IOP PUBLISHING PHYSIOLOGICAL MEASUREMENT

Physiol. Meas. 30 (2009) S201–S224 doi:10.1088/0967-3334/30/6/S14

A modelling study to inform specification and optimalelectrode placement for imaging of neuronaldepolarization during visual evoked responses byelectrical and magnetic detection impedancetomography

O Gilad1,2,5, L Horesh3 and D S Holder1,4

1 Department of Medical Physics & Bioengineering, University College London, London, UK2 The Abramson Center for Medical Physics, Tel-Aviv University, Israel3 Scientific Computing, Mathematics and Computer Science, Emory University, Atlanta,GA, USA4 Department of Clinical Neurophysiology, University College London Hospitals, London, UK

E-mail: o.gilad@ucl.ac.uk, horesh@mathcs.emory.edu and d.holder@ucl.ac.uk

Received 12 December 2008 accepted for publication 25 February 2009Published 2 June 2009Online at stacks.iop.org/PM/30/S201

AbstractElectrical impedance tomography (EIT) has the potential to achieve non-invasive functional imaging of fast neuronal activity in the human brain dueto opening of ion channels during neuronal depolarization. Local changes ofresistance in the cerebral cortex are about 1%, but the size and location ofchanges recorded on the scalp are unknown. The purpose of this work wasto develop an anatomically realistic finite element model of the adult humanhead and use it to predict the amplitude and topography of changes on thescalp, and so inform specification for an in vivo measuring system. A detailedanatomically realistic finite element (FE) model of the head was produced fromhigh resolution MRI. Simulations were performed for impedance changes inthe visual cortex during evoked activity with recording of scalp potentials byelectrodes or magnetic flux density by magnetoencephalography (MEG) inresponse to current injected with electrodes. The predicted changes werevalidated by recordings in saline filled tanks and with boundary voltagesmeasured on the human scalp. Peak changes were 1.03 ± 0.75 μV (0.0039 ±0.0034%) and 27 ± 13 fT (0.2 ± 0.5%) respectively, which yielded an estimatedpeak signal-to-noise ratio of about 4 for in vivo averaging over 10 min and1 mA current injection. The largest scalp changes were over the occipitalcortex. This modelling suggests, for the first time, that reproducible changescould be recorded on the scalp in vivo in single channels, although a higherSNR would be desirable for accurate image production. The findings suggest

5 Author to whom any correspondence should be addressed.

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http://dx.doi.org/10.1088/0967-3334/30/6/S14mailto:o.gilad@ucl.ac.ukmailto:horesh@mathcs.emory.edumailto:d.holder@ucl.ac.ukhttp://stacks.iop.org/PM/30/S201

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that an in vivo study is warranted in order to determine signal size but methodsto improve SNR, such as prolonged averaging or other signal processing maybe needed for accurate image production.

Keywords: electrical impedance tomography, neural imaging, evokedresponses, brain modelling, finite elements

(Some figures in this article are in colour only in the electronic version)

1. Introduction

1.1. Possible use of EIT for imaging fast neural activity in the brain

Functional neuroimaging has improved greatly in the past two decades but the ‘holy grail’would be to image neuronal activity non-invasively with a temporal and spatial resolution ofabout 1 ms and 1 mm respectively. Currently, there has been great interest in such ‘neuralimaging’ with proposals for the use of MRI (Bodurka et al 1999, Bodurka and Bandettini 2002,Kamei et al 1999, Kilner et al 2004, Kim and Ogawa 2002), infrared (Cohen 1973, Stepnoskiet al 1991) or inverse source modelling (Baillet et al 2001, Cohen 1968, Dale et al 2000,Dale and Halgren 2001, Hamalainen 1992, Hamalainen et al 1993, Michel et al 2004) for thispurpose, but no method has yet been shown to be successful. Electrical impedance tomography(EIT) is a novel medical imaging method which has the potential to achieve the desiredtemporal resolution, by imaging the electrical impedance changes (Holder 1987) which occurover milliseconds when neuronal ion channels open during activity and the cell membraneresistivity decreases (Cole and Curtis 1939). This work arose from an attempt to recordsuch changes, for the first time, in human subjects during visual evoked potentials, with non-invasive scalp electrodes or detection of magnetic flux density by magnetoencephalography(MEG). Prior to attempting this study, we wanted to model the expected changes in orderto estimate if such a study appeared feasible and suggest optimal electrode placement. Inthe event, we proceeded to the planned human study; these empirical findings are presentedelsewhere (Gilad et al 2009, Gilad and Holder 2009).

EIT provides information regarding the internal electrical properties inside a body basedon non-invasive voltage measurements on its boundary. Data acquisition is performed throughan array of electrodes which are attached to the surface of the imaged object. Sequences ofsmall insensible currents, typically of about 1 mA, are injected into the object through theseelectrodes and the corresponding boundary electric potentials are measured over a predefinedset of electrodes. The process is repeated for numerous different configurations of appliedcurrent. The internal admittivity or impedivity distribution can be inferred using this boundarydata. EIT was first proposed as a medical imaging method by Henderson and Webster (1978)and was initially applied to chest imaging (Brown et al 1985, Brown and Seagar 1987,Metherall et al 1996). Potential applications of EIT for imaging brain function and pathologyinclude detection and monitoring of cerebral ischaemia and haemorrhage (Gibson et al 2000,Holder 1992a, Horesh et al 2005, McArdle et al 1988, McEwan et al 2006, Romsauerovaet al 2006), localization of epileptic foci (Bagshaw et al 2003, Fabrizi et al 2006b), normalhaemodynamic brain function (Tidswell et al 2001) and neuronal activity (Boone and Holder1995, Holder 1987).

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The principle by which EIT could image neuronal activity rests on the application oflow frequency currents below about 100 Hz which remain in the extracellular space underresting conditions because they cannot enter significantly into the intracellular space acrossthe capacitative cell membrane. During the action potential or neuronal depolarization, themembrane resistance diminishes by about 80× (Cole and Curtis 1939) so that the appliedcurrent enters the intracellular space as well. Over a population of neurons, this will leadto a net decrease in the resistance during coherent neuronal activity, such as cortical evokedresponses, as the intracellular space will provide additional conductive ions (Boone and Holder1995, Liston et al 2000, 2009, Liston 2004). Biophysical analysis indicates that recordingneeds to be below 100 Hz. At higher frequencies, applied current would enter the intracellularcompartment across the capacitance of cell membranes at rest, so there would then be aninsignificant change in resistance as ion channels opened.

