A cable theory based biophysical model of resistance change in crab peripheral nerve and human cerebral cortex during neuronal depolarisation: implications for electrical impedance tomography of fast neural activity in the brain

Optimization of the electrode drive pattern for imaging fascicular compound action potentials in peripheral nerve with fast neural electrical impedance tomography

OBJECTIVE

The main objective of this study was to investigate which injection pattern led to the best imaging of fascicular compound activity in fast neural EIT of peripheral nerve using an external cylindrical 2  ×  14-electrodes cuff. Specifically, the study addressed the identification of the optimal injection pattern and of the optimal region of the reconstructed volume to image fascicles.

APPROACH

The effect of three different measurement protocol features (transversal/longitudinal injection, drive electrode spacing, referencing configuration) over imaging was investigated in simulation with the use of realistic impedance changes and noise levels. Image-based metrics were employed to evaluate the quality of the reconstructions over the reconstruction domain. The optimal electrode addressing protocol suggested by the simulations was validated in vivo on the tibial and peroneal fascicles of rat sciatic peripheral nerves (N  =  3) against MicroCT reference images.

MAIN RESULTS

Injecting current transversally, with spacing of  ⩾4 electrodes apart (⩾100°) and single-ring referencing of measurements, led to the best overall localization when reconstructing on the edge of the electrode array closest to the reference. Longitudinal injection protocols led to a higher SNR of the reconstructed image but poorer localization. All in vivo EIT recordings had statistically significant impedance variations (p   <  0.05). Overall, fascicle center-of-mass (CoM) localization error was estimated at 141  ±  56 µm (-26  ±  94 µm and 5  ±  29° in radial coordinates). Significant difference was found (p   <  0.05) between mean angular location of the tibial and peroneal CoMs.

SIGNIFICANCE

This study gives the reader recommendations for performing fast neural EIT of fascicular compound activity using the most effective protocol features.

Increasing signal amplitude in electrical impedance tomography of neural activity using a parallel resistor inductor capacitor (RLC) circuit

OBJECTIVE

To increase the impedance signal amplitude produced during neural activity using a novel approach of implementing a parallel resistor inductor capacitor (RLC) circuit across the current source used in electrical impedance tomography (EIT) of peripheral nerve.

APPROACH

The frequency response of the impedance signal was characterized in the range 4-18 kHz, then a frequency range with significant capacitive charge transfer was selected for experiment with the RLC circuit. Design of the RLC circuit was aided by in vitro impedance measurements on nerve and nerve cuff in the range 5 Hz to 50 kHz.

MAIN RESULTS

The frequency response of the impedance signal across 4-18 kHz showed maximum amplitude at 6-8 kHz, and steady decline in amplitude between 8 and 18 kHz with  -6 dB reduction at 14 kHz. The frequency range 17  ±  1 kHz was selected for the RLC experiment. The RLC experiment was performed on four subjects using an RLC circuit designed to produce a resonant frequency of 17 kHz with a bandwidth of 3.6 kHz, and containing a 22 mH inductive element and a 3.45 nF capacitive element with  +0.8/-  3.45 nF manual tuning range. With the RLC circuit connected, relative increases in the impedance signal (±3σ noise) of 44% (±15%), 33% (±30%), 37% (±8.6%), and 16% (±19%) were produced.

SIGNIFICANCE

The increase in impedance signal amplitude at high frequencies, generated by the novel implementation of a parallel RLC circuit across the drive current, improves spatial resolution by increasing the number of parallel drive currents which can be implemented in a frequency division multiplexed (FDM) EIT system, and aids the long term goal of a real-time FDM EIT system by reducing the need for ensemble averaging.

