-like processes, as a negative DC shift occurred. Similar chan-
Impedance Imaging of Brain Function
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Figure 3. EIT images during cerebral ischaemia. Global cerebral ischaemia was produced in anaesthetized rats by reversibly occluding the vertebral and carotid arteries for 15 min. The image is displayed as a contour m a p ; x and y axes represent the electrode plane, and the z axis represents impedance change. A bimodal i m p e d a n c e increase was observed, which is largest in the occipital region. Increases are largest in the midline. Thisis probably because the volume of sensitivity is biconvex. (After (Holder, 1992a)).
ges have been observed in cat hippocampus, amygdala, and cortex (Elazar et al. 1966), and cat cortex (Shalit 1965). Impedance increases of about 3% have recently been recorded in humans during seizures (Holder, Binnie and Polkey in press). All these changes are large enough to be detected by EIT systems. Determination of the accuracy of the images is in progress. Imaging of experimental epilepsy and spreading depression are being performed in this laboratory. Reversible impedance increases of the order of one hundred per cent have been observed during global cerebral ischaemia in the anaesthetized rat (figure
3). If imaging through the scalp becomes possible, continuous monitoring of such changes to detect cerebral ischaemia after head injury or during artificially induced hypotension at operation may be a useful tool. It may also be possible to image during migraine attacks, to elucidate if s p r e a d i n g d e p r e s s i o n is actually the mechanism of the aura in humans. Clinically useful application may be possible with the Sheffield system as it stands. At present, it is essential to localize epileptic foci in intractable epileptics prior to curative neurosurgery. It is usually necessary to use intracranial electrodes which are inserted at a preliminary operation. The EEG is then measured over a period of days while the patient is ambulatory on the ward. While subdural electrodes carry a low risk, depth electrodes which penetrate into the cerebral substance carry a significant morbidity and mortality. Haemorrhage resulting in permanent neurological damage occurred in 0.8% in one report (879 patients); in another, 2 patients of a series of 140 died (see Van Buren 1987). In addition, the success rate of surgery is only about 70%
(Polkey 1988). The cause of this is not entirely clear, but it may be partly because intracranial electrodes can only sample at a limited number of sites. It may be possible to use EIT with an occipitofrontal ring of subdural electrodes to localize the seizure focus, on the basis that there should be a single discrete impedance change at the onset of the seizure, which could be localized by the Sheffield system. This should be justifiable ethically, as the electrodes would be similar to those already in use. It could be performed in ambulatory patients in the same way as EEG telemetry. Its advantages would be that depth electrodes need not be used, and information could be obtained from all sites in the sensitive volume of brain. Slow i m p e d a n c e c h a n g e s d u r i n g f u n c t i o n a l activity
Impedance has been shown to change in the brain during physiological stimulation. Adey et al. (1962) measured impedance at 1 kHz using chronically implanted electrodes in the limbic system of the cat. They observed impedance decreases of about 2% which lasted for several seconds during physiological stimuli, such as presentation of milk or exposure of a female to a male. Aladjalova (1964) observed similar impedance changes in cerebral cortex after direct electrical stimulation. The cause of such changes is unclear. The most likely explanation is that blood volume and flow alter. Changes in blood volume will alter tissue impedance, either by replacing a fluid of different resistivity (such as CSF), or by changing the cross-sectional area available to current flow. Changes in blood flow can also alter impedance, because erythrocyte alignment alters (Coulter and Pappenheimer 1949). It is well established that blood
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flow and volume increase in the brain during functional activity. This forms the basis of much of the functional brain imaging by PET. It is unclear whether EIT could ultimately have a superior spatial resolution, but, if feasible, it m a y provide a more practical and less expensive method. Functional activity with the time course of the action potential
In both the possible applications described above, similar changes can at present be imaged by other, existing, methods; the advantages of EIT would be of a practical nature. There, is, however, a third possible application of EIT in neuroscience, in which it would have a unique advantage in being able to image nervous activity with a temporal resolution of milliseconds. This application is more technically demanding but, if possible, would provide a substantial advance in neuroscience technology. The application would be based on the well known change in impedance of neural membranes which occurs on depolarization as ion channels open. In the squid axon, impedance falls forty-fold (Cole and Curtis 1938) when measured directly across the axon. There should therefore be an impedance change across populations of cells in nervous tissue during activity. The effect could be due to action potentials in white matter, or to summated effects of synaptic activity in grey matter, which is the origin of the EEG (see Kiloh et al. 1981). At the frequencies of measurement with EIT, most current passes in the highly conductive extracellular space. The amplitude of the impedance changes across tissue is therefore likely to be small. It is at present unclear how large this effect is. Klivington and Galambos (1968) m e a s u r e d i m p e d a n c e changes d u r i n g physiologically evoked activity in the auditory cortex of anaesthetized cats at 10 kHz. A maximum decrease of about 0.005% was observed, which had a similar time course to the evoked cortical response. Similar changes were measured in visual cortex during visual evoked responses (Klivington and Galambos 1967) and less reproducible impedance decreases of up to 0.02% were observed in subcortical nuclei during auditory or visual evoked responses in unanaesthetized cats (Galambos and Velluti 1968). Freygang and Landau (1955) observed a maximum decrease in impedance of 3.1% measured with square wave pulses 0.3 - 0.7 msec long during the evoked cortical response in the cat. Chailakhian and Iur'ev (1957) observed an impedance decrease of 0.030.1% and reactance decrease of 0.1-0.3% during the action potential in crab nerve measured at 35 kHz. It is unlikely that even improved EIT systems in the future could detect deep impedance changes of 0.01%.