1.2. Likely magnitude of resistance changes in the cerebral cortex and when measurednon-invasively on the scalp

The magnitude of such fast changes in the brain is not entirely clear. Reports in the literaturevary from 3.1% with 0.3–0.7 ms square wave pulses (Freygang and Landau 1955) to 0.003%at 10 kHz (Klivington and Galambos 1967, 1968). However, at 50 kHz, no changes greaterthan 0.01% were observed (Holder 1989, Holder and Gardner-Medwin 1988). The likelyamplitude of the changes has been investigated by modelling and animal studies in our group.Mathematical modelling, based on cable theory, estimated local resistivity changes near dc tobe 3.7% for peripheral nerve bundles and 0.06–1.7% for the cortex during evoked potentials(EP) (Boone and Holder 1995, Liston et al 2000, 2009, Liston 2004). These predictionsare in broad agreement with near dc decreases recorded experimentally of 0.5–1.0% in crabperipheral nerve (Boone 1995, Holder 1992b, Liston 2004) and 0.01–0.03% on the surface ofrabbit cortex during somatosensory evoked responses (Boone 1995). Overall, therefore, thetrue size of the changes in cortex is unclear but a reasonable working figure for the purposesof this work was taken to be 1% with recording with an applied current below 100 Hz.

Local resistance changes in the cerebral cortex may be expected to be diminishedsubstantially when recorded on the scalp, because of partial volume effects, diversion ofapplied current by the resistance of the skull and a low pass spatial filtering effect of the skulland scalp on the resulting fields. In previous studies from our group, we have attempted toestimate this effect. Liston estimated the boundary voltage changes to drop by a factor of 10to 0.006–0.17% (Liston 2004). This was suggested since cortical resistivity changes of 5%,related to blood volume changes, caused peak voltage changes on the scalp about 10× smallerin an experimental study in adult human subjects during visual, somatosensory or motoractivity (Tidswell et al 2001). These slow changes occurring over seconds during evokedresponses could be comparable to findings from fMRI studies (Tidswell et al 2001). These arelikely to accompany the fast changes due to neuronal depolarization and potentially mask itduring measurement. However, it should be possible to clearly distinguish them by temporalfiltering as their time courses are very different—seconds as opposed to tens of milliseconds(Gilad et al 2009, Gilad and Holder 2009).

Ahadzi et al (2004a) then generated an anatomically realistic model of the human headusing a finite element (FE) formulation for solution of the EIT problem (hereafter EIT forwardproblem). This model yielded the expected boundary voltage changes on the scalp, whena 1% local resistivity changes occurred at the visual cortex during the VEP. Boundaryvoltage changes were estimated to be 0.02–0.04% for optimal four terminal resistivitymeasurements.

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1.3. Proposed use of EIT and MEG for imaging fast neural activity

Most EIT acquisition procedures have been undertaken with injection and recording of currentand voltage by electrodes (Holder 2004). More recently, there has been interest in the use ofmagnetic methods for current injection by coils (Freeston and Tozer 1995, Gencer and Tek1999, Karbeyaz and Gencer 2003, Merwa et al 2004, Ozparlak and Ider 2005, Rosell-Ferreret al 2006, Zlochiver et al 2004) or recording of induced current by MRI (Birgul et al 2003,Ider et al 2003, Joy et al 1989, Ozparlak and Ider 2005), coils (Gencer and Tek 1999, Irelandet al 2004, Karbeyaz and Gencer 2003, Levy et al 2002, Merwa et al 2004, Rosell-Ferreret al 2006, Tozer et al 1999), MEG (Ahadzi et al 2004b, Ahlfors and Ilmoniemi 1992). Suchmethods hold considerable potential advantages for this proposed application because the skullis transparent to magnetic fields (Hamalainen et al 1993). The advantages and limitations ofthe different approaches are discussed elsewhere (Ireland et al 2004). It might thus be possibleto improve signal detection substantially by using magnetic signal detection.

The term magnetic detection EIT (MD-EIT) (Ireland et al 2004, Tozer et al 1999) wasdefined for the case of current injection with electrodes. The use of MD-EIT for biomedicalapplications was first proposed by Ahlfors and Ilmoniemi (1992) with MEG and for geophysicsapplications with a technique termed magnetometric resistivity (MMR) (Edwards 1974).

For this application, current injection by electrodes is necessary, as it would not be possibleto inject sufficient current in a practical way by coils at the required very low frequencies.The resulting magnetic flux density could be detected by MEG (Ahlfors and Ilmoniemi 1992),which is ideally suited to the detection of small low frequency fields. This technique employsarrays of up to 275 superconducting quantum interference devices (SQUIDs) which are placednear the scalp and the apparatus in enclosed in a magnetically shielded room. It has beenused over the past two decades to detect the magnetic fields which arise spontaneously fromelectrical activity in the brain.

The use of MD-EIT with MEG as the sensing device to detect and image impedancechanges related to neuronal activity was initially proposed in our group by Ahadzi et al(2004b). In an initial simulation study to determine whether such a task was theoreticallyplausible, the head was modelled as concentric spheres to mimic the scalp, skull, cerebrospinalfluid and brain using the finite element method, and the magnetic flux density 1 cm awayfrom the scalp was estimated. An impedance change of 1% in a 2 cm radius (volume33.5 cm3) in the brain was modelled as the region of depolarization and a constant currentof 100 μA was injected into the head from diametrically opposite electrodes. The modelpredicted that the static magnetic flux density is about 10 pT and changed by about 3 fT(0.03%) on depolarization. As the noise in a typical MEG system in the frequency band1–100 Hz is about 7 fT, the authors concluded that these predicted changes are at the limit ofdetectability, similar to the situation in conventional EIT measurements. However, they alsonoted that there may be advantages to MEG since the magnetic field directly traverses theskull, and instrumentation errors from the electrode–skin interface will be obviated (Ahadziet al 2004b).

1.4. Purpose

The purpose of this work was to develop and validate an anatomically realistic numericalmodel of the adult human head and use it to estimate the changes recorded on the scalpduring cortical evoked activity using EIT or MD-EIT. Our intention was to estimate answersto the following issues. (1) Would a human study be feasible, i.e. would the estimated signalchanges be discernible from baseline noise? (2) In a human study with scalp electrodes, a

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limited number of about 32 channels is practical—what would be the optimal placement ofthese? (3) Would EIT or MD-EIT be more likely to produce a larger signal-to-noise ratio(SNR)? (4) What would be the effect on the estimated signal size of avoidance of electrodeplacement near cranial orifices such as the orbital foraminae? (5) Previous work (Gilad et al2007) has suggested that more current can be injected through larger electrodes. What wouldbe the expected effect of use of electrodes of differing sizes? (6) Would the predicted changesyield a SNR sufficient to produce reliable EIT images?