Microelectrode array electrical impedance tomography for fast functional imaging in the thalamus

Electrical Impedance Tomography (EIT) has the potential to be able to observe functional tomographic images of neural activity in the brain at millisecond time-scales. Prior modelling and experimental work has shown that EIT is capable of imaging impedance changes from neural depolarisation in rat somatosensory cortex. Here, we investigate the feasibility of EIT for imaging impedance changes using a stereotaxically implanted microelectrode array in the thalamus. Microelectrode array EIT was simulated using an anatomically accurate marmoset brain model. Impedance imaging was validated and detectability estimated using physiological noise recorded from the marmoset visual thalamus. The results suggest that visual-input-driven impedance changes in visual subcortical bodies within 300 μm of the implanted array could be reliably reconstructed and localised, comparable to local field potential measurements. Furthermore, we demonstrated that microelectrode array EIT could reconstruct concurrent activity in multiple subcortical bodies simultaneously.

Model of Impedance Changes in Unmyelinated Nerve Fibers

OBJECTIVE

Currently, there is no imaging method that is able to distinguish the functional activity inside nerves. Such a method would be essential for understanding peripheral nerve physiology and would allow precise neuromodulation of organs these nerves supply. Electrical impedance tomography (EIT) is a method that produces images of electrical impedance change (dZ) of an object by injecting alternating current and recording surface voltages. It has been shown to be able to image fast activity in the brain and large peripheral nerves. To image inside small autonomic nerves, mostly containing unmyelinated fibers, it is necessary to maximize SNR and optimize the EIT parameters. An accurate model of the nerve is required to identify these optimal parameters as well as to validate data obtained in the experiments.

METHODS

In this study, we developed two three-dimensional models of unmyelinated fibers: Hodgkin-Huxley (HH) squid giant axon (single and multiple) and mammalian C-nociceptor. A coupling feedback system was incorporated into the models to simulate direct and alternating current application and simultaneously record external field during action potential propagation.

RESULTS

Parameters of the developed models were varied to study their influence on the recorded impedance changes; the optimal parameters were identified. The negative dZ was found to monotonically decrease with frequency for both HH and C fiber models, in accordance with the experimental data.

CONCLUSION AND SIGNIFICANCE

The accurate realistic model of unmyelinated nerve allows the optimization of EIT parameters and matches literature and experimental results.

Membrane resistance and shunting inhibition: where biophysics meets state-dependent human neurophysiology

Activation of neurons not only changes their membrane potential and firing rate but as a secondary action reduces membrane resistance. This loss of resistance, or increase of conductance, may be of central importance in non‐invasive magnetic or electric stimulation of the human brain since electrical fields cause larger changes in transmembrane voltage in resting neurons with low membrane conductances than in active neurons with high conductance. This may explain why both the immediate effects and after‐effects of brain stimulation are smaller or even reversed during voluntary activity compared with rest. Membrane conductance is also increased during shunting inhibition, which accompanies the classic GABA_A IPSP. This short‐circuits nearby EPSPs and is suggested here to contribute to the magnitude and time course of short‐interval intracortical inhibition and intracortical facilitation.

Empirical validation of statistical parametric mapping for group imaging of fast neural activity using electrical impedance tomography

Electrical impedance tomography (EIT) allows for the reconstruction of internal conductivity from surface measurements. A change in conductivity occurs as ion channels open during neural activity, making EIT a potential tool for functional brain imaging. EIT images can have  >10 000 voxels, which means statistical analysis of such images presents a substantial multiple testing problem. One way to optimally correct for these issues and still maintain the flexibility of complicated experimental designs is to use random field theory. This parametric method estimates the distribution of peaks one would expect by chance in a smooth random field of a given size. Random field theory has been used in several other neuroimaging techniques but never validated for EIT images of fast neural activity, such validation can be achieved using non-parametric techniques. Both parametric and non-parametric techniques were used to analyze a set of 22 images collected from 8 rats. Significant group activations were detected using both techniques (corrected p  <  0.05). Both parametric and non-parametric analyses yielded similar results, although the latter was less conservative. These results demonstrate the first statistical analysis of such an image set and indicate that such an analysis is an approach for EIT images of neural activity.

