A fast parallel solver for the forward problem in electrical impedance tomography

A combined cuff electrode array for organ-specific selective stimulation of vagus nerve enabled by Electrical Impedance Tomography

Previously developed spatially-selective Vagus Nerve Stimulation (sVNS) allows the targeting of specific nerve fascicles through current steering in a multi-electrode nerve cuff but relies on a trial-and-error strategy to identify the relative orientation between electrodes and fascicles. Fast Neural Electrical Impedance Tomography (FN-EIT) has been recently used for imaging neural traffic in the vagus nerves of pigs in a cross-correlation study with sVNS and MicroCT fascicle tracking. FN-EIT has the potential for allowing targeted sVNS; however, up to now, stimulation and imaging have been performed with separate electrode arrays. In this study, different options were evaluated in-silico to integrate EIT and stimulation into a single electrode array without affecting spatial selectivity. The original pig vagus EIT electrode array geometry was compared with a geometry integrating sVNS and EIT electrodes, and with direct use of sVNS electrodes for EIT imaging. Modelling results indicated that both new designs could achieve image quality similar to the original electrode geometry in all tested markers (e.g., co-localisation error <100 µm). The sVNS array was considered to be the simplest due to the lower number of electrodes. Experimental results from testing evoked EIT imaging of recurrent laryngeal activity using electrodes from the sVNS cuff returned a signal-to-noise ratio similar to our previous study (3.9 ± 2.4 vs. 4.1 ± 1.5, N = 4 nerves from 3 pigs) and a lower co-localisation error (≈14% nerve diameter vs. ≈25%, N = 2 nerves from 2 pigs). Performing FN-EIT and sVNS on the same nerve cuff will facilitate translation to humans, simplify surgery and enable targeted neuromodulation strategies.

Organotopic organization of the porcine mid-cervical vagus nerve

Introduction

Despite detailed characterization of fascicular organization of somatic nerves, the functional anatomy of fascicles evident in human and large mammal cervical vagus nerve is unknown. The vagus nerve is a prime target for intervention in the field of electroceuticals due to its extensive distribution to the heart, larynx, lungs, and abdominal viscera. However, current practice of the approved vagus nerve stimulation (VNS) technique is to stimulate the entire nerve. This produces indiscriminate stimulation of non-targeted effectors and undesired side effects. Selective neuromodulation is now a possibility with a spatially-selective vagal nerve cuff. However, this requires the knowledge of the fascicular organization at the level of cuff placement to inform selectivity of only the desired target organ or function.

Methods and results

We imaged function over milliseconds with fast neural electrical impedance tomography and selective stimulation, and found consistent spatially separated regions within the nerve correlating with the three fascicular groups of interest, suggesting organotopy. This was independently verified with structural imaging by tracing anatomical connections from the end organ with microCT and the development of an anatomical map of the vagus nerve. This confirmed organotopic organization.

Discussion

Here we show, for the first time, localized fascicles in the porcine cervical vagus nerve which map to cardiac, pulmonary and recurrent laryngeal function (N = 4). These findings pave the way for improved outcomes in VNS as unwanted side effects could be reduced by targeted selective stimulation of identified organ-specific fiber-containing fascicles and the extension of this technique clinically beyond the currently approved disorders to treat heart failure, chronic inflammatory disorders, and more.

Improvement of performance and sensitivity of 2D and 3D image reconstruction in EIT using EFG forward model

This paper presents a pure element-free Galerkin method (EFGM) forward model for image reconstruction in 2D and 3D electrical impedance tomography (EIT) using an adaptive current injection method. In EIT systems with the adapting current injection method, both static and dynamic images can be reconstructed; however, determination of electrode contact impedances in the complete electrode model is difficult and the Gap model is used. In this paper, in the EIT forward problem a weak form functional based on the Gap model and a pure EFGM approach are developed, and in the EIT inverse problem, Jacobian matrix is computed by the EFGM, and a fast integration technique is introduced to calculate the entries of the Jacobian matrix within an adequate computation time. The influence of increasing the density of nodes at and near the electrodes with steep electric potential gradients on the accuracy of FEM and EFGM forward solutions is investigated, and the performance of the image reconstruction algorithm with the proposed fast integration technique is examined. The numerical results reveal that the proposed EFGM forward model with the fast integration technique has an efficient performance both in terms of mean relative imaging errors and computational time.