1.5. Design and rationale of study

Numerical simulations were performed using an anatomically realistic FE model of the head.Expected changes on the scalp were calculated for an estimated resistance change in the visualcortex during visual evoked responses such as those used routinely in clinical practice inresponse to viewing a reversing black and white chequerboard. This was also used to predictthe optimal electrode placement for human studies for a specific set of 31 electrode positions.One FE model was used throughout but solutions were generated for minimum, median andmaximum conductivity values derived from a literature review for each of the compartmentscorresponding to the scalp, skull, and grey and white matter of the brain.

For the electric case, boundary voltages on the scalp were calculated by solvingthe generalized Laplace partial differential equation, using the complete electrode modelformulation (Vauhkonen et al 1999). For the magnetic case, magnetic flux density changeswere calculated using a Biot–Savart integral and the current densities calculated for the electriccase. A realistic model of the magnetic sensors was generated for a specific MEG machineavailable for our experimental studies.

The accuracy of these numerical models was assessed in a spherical saline filled tank inwhich a sponge was used to simulate a resistance change similar in volume to that expectedduring visual evoked responses for both the electric and magnetic cases. It was also assessed bycomparing predicted boundary voltages with those recorded from the scalp in human studiesfor the electric case only.

Simulations were also undertaken for different electrode diameters and with electrodesplaced or omitted on the scalp near skull foraminae.

Novelty over previous electric (Ahadzi et al 2004a) or magnetic (Ahadzi et al 2004b)modelling studies. For the electric case, all possible electrode protocols were tested and themain source of variance due to uncertainty in conductivities was taken into account. Extensivevalidations of the model predictions were performed using tank and human measurements.For the magnetic case, the novelty included the use of a realistic head model and MEGsensors, inclusion of all possible current injection electrodes and magnetic sensors protocols,and analytical and experimental validations.

2. Methods

2.1. Modelling the electric case

A numerical anatomically realistic FE model of the head was created from segmentationof an adult human MRI using I-DEAS software (Tizzard et al 2005). The mesh contained53 336 elements, which comprised scalp, skull, CSF and ventricles, grey and white matter,eyes, optic canal, olfactory tracts and the auditory meatus (Horesh et al 2005, Tizzard et al2005). The mesh resolution varied between 0.1 mm3 over fine structures such as the skull andcerebrospinal fluid, to 500 mm3 (0.5 cm3) in the centre of the brain; this permitted accurate

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(a) (b)

Figure 1. (a) Modelled primary visual cortex area V1. (b) Outer scalp surface of the mesh usedand the electrode placement for the case of 31 electrodes of 21 mm diameter. Axes are distance inmeters. Reproduced from Gilad et al (2007) with permission.

representation of fine structures and boundaries between tissues having a high conductivitycontrast (scalp–skull, skull–CSF and CSF–brain interfaces) while keeping the overall meshsize to a reasonable size. For validating our choice of mesh resolution of 53 336 elements, pilotsimulations with a refined version of 136 442 elements gave similar changes (

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Table 1. Conductivities used for the head model.

Tissue σ a (S m−1) Source and remarks

Scalp 0.1, 0.30, 0.45 (Burger and Van Dongen 1960, Burger andVan Milaan 1943, Gabriel et al 1996)

Skull 0.005, 0.015, (Akhtari et al 2002, Gabriel et al 1996,0.030 Hagberg et al 2006, Hoekema et al 2003, Law

1993, Oostendorp et al 2000, Parkes et al 2007)CSF 1.79 (Baumann et al 1997)Grey matter 0.20, 0.30, (Freygang and Landau 1955, Ranck 1963,

0.45 Van Harreveld et al 1963)White matter, optic canal 0.18, 0.25, (Gabriel et al 1996, Ranck and

and auditory meatus 0.30 BeMent 1965)Eye 1.15 (Horesh 2006) superposition of cornea, lens,

retina, sclera, vitreous and aqueous humoursOlfactory tract Average of skull and white matter

a The minimum, median and maximum for each tissue are presented. These were obtained from aliterature review for properties below 1 kHz.

diameter was set to 11 or 21 mm as two electrode designs were used in the experimentalwork (Gilad et al 2007). Boundary voltages were calculated for multiple current injectionand voltage measurement electrode pairs using the UCL SuperSolver package developed inour group (Horesh et al 2006). This is based on EIDORS 3D (Polydorides and Lionheart2002), and the generalized Laplace equation was solved using the Neumann to Dirichletmap to obtain the electric potentials at each element. The numerical solution was performedwith a preconditioned conjugate gradient linear solver. The relative residual tolerance wasset and monitored to be below 10−12. An incomplete Cholesky factorization was used as apreconditioner, with a drop tolerance threshold of 10−5 (Horesh et al 2006). The injectedcurrent level was set to 1 mA which is the maximal level which was estimated not to alterbrain activity (Gilad et al 2007). The calculated voltages could then be linearly scaled fordifferent current levels.

The conductivity values of the different compartments of the model were obtained fromthe published literature (Horesh 2006, chapter 2) and taken as isotropic. Solutions werecalculated for the minimum, median and maximum values for each of scalp, skull, grey andwhite matter, which yielded 34 = 81 solutions (table 1).

Calculations were made for all 31 × 30/2 = 465 possible current injection pairs, withand without a perturbation of 1% increase in the conductivity of the visual cortex. For eachcurrent injection pair, the boundary voltages across all possible 29 × 28/2 = 406 pairs of theremaining 29 electrodes were calculated. One of each pair of reciprocal electrode combinationwas discarded as they produce the same results. The magnitude of the voltage changes was thedifference δ between the boundary voltages without the perturbation and with the perturbation.δ was therefore calculated for all the electrode combinations (465 current pairs × 406 voltagepairs/2 reciprocal electrode combinations = 94 395). This entire protocol was repeated for 81different conductivity combinations σ i (i = 1, 2, . . . , 81) and then for two different electrodediameters.