Imaging fast electrical activity in the brain with electrical impedance tomography

Imaging of neuronal depolarization in the brain is a major goal in neuroscience, but no technique currently exists that could image neural activity over milliseconds throughout the whole brain. Electrical impedance tomography (EIT) is an emerging medical imaging technique which can produce tomographic images of impedance changes with non-invasive surface electrodes. We report EIT imaging of impedance changes in rat somatosensory cerebral cortex with a resolution of 2ms and <200μm during evoked potentials using epicortical arrays with 30 electrodes. Images were validated with local field potential recordings and current source-sink density analysis. Our results demonstrate that EIT can image neural activity in a volume 7×5×2mm in somatosensory cerebral cortex with reduced invasiveness, greater resolution and imaging volume than other methods. Modeling indicates similar resolutions are feasible throughout the entire brain so this technique, uniquely, has the potential to image functional connectivity of cortical and subcortical structures.

Modeling the effect of dendritic input location on MEG and EEG source dipoles

The cerebral sources of magneto- and electroencephalography (MEG, EEG) signals can be represented by current dipoles. We used computational modeling of realistically shaped passive-membrane dendritic trees of pyramidal cells from the human cerebral cortex to examine how the spatial distribution of the synaptic inputs affects the current dipole. The magnitude of the total dipole moment vector was found to be proportional to the vertical location of the synaptic input. The dipole moment had opposite directions for inputs above and below a reversal point located near the soma. Inclusion of shunting-type inhibition either suppressed or enhanced the current dipole, depending on whether the excitatory and inhibitory synapses were on the same or opposite side of the reversal point. Relating the properties of the macroscopic current dipoles to dendritic current distributions can help to provide means for interpreting MEG and EEG data in terms of synaptic connection patterns within cortical areas.

Investigation of potential artefactual changes in measurements of impedance changes during evoked activity: implications to electrical impedance tomography of brain function

Electrical impedance tomography (EIT) could provide images of fast neural activity in the adult human brain with a resolution of 1 ms and 1 mm by imaging impedance changes which occur as ion channels open during neuronal depolarization. The largest changes occur at dc and decrease rapidly over 100 Hz. Evoked potentials occur in this bandwidth and may cause artefactual apparent impedance changes if altered by the impedance measuring current. These were characterized during the compound action potential in the walking leg nerves of Cancer pagurus, placed on Ag/AgCl hook electrodes, to identify how to avoid artefactual changes during brain EIT. Artefact-free impedance changes (δZ) decreased with frequency from −0.045 ± 0.01% at 225 Hz to −0.02 ± 0.01% at 1025 Hz (mean ± 1 SD, n = 24 in 12 nerves) which matched changes predicted by a finite element model. Artefactual δZ reached c.300% and 50% of the genuine membrane impedance change at 225 Hz and 600 Hz respectively but decreased with frequency of the applied current and was negligible above 1 kHz. The proportional amplitude (δZ (%)) of the artefact did not vary significantly with the amplitude of injected current of 5–20 µA pp. but decreased significantly from −0.09 ± 0.024 to −0.03 ± 0.023% with phase of 0 to 45°. For fast neural EIT of evoked activity in the brain, artefacts may arise with applied current of >10 µA. Independence of δZ with respect to phase but not the amplitude of applied current controls for them; they can be minimized by randomizing the phase of the applied measuring current and excluded by recording at >1 kHz.

Real-time imaging of cerebral infarction in rabbits using electrical impedance tomography

Objective

To investigate the possible use of electrical impedance tomography (EIT) in monitoring focal cerebral infarction in a rabbit model.

Methods

A model of focal cerebral infarction was established in eight New Zealand rabbits using a photochemical method without craniectomy. Focal cerebral infarction was confirmed by histopathological examination. Intracranial impedance variation was measured using 16 electrodes placed in a circle on the scalp. EIT images were obtained using a damped least-squares reconstruction algorithm. The average resistivity value (ARV) of the infarct region on EIT images was calculated to quantify relative resistivity changes. A symmetry index was calculated to evaluate the relative difference in resistivity between the two sides of the cerebrum.

Results

EIT images and ARV curves showed that impedance changes caused by cerebral infarction increased linearly with irradiation time. A difference in ARV was found between measurements taken before and after infarct induction.

Conclusions

Focal cerebral infarction can be monitored by EIT in the proposed animal model. The results are sufficiently encouraging that the authors plan to extend this study to humans, after further technical improvements.