Advances in electrical impedance tomography-based brain imaging

Novel advances in the field of brain imaging have enabled the unprecedented clinical application of various imaging modalities to facilitate disease diagnosis and treatment. Electrical impedance tomography (EIT) is a functional imaging technique that measures the transfer impedances between electrodes on the body surface to estimate the spatial distribution of electrical properties of tissues. EIT offers many advantages over other neuroimaging technologies, which has led to its potential clinical use. This qualitative review provides an overview of the basic principles, algorithms, and system composition of EIT. Recent advances in the field of EIT are discussed in the context of epilepsy, stroke, brain injuries and edema, and other brain diseases. Further, we summarize factors limiting the development of brain EIT and highlight prospects for the field. In epilepsy imaging, there have been advances in EIT imaging depth, from cortical to subcortical regions. In stroke research, a bedside EIT stroke monitoring system has been developed for clinical practice, and data support the role of EIT in multi-modal imaging for diagnosing stroke. Additionally, EIT has been applied to monitor the changes in brain water content associated with cerebral edema, enabling the early identification of brain edema and the evaluation of mannitol dehydration. However, anatomically realistic geometry, inhomogeneity, cranium completeness, anisotropy and skull type, etc., must be considered to improve the accuracy of EIT modeling. Thus, the further establishment of EIT as a mature and routine diagnostic technique will necessitate the accumulation of more supporting evidence.

Simplifying the hardware requirements for fast neural EIT of peripheral nerves

OBJECTIVE

The main objective of this study was to assess the feasibility of lowering the hardware requirements for fast neural EIT in order to support the distribution of this technique. Specifically, the feasibility of replacing the commercial modules present in the existing high-end setup with compact and cheap customized circuitry was assessed.

APPROACH

Nerve EIT imaging was performed on rat sciatic nerves with both our standard ScouseTom setup and a customized version in which commercial benchtop current sources were replaced by custom circuitry. Electrophysiological data and images collected in the same experimental conditions with the two setups were compared. Data from the customized setup was subject to a down-sampling analysis to simulate the use of a recording module with lower specifications.

MAIN RESULTS

Compound action potentials (573±287µV and 487±279µV, p=0.28) and impedance changes (36±14µV and 31±16µV, p=0.49) did not differ significantly when measured using commercial high-end current sources or our custom circuitry, respectively. Images reconstructed from both setups showed neglibile (<1voxel, i.e. 40µm) difference in peak location and a high degree of correlation (R2=0.97). When down-sampling from 24 to 16 bits ADC resolution and from 100KHz to 50KHz sampling frequency, signal-to-noise ratio showed acceptable decrease (<-20%), and no meaningful image quality loss was detected (peak location difference <1voxel, pixel-by-pixel correlation R2=0.99).

SIGNIFICANCE

The technology developed for this study greatly reduces the cost and size of a fast neural EIT setup without impacting quality and thus promotes the adoption of this technique by the neuroscience research community.

Fascicle localisation within peripheral nerves through evoked activity recordings: A comparison between electrical impedance tomography and multi-electrode arrays

BACKGROUND

The lack of understanding of fascicular organisation in peripheral nerves limits the potential of vagus nerve stimulation therapy. Two promising methods may be employed to identify the functional anatomy of fascicles within the nerve: fast neural electrical impedance tomography (EIT), and penetrating multi-electrode arrays (MEA). These could provide a means to image the compound action potential within fascicles in the nerve.

NEW METHOD

We compared the ability to localise fascicle activity between silicon shanks (SS) and carbon fibre (CF) multi-electrode arrays and fast neural EIT, with micro-computed tomography (MicroCT) as an independent reference. Fast neural EIT in peripheral nerves was only recently developed and MEA technology has been used only sparingly in nerves and not for source localisation. Assessment was performed in rat sciatic nerves while evoking neural activity in the tibial and peroneal fascicles.

RESULTS

Recorded compound action potentials were larger with CF compared to SS (∼700 μV vs ∼300 μV); however, background noise was greater (6.3 μV vs 1.7 μV) leading to lower SNR. Maximum spatial discrimination between Centres-of-Mass of fascicular activity was achieved by fast neural EIT (402 ± 30 μm) and CF MEA (414 ± 123 μm), with no statistical difference between MicroCT (625 ± 17 μm) and CF (p > 0.05) and between CF and EIT (p > 0.05). Compared to CF MEAs, SS MEAs had a lower discrimination power (103 ± 51 μm, p < 0.05).