2.1.1. Effect of orifices. In order to maximize the signal, it is desirable to inject the highestcurrent that is safe and can be tolerated by the subject. In a previous study, this was shown tobe 1 mA but this could not be applied through electrodes near transcranial shunt paths such

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as the optic forminae or auditory canals, since this could produce a current density above thelevel estimated to alter brain activity (Gilad et al 2007). For evaluating this potential effect,the above calculations were repeated after excluding from the current injection protocol eightelectrodes which were up to 5 cm away from the eyes or ears. This gave 23 × 22/2 =253 current pairs out of the original 465 pairs. In this case, the total number of electrodecombinations was 253 × 406/2 = 51 359 and after selecting the independent combinationwith the highest changes this reduced to 22 × 28 = 616 combinations.

2.1.2. Optimal electrode combinations. For the given set of 31 electrode positions, the 10electrode combinations which gave the largest absolute changes for the median conductivitieswere selected. This was repeated for the two electrode diameters and with and without theelectrodes closest to the orifices.

2.1.3. Data analysis. The estimation above produced 94 395 absolute voltage differences|δ|σi for each of the 81 conductivity sets σ i and one of the two electrode diameters. Inorder to simplify presentation, these calculations were reduced. Most of the 94 395 electrodecombinations were linearly dependent in a sense that they could be reproduced by a linearcombination of other electrode combinations. For example, [I 1,2; V 3,4] could be reproducedby subtracting the voltages from [I 1,2; V 3,5] and [I 1,2; V 5,4] (I = current injection pair;V = voltage measurement pair). This set was reduced to the minimum number of electrodecombinations which were linearly independent and yielded the largest calculated absolutechanges. As there were 30 independent current pairs and 28 independent voltage pairs, thisresulted in 840 four electrode combinations.

Two statistical measures were calculated from these. (a) The ‘mean’ of all 840 largestindependent channels or (b) the single ‘maximal’ change, which was the single largest changein one electrode combination from all 840 channels. These were defined as ‘mean’ or‘maximal’ di. This voltage value was also converted to percentage units by normalizing tothe mean boundary voltages. A final representative value for all such changes over the 81modelled conductivity combinations was defined as D. A separate value for mean or maximalD then existed for inclusion or exclusion of electrodes near cranial foraminae and for 11 or21 mm electrodes. Unless otherwise stated, data presented are for D for the case of 21 mmelectrodes with exclusion of electrodes near cranial foraminae. All data are presented asmean ± 1 SD.

2.2. Validation for the electric case

2.2.1. Saline filled tank. A spherical tank of 0.19 m diameter was filled with 0.2% saline(conductivity 0.39 S m−1) and 31 Ag/AgCl 2 mm diameter ball electrodes placed over onehemisphere. The local resistivity perturbation in the visual cortex was simulated using anellipsoid of polyurethane sponge, height 50 mm and diameter 26.6 mm, with a volume of18.5 cm3 made of 5% weight/volume polyurethane which produced a 19% increase inresistivity. n = 95 combinations of current injection and voltage measurement pairs wererecorded and averaged for 1 min using a 1 Hz bipolar square wave current of 100 μA and aSD128 EEG system (Micromed, Italy). This was repeated with and without the presence ofthe sponge.

A mesh of 225 000 elements with the same dimensions, electrode positions, conductivityand modelled perturbation was used to calculate the predicted voltages with the numericalsolver. For both boundary voltages and boundary voltage changes due to the perturbation,linear regression parameters were calculated between the measured and predicted values as

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well as the correlation coefficient R, p-value for no correlation, standard errors Ea and Eb forthe regression parameters and standard deviation SD around the regression line.

2.2.2. Human studies. Twenty recordings of boundary voltages were made from sevensubjects (two male, five females, age 25–42 years) who gave informed consent. The studywas approved by the ethics committee of our university. A square wave current at 1 Hz wasapplied to one of the two positions over the occipital cortex, located bi-laterally 5 and 10 cm,or 10 and 5 cm from Oz (5 cm above the inion bone); the resulting voltages were recordedwith an EEG system (SD32R or SD128, Micromed, Italy) from 19 other electrodes placedover the occipital cortex, yielding 18 linearly independent measurement pairs. Measurementsin two subjects were repeated two and three times on different days. Since each recordingsession included two recordings with the same electrode positions, these data were consideredas ten recordings, each with 36 measurements (n = 360).

These boundary voltage recordings were the control recordings without visual stimulationtaken together with active recordings (with stimulation) for measuring the fast changes.These are fully presented elsewhere (Gilad and Holder 2009). Applied current varied from100 μA to 1000 μA as different subjects tolerated different amounts (Gilad et al 2007).Although the International Electrotechnical Commission standard specifies a ‘patient auxiliarycurrent’ limit of 100 μA from 0.1 Hz to 1 kHz, based on limitation of the injected currentto 10% of the average threshold of sensation (IEC60601-1{ed3.0} 2005), current densityacross the electrode–skin interface is the critical parameter for controlling skin sensation.Careful electrode design for producing uniform current density could in practice allow up to1000 μA to be applied to the scalp without sensation (Gilad et al 2007).

The measured voltages were normalized to a current level of 100 μA and compared topredicted voltages obtained with the realistic head model and real electrode positions measuredon the individual subject, projected on the standard head mesh for conductivities of 0.1, 0.015,0.30 and 0.25 S m−1 for scalp, skull, grey and white matter, respectively.

2.3. Modelling the magnetic case

In the magnetic case, current was injected with electrodes and the magnetic flux density wasmeasured outside the head. The head model, conductivities, electrode placement, currentlevel and injection protocol and visual cortex perturbation were the same as those used in theelectric case. Only 21 mm diameter electrodes were used since the results for the electric casewith 11 and 21 mm were similar. The first step for calculating the magnetic flux density wasto derive the current density in every volume element of the head model. The forward solverfor the electric case provided the electric (E) field at each volume element and the continuumform of Ohm’s law (J = σE) was used to translate this into current densities.

The MEG system available for experimental studies was a CTF MEG 275 (VSM MedTechLtd, Coquitlam, BC, Canada (Vrba and Robinson 2001)) located at the Functional ImagingLaboratory, UCL, UK. The specifications of this system were used for this modelling studyin order to be comparable to experimental measurements. This system is equipped with 275gradiometers made of two parallel coils of radii R = 9 mm which sense the difference in theradial component of the magnetic flux density between the first coil close to the head and thesecond coil located D = 50 mm away from the first coil (figures 2(a), (b)).

The head mesh position within the coil array was taken as the average position from humanmeasurements. For this position, the distances between the lower coils and the scalp were25–45 mm and 25–37 mm for the occipital and parietal sensors, respectively, most relevantfor this study. Out of these distances, 17 mm was the distance between the coil and the innersurface of the MEG helmet.