Holder
However, it should be possible to increase the signal by recording at lower frequencies. This is because the nerve membrane behaves as a capacitance and resistance in parallel. At higher frequencies, any effects of changes in the resistive component due to opening of ion channels is short-circuited by current passing through membrane capacitance. In the evoked response study in the cat, an inverse log-log relationship between peak impedance decrease and oscillator frequency was observed. This corresponded to a peak impedance decrease of about 0.002% at 50 kHz, and .014% at 1 kHz (Galambos and Veiluti 1968). Impedance decreases of 0.7% have been recorded during the action potential in crab nerve with a DC measuring potential; no changes larger than baseline variability of 0.02% could be detected at 50 kHz (Holder 1992d). The proposed application would be to record EIT images from one or more rings of electrodes, either around the brain in experimental animals or human surgical subjects, or, ultimately, around the scalp. Data would be gathered after a repeated stimulus, in the same way as somatosensory or visual evoked responses. An EIT image would subsequently be reconstructed for each millisecond or so of the recording window. In this way, it would be possible to determine the waveform of activity in any selected pathway during evoked responses.
Conclusion Electrical Impedance Tomography is a new imaging method, whose clinical utility has so far only been demonstrated for imaging of gastric emptying. At present, it has a poor spatial resolution, but this may be expected to improve substantially in the next few years. Its advantages are that it is small, portable and non-invasive. Presently available systems cannot image through the skull. One important application which could well be realized in the immediate future is for localization of epileptic foci in ambulatory patients using a ring of subdural electrodes. Possible future applications include epileptic source localization with scalp or skull electrodes, monitoring for cerebral ischaemia, and imaging of slow or rapid impedance changes during functional activity. The latter would represent a major advance in neuroscience technology.
References Adey, W.R., Kado, R. T. and Didio, J. Impedance measurements in brain tissue of animals using microvolt signals. Exp. Neurol., 1962, 5: 47-66. Aladjalova, N.A. Slow electrical processes in the brain. Prog. Brain Res. 1964, 7: 156-206. Barber, D.C. and Brown, B. H. Applied potential tomography. J. Phys. E: Sci. Instrum. 1984, 17: 723-733.
Impedance Imaging of Brain Function
Barber, D.C. and Seagar, A.D. Fast reconstruction of impedance images. Clin. Phys. Physiol. Meas. 8 Suppl., 1987, A: 47-54 Brown, B.H. and Seagar, A. D. The Sheffield data collection system. Clin. Phys. Physiol. Meas. 8 Suppl., 1987, A:91-98. Brown, B.H., Lindley, E., Knowles, R. and Wilson, A.J.A body worn APT system for space use Proc of 3rd EC conference on EIT, Copenhagen. COMAC-BME DG XII/F/3 Brussels. 1990: 162-167. Bures, J., Buresova, O. and Krivanek, J. The mechanism and applications of Leao's spreading depression of electroencephalographic activity. Academic Press, New York, 1974. Chailakhian, L.M., and Iur'ev, S. A. An investigation of the time relations of the action potential and impedance changes on excitation in the frog nerve. Biofizika 1957, 2: 417-426. Cole, K.S. and Curtis, H.J. Electric impedance of the squid giant axon during activity. J. Gen. Physiol., 1939, 22: 649-670. Coulter, N.A. and Pappenheimer, J.R. Development of turbulence in flowing blood. Am. J. Physiol., 1949,159: 401-408. Elazar, Z., Kado, R.T. and Adey, W.R. Impedance changes during epileptic seizures. Epilepsia, 1966, 7: 291-307. Eyuboglu, B.M., Brown, B.H. and Barber, D.C. Limitations to SV determination from APT images. IEEE Eng. Med. Biol. Soc. 11th Ann. Int. Conf., 1989: 442-443. Freygang, W.H. and Landau, W.M. Some relations between resistivity and electrical activity in the cerebral cortex of the cat. J. Cell. Comp. Physiol., 1955, 45: 377-392. Fuks, L.F., Cheney, M., Isaacson, D., Gisser, D.G. and Newell, J.C. Detection and imaging of electric conductivity and permittivity at low frequency. IEEE Trans Biomed Eng., 1991, 38: 1106-1110. Galambos, R. and Velluti, R. Evoked resistance shifts in unanaesthetized cats. Exp. Neurol., 1968, 22: 243-252. Gamache, F.W., Dold, G.M. and Myers, R.E. Changes in cortical impedance and EEG activity induced by profound hypotension. Am. J. Physiol. 1975, 228: 1914-1920. Goble, J. and Isaacson, D. Fast reconstruction algorithms for three-dimensional electrical impedance tomography. Proc 12th Ann Int Conf IEEE Engineering in Medicine and Biology Soc., 1990, 10: 285-286. Griffiths, H. and Zhang, Z. A dual-frequency electrical impedance tomography system. 1989, 34: 1465-76. Hansen, J.H. and Olsen, C.E. Brain extracellular space during spreading depression and ischemia. Acta. Physiol. Scand., 1989, 108: 355-365. Holder, D.S. Electrical impedance tomography with cortical or scalp electrodes during global cerebral ischaemia in the anaesthetized rat. Clin Phys Physiol Meas., 1992a, 13: 87-98. Holder, D.S. Detection of cerebral ischaemia in the anaesthetized rat by impedance measurement with scalp electrodes : implications for non-invasive imaging of stroke by electrical impedance tomography. Clin. Phys. Physiol. Meas., 1992b, 13:63 - 76. Holder, D.S. Detection of cortical spreading depression in the anaesthetized rat by impedance measurement with scalp electrodes : implications for non-invasive imaging of the brain with electrical impedance tomography. Clin. Phys. Physiol. Meas., 1992c, 13:77 - 86. Holder, D.S. Impedance changes during the compound action potential in crab nerve measured with 50 khz or direct
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current: implications for impedance imaging of neuronal depolarization in the brain. Med. Biol. Eng. Comput., 1992d, 30: 140-146. Holder, D.S. Detection of cerebral ischaemia in the anaesthetized rat by impedance measurement with scalp electrodes: implications for non-invasive imaging of stroke by electrical impedance tomography. Clin. Phys. Physiol. Meas., 1992b, 13:63 - 76. Holder, D.S. (Ed.) Clinical and physiological applications of electrical impedance tomography. UCL press: London (in press). Holder, D.S., Binnie, C.D., Polkey, C.P. The possible application of EIT to imaging epileptic foci. Proc COMAC in Biomagnetism, Cambridge: 1991 (in press). Hossman, K. Cortical steady potential, impedance and excitability changes during and after total ischaemia of cat brain. Exp. Neurol. 1971, 32:163-175 Kiloh, LG., McComas, A.J., Osselton, J.W. and Upton, A.R.M. Clinical Electroencephalography. Butterworths: London, 1981. Klivington, K. A. and Galambos, R. Resistance shifts accompanying the evoked cortical response in the cat. Science 1967, 157: 211-213. Klivington, K. A. and Galambos, R. Rapid resistance shifts in cat cortex during click-evoked responses. J. Neurophysiol., 1968, 31: 565-573. McArdle, F.J., Brown, B.H. and Angel, A. Imaging resistivity changes of the adult brain during the cardiac cycle. IEEE Eng. in Med. Biol. 11th Ann. Int. Conf. 1989: 480-481. Murphy, D. Burton, P. Coombs, R., Tarassenko, L. and Rolfe, P. Impedance imaging in the newborn Clin. Phys. Physiol. Meas. 1987, 8 Suppl. A: 131-140. Paulson, K., Breckon, W. and Pidcock, M. Concurrent EIT reconstruction. Proc of 3rd EC conference on EIT, Copenhagen. COMAC-BME DG XII/F/3 Brussels 1990: 136-143. Pearce, J.M.S. Is migraine explained by Leao's spreading depression? Lancet 1985: 763-765. Polkey, C.P. Neurosurgery. In : A textbook of epilepsy. J. Laidlaw, A. Richens, and J. Oxley, (Ed.), Churchill Livingstone:Edinburgh, 1988, 484-510. Riu, P.J., Rosell, J., Lozano, A. and Palls-Areny, R. A broadband system for multifrequency static imaging in EIT. Clin. Phys. Physiol. Meas., (in press). Shalit, M.N. The effect of metrazol on the hemodynamics and impedance of the cat's brain cortex. J. Neuropath. Exp. Neurol., 1965, 24: 75-84. Van Buren, J.M. Complications of surgical procedures in the diagnosis and treatment of epilepsy. In: J. Engel Jr. (Ed.), Surgical treatment of the epilepsies. Raven Press: New York, 1987. Van Harreveld, A. and Schad6, J.P. Changes in the electrical conductivity of cerebral cortex during seizure activity. Exp. Neurol., 1962, 5: 383-400. Wang, M., Dickin, F.J. and Beck, M. Improved electrical impedance tomography data collection system and measurement protocols. Proc. ECAPT meeting, Manchester, 1992 (in press). Webster, J.G. Electrical Impedance Tomography. Adam Hilger: Bristol, 1990.
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Electrical Impedance Tomography (Eli) of Brain Function D.S. Holder*
Summary: Electrical impedance tomography (EIT) is a recently developed technique which enables the internal impedance of an object to be imaged non-invasively. Images are at present reconstructed from measurements made at 51 kHz with a ring of sixteen electrodes placed around the subject. A minimum data set is acquired in 40 msec, and an image can be reconstructed in about 5 sec. The technique is rapid, safe, portable and inexpensive, and so is ideal for non-invasive continuous imaging at the bedside. It cannot be used at present to image changes in the brain with scalp electrodes, as the relative resistance of the skull is too great. It should be possible to use it in the near future with a ring of subdural electrodes to produce images of brain regions undergoing anoxic depolarization in conditions such as epilepsy or stroke. It may be possible to use it in the future to image impedance changes related either to blood flow or depolarization during functional activity. Images of depolarization could be produced with a temporal resolution of milliseconds and would form a substantial advance in neuroscience methodology. Keywords: Impedance; Electrical impedance tomography; Neuroimaging; Neurophysiology; Cerebral function; Epilepsy.
Introduction to Electrical Impedance Tomography (EIT) By Ohm's law, the resistance of an object can be calculated if the voltage across it and the current passed are known. In principle, this could be done with just two electrodes, but the measured resistance then includes that of the electrode-tissue interfaces as well as the subject. M e a s u r e m e n t is b e s t p e r f o r m e d w i t h four electrodes, which avoids this problem (figure 1). Inpractice, alternating current at above 10 kHz is used for most biological measurement, because there is less risk of exciting nerves, and electrode problems are reduced. With alternating current, both resistances and capacitances influence the passage of current. The two components resistive and capacitative - may be separated electronically. "Impedance" refers to their combined effect in impeding the flow of current. In practice, at the frequencies used in EIT, resistive effects are paramount, and impedance may be approximated to resistance. The term "impedance" will be used synonymously with "resistance" below. When current is applied in this w a y to a conducting
*Departments of Physiology, University College and Clinical Neurophysiology, The Maudsley Hospital, London, UK. Accepted for publication: July 13, 1992. Corrrespondence and reprint requests should be addressed to D.S. Holder, Department of Physiology, University College, London, WCIE 6BT, UK. Copyright © 1992 Human Sciences Press, Inc.
subject, it flows in three dimensions. Most will flow directly between the electrodes, but some will travel by more circuitous routes. In fact, some current will flow in a graded w a y in all parts of the subject, but the majority may be thought of as flowing in a spindle or banana shaped volume (figure 1). The principle of EIT is that a large number of such impedance measurements are made from electrodes placed on the boundary of an object. Each measurement represents the impedance of a banana or spindle shaped volume of tissue, weighted according to the distribution of current flow. These canbe reconstructed into an image by computer. There is a fundamental difference to attempted imaging of endogenously produced electric or magnetic fields. It is mathematically impossible to produce unique reconstructions of the multiple unknown sources which occur in EEG or MEG. Hypothetical source localization is possible if certain assumptions are made about the number and nature of the sources, but it is not usually possible to justify these in any particular case. In contrast, in EIT the position and nature of the current source is known, so reconstruction is in principle unique, although it may be difficult in practice. At present, images are two-dimensional i.e., they are made as if all current flowed in the plane of the electrodes, so that the image represents impedance changes in the electrode plane only. As current flows in 3-D, this is an over-simplification (see below). Whilst there are many ways of achieving this in theory, the following description refers to the only device which is commercially available for clinical use - the "Sheffield
88
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Figure 1. a) Ohm's law. In the simplest case, an unknown resistance may be measured by applying a known voltage from a battery. The resulting current flows in inverse proportion to the resistance, b) Biological impedance measurement. A constant current is applied to the unknown subject via two electrodes. Current flows in three dimensions (shown here diagrammatically only as two). The impedance can be calculated because it is proportional to the voltage measured from two other electrodes. This"four electrode'" method minimizes artefacts due to variations in the impedances of the electrodes themselves: A constant current is applied irrespective of the current electrode impedances, and the impedance of the voltage measuring electrodes becomes negligible in comparison to the much larger input impedance of modern voltage measuring circuits.
EIT system" (Barber and Seagar 1987; Brown and Seagar 1987). Sixteen electrodes are equally spaced around the subject. A current of 5 mA or less at 51 kHz is passed between two adjacent electrodes, and the resistive component of the potential difference is then recorded in turn from each of the thirteen adjacent pairs of other available electrodes. The system is controlled by an IBM compatible microcomputer with an Inte180186 processor. A minimum data set may be collected in 40 msec. Multiple sets of data-usually over a few seconds - may be averaged in order to reduce noise. The algorithm is illustrated in Figure 2. It is not theoretically optimum, but is rapid and practicable. In particular, it is relatively robust in situations, such as in clinical subjects, where electrode placement is not exact. One image can be reconstructed in about 5 sec. About thirty of these Sheffield EIT systems have been constructed and are being assessed worldwide. The system is not in routine clinical use for any purpose, but is used in clinical research for monitoring gastric emptying. Preliminary examples of EIT images of the thoracic impedance gated to the ECG or respiration, and the upper arm d u r i n g fracture healing have been published (Webster 1990; Holder (in press)). Preliminary images of intraventricular haemorrhage in the neonate (Murphy et al. 1987), or ECG gated changes in the adult head (McArdle et al. 1989) have been published, but are single examples and their relationship to underlying tissue properties was not established.
The Sheffield EIT system is a prototype device and has several specific limitations as a result of its design: 1) Spatial resolution. The spatial resolution (defined as the distance apart two objects need to be to be separated by an impedance value of 1/e of the peak changes) for a point impedance disturbance in a tank of saline might be expected to be roughly 20% of the tank diameter at the centre or 10-16% near the edge (Eyuboglu et al. 1989; Holder 1992a). 2) Off-plane impedance changes. Impedance changes out of the plane of the electrodes would be expected to produce changes in the image, as current spreads in all directions. Eyuboglu et al. (1989) found that impedance changes from a progressively smaller central area were represented in the image, as an impedance disturbance progressively moved off-plane. Therefore an impedance change which was actually the full diameter of the electrode array, but off-plane, would appear in the image as a central impedance disturbance. 3) Distortion due to assumption of initial constant resistivity. Any inhomogeneity in the baseline resistivity of the subject will produce greater inaccuracy, as the program used assumes homogeneous resistivity in calculating the equipotential lines on which back projection is based. 4) Imaging of impedance differences only. The imaging procedure has been designed to image only the difference between a specified reference image and subsequent images. 5) Assumption of a circular electrode array. It is assumed that the electrodes are equally spaced and form a circle. Any deviation from this will
Impedance Imaging of Brain Function
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9 Figure 2. The reconstruction algorithm, a) Data collection procedure, b) It is assumed that the object has an initially constant resistivity. The current applied to an adjacent electrode pair is equivalent to a dipole, and p r o d u c e s t h e illustrated lines of isopotential. (These are calculated in advance and included in the algorithm). The empirical principle of the algorithm is that a small resistance c h a n g e within such a sector produces a proportional c h a n g e in the potential difference between the electrodes on the boundary of the sector enclosing the change. The boundaries of the sector are taken to be the isopotential lines which end on the electrodes. This is illustrated for a circular resistance change in the sector ending at electrodes 6 and 7 when current was applied to electrodes 16 and 1. c) Reconstruction is performed by back-projecting e a c h c h a n g e in PD along its corresponding sector, and then adding all the resulting changes. This produces a blurred reconstructed image, which is improved by weighting the contribution of each pixel, and with the use of an empirical de-blurring filtering function. This is illustrated for the object in (b). Each sector containing altered resistance is b o u n d e d by a heavy line.
result in a distortion in the image. These limitations pose problems for current research with the Sheffield EIT system, but there are good grounds for anticipating substantial technical improvements in the future. Major areas of development at present include: 1) I m p r o v e d data acquisition. Use of 128 electrodes could in theory produce a spatial resolution of 1% of the diameter of the electrode array (Barber and Brown 1984). Preliminary results with 32 electrode systems have been reported (Fuks et al. 1991). Alternative current drive arrangements should give better signal-tonoise ratios in the centre of the image, and absolute images may become possible (see Webster 1990). 2) Improved reconstruction algorithms. The Sheffield system only uses one iteration. Superior iterative algorithms have been proposed. These require greater computing power and time, but rapid reconstruction should become possible, especially with the use of parallel computers
(Paulson et al. 1990;see Webster 1990). Other areas under development include imaging at multiple frequencies (Griffiths and Zhang 1989; Riu et al. (in press); Wang et al. 1992) and in three dimensions (Goble and Isaacson 1990). At the present time, EIT cannot therefore compete with most other brain imaging methods in terms of spatial resolution. It does, however, have the following potential advantages: 1) It is non-invasive. Currents used (less than 100 ~A peak-to-peak at 51 kHz on the brain) are safer than limits required by British Standards and do not damage or excite tissue. 2) The equipment is portable. The Sheffield system comprises a multiplexer about the size of a video recorder, attached to a microcomputer. It can be placed at the bedside or on a laboratory bench. The electronics can be made smaller if needed (Brown et al. 1990). 3) The system costs about £15,000 sterling at present. It is therefore far less expen-
90 sive than other imaging devices such as X-ray computer tomography or Positron Emission Tomography (PET). 4) The temporal resolution is 40 msec (25 frames may be collected per second). Temporal resolution of a few tens of microseconds could be produced by averaging after repeated stimuli; individual potential measurements could be saved in separate m e m o r y bins and combined subsequently. 5) Small impedance changes of less than 1% can be reliably discriminated (Holder 1992a). 6) Impedance changes in a characteristic w a y in certain physiological conditions. EIT could therefore provide a uniquely practical imaging method in a clinical or research situation where continuous images are required over a protracted period.
The Possible use of EIT to Image Impedance Changes in the Brain During Functional Activity At present, there are excellent ways of imaging structural abnormalities in the brain by X-ray CT or MRI. EIT may prove to have clinical utility as a practical monitoring method for early diagnosis in conditions such as intraventricular haemorrhage in the neonate (Murphy et al. 1987), but its relatively poor spatial resolution makes it unlikely that it will ever replace existing methods for routine high-resolution structural diagnosis. Changes related to blood flow may already be imaged by Positron Emission Tomography or Single Photon Emission Computed Tomography. These have a temporal resolution of tens of seconds or more and a spatial resolution of several millimeters, and are large, expensive and immovable. At present, the use of EIT for this purpose remains to be established, but its portability and superior temporal resolution m a y permit it to become a useful alternative imaging method. In other situations, its superior temporal resolution may render it qualitatively superior to PET or SPECT. The immediate application of EIT with the Sheffield system for imaging in the adult head will be restricted due to its technical limitations. It would, of course, be convenient to image with scalp electrodes. Unfortunately, because of the assumption of uniform initial resistivity, spatial resolution of brain changes is degraded unacceptably (Holder 1992a). The spatial resolution of the Sheffield system is about 20% for distinguishing two discrete disturbances, but it can localize the centre of a single disturbance with an accuracy of 5% of the electrode array diameter in a saline tank (Holder 1992a). With the Sheffield system, it should therefore be possible to produce reasonable images in the laboratory or in patients if electrodes can be positioned on the brain. Imaging with scalp electrodes should become possible in the future, w h e n c u r r e n t drive arrangements and
Holder
reconstruction algorithms are improved.
Impedance changes due to cell swelling during stroke, spreading depression or epilepsy When cerebral grey matter outruns its energy supply, a characteristic sequence of events takes place. This is termed "anoxic depolarization", because it occurs during pure hypoxia, but the term has been extended to include the similar events which occur in ischaemia, spreading depression or epilepsy. These events have been most studied in the cerebral cortex, but also occur in other areas of grey matter in the brain. When measured in the cerebral cortex, the characteristic event is that spontaneous electrical activity ceases and a sustained negative shift of tens of millivolts is recorded with an electrode on the cortical surface. These events are accompanied by a substantial m o v e m e n t of ions and water, as ionic homeostasis fails. Water follows sodium and chloride into cells, so that the extracellular space shrinks by about 50% (Hansen and Olsen 1980).. At frequencies up to 100 kHz, the great majority of current applied to the brain passes through the extracellular fluid. This component of current will be resistive and so is measured by the Sheffield EIT system, which measures the in-phase component of the impedance. During anoxic depolarization, the impedance of grey matter in brain therefore increases, because the extracellular space shrinks. (Changes in temperature, the impedance of neuronal membranes, and blood volume may also contribute, but the effect due to cell swelling is greatly predominant.) Large impedance increases of about 20 - 100% occur during cerebral ischaemia in species such as the rat (Holder, 1992b), cat (Hossman 1971) and m o n k e y (Gamache et al. 1975). Spreading depression is a phenomenon which can be elicited in the grey matter of experimental animals by applying potassium chloride solution or mechanical trauma. Intense activity of depolarized cells occurs, so that potassium and excitatory amino-acids pass into the extracellular space. These then excite neighbouring cells by diffusion. In this way a concentric "ripple" of activity moves out from the site of initial disturbance like a ripple in a pond. It moves at about 3mm per rain, and has been postulated to be the cause of the migraine aura in humans (Pearce 1985). Impedance increases of about 40% occur in various species (Holder 1992c; Bures et al. 1974). During epilepsy induced in experimental animals, reversible cortical impedance increases of 5 - 20% have been observed during measurement at I kHz with a two electrode system in the rabbit or cat (Van Harreveld and Schad6 1962). The changes had a duration similar to the period of epileptic EEG activity and were due to anoxic depolarization-like processes, as a negative DC shift occurred. Similar chan-
Impedance Imaging of Brain Function
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Figure 3. EIT images during cerebral ischaemia. Global cerebral ischaemia was produced in anaesthetized rats by reversibly occluding the vertebral and carotid arteries for 15 min. The image is displayed as a contour m a p ; x and y axes represent the electrode plane, and the z axis represents impedance change. A bimodal i m p e d a n c e increase was observed, which is largest in the occipital region. Increases are largest in the midline. Thisis probably because the volume of sensitivity is biconvex. (After (Holder, 1992a)).
ges have been observed in cat hippocampus, amygdala, and cortex (Elazar et al. 1966), and cat cortex (Shalit 1965). Impedance increases of about 3% have recently been recorded in humans during seizures (Holder, Binnie and Polkey in press). All these changes are large enough to be detected by EIT systems. Determination of the accuracy of the images is in progress. Imaging of experimental epilepsy and spreading depression are being performed in this laboratory. Reversible impedance increases of the order of one hundred per cent have been observed during global cerebral ischaemia in the anaesthetized rat (figure
3). If imaging through the scalp becomes possible, continuous monitoring of such changes to detect cerebral ischaemia after head injury or during artificially induced hypotension at operation may be a useful tool. It may also be possible to image during migraine attacks, to elucidate if s p r e a d i n g d e p r e s s i o n is actually the mechanism of the aura in humans. Clinically useful application may be possible with the Sheffield system as it stands. At present, it is essential to localize epileptic foci in intractable epileptics prior to curative neurosurgery. It is usually necessary to use intracranial electrodes which are inserted at a preliminary operation. The EEG is then measured over a period of days while the patient is ambulatory on the ward. While subdural electrodes carry a low risk, depth electrodes which penetrate into the cerebral substance carry a significant morbidity and mortality. Haemorrhage resulting in permanent neurological damage occurred in 0.8% in one report (879 patients); in another, 2 patients of a series of 140 died (see Van Buren 1987). In addition, the success rate of surgery is only about 70%
(Polkey 1988). The cause of this is not entirely clear, but it may be partly because intracranial electrodes can only sample at a limited number of sites. It may be possible to use EIT with an occipitofrontal ring of subdural electrodes to localize the seizure focus, on the basis that there should be a single discrete impedance change at the onset of the seizure, which could be localized by the Sheffield system. This should be justifiable ethically, as the electrodes would be similar to those already in use. It could be performed in ambulatory patients in the same way as EEG telemetry. Its advantages would be that depth electrodes need not be used, and information could be obtained from all sites in the sensitive volume of brain. Slow i m p e d a n c e c h a n g e s d u r i n g f u n c t i o n a l activity
Impedance has been shown to change in the brain during physiological stimulation. Adey et al. (1962) measured impedance at 1 kHz using chronically implanted electrodes in the limbic system of the cat. They observed impedance decreases of about 2% which lasted for several seconds during physiological stimuli, such as presentation of milk or exposure of a female to a male. Aladjalova (1964) observed similar impedance changes in cerebral cortex after direct electrical stimulation. The cause of such changes is unclear. The most likely explanation is that blood volume and flow alter. Changes in blood volume will alter tissue impedance, either by replacing a fluid of different resistivity (such as CSF), or by changing the cross-sectional area available to current flow. Changes in blood flow can also alter impedance, because erythrocyte alignment alters (Coulter and Pappenheimer 1949). It is well established that blood
92
flow and volume increase in the brain during functional activity. This forms the basis of much of the functional brain imaging by PET. It is unclear whether EIT could ultimately have a superior spatial resolution, but, if feasible, it m a y provide a more practical and less expensive method. Functional activity with the time course of the action potential
In both the possible applications described above, similar changes can at present be imaged by other, existing, methods; the advantages of EIT would be of a practical nature. There, is, however, a third possible application of EIT in neuroscience, in which it would have a unique advantage in being able to image nervous activity with a temporal resolution of milliseconds. This application is more technically demanding but, if possible, would provide a substantial advance in neuroscience technology. The application would be based on the well known change in impedance of neural membranes which occurs on depolarization as ion channels open. In the squid axon, impedance falls forty-fold (Cole and Curtis 1938) when measured directly across the axon. There should therefore be an impedance change across populations of cells in nervous tissue during activity. The effect could be due to action potentials in white matter, or to summated effects of synaptic activity in grey matter, which is the origin of the EEG (see Kiloh et al. 1981). At the frequencies of measurement with EIT, most current passes in the highly conductive extracellular space. The amplitude of the impedance changes across tissue is therefore likely to be small. It is at present unclear how large this effect is. Klivington and Galambos (1968) m e a s u r e d i m p e d a n c e changes d u r i n g physiologically evoked activity in the auditory cortex of anaesthetized cats at 10 kHz. A maximum decrease of about 0.005% was observed, which had a similar time course to the evoked cortical response. Similar changes were measured in visual cortex during visual evoked responses (Klivington and Galambos 1967) and less reproducible impedance decreases of up to 0.02% were observed in subcortical nuclei during auditory or visual evoked responses in unanaesthetized cats (Galambos and Velluti 1968). Freygang and Landau (1955) observed a maximum decrease in impedance of 3.1% measured with square wave pulses 0.3 - 0.7 msec long during the evoked cortical response in the cat. Chailakhian and Iur'ev (1957) observed an impedance decrease of 0.030.1% and reactance decrease of 0.1-0.3% during the action potential in crab nerve measured at 35 kHz. It is unlikely that even improved EIT systems in the future could detect deep impedance changes of 0.01%.
Holder
However, it should be possible to increase the signal by recording at lower frequencies. This is because the nerve membrane behaves as a capacitance and resistance in parallel. At higher frequencies, any effects of changes in the resistive component due to opening of ion channels is short-circuited by current passing through membrane capacitance. In the evoked response study in the cat, an inverse log-log relationship between peak impedance decrease and oscillator frequency was observed. This corresponded to a peak impedance decrease of about 0.002% at 50 kHz, and .014% at 1 kHz (Galambos and Veiluti 1968). Impedance decreases of 0.7% have been recorded during the action potential in crab nerve with a DC measuring potential; no changes larger than baseline variability of 0.02% could be detected at 50 kHz (Holder 1992d). The proposed application would be to record EIT images from one or more rings of electrodes, either around the brain in experimental animals or human surgical subjects, or, ultimately, around the scalp. Data would be gathered after a repeated stimulus, in the same way as somatosensory or visual evoked responses. An EIT image would subsequently be reconstructed for each millisecond or so of the recording window. In this way, it would be possible to determine the waveform of activity in any selected pathway during evoked responses.
Conclusion Electrical Impedance Tomography is a new imaging method, whose clinical utility has so far only been demonstrated for imaging of gastric emptying. At present, it has a poor spatial resolution, but this may be expected to improve substantially in the next few years. Its advantages are that it is small, portable and non-invasive. Presently available systems cannot image through the skull. One important application which could well be realized in the immediate future is for localization of epileptic foci in ambulatory patients using a ring of subdural electrodes. Possible future applications include epileptic source localization with scalp or skull electrodes, monitoring for cerebral ischaemia, and imaging of slow or rapid impedance changes during functional activity. The latter would represent a major advance in neuroscience technology.
References Adey, W.R., Kado, R. T. and Didio, J. Impedance measurements in brain tissue of animals using microvolt signals. Exp. Neurol., 1962, 5: 47-66. Aladjalova, N.A. Slow electrical processes in the brain. Prog. Brain Res. 1964, 7: 156-206. Barber, D.C. and Brown, B. H. Applied potential tomography. J. Phys. E: Sci. Instrum. 1984, 17: 723-733.
Impedance Imaging of Brain Function
Barber, D.C. and Seagar, A.D. Fast reconstruction of impedance images. Clin. Phys. Physiol. Meas. 8 Suppl., 1987, A: 47-54 Brown, B.H. and Seagar, A. D. The Sheffield data collection system. Clin. Phys. Physiol. Meas. 8 Suppl., 1987, A:91-98. Brown, B.H., Lindley, E., Knowles, R. and Wilson, A.J.A body worn APT system for space use Proc of 3rd EC conference on EIT, Copenhagen. COMAC-BME DG XII/F/3 Brussels. 1990: 162-167. Bures, J., Buresova, O. and Krivanek, J. The mechanism and applications of Leao's spreading depression of electroencephalographic activity. Academic Press, New York, 1974. Chailakhian, L.M., and Iur'ev, S. A. An investigation of the time relations of the action potential and impedance changes on excitation in the frog nerve. Biofizika 1957, 2: 417-426. Cole, K.S. and Curtis, H.J. Electric impedance of the squid giant axon during activity. J. Gen. Physiol., 1939, 22: 649-670. Coulter, N.A. and Pappenheimer, J.R. Development of turbulence in flowing blood. Am. J. Physiol., 1949,159: 401-408. Elazar, Z., Kado, R.T. and Adey, W.R. Impedance changes during epileptic seizures. Epilepsia, 1966, 7: 291-307. Eyuboglu, B.M., Brown, B.H. and Barber, D.C. Limitations to SV determination from APT images. IEEE Eng. Med. Biol. Soc. 11th Ann. Int. Conf., 1989: 442-443. Freygang, W.H. and Landau, W.M. Some relations between resistivity and electrical activity in the cerebral cortex of the cat. J. Cell. Comp. Physiol., 1955, 45: 377-392. Fuks, L.F., Cheney, M., Isaacson, D., Gisser, D.G. and Newell, J.C. Detection and imaging of electric conductivity and permittivity at low frequency. IEEE Trans Biomed Eng., 1991, 38: 1106-1110. Galambos, R. and Velluti, R. Evoked resistance shifts in unanaesthetized cats. Exp. Neurol., 1968, 22: 243-252. Gamache, F.W., Dold, G.M. and Myers, R.E. Changes in cortical impedance and EEG activity induced by profound hypotension. Am. J. Physiol. 1975, 228: 1914-1920. Goble, J. and Isaacson, D. Fast reconstruction algorithms for three-dimensional electrical impedance tomography. Proc 12th Ann Int Conf IEEE Engineering in Medicine and Biology Soc., 1990, 10: 285-286. Griffiths, H. and Zhang, Z. A dual-frequency electrical impedance tomography system. 1989, 34: 1465-76. Hansen, J.H. and Olsen, C.E. Brain extracellular space during spreading depression and ischemia. Acta. Physiol. Scand., 1989, 108: 355-365. Holder, D.S. Electrical impedance tomography with cortical or scalp electrodes during global cerebral ischaemia in the anaesthetized rat. Clin Phys Physiol Meas., 1992a, 13: 87-98. Holder, D.S. Detection of cerebral ischaemia in the anaesthetized rat by impedance measurement with scalp electrodes : implications for non-invasive imaging of stroke by electrical impedance tomography. Clin. Phys. Physiol. Meas., 1992b, 13:63 - 76. Holder, D.S. Detection of cortical spreading depression in the anaesthetized rat by impedance measurement with scalp electrodes : implications for non-invasive imaging of the brain with electrical impedance tomography. Clin. Phys. Physiol. Meas., 1992c, 13:77 - 86. Holder, D.S. Impedance changes during the compound action potential in crab nerve measured with 50 khz or direct
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current: implications for impedance imaging of neuronal depolarization in the brain. Med. Biol. Eng. Comput., 1992d, 30: 140-146. Holder, D.S. Detection of cerebral ischaemia in the anaesthetized rat by impedance measurement with scalp electrodes: implications for non-invasive imaging of stroke by electrical impedance tomography. Clin. Phys. Physiol. Meas., 1992b, 13:63 - 76. Holder, D.S. (Ed.) Clinical and physiological applications of electrical impedance tomography. UCL press: London (in press). Holder, D.S., Binnie, C.D., Polkey, C.P. The possible application of EIT to imaging epileptic foci. Proc COMAC in Biomagnetism, Cambridge: 1991 (in press). Hossman, K. Cortical steady potential, impedance and excitability changes during and after total ischaemia of cat brain. Exp. Neurol. 1971, 32:163-175 Kiloh, LG., McComas, A.J., Osselton, J.W. and Upton, A.R.M. Clinical Electroencephalography. Butterworths: London, 1981. Klivington, K. A. and Galambos, R. Resistance shifts accompanying the evoked cortical response in the cat. Science 1967, 157: 211-213. Klivington, K. A. and Galambos, R. Rapid resistance shifts in cat cortex during click-evoked responses. J. Neurophysiol., 1968, 31: 565-573. McArdle, F.J., Brown, B.H. and Angel, A. Imaging resistivity changes of the adult brain during the cardiac cycle. IEEE Eng. in Med. Biol. 11th Ann. Int. Conf. 1989: 480-481. Murphy, D. Burton, P. Coombs, R., Tarassenko, L. and Rolfe, P. Impedance imaging in the newborn Clin. Phys. Physiol. Meas. 1987, 8 Suppl. A: 131-140. Paulson, K., Breckon, W. and Pidcock, M. Concurrent EIT reconstruction. Proc of 3rd EC conference on EIT, Copenhagen. COMAC-BME DG XII/F/3 Brussels 1990: 136-143. Pearce, J.M.S. Is migraine explained by Leao's spreading depression? Lancet 1985: 763-765. Polkey, C.P. Neurosurgery. In : A textbook of epilepsy. J. Laidlaw, A. Richens, and J. Oxley, (Ed.), Churchill Livingstone:Edinburgh, 1988, 484-510. Riu, P.J., Rosell, J., Lozano, A. and Palls-Areny, R. A broadband system for multifrequency static imaging in EIT. Clin. Phys. Physiol. Meas., (in press). Shalit, M.N. The effect of metrazol on the hemodynamics and impedance of the cat's brain cortex. J. Neuropath. Exp. Neurol., 1965, 24: 75-84. Van Buren, J.M. Complications of surgical procedures in the diagnosis and treatment of epilepsy. In: J. Engel Jr. (Ed.), Surgical treatment of the epilepsies. Raven Press: New York, 1987. Van Harreveld, A. and Schad6, J.P. Changes in the electrical conductivity of cerebral cortex during seizure activity. Exp. Neurol., 1962, 5: 383-400. Wang, M., Dickin, F.J. and Beck, M. Improved electrical impedance tomography data collection system and measurement protocols. Proc. ECAPT meeting, Manchester, 1992 (in press). Webster, J.G. Electrical Impedance Tomography. Adam Hilger: Bristol, 1990.