COMPARISON WITH EXISTING METHODS

EIT and CF MEAs showed localisation power closest to MicroCT. Silicon MEAs adopted in this study failed to discriminate fascicle location. Re-design of probe geometry may improve results.

CONCLUSIONS

Nerve EIT is an accurate tool for assessment of fascicular position within nerves. Accuracy of EIT and CF MEA is similar to the reference method. We give technical recommendations for performing multi-electrode recordings in nerves.

Electrical Tomography Reconstruction Using Reconfigurable Waveforms in a FPGA

The principal objective of this research is to conceive a mobile system based on electrical tomography for subsurface imaging and monitoring in order to enable simultaneous recording of electrical potentials of cardiac and pulmonary activity. For an exploration of excitation waveforms in electrical tomography, specialized hardware is required. As the main principle of tomography is the measurement of electrical perturbations on an unknown object, it is crucial to synchronize excitation and sensing processes in a very precise way for the purpose of acquiring meaningful data. To cope with this problem, an FPGA device is used, with an architecture that allows us to trigger excitation signals and to read sensed data simultaneously via independent processes that share the same clock. In this way, waveform reconfiguration on frequency and shape can be provided and studied. The system is connected to a standard microcontroller SoC with a simple API that allows for IoT capabilities for on-line operation and tracking, given that the design is targeted for in vivo medical monitoring. As a result of the research work, a measuring device was developed, the surface data analyzed and the image was reconstructed using the selected configuration.

Imaging of focal seizures with Electrical Impedance Tomography and depth electrodes in real time

Intracranial EEG is the current gold standard technique for localizing seizures for surgery, but it can be insensitive to tangential dipole or distant sources. Electrical Impedance Tomography (EIT) offers a novel method to improve coverage and seizure onset localization. The feasibility of EIT has been previously assessed in a computer simulation, which revealed an improved accuracy of seizure detection with EIT compared to intracranial EEG. In this study, slow impedance changes, evoked by cell swelling occurring over seconds, were reconstructed in real time by frequency division multiplexing EIT using depth and subdural electrodes in a swine model of epilepsy. EIT allowed to generate repetitive images of ictal events at similar time course to fMRI but without its significant limitations. EIT was recorded with a system consisting of 32 parallel current sources and 64 voltage recorders. Seizures triggered with intracranial injection of benzylpenicillin (BPN) in five pigs caused a repetitive peak impedance increase of 3.4 ± 1.5 mV and 9.5 ± 3% (N =205 seizures); the impedance signal change was seen already after a single, first seizure. EIT enabled reconstruction of the seizure onset 9 ± 1.5 mm from the BPN cannula and 7.5 ± 1.1 mm from the closest SEEG contact (p<0.05, n =37 focal seizures in three pigs) and it could address problems with sampling error in intracranial EEG. The amplitude of the impedance change correlated with the spread of the seizure on the SEEG (p <<0.001, n =37). The results presented here suggest that combining a parallel EIT system with intracranial EEG monitoring has a potential to improve the diagnostic yield in epileptic patients and become a vital tool in improving our understanding of epilepsy.

Imaging slow brain activity during neocortical and hippocampal epileptiform events with electrical impedance tomography

OBJECTIVE

Electrical impedance tomography (EIT) is an imaging technique that produces tomographic images of internal impedance changes within an object using surface electrodes. It can be used to image the slow increase in cerebral tissue impedance that occurs over seconds during epileptic seizures, which is attributed to cell swelling due to disturbances in ion homeostasis following hypersynchronous neuronal firing and its associated metabolic demands. In this study, we characterised and imaged this slow impedance response during neocortical and hippocampal epileptiform events in the rat brain and evaluated its relationship to the underlying neural activity.

APPROACH

Neocortical or hippocampal seizures, comprising repeatable series of high-amplitude ictal spikes, were induced by electrically stimulating the sensorimotor cortex or perforant path of rats anaesthetised with fentanyl-isoflurane. Transfer impedances were measured during ≥30 consecutive seizures, by applying a sinusoidal current through independent electrode pairs on an epicortical array, and combined to generate an EIT image of slow activity.

