A comparison of the spatial sensitivity of EEG and EIT

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1 A comparison of the spatial sensitivity of EEG and EIT Thomas C. Ferree, Matthew T. Clay and Don M. Tucker Electrical Geodesics, Riverfront Research Park, Eugene, Oregon Computational Science Institute, University of Oregon Department of Mathematics, University of Oregon Department of Psychology, University of Oregon Abstract We use lead field theory to compute spatial sensitivity distributions for two electrical brain imaging methodologies: electroencephalography (EEG) and electrical impedance tomography (EIT). These methods are applicable to evoked responses as well as detection and monitoring of ischemic and hemorrhagic stroke. We compare maximum sensitivities, halfsensitivity volumes, and depth of sensitivity. We quantify the dependence of each on skull conductivity, since the skull is the main challenge to noninvasive imaging in humans. We find that for some EIT four-electrode configurations, the sensitivity distributions are similar to those of two-electrode EEG. However, the wide variety of four-electrode configurations available in EIT suggest that some brain regions may be best isolated by EIT. Taken together EEG and EIT could improve clinical practice by providing both redundant and complementary measures of brain physiology. Introduction To be submitted to IEEE Transactions on Medical Imaging Basic researchers and clinicians agree that a combination of imaging modalities can be advantageous for imaging human brain function. This is first because different modalities usually image distinct physiological processes, and second because even when two modalities are imaging essentially the same physiological process, each will have relative strengths and weaknesses in its spatial sensitivity distributions. The question of which modalities to emphasize depends upon the scientific question being asked. We seek here an electrical brain imaging system applicable to cognitive science, acute stroke assessment, and long-term brain monitoring. Electroencephalography (EEG) measures scalp potential differences arising from the synchronous oscillations of nearby cortical pyramidal neurons. It has long been used for functional brain imaging in psychology, since it can track changes in brain state over the millisecond time scales necessary to resolve cognitive events. In its most common application, evoked response potentials (ERPs) are obtained by averaging scalp EEG time series which have been aligned according to stimulus or response times. Localization of brain activity underlying the scalp topography is a challenging problem under intense investigation, which we do not address here. We focus instead on the spatial sensitivity of EEG, which involves only the forward solution. Electrical impedance tomography (EIT) has become a broadly used term to mean the measurement of tissue conductivity or changes in tissue conductivity. It has long been applied in the thorax to image cardiac function and cardiac stroke. More recently, Holder has shown that 1

2 brain tissue impedance chances occur on millisecond time scales relative to stimulus time and cognitive events (). The suggested mechanism of such impedance changes is a cell swelling. This is because, for frequencies below 100 khz, essentially all impressed current passes through extracellular space only, i.e., does not flow across the cell membrane (). Cell swelling reduces the extracellular space and decreases the bulk tissue conductivity. While these changes are typically small (< 0.1%) it may be that, with further advances in acquisition and inverse methods, EIT may become useful for cognitive research. A major outstanding problem in clinical practice is acute ischemic stroke. In ischemic stroke, brain tissue is deprived of oxygen, typically due to an arterial blockage. This results in neuronal cell death if not treated promptly. While magnetic resonance imaging (MRI) and x-ray computed tomography (CT) show dead tissue, they do not show cells which are in the acute ischemic state, and it is these cells which are the best candidates for rescue. The development of new thrombolytic drugs, e.g., t-pa, hold great promise for treating ischemia (), but unfortunately thrombolytics also increase the risk of brain hemorrhage (). It is therefore essential to monitor the recovery of stroke patients using compatible modalities which are sensitive to both ischemia and hemorrhage. The outcome of monitoring should be quantitative measures of decline or improvement of ischemia, as well as a reliable alarm signaling high probability of developing hemorrhage. This can be accomplished with a combined EEG and EIT brain monitoring system. Cortical ischemia is accompanied by