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(a) (b)

Figure 2. (a) Two layers of 275 coils were placed around the realistic head mesh. (b) Radial andtangential components of the magnetic flux density at the centres of the two gradiometer coils.

The magnetic flux density B at the centre of each coil was calculated using the discreteform of the Biot–Savart law (Lee et al 2003) and the current density J. The differencebetween the two radial components (figure 2(b)) was calculated with and without theperturbation in visual cortex conductivity during neuronal activity which changes J. Thisestimated difference δrad was repeated for all 31 × 30/2 = 465 possible current injection pairsgenerated from the 31 electrodes, all 275 magnetic sensors and the 81 different conductivitycombinations.

Calculating the magnetic flux density at the centre of the coils was only a firstapproximation since the flux density is not necessarily homogeneous across the coil plane.However, this was shown to be negligible using a pilot numerical study with a planner meshmodel of the coils.

2.3.1. Data analysis. The analysis of the magnetic flux density changes was similar to thatfor the electric case. The estimation above produced 465 × 275 = 127 875 absolute magneticflux density differences |δrad|σi for each of the 81 conductivity sets σ i.

Mean or maximal field changes di were again calculated for the linearly independentelectrode/MEG sensor combinations with the largest changes (30 × 275 = 8250 values).These were also converted to percentage units by normalizing to the non-perturbed magneticflux density. A final representative value for all such changes over the 81 modelled conductivitycombinations was defined as D. A separate value for mean or maximal D then existed forinclusion or exclusion of eight electrodes near cranial foraminae. The latter case had 22 ×275 = 6050 values for calculating the mean di.

Unless otherwise stated, results presented are for avoidance of current injection nearcranial orifices. Data are again presented as mean ± 1 SD.

2.4. Validation for the magnetic case

In order to validate the numeric Biot–Savart estimation independently, results were comparedfor fields calculated from a model of a wire, 10 cm long, carrying electrical current andan analytic solution of the Biot–Savart law. A finite element model was constructed withcylindrical elements of 1 mm radius and 0.1 mm height carrying uniform current density, andfields were calculated for a MEG sensor at distances from 1 to 10 cm away.

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Additional validation was undertaken using a spherical tank, 148.6 mm in diameter,filled with 0.2% saline (conductivity 0.39 S m−1). Two Ag/AgCl, 10 mm diameter, surfaceelectrodes were glued on the inner surface of the tank at [−53, −51, 3] and [−61, 30, 22]mm in Cartesian coordinates relative to the centre of the tank (8 cm and 70◦ apart). Thesewere connected by two leads which exited from the tank at the electrode positions and thenpassed externally to the centre point between the two electrodes. They were then twisted and alength of 5 m passed through the magnetically shielded room and was connected to the currentinjection apparatus.

The high current density at the electrodes and the untwisted part of the leads and theproximity of these to the magnetic sensors resulted in a high standing magnetic flux densitycomponent which was not related to the current flow in the volume conductor. However, thiseffect was obviated by the subtraction of measurements of a sponge perturbation in differingpositions.

The local resistivity perturbation was simulated using a sponge sphere of volume9.85 cm3 and 19% increase in resistivity which was suspended on a plastic fishing linetied along the diameter of the z-axis of the tank. The line ran through a loop at the bottomof the tank and two 1 mm diameter holes at the top of the tank. This allowed positioning ofthe sponge along the z-axis with a limited precision of about 5 mm due to the elasticity ofthe fishing line and the sponge. The positions of the electrodes, z-axis and three localizationcoils used by the MEG system to locate the tank in the sensor array were measured with a 3DPolhemus digitization system (3SPACE ISOTRAK II, Polhemus Inc., Colchester, VT, USA)with a specified accuracy of 2.5 mm.

Twelve recordings of 80 s were made while the sponge was moved alternately betweena central and superior position 60 mm apart. In each recording, a current of 1 mA generatedby a DS-5 unit (Digitimer, Welwyn Garden City, UK) was delivered at 23.53 Hz throughthe two electrodes and the magnetic flux density was digitized by the MEG system at 1200samples s−1, 32 bit and 0.317 fT resolution. For each of the 275 channels in each recording,the measured magnetic flux density was calculated as the mean of the amplitude demodulationover 80 s. This was then subtracted between the six pairs of recordings at the two spongepositions. The mean difference between the two positions was calculated together with thestandard deviation SD1 reflecting the variation across experimental repetitions.

Numerical calculations of the magnetic flux density difference between the two spongepositions were made as described in the previous section using a spherical mesh with allocatedconductivity, electrode positions, sponge perturbation geometry and positions and the positionof the tank within the scanner. Linear regression was used to compare the measured andpredicted absolute magnetic flux density changes for the channels with SD1 < 200 fT. Theregression parameters (mean ± SE), correlation coefficient and standard deviation SD2 of thedata points around the regression line were calculated.

For evaluating the effect of the limited precision of the sponge positioning along the z-axis(SD3), these calculations were repeated after lowering the registered top sponge position by5 mm.

3. Results

3.1. Modelling the electric case

3.1.1. Magnitude of the changes. The mean D was 0.54 ± 0.36 μV; 0.0018 ± 0.0014% (n =616 × 81 = 49 896) (figure 3). The corresponding maximal change was about twice greater,1.03 ± 0.75 μV; 0.0039 ± 0.0034% (n = 81).

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

δ [μV]

Nor

mal

ized

Inc

iden

ce

All electrode combinations

Independent electrode combinations

Figure 3. Normalized incidence of the voltage changes from all electrode combinations (n =51 359) and from the subset of independent combinations most sensitive to the visual cortex (n =616). This is for the case of 21 mm diameter, median conductivity values and excluding currentinjection close to the orifices.

Table 2. Mean (maximum) voltage changes for all independent electrode combinations and allconductivity sets.

Casea D (μV) D (%)

11/23 0.56 ± 0.38 (1.08 ± 0.80) 0.0020 ± 0.0016 (0.0043 ± 0.0035)11/31 0.50 ± 0.34 (1.08 ± 0.80) 0.0020 ± 0.0016 (0.0043 ± 0.0035)21/23 0.54 ± 0.36 (1.03 ± 0.75) 0.0018 ± 0.0014 (0.0039 ± 0.0034)21/31 0.49 ± 0.34 (1.03 ± 0.75) 0.0018 ± 0.0014 (0.0039 ± 0.0034)a Electrode diameter/number of electrodes (23—after excluding electrodes near orifices).