MAIN RESULTS

The slow impedance responses were consistently time-matched to the end of seizures and EIT images of this activity were reconstructed reproducibly in all animals (p < 0.03125, N = 5). These displayed foci of activity that were spatially confined to the facial somatosensory cortex and dentate gyrus for neocortical and hippocampal seizures, respectively, and encompassed a larger volume as the seizure progressed. Centre-of-mass analysis of reconstructions revealed that this activity corresponded to the true location of the epileptogenic zone, as determined by EEG recordings and fast neural EIT measurements which were obtained simultaneously.

SIGNIFICANCE

These findings suggest that the slow impedance response presents a reliable marker of hypersynchronous neuronal activity during epileptic seizures and can thus be utilised for investigating the mechanisms of epileptogenesis in vivo and for aiding localisation of the epileptogenic zone during presurgical evaluation of patients with refractory epilepsies.

Imaging fascicular organization of rat sciatic nerves with fast neural electrical impedance tomography

Imaging compound action potentials (CAPs) in peripheral nerves could help avoid side effects in neuromodulation by selective stimulation of identified fascicles. Existing methods have low resolution, limited imaging depth, or are invasive. Fast neural electrical impedance tomography (EIT) allows fascicular CAP imaging with a resolution of <200 µm, <1 ms using a non-penetrating flexible nerve cuff electrode array. Here, we validate EIT imaging in rat sciatic nerve by comparison to micro-computed tomography (microCT) and histology with fluorescent dextran tracers. With EIT, there are reproducible localized changes in tissue impedance in response to stimulation of individual fascicles (tibial, peroneal and sural). The reconstructed EIT images correspond to microCT scans and histology, with significant separation between the fascicles (p < 0.01). The mean fascicle position is identified with an accuracy of 6% of nerve diameter. This suggests fast neural EIT can reliably image the functional fascicular anatomy of the nerves and so aid selective neuromodulation.

Multi-frequency symmetry difference electrical impedance tomography with machine learning for human stroke diagnosis

OBJECTIVE

Multi-frequency symmetry difference electrical impedance tomography (MFSD-EIT) can robustly detect and identify unilateral perturbations in symmetric scenes. Here, an investigation is performed to assess if the algorithm can be successfully applied to identify the aetiology of stroke with the aid of machine learning.

METHODS

Anatomically realistic four-layer finite element method models of the head based on stroke patient images are developed and used to generate EIT data over a 5 Hz-100 Hz frequency range with and without bleed and clot lesions present. Reconstruction generates conductivity maps of each head at each frequency. Application of a quantitative metric assessing changes in symmetry across the sagittal plane of the reconstructed image and over the frequency range allows lesion detection and identification. The algorithm is applied to both simulated and human (n = 34 subjects) data. A classification algorithm is applied to the metric value in order to differentiate between normal, haemorrhage and clot values.

MAIN RESULTS

An average accuracy of 85% is achieved when MFSD-EIT with support vector machines (SVM) classification is used to identify and differentiate bleed from clot in human data, with 77% accuracy when differentiating normal from stroke in human data.

CONCLUSION

Applying a classification algorithm to metrics derived from MFSD-EIT images is a novel and promising technique for detection and identification of perturbations in static scenes.

SIGNIFICANCE

The MFSD-EIT algorithm used with machine learning gives promising results of lesion detection and identification in challenging conditions like stroke. The results imply feasible translation to human patients.

Bi-Frequency Symmetry Difference EIT-Feasibility and Limitations of Application to Stroke Diagnosis

OBJECTIVE

Bi-Frequency Symmetry Difference (BFSD)-EIT can detect, localize and identify unilateral perturbations in symmetric scenes. Here, we test the viability and robustness of BFSD-EIT in stroke diagnosis.

METHODS

A realistic 4-layer Finite Element Method (FEM) head model with and without bleed and clot lesions is developed. Performance is assessed with test parameters including: measurement noise, electrode placement errors, contact impedance errors, deviations in assumed tissue conductivity, deviations in assumed anatomy, and a frequency-dependent background. A final test is performed using ischemic patient data. Results are assessed using images and quantitative metrics.

RESULTS

BFSD-EIT may be feasible for stroke diagnosis if a signal-to-noise ratio (SNR) of ≥60 dB is achievable. Sensitivity to errors in electrode positioning is seen with a tolerance of only ±5 mm, but a tolerance of up to ±30 mm is possible if symmetry is maintained between symmetrically opposite partner electrodes. The technique is robust to errors in contact impedance and assumed tissue conductivity up to at least ±50%. Asymmetric internal anatomy affects performance but may be tolerable for tissues with frequency-dependent conductivity. Errors in assumed external geometry marginally affect performance. A frequency-dependent background does not affect performance with carefully chosen frequency points or use of multiple frequency points across a band. The Global Left-Hand Side (LHS) & Right-Hand Side (RHS) Mean Intensity metric is particularly robust to errors.