at least two distinct physiological changes which are detectable using electrical methods. The first is a change in the oscillatory dynamics of cortical neurons. The EEG power spectrum arising from ischemic tissue exhibits a characteristic shift to lower frequencies (). By low-pass filtering the data and using existing inverse methods it may be possible to detect and approximately localize ischemic tissue using the EEG (Luu et al., 2000). Measures of the EEG time series other than simple Fourier analysis may also be helpful in this regard (). The second is cell swelling within ischemic tissue. Like functional activity, tissue ischemia is accompanied by changes in impedance (). As cells fail metabolically and their resting potential drifts upward, excessive water follows sodium and chloride ions into the cell and causes cell swelling. Impedance changes due to ischemia are significantly larger (50%) than those due to functional brain activity (). Since it is not known whether how oscillatory changes are related to impedance changes during ischemic progression, a combined EEG/EIT imaging approach would likely give a more complete picture. Following treatment with thrombolytics, one expects to see an improvement in brain state which should be detectable and quantifiable by both EEG and EIT. An equally if not more important goal of monitoring derives from the fact that thrombolytic drugs cause brain hemorrhage in approximately 6% of patients (). A robust hemorrhage detection methodology even without localization could alert a physician to a deteriorating situation. Approximate localization could improve the situation in ambulances and field hospitals where x-ray CT may not be immediately available. Since the conductivity of blood is about 2.5 times higher than that of intact brain tissue (), an impedance change due to brain tissue being displaced by blood can be expected to have the opposite sign from ischemia (???). We define three measures of sensitivity. The first is the maximum sensitivity. This is found by computing the scalar sensitivity at a large number of points in the brain cavity. Since such a sensitivity function must be multiplied by a physiological signal to determine absolute detectability on the scalp, these results are used here only to assess relative strengths and weaknesses of each modality. The second is the half-sensitivity volume (HSV), defined as the set of points in the brain cavity for which the scalar sensitivity is at least one-half its maximum 2

3 value (Malmivuo and Plonsey, 1995). The choice of threshold is of course arbitrary, but this provides a well-defined measure of the volume of brain tissue probed by a particular modality. Finally, we define the depth of sensitivity as the maximum depth of all points comprising the HSV.. There are both similarities and differences in the physiological mechanisms giving rise to EEG and EIT signals. Similarities and differences in the spatial sensitivity of the two techniques further enriches their interrelationship. In EEG, the potential difference is measured between two locations on the scalp, and as such it is fundamentally a bipolar measurement. In EIT, current is injected through one pair of electrodes and the potential difference is measured across a different pair. As such, EIT is fundamentally a quadrupolar measurement, and has many more possible configurations than EEG. We will show below that the spatial sensitivities of EEG and EIT are in some situations redundant and in other situations complementary. Since cognitive task are also used to assess stroke damage and recovery, a combined EEG/EIT imaging system could significantly improve stroke care. Because of their fundamental relationship through the physics of electric fields, these technologies can be combined effectively and economically. Theory Scalp EEG is made possible by the cellular-level anatomy of mammalian cortical tissue. The apical dendrites of cortical pyramidal cells are aligned along the local normal to the cortical surface. Synchronously active cells generate extracellular currents which superimpose to generate electric and magnetic fields detectable at a distance. Figure 1 shows a distribution of EEG current sources in relation to the cortical sheet. Figure 1. Schematic diagram of the human head, showing two EEG electrodes and the position and alignment of EEG current sources in the cortical sheet. Adapted from Nunez (1995). The electric potential Φ in the extracellular space is determined by the solution to Poisson s equation 2 Φ = 1 r r J s where Js is the source density due to neuronal transmembrane currents, and σ is the local tissue conductivity (Nunez, 1981). A multipole expansion of an arbitrary current distribution has the dipole as its leading order term (Jackson, 1975), hence the general solution for potentials in the conductive head volume can be written as the sum of solutions for a single dipole source. The following discussion of lead fields is given in the context of a single dipole, but such dipoles should be viewed here only as the fundamental unit of an arbitrary source current distribution. 3