3.1.2. Effect of electrode diameter and orifices. The mean changes for the larger (21 mm)electrode diameter decreased by 4% (0.56 ± 0.38 versus 0.54 ± 0.36 μV for 23 electrodes)or 2% (0.50 ± 0.34 versus 0.49 ± 0.34 μV for 31 electrodes). When electrodes close to theorifices were omitted, the mean changes were 10% higher (0.54 ± 0.36 versus 0.49 ± 0.34 μVfor 21 mm), although the maximal changes were identical (1.03 ± 0.75 μV). This suggests thatthe electrodes close to the orifices are less sensitive to changes in the visual cortex comparedto the remaining electrodes (table 2).

3.1.3. Optimal electrode placement. For the 21 mm diameter electrodes, the electrodecombination which gave the largest peak change for the median conductivities was withcurrent injection over the occipital region with an adjacent pair of electrodes 5 cm apart (29and 30) and recording immediately lateral to these (23 and 27) (figure 4). The electrodecombinations for the ten largest changes were over much of the occipital area (table 3). Thesecombinations included current injection from semi-adjacent electrodes, 10 cm apart, over theocciput and recording from electrodes near to these. The current electrodes could be replacedwith the measurements according to the reciprocity principle.

Modelling for imaging neuronal depolarization by electrical and magnetic detection impedance tomography S213

Figure 4. The electrode combination which gave the largest peak change for the medianconductivities (bent arrows). The cluster of dots marks the surface projection of the modelledvisual cortex. The view is of the back of the head and the axes are in metres.

Table 3. Ten uppermost sensitive electrode combinations for 21 mm diameter and medianconductivities.

δ (μV) δ (%) Current pair Measure pair

0.78 0.0034 29 30 23 270.77 0.0014 23 30 19 270.76 0.0014 24 30 23 310.75 0.0011 23 31 19 300.74 0.0011 24 30 19 310.74 0.0015 27 28 26 290.73 0.0020 23 30 24 270.73 0.0014 19 30 23 270.72 0.0010 23 30 19 310.72 0.0012 22 28 26 29

For electrodes 11 mm in diameter, the combinations which produced the largest changeswere identical to the case with the 21 mm electrodes. Of the remaining eight, six wereidentical. For both electrode diameters, identical optimal electrode combinations wereobtained independently of placement of electrodes closest to the orifices.

3.2. Validation for the electric case

For the tank measurements, the correlation between measured and predicted boundary voltageswas R = 0.98 (p < 10−67; N = 95), with a slope of 1.02 ± 0.02 (figure 5). For the changes

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-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8-1.2

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Figure 5. Measured versus predicted boundary voltages for the spherical tank.

-2 -1 0 1 2 3 4 5-2

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Figure 6. Measured versus predicted boundary voltage changes for the spherical tank with spongeperturbation.

due to sponge perturbation, the correlation was R = 0.87 (p < 10−28; N = 95), with a slope of1.04 ± 0.06 (figure 6). For the human measurements, the correlation between measured andpredicted boundary voltages was R = 0.93 (p < 10−9; N = 10 experiments, each with n = 36data points), with a slope of 1.0 ± 0.3 (figure 7).

3.3. Modelling the magnetic case

Mean D changes were 4.7 ± 1.9 fT; 0.007 ± 0.003% (n = 6050 × 81 = 490 050). Themaximal changes were sixfold higher 27 ± 13 fT (n = 81). However, the maximal change

Modelling for imaging neuronal depolarization by electrical and magnetic detection impedance tomography S215

-10 -5 0 5 10

-10

-5

0

5

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Me

asu

red

Vo

lta

ge

[m

V]

Figure 7. Measured versus predicted boundary voltages for ten human experiments.

Table 4. Mean (maximum) magnetic flux density changes for all independent current combinationsand all conductivity sets.

Casea D (fT) D (%)

21/23 4.7 ± 1.9 (27 ± 13) 0.007 ± 0.003 (0.2 ± 0.5)21/31 4.5 ± 1.9 (27 ± 13) 0.007 ± 0.003 (0.2 ± 0.5)a Electrode diameter/number of electrodes (23—after excluding electrodes near orifices).

expressed as a percentage was 0.2 ± 0.5%, 30-fold higher than that for the mean, since thestatic magnetic flux density was low for these maximal changes (table 4).

3.3.1. Effect of orifices. When electrodes close to the orifices were omitted, the meanchanges were 4% higher (4.7 ± 1.9 versus 4.5 ± 1.9 fT), although the maximal changes wereidentical (27 ± 13 fT) (table 4).

3.3.2. Optimal electrode and magnetic sensor placement. The current injection electrodepairs which gave the four uppermost changes for the median conductivities were semi-adjacent(5–10 cm apart) over the occipital region: pairs [23 26], [23 27], [23 30] and [29 30](figure 4). In all these cases, the most sensitive magnetic sensors were over the midline atthe border between the parietal and occipital sensor groups (e.g. figure 8). This area was justabove the modelled visual cortex.

3.4. Validation for the magnetic case

For the comparison of the estimation of magnetic flux density from a current carrying linearwire, the proportionate error between the analytic equation and the numerical calculation was1 × 10−7 for a modelled MEG sensor 1–10 cm distant.

For the changes due to sponge perturbation, the correlation between measured andpredicted absolute magnetic flux density changes for channels with SD1 < 200 fT was

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Figure 8. Example for distribution of absolute changes in the radial component across the magneticsensors over the back of the head. This is for the median conductivities and current injection pair[23 30] marked as solid polygons on the head surface. The axes are in metres.

R = 0.81 (p < 10−42; N = 189), with a slope of 1.06 ± 0.06 and offset 75 ± 5 fT, andstandard deviation around the regression line was SD2 = 65 fT (figure 9).

4. Discussion

4.1. Summary of results

For the electric case, the modelled mean D changes were 0.54 μV (0.0018%). With respectto variable conductivities due to uncertainty in the literature, this varied with a SD of 0.36μV (0.0014%). The maximal changes were about twice these. The mean changes were about4% smaller for the larger diameter electrodes and about 10% higher when omitting electrodesnear the orifices. The combinations which gave the largest peak changes were with currentinjection over the occipital region with an adjacent (5 cm apart) or semi-adjacent (10 cm apart)pair of electrodes and recording immediately lateral to these. For the studies intended tovalidate the modelling method, there was a high correlation between measured and predictedboundary voltages for both human measurements and tank studies.

For the magnetic case, the modelled mean D changes in magnetic flux density were4.7 ± 1.9 fT (0.007 ± 0.003%). The maximal changes were about sixfold higher. The meanchanges were about 4% higher when omitting electrodes near the orifices. The combinationswhich gave the largest peak changes were with current injection over the occipital regionwith an adjacent (5 cm apart) or semi-adjacent (10 cm apart) pair of electrodes and recordingwith magnetic sensors above the visual cortex (figure 8). For the sponge perturbation studyintended to validate the modelling method, there was a high correlation between measuredand predicted magnetic flux density changes.

4.2. Technical issues

4.2.1. Accuracy of the forward models. For these data to be useful, it is clearly essentialthat the numerical model used provided an accurate reflection of the realistic values. The

Modelling for imaging neuronal depolarization by electrical and magnetic detection impedance tomography S217

0 100 200 300 4000

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Figure 9. Measured versus predicted absolute magnetic flux density changes for the spherical tank(radial component). Solid dots are channels with SD1 < 200 fT.

numerical results were therefore validated by taking measures of mesh quality, and by empiricalrecordings. Mesh density was determined by comparing pilot results from models of increasingmesh density.

For the electric case, the measures of mesh quality were very high, which suggestedthat computational errors were likely to be insignificant (EDS 2003, Tizzard et al 2005). Inthe saline filled tank, the modelled and measured voltages were highly correlated. However,in human studies, the correlation was less good-–there was a dispersion of 30% around theunity slope across recordings from different subjects. These factors may be ascribed to thefollowing limitations of the model: (1) inaccurate registration of conductivities in differentcompartments of the mesh, (2) usage of single standard head geometry in the mesh which didnot take into account individual differences in anatomy (Marson et al 2008), (3) projection ofthe electrode positions from the individual head geometry onto the standard mesh (Yerworthet al 2004) and (4) no allowance for tissue anisotropy; recent work has indicated that thiscan make a significant contribution (Abascal et al 2007, 2008). There were probably alsoexperimental errors in the human recordings due to movement artefact and uncertainty in theprecise position of electrodes when measured with a mechanical digitizing arm. In spite ofthese limitations, the high correlation (R = 0.93) and bias factors of 30% suggest that themodel can predict the changes in boundary voltages due to neuronal activity within the correctorder of magnitude.

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For the magnetic case, the same FE mesh was used; the principal difference was the useof a discrete form of the Biot–Savart law to calculate magnetic flux densities. This lattercalculation was verified through comparison to an analytical solution for the simple case ofcurrent flowing through a wire. Validation in a saline filled tank was made difficult becausesignificant environmental and instrumentation noise was transmitted through current injectionelectrodes. This was due to leads connected to a mains driven current source located outsidethe magnetic shielded room (DS-5). This additional noise was of the same magnitude asthe background brain activity. In the future, it could be minimized by using a battery drivencurrent source located within the magnetic shielded room. In addition, there were largestanding magnetic flux densities due to current flow in the leads leading to the tank. Thesecaused a significant offset. In spite of these factors, there was a significant correlation betweenmodelled and measured fields.

Overall, allowing for experimental error, it therefore appears reasonable that the modelused is likely to have made predictions of the fields which are accurate to within an order ofmagnitude, which should be sufficient for the purposes of this work.

4.2.2. Units. It is not straightforward to decide in which form data are best presented. Inprinciple, changes in the field due to insertion of a perturbation are most easily appreciatedif expressed as a proportional change in per cent. This is because, for a simple case ofresistance measurement with a constant current source, this accurately reflects the changein transfer resistance. This convention has been widely used in EIT publications but mayprovide misleading results for 3D fields encountered in practice. This is because the patternof current flow may change as well and a field which is close to an isopotential or isomagneticpoint may show a spuriously large change if expressed as a fraction of the baseline. Inaddition, the absolute magnitude of the units is a critical value in determining whether signalsmay be distinguished from noise. The approach in this work has been to calculate theabsolute change in the first instance and use the greatest of such values to determine the setof linearly independent electrode or magnetic sensor combinations. In principle, this shouldavoid incorporation of spuriously large proportional changes. The selected largest change orchanges are then presented both in physical units and as percentage changes. An exampleof this is the values given in table 3 for the top ten highest changes. The variation in thevoltage changes is only 10% (0.72–0.78 μV) whereas the variation in the percentage changesis almost 300% (0.0012–0.0034%). Therefore, values in physical units were used to interpretthe results while including percentage values to be consistent with the convention and to givea comprehensible indication of the modelled change in transfer impedance.

4.3. Implications for a human study

4.3.1. Is the SNR likely to be sufficient to provide reliable results in single channelmeasurements? For the electric case, the physiological noise level obtained from backgroundbrain activity in the occipital area when eyes are open is about 10 μV with a bandwidth ofabout 100 Hz. It is generally uncorrelated, so it would reduce by the root square with averaging(Sokal and Rohlf 1995). For a realistic human study which requires voluntary cooperation,averaging may be undertaken for trials up to 10 min in duration. For visual evoked responsesrecorded with EIT, this would provide about 1000 stimuli over 10 min, and so the noise wouldbe expected to reduce to 10 μV/√1000 = 0.3 μV. This may be expected to produce a SNRof 1.7 for the mean D changes and 3.5 for the maximal values. For the magnetic case, thephysiological noise level is about 200 fT (Cohen 1968, Hamalainen et al 1993) and after

Modelling for imaging neuronal depolarization by electrical and magnetic detection impedance tomography S219

averaging 1000 stimuli for 10 min, this would reduce to 200 fT/√1000 = 6.3 fT. This maybe expected to produce a SNR of 0.74 for the mean D changes but 4.3 for the maximal values.

Ideally, a much larger SNR would be desirable but this suggests that it would at least beplausible to anticipate statistically significant changes in an empirical human study. Changesof this magnitude are regularly encountered in fMRI or PET studies. Even if changes inindividual subjects may be insignificant, well-established methods such as group averaging orICA could be used to improve overall significance.

4.3.2. Effects of cranial foraminae and electrode placement near them. Modelling hasshown that current injection near cranial foraminae would lead to increased current densitiesin the brain nearby, so that the use of such electrodes should be avoided (Gilad et al 2007).Fortunately, this study has indicated that these had a minor effect on the results for bothelectric and magnetic cases. It therefore appeared reasonable that they could be excluded fromexperimental protocols without significant loss of sensitivity to changes in the visual cortex.The figures given above in section 3 therefore employed 23 rather than 31 current injectionelectrodes so that the number of linearly independent current and measurement combinationsbe 22 × 28 = 618 and 22 × 275 = 6050 for the electric and magnetic cases respectively.

4.3.3. Optimal electrode size. From the electric case study, the sensitivity for internalimpedance changes under the model conditions was only weakly dependent on the area of thesurface electrodes. These results agree with a previous 2D simulation study on errors of staticEIT, showing that for changes of −33 and +166% in the electrode diameter, there were nosignificant changes in the reconstructed image (Kolehmainen et al 1997).

From a theoretical point of view, the amount of current that can be injected is limited bothby the current density at the surface of the brain, in order to avoid neural stimulation, and bycurrent density on the skin, where stimulation of cutaneous receptors can cause discomfort.From both points of view, a larger surface area, ideally with use of a resistive material todiffuse current density, is preferable (Gilad et al 2007). On the other hand, it is preferable toemploy small electrodes as this allows higher spatial resolution. Nevertheless, for ill-posedproblems, and in particular EIT, the spatial resolution is intrinsically bounded and so it appearsthat larger electrodes could be used with minor compromise (Haber et al 2008).

4.4. Implications for imaging of fast neural activity by EIT

4.4.1. Likelihood of eventual success in producing images. This modelling study has focusedsolely on the SNR in the raw transfer impedances from differing electrode combinations. Howthis translates into reliable images is a complex matter outside the scope of this study andis discussed elsewhere (Horesh et al 2009, Haber et al 2008). In principle, it might beexpected that the imaging process can yield acceptable images from noisy data because manychannels with some redundancy are used, and this will have an averaging effect on randomnoise. In addition, the use of established methods, such as principal component analysis(PCA) (Abascal 2007, Fabrizi et al 2008), in the linear reconstruction algorithm used forour brain EIT images, may be expected to condition the data further. The effect of SNR onimage reconstruction has been investigated in our group with a simulation study for the caseof temporal lobe epilepsy (Fabrizi et al 2006a). Using a similar numerical model to that inthis study, scalp voltage changes were calculated when differing volumes of brain changedresistance by about 10%, as in epileptic seizures. Images were reconstructed using a linearmethod with truncated singular value decomposition after realistic noise was added. A peakSNR of 4 in scalp potential measurements appeared to be required for obtaining reliable

S220 O Gilad et al

image reconstruction. This average was for the highest 10% of the voltage changes out ofa protocol which comprised 258 current injection and voltage measurement combinations(Fabrizi et al 2006a). This electrode protocol consisted of 21 current pairs, each with 12voltage measurement pairs. Due to reciprocity, similar results could be obtained with 12current pairs, each with 21 voltage measurements. Since multiple voltage measurementscould be done in parallel, the limiting factor was the number of current pairs which needs tobe recorded serially. Additional improvement may also be achieved by the development ofspatio-temporal constraint-optimization based image reconstruction, in which functional andphysiological constraints can be imposed onto the reconstruction process.

In this study, the maximal SNR after 10 min of averaging was about 4 in both cases.This refers to the peak change in the most sensitive channels, whereas, in the above study, anSNR of 4 was needed in the most sensitive 10%. It is therefore likely that a longer period ofaveraging would be needed, or data would need to be pooled from multiple subjects to achievethis in just one channel for the electric case. Unfortunately, imaging would need recordingfrom multiple current combinations. This would make the period of averaging several hours,which is impractical.

Overall, the findings from this study suggest that a human study is certainly warranted toascertain if these changes can be reliably measured in vivo. However, the prospect of imagingof such changes, which would constitute a dramatic advance in neuroscience technology,appears to be impractical as it is difficult to envisage human subjects tolerating several hoursof averaging. However, there are several factors which might be still varied to achieve theultimate goal—imaging could be undertaken in animal studies when prolonged averaging couldbe performed and greater current applied, or it may be that the magnitude of the resistancechange is greater than the estimate, or that other methods could be discovered to increase itsamplitude.

4.4.2. Is EIT or MD-EIT likely to yield a greater signal-to-noise ratio? Overall, the electric(EIT) and magnetic (MD-EIT) methods may be estimated to produce a similar SNR. This issurprising, as the recording of magnetic fields has the theoretical advantage that they penetratethe skull without resistance. This finding may be explained because the principal source ofnoise in EEG or MEG recording appears to derive from cerebral cortical activity, rather thanfixed instrumentation noise. As a result, the impedance change signal in MEG is greaterbecause it is not diffused by the skull but, equally, the cortical activity is greater by the samedegree.

There, therefore, does not appear to be any great advantage in using the scarce resourceof a MEG system. However, MEG has the practical advantage of ten times more recordingsensors compared to a typical EIT setting and no time is required to attach the recordingsensors.

The original purpose of developing this method was to enable tomographic imaging offast neural activity in the brain. At present, it is not clear if this method could yield imageswith scalp electrodes (EIT) or the magnetic variant MD-EIT, which are sufficiently accuratefor clinical or experimental routine use. The method is presented in the hope of stimulatingfurther development with which technical innovations might improve the signal-to-noise ratio.Even if non-invasive imaging is not possible, this method could be used for recording fromperipheral nerve, which would give different information to nerve conduction studies, or elsebe used for EIT with intracranial electrodes in animal studies or the available special situationof epilepsy patients with implanted subdural electrodes. The latter studies are in progress(Gilad et al 2008). If reliable images can be produced in these research applications, thisshould still constitute a significant addition to neuroscience technology.

Modelling for imaging neuronal depolarization by electrical and magnetic detection impedance tomography S221

Acknowledgments

This work was supported in part by the Epilepsy Research Foundation, UK, Ministry ofScience & Technology, Israel, and the National Institutes of Health (NIH), USA, under grant5R01EB006597-03 from the National Institute of Biomedical Imaging and Bioengineering(NIBIB) and the National Eye Institute (NEI).

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1. Introduction1.1. Possible use of EIT for imaging fast neural activity in the brain1.2. Likely magnitude of resistance changes in the cerebral cortex and when measured non-invasively on the scalp1.3. Proposed use of EIT and MEG for imaging fast neural activity1.4. Purpose1.5. Design and rationale of study

2. Methods2.1. Modelling the electric case2.2. Validation for the electric case2.3. Modelling the magnetic case2.4. Validation for the magnetic case

3. Results3.1. Modelling the electric case3.2. Validation for the electric case3.3. Modelling the magnetic case3.4. Validation for the magnetic case

4. Discussion4.1. Summary of results4.2. Technical issues4.3. Implications for a human study4.4. Implications for imaging of fast neural activity by EIT

AcknowledgmentsReferences