CONCLUSION

BFSD-EIT is a promising technique for stroke diagnosis, provided parameters are within the tolerated ranges.

SIGNIFICANCE

BFSD-EIT may prove an important step forward in imaging of static scenes such as stroke.

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.

Bi-frequency symmetry difference electrical impedance tomography-a novel technique for perturbation detection in static scenes

OBJECTIVE

A novel method for the imaging of static scenes using electrical impedance tomography (EIT) is reported with implementation and validation using numerical and phantom models. The technique is applicable to regions featuring symmetry in the normal case, asymmetry in the presence of a perturbation, and where there is a known, frequency-dependent change in the electrical conductivity of the materials in the region.

APPROACH

The stroke diagnostic problem is used as a motivating sample application. The head is largely symmetrical across the sagittal plane. A haemorrhagic or ischaemic lesion located away from the sagittal plane will alter this natural symmetry, resulting in a symmetrical imbalance that can be detected using EIT. Specifically, application of EIT stimulation and measurement protocols at two distinct frequencies detects deviations in symmetry if an asymmetrically positioned lesion is present, with subsequent identification and localisation of the perturbation based on known frequency-dependent conductivity changes. Anatomically accurate computational models are used to demonstrate the feasibility of the proposed technique using different types, sizes, and locations of lesions with frequency-dependent (or independent) conductivity. Further, a realistic experimental head phantom is used to validate the technique using frequency-dependent perturbations emulating the key numerical simulations.

MAIN RESULTS

Lesion presence, type, and location are detectable using this novel technique. Results are presented in the form of images and corresponding robust quantitative metrics. Better detection is achieved for larger lesions, those further from the sagittal plane, and when measurements have a higher signal-to-noise ratio.

SIGNIFICANCE

Bi-frequency symmetry difference EIT is an exciting new modality of EIT with the ability to detect deviations in the symmetry of a region that occur due to the presence of a lesion. Notably, this modality does not require a time change in the region and thus may be used in static scenarios such as stroke detection.

Electrode fabrication and interface optimization for imaging of evoked peripheral nervous system activity with electrical impedance tomography (EIT)

OBJECTIVE

Non-invasive imaging techniques are undoubtedly the ideal methods for continuous monitoring of neural activity. One such method, fast neural electrical impedance tomography (EIT) has been developed over the past decade in order to image neural action potentials with non-penetrating electrode arrays.

APPROACH

The goal of this study is two-fold. First, we present a detailed fabrication method for silicone-based multiple electrode arrays which can be used for epicortical or neural cuff applications. Secondly, we optimize electrode material coatings in order to achieve the best accuracy in EIT reconstructions.

MAIN RESULTS

The testing of nanostructured electrode interface materials consisting of platinum, iridium oxide, and PEDOT:pTS in saline tank experiments demonstrated that the PEDOT:pTS coating used in this study leads to more accurate reconstruction dimensions along with reduced phase separation between recording channels. The PEDOT:pTS electrodes were then used in vivo to successfully image and localize the evoked activity of the recurrent laryngeal fascicle from within the cervical vagus nerve.

SIGNIFICANCE

These results alongside the simple fabrication method presented here position EIT as an effective method to image neural activity.

Imaging fast electrical activity in the brain during ictal epileptiform discharges with electrical impedance tomography

Electrical Impedance Tomography (EIT) is an emerging medical imaging technique which can produce tomographic images of internal impedance changes within an object using non-penetrating surface electrodes. It has previously been used to image impedance changes due to neuronal depolarisation during evoked potentials in the rat somatosensory cortex with a resolution of 2 ms and <200 μm, using an epicortical electrode array. The purpose of this work was to use this technique to elucidate the intracortical spatiotemporal trajectory of ictal spike-and-wave discharges (SWDs), induced by electrical stimulation in an acute rat model of epilepsy, throughout the cerebral cortex. Seizures lasting 16.5 ± 5.3 s with repetitive 2-5 Hz SWDs were induced in five rats anaesthetised with fentanyl-isoflurