A POTENTIAL METHOD FOR IMAGING NEURONAL DEPOLARISATION IN THE BRAIN BY ELECTRICAL IMPEDANCE TOMOGRAPHY

Adam Liston, Louise Enfield^* ,Richard Bayford, David Holder^*,
Middlesex University (^*University College London), Department of Clinical Neurophysiology, 3rd floor Outpatients Building, Middlesex Hospital, Cleveland St., London W1N 8AA United Kingdom
liston@madeira.physiol.ucl.ac.uk, louise@madeira.physiol.ucl.ac.uk

Abstract: Electrical Impedance Tomography (EIT) is a medical imaging method which has the potential to image resistance changes which occur during neuronal depolarisation in the cortex and last tens of milliseconds. Their magnitude was estimated with a mathematical model, based on cable theory, of impedance changes at DC during depolarisation, first in crab peripheral nerve and then in cerebral cortex. The signal reducing effects of both the membrane capacitance and the fraction of active neurons were estimated and resistivity decreases were predicted of 0.4%–1.6% in cerebral cortex, which corresponded to 0.04% –0.16% on the scalp. The model was verified with recordings in the walking leg nerve of the edible crab. The model predicted a decrease of 1.6% during the action potential and 0.6% was observed. The predicted scalp change is at the limit of detectability of present EIT systems but this may become possible with future technical developments.   

1. Introduction

Electrical Impedance Tomography (EIT) is a recently developed, non-invasive, portable imaging technique which enables tomographic images of electrical impedance to be reconstructed from voltages measured by electrodes placed on the body. Our group has been developing its use for imaging brain function and our main interest has been imaging impedance changes due to blood flow changes and cell swelling. These physiological events cause resistance changes of order 10%, which occur over tens of seconds. It would be of great use if an imaging technique could combine the spatial and temporal resolution of fMRI and EEG to map neuronal activity itself, rather than its consequences. It is possible that EIT may do so.

When a neuron depolarises, ion channels open in the dendritic membrane and its resistance decreases over tens of milliseconds. During this time, there is a localised decrease in resistivity because more current is driven into and through the intracellular space. A technique such as EIT has the capability of measuring with sufficient time-resolution to detect this change as it occurs in the brain. However, the change is expected to be much smaller than those already imaged.

The purpose of this work was to estimate the likely magnitude of the resistivity changes which occur during neuronal depolarisation in order to assess whether or not EIT is adequately sensitive.  The size of the impedance change was modeled using cable theory, and this was then empirically verified with measurements in unmyelinated crab nerve. Both modeling and experimental work were done using DC current. The impedance change occurs during the action potential because current is restricted to the extracellular space at rest but then can pass through the intracellular space during neuronal activity when ion channels open. This effect is greatest at DC, because current passes the cell membrane capacitance at higher frequencies [2].

 2. Crab Nerve Studies

Measurements of this impedance decrease were made using unmyelinated, compound walking leg nerves of the edible crab, Cancer Pegarus, placed on an array of 15 silver-silver chloride electrodes and bathed in crab Ringer Solution (Figure 1).

Figure 1. The crab nerve bundle lying across the silver –silver chloride electrode array

Impedance was measured using 6 electrodes.  The nerve was stimulated with S1 and S2.  A current was applied to D1 and D2 which was less than half of the threshold for an action potential, and resistance was calculated from the resulting voltage recorded between R1 and R2 (Fig. 2).

Figure 2. Experimental array used to stimulate and record the responses from the nerve fibre bundle.

The average impedance change measured was 0.6% when there was a distance of 50mm between R1 and R2. Decreasing the size of the gap to 40mm and 25mm lead to a variation of less than 0.05% in the size of the impedance decrease.

When the impedance measuring current was between 12.5 - 50% of threshold, impedance decreases were constant in the range 0.55 - 0.7%.

3. The Model

The following describes the development of a model of the resistivity changes that occur when cortical neurons depolarise. Their geometry is more complex than that of the peripheral axon and experimental verification of predictions is difficult.

The neurons in the cortex are randomly orientated and it has been shown that their conductivity is one-third that if they were all parallel. Published values were used for the geometry and electrical properties of cortical dendrites and bulk resistivity was calculated using Matlab on a PC. The calculation was repeated for depolarising neuronal membrane. Two factors were added to the calculation, one to account for membrane capacitance which has a tendency to resist voltage changes and reduces the measurable signal. and another to account for those neurons which do not depolarise (for this model, it was estimated that 10% of the neurons depolarise). The signal would also be further reduced because of the distance of the measurement electrodes from the change and because between the two lies the highly resistive skull. The model predicts a localised resistivity change and the scalp signals it causes have yet to be predicted rigorously. A crude estimate was made of the relation between the two and a ratio of 10:1 has been suggested.

The model predicted bulk resistivity of grey matter to be 210-350 Wcm. Capacitance was predicted to reduce the signal associated with the resistance change to a fraction 0.47-0.94 and incomplete depolarisation to a fraction 0.1 for evoked responses. Therefore the effective resistivity change during evoked activity of a region of cortex, as measured at DC, is between –0.4% and –1.6%. This translates into scalp signals of between –0.04% and –0.16%.

4. Discussion

4.1 Validation of experimental work

The results from the experiments on the crab nerve are in agreement from previous modeling work [2] and the model in this work.

4.2 Validation and Criticism of the model

Predictions of bulk resistivity of grey matter were consistent with published values in the literature, which are between 200 at high frequency and 350 at low frequency .However it is difficult to validate the predictions as previous measurements have been made at higher frequencies and with different electrode configurations which will affect the measurements of resistance In preliminary measurements Boone observed [2] a decrease at DC of 0.01-0.03% during evoked responses in rabbit cortex but these results require confirmation.

The dendritic membrane resistance change during depolarisation is unknown and difficult to measure. However, there is a near linear relation between the percentage membrane resistivity change and the bulk resistivity change so their result suffices as an order of magnitude estimate.

4.3 Future Work

To predict scalp voltage changes more completely and accurately, an analytical or Finite Element Method (FEM) forward model could be used with inclusion of a simulated resistance change of order that predicted by the cable model above. Our group expects soon to make DC single channel scalp measurements of the fast cortical resistance changes which accompany evoked responses in humans.

5. Conclusion

The scalp signals generated by the predicted resistivity changes are at the limit of detectability using hardware presently available and image reconstruction is difficult even with the larger signals obtained previously. At present, the predicted resistivity decrease could not be imaged but improvements in EIT technology may allow the technique to be used in the future to produce images of the fast resistance changes associated with neuronal depolarisation.

References

[1] Rall (1975). The nervous system I - Core conductor theory and cable properties of neurons. Handbook of physiology: 39-97.

[2] Boone, K. (1995) The Possible Use of Applied Potential Tomography for imaging action potentials in the brain Clinical Neurophysiology London, UCL