4 We are not arguing that brain activity can be described in general by a small number of current dipoles. In spherical and realistic head models, the linearity of Poisson s equation allows the potential difference across two scalp electrodes due to a single dipole to be written as Φ = r p L r where p is the current dipole moment, and L is called the lead field for a particular electrode pair and dipole location (). This lead field vector forms the basis of all the analyses which quantify the spatial sensitivity of scalp EEG and EIT. Intuitively, the lead field may be computed by putting a dipole at a particular location in the head volume and computing the potential difference across many pairs of electrodes. If one of the electrodes is kept fixed then this produces the scalp topography for a particular reference electrode and is equivalent to the conventional way of thinking about the forward solution for scalp EEG. It is also possible to reverse the perspective, keeping the electrode pair fixed and varying the dipole location. In this way, the variation in potential difference as a function of dipole location and orientation determines the spatial sensitivity of a particular electrode pair. The reciprocity theorem for volume conductors of arbitrary geometry (Helmholtz, 1853) facilitates the computation of the lead field vector for a particular electrode pair. It shows that the lead field L is determined entirely by the geometry and conductivity of the head volume, and the resulting expression is r L = r J i I i where J i is the impressed current density which would be generated at the dipole location if a total impressed current I i were injected through the electrode pair. By virtue of the vector dot product between the lead field and the dipole moment vectors, the potential difference across two electrodes has a rather trivial dependence on dipole orientation. That is to say, given the lead field vector, it is trivial to understand how the potential difference depends upon dipole orientation. Of course, Figure 1 shows that the allowed dipole orientations are determined by the gross anatomy of the cortex, which is geometrically complex. In the results below, we ignore this effect, understanding that it is straightforward to add this constraint given a segmented image of the cortical surface. We therefore focus on the magnitude of the lead field vector and quantify the spatial sensitivity of scalp EEG independent of orientation. The spatial sensitivity of EIT is determined by lead field vector for the injection and measurement pairs. Figure 2 shows the experimental configuration that underlies EIT. The lines represent surface electrodes, and arrowheads indicate the direction of the impressed current flow. It is assumed that there are no current sources in the volume, since in practice we inject current at high enough frequencies (>100 Hz) that the impressed potential can be separated from the background EEG. 4

5 A A I 1 C Φ2 B Φ 1 B D C D I 2 t=t 1 t=t 2 Figure 2. Electrode arrangement for reciprocity theorem and detection of local impedance changes. At time t 1, current I 1 is injected and Φ 1 is measured; at time t 2, current I 2 is injected and Φ 2 is measured. Let Φ 1 be the potential difference across electrodes C and D at time t 1, when current I 1 is injected through electrodes A and B, and let Φ 2 be the potential difference across electrodes A and B at time t 2, when current I 2 is injected through electrodes C and D. We assume throughout that the conductivity is a scalar function of position. Geselowitz (1971) and Lehr (1972) have show that if between these times the scalar conductivity changes from σ 1 to σ 2 then the potential differences are related by Z 2 Z 1 = ( 2 1 ) L r 1 L r 2 d 3 r brain where Z 1 and Z 2 are the four-electrode mutual impedances at the respective time points. The key point is that the conductivity change is weighted at each point by the scalar dot product of the lead fields for each electrode pair. When t 1 and t 2 are considered as two sequential time points, the method is often called electrical impedance plethysmography (EIP). It is directly applicable to functional brain imaging and stroke monitoring, since each of these involve impedance changes over time. The same formulation is also fundamental to conventional EIT, wherein one seeks absolute measures of tissue conductivity. A straightforward iterative algorithm has been shown to produce static images of conductivity by evolving conductivity guesses toward reproducing the scalp potentials (). This is applicable at patient presentation to determine baseline tissue properties and thereby improve the calculation of the lead fields for EIP, or to detect existing ischemia or hemorrhage. We use the term EIT here to refer collectively to imaging of static and dynamic conductivity. For EIT, the spatial dependence of a particular four-electrode configuration is determined locally by the dot product of the corresponding lead fields. We define the EIT scalar sensitivity function S as S( r ) L r 1 ( r ) L r 2 ( r ) One can define a half-sensitivity volume (HSV) in much the same way as for EEG, but for EIT the vector magnitude is replaced by the scalar absolute value. Maximum sensitivity and depth of sensitivity are also defined similarly. In contrast to the EEG problem, there is no directional component to conductivity changes which would correspond to dipole orientation. The numerical results below show the product of the relevant lead fields for several examples of EIT four-electrode configurations. We show the dependence of these sensitivity measures as a 5

6 function of electrode positions and skull conductivity for two complementary electrode configurations. Numerical results The major obstacle to noninvasive electrical imaging of the brain is the low conductivity of the skull. To address this point and provide a simple comparison between EEG and EIT it is sufficient to use a spherical head model. We computed the lead field vector using the forward solutions derived in Ferree et al. (2000) for current injected into the scalp. We took the spatial gradient and compute the lead field vector by dividing by the injected current. To establish the numerical accuracy of our implementation, we compared the scalp potential computed via the dot product of the lead field vector and a current dipole with that produced using standard expressions in the literature (Sun, ). The scalp potentials were typically in four significant figures agreement. The parameters in the model were chosen as follows. The outer radii of the four tissue layers were 8.0 cm (brain), 8.2 cm (CSF), 8.7 cm (skull) and 9.2 cm (scalp). The conductivity values σ were determined from the literature review described in Ferree et al. (2000). The nominal values were 0.25 S/m (brain), 1.79 S/m (CSF), S/m (skull) and 0.44 S/m (scalp). For all tissue except these skull, these values are similar to those currently used in most simulations. The skull value given above is a factor 1/24 that of the scalp, which is in agreement with the most current available literature (Law, 1993). This is significantly larger than that used in most simulations, which typically assume a factor 1/80. The results below are therefore given for factors of 1/24 and 1/80, and the effects of skull conductivity are discussed. Figure 3 shows the EEG lead field vectors within the HSV for three revealing electrode configurations. The sequence of figures shows that the HSV is a single contiguous volume for nearby electrode pairs, and bifurcates near 60 degrees to become two separate volumes for more distant pairs. Nearby electrodes are primarily sensitive to tangential dipoles in the region between them, but are also sensitive to radial dipoles at the locations underneath each electrode. In contrast, distant electrodes are primarily sensitivity to radial dipoles, but are also sensitive to tangential components are the periphery of the HSV. (a) (b) (c) Figure 3. The EEG lead field vector L within the HSV for a spherical head model and skull/scalp ratio 1/24. The electrode separation angles are 10 (a), 60 (b) and 90 (c) degrees. The circles on the scalp surface indicate the location of EEG electrodes. The lengths of the arrows show the magnitude of the lead field vector, and the directions of the arrows show its direction. 6

7 Figure 4 summarizes the sensitivity information for EEG electrode separations between 1 and 180 degrees. The HSV (Figure 4a) increases as a function of angle until the bifurcation occurs, then decreases slightly. For very small separation angles, the HSV reaches a minimum which allows a quantification of the optimal sensitivity for conventional and high-density electrode arrays. For conventional 20-electrode systems, for which nearby pairs are separated by 30 degrees, we find an optimal spatial resolution of cubic cm. For modern 130-electrode systems, for which nearby pairs are separated by only 10 degrees, we find an optimal spatial resolution of 6-8 cubic cm. The general behavior of the HSV and this small-angle saturation can be understood in two complementary ways. In terms of the lead field vector computed via scalp current injection, for nearby electrodes more of the current is shunted through the scalp and the amount that passes though the skull to contribute to the HSV becomes indicative of the local skull conductivity only. In terms of the corresponding EEG scalp potentials, the potential difference becomes less for nearby electrodes just based upon the definition of potential difference. The point of saturation is indicative of the fact that the skull acts like a spatial lowpass filter for the more variable subdural potential, and eventually the electrode separation is beneath the highest spatial frequency comprising the scalp potential. The maximum sensitivity (Figure 4b) and depth of sensitivity (Figure 4c) both increase monotonically as a function of angle, but effectively saturate by 60 degrees. Together these imply that in general EEG is more sensitive to deeper dipoles, although their location is less easily resolved by virtue of the larger HSV of distant electrodes. The depth of sensitivity shows a saturation at small angles similar to that seen in the HSV. It is interesting that the maximum sensitivity does not also show this behavior. The lower the skull conductivity, the larger the HSV and depth of sensitivity, and the lower the maximum sensitivity. Overall the dependence of the HSV on skull conductivity is the strongest: when the skull conductivity is decreased by a factor 80/24=3.33, the HSV increases by roughly the same amount, while the maximum sensitivity and depth of sensitivity change only twofold. (a) (b) (c) Figure 4. Half-sensitivity volume (a), maximum sensitivity (b), and depth of sensitivity (c) as a function of angle between EEG electrodes, for skull/scalp conductivity ratios 1/24 and 1/80. Two EEG electrodes always defined a plane, and in a spherical head model all such planes are equivalent. Though Figure 3 shows the lead fields in a planar slice, and sensitivity measures shown in Figure 4 were computed in the full three-dimensions of our spherical head model. In EIT there are many more electrode arrangements possible than in EEG. We have chosen two subsets for comparison, each with all four electrodes restricted to a plane. Even with these planar electrode configurations, the lead fields and sensitivity measures were computed in three-dimensions just as for EEG. The particular subsets considered, however, are similar to 7

8 those used commonly in the EIT literature, where EIT images are often computed with only twodimensional models and considerations. The first EIT electrode configuration we consider is referred to as the neighboring configuration (Malmivuo and Plonsey, 1995). This terminology refers to the fact that the injection electrodes are nearest neighbors, and the measurement electrodes are nearest neighbors. The lead fields and sensitivity measures are then considered as a function of the angle between and injection and measurement pairs. Neighboring pairs were assumed to be separated by 10 degrees, as is the case for modern 130-channel electrode arrays. Figure 5 shows the scalar sensitivity function, defined as the dot product of the lead fields for injection and measurement pairs, within the HSV as a function of the angle between injection and measurement pairs. The dependence on angle is seen to be qualitatively similar to that of EEG. Below 50 degrees the HSV is a single contiguous volume, then bifurcates near 50 degrees into two separate volumes. (a) (b) (c) Figure 5. The scalar sensitivity function within the HSV in a spherical head model and skull/scalp ratio 1/24. Injection (white circles) and measurement (black circles) electrodes are each neighboring and are separated by 10 degrees. The angle between injection and measurement pairs are 30 (a), 50 (b) and 90 (c) degrees from center to center. Figure 6 summarizes the sensitivity information for all injection-measurement pair separations between 1 and 180 degrees. Below 10 degrees the behavior is qualitatively different from that above 10 degrees, because below 10 degrees one measurement electrode sits between the two injection electrodes, or visa versa. To simplify the discussion we focus on the latter case only. The HSV (Figure 6a) is qualitatively similar to that of EEG (Figure 4a), but with the bifurcation occurring at slightly smaller angles. The maximum sensitivity (Figure 6b) is opposite that of EEG, decreasing rapidly at larger angles. This is because the lead fields of injection and measurement pairs are each largely confined to the vicinity of their respective electrode pair (see Figure 3) and do not overlap significantly at larger angles. The depth of sensitivity increases as a function of angle in a way very similar to that of EEG. The dependence on conductivity of each of these measures is also like that of EEG. The lower the skull conductivity, the larger the HSV and depth of sensitivity, and the lower the maximum sensitivity. In contrast to EEG, the dependence of the maximum sensitivity on skull conductivity is the strongest: when the skull conductivity is decreased by a factor 80/24=3.33, the HSV increases roughly twofold and the depth of sensitivity increases only slightly, while the maximum sensitivity decreases drastically at angles below 60 degrees. 8

9 In the introduction we described how ischemic tissue exhibits physiological changes that are accessible to both EEG and EIT, and that simultaneous measures would be beneficial in clinical applications, even if largely redundant. It is therefore desirable to make quantitative comparisons of EEG and nearest neighbor EIT. This is straightforward for the HSV and depth of sensitivity, since these measures are expressed in the same units. Comparing Figures 4a and 6a, the HSV for neighboring EIT overall is roughly a factor of 5 smaller than that of EEG. This suggests that the use of EIT for diagnosis and monitoring of cortical ischemia could significantly improve localization efforts. Comparing Figures 4c and 6c, the depth of sensitivity of EEG is approximately 1.25 times that of neighboring EIT if the skull/scalp ratio is near 1/24, and is approximately 1.50 times that of EIT if the skull/scalp ratio is near 1/80. Thus EEG is sensitive to somewhat deeper sources than neighboring EIT. We will see that this situation is reversed, however, for the diametric EIT configuration discussed next. A quantitative comparison of the absolute sensitivity of EEG and EIT is confounded by the fact that the vector lead field sensitivity of EEG and the scalp lead field sensitivity of EIT have different units. We return to this point in detail in the Discussion section. (a) (b) (c) Figure 6. Half-sensitivity volume (a), maximum sensitivity (b), and depth of sensitivity (c) as a function of angle between injection and measurement electrode pairs, for neighbor EIT with skull/scalp conductivity ratio 1/24 and 1/80. Figure 7 shows the The sensitivity distribution is fundamentally different than anything seen in EEG, or in nearest neighbor EIT, because the distribution is not simply bimodal. This example is particularly interesting because at some locations there is significant sensitivity to deeper tissues and relatively low sensitivity to more superficial tissue. Such configurations hold promise for zooming in on brain activity deeper within the skull. Figure 8 summarizes the sensitivity information for all electrode separations between 0 and 180 degrees, for the opposite-electrode configuration of the sort shown in Figure 5 (c). For 30 degrees we find a maximum spatial resolution of 62 cubic cm. For 10 degrees, we find a maximum spatial resolution of 11 cubic cm. These are much larger than the EEG case and nearest neighbor EIT cases. 9

10 (a) (b) (c) Figure 8. Half-sensitivity volume (a), maximum sensitivity (b), and maximum depth of HSV (c) as a function of angle between electrodes, for opposed EIT electrode configurations and conductivity ratio 1/24 and 1/80. The maximum absolute sensitivity (b) is maximum for angles near zero and 180 degrees, when the diametric pairs are nearly parallel. The higher the skull conductivity for any configuration, the lower the overall sensitivity. For any skull conductivity, where there is appreciable maximum sensitivity the HSV is relatively small and superficial. Near perpendicular configurations the HSV is much larger and Acknowledgements This work was supported by NIH grants R43-NS and R43-AG Discussion We have described the similarities and difference of the spatial sensitivity of noninvasive human EEG and EIT. We have studied the EEG case exhaustively and quantified the maximum sensitivity, half-sensitivity volume and depth of sensitivity. We see a strong dependence on skull conductivity, emphasizing the need for methods of measuring the parameter. Due to the fundamental dependence of the EIT scalar lead field on three angles rather than one, even in a spherical head model, we have studied the EIT case only for particular configurations. Still, this analysis shows that EIT supports sensitivity distributions which similar to those of EEG, but also which are qualitatively different than those of EEG. Thus the two methods can be view as complementary and a combination of EEG and EIT would seem optical for imaging cortical ischemia. Regarding optimal sampling density of EEG, the plateau in the HSV for small angles can be somewhat misleading, if this is used to conclude that no benefit is to be gained for more dense electrode arrays. Independent of the benefits gained in robustness to bad channels, etc., Figure 4 strongly suggests that it will be advantageous to have 5 degree electrode separations, but that more dense arrays will provide only marginal benefit. As a particular example, consider the detection of superficial tangential dipoles by nearest neighbor pairs. The sensitivity to tangential dipoles is restricted to the region between the electrodes. The next neighboring pair of electrodes will also be sensitive to superficial dipoles, but in a location which is translated on the order of the inter-electrode spacing. In order to optimally detect tangential dipoles under a particular electrode, one must use the electrodes which neighbor it on either side. The larger separation of those electrodes will result in a more diffuse HSV and deeper sensitivity. With twice the sampling density, it would be possible to choose an intermediate pair for optimal detection of 10

11 tangential dipoles under a particular electrode, without compromising on spatial resolution. The 10 degree separation of 130 electrode arrays A quantitative comparison of the absolute sensitivity of EEG and EIT is confounded by the fact that the vector lead field sensitivity of EEG and the scalp lead field sensitivity of EIT have different units. In addition, the physiological origin of EEG and EIT signals are different, e.g., a comparison made in the context of evoked responses may lead to completely different conclusions than that made in the context of cortical ischemia. To make such a comparison rigorously, one must make quantitative estimates of the EEG and EIT signals arising from ischemic tissue, for example. Ideally, the estimates should be cast in the language of signal to noise ratios for comparison of absolute detectability across modalities. It has been reported that ischemic tissue can exhibit impedance increases of as much as 50%. At present, however, there is no information available on the dipole strengths expected to arise from the pathological EEG oscillations of ischemic tissue??? We therefore restricted the present study to issues of spatial sensitivity and their bearing on stroke localization. It would be interesting to extend this comparison to include optical imaging (OI). OI has the potential to detecting cell swelling as occurs in cortical ischemia. In this way the underlying mechanism of OI in the context is most like that of EIP or EIT. Yet OI is fundamentally a bipolar measurement, in that the signal is detected via light from a single emitter incident on a single detector. In this way, the sensitivity distribution of OI can be expected to most like that of EEG. It seems that by comparing the sensitivity distributions of EEG and EIT with OI it may be possible to better assess their relative strengths for detecting and monitoring cortical ischemia. References Baumann, S. B., D. R. Wonzy, S. K. Kelly and F. M. Meno (1997). The electrical conductivity of human cerebrospinal fluid at body temperature. IEEE Transactions on Biomedical Engineering 44(3): Clay, M. T., T. C. Ferree and D. M. Tucker (2000). Imaging ischemia and hemorrhage through the human skull with electrical impedance tomography. In preparation. Ferree, T. C., K. J. Eriksen and D. M. Tucker (2000). Regional head tissue conductivity estimation for improved EEG analysis. IEEE Transactions on Biomedical Engineering. In press. Foster, K. R. and H. P. Schwan (1989). Dielectric properties of tissues and biological materials: A critical review. Critical Reviews in Biomed. Eng. 17(1): Geddes, L. A. and L. E. Baker (1967). The specific resistance of biological materials: A compendium of data for the biomedical engineer and physiologist. Med. Biol. Eng. 5: Geselowitz, D. B. (1971). An application of electrocardiographic lead theory to impedance plethysmography. IEEE Transactions on Biomedical Engineering 18(1): Helmholtz, H. L. F. (1853). Ueber einige Gesetze der Vertheilung elektrischer Strome in korperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche. Ann. Physik und Chemie 89: ,

12 Law, S. K. (1993). Thickness and resistivity variations over the upper surface of the human skull. Brain Topography 6(2): Lehr, J. (1972). A vector derivation useful in impedance plethysmographic field calculations. IEEE Transactions on Biomedical Engineering 19(2): Luu et al. (2000). Malmivuo Malmivuo and Plonsey (1995). Nelder, J. A. and R. Mead (1965). Computer Journal 7 : Nunez, P. L. (1987). A method to estimate local skull resistance in living subjects. IEEE Transactions on Biomedical Engineering 34(11): Plonsey R. (1969). Bioelectric phenomena. Mc-Graw Hill, New York. Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery (1992). Numerical recipes in C. Cambridge University Press. Rush, S. and D. A. Driscoll (1969). EEG electrode sensitivity - an application of reciprocity. IEEE Transactions on Biomedical Engineering 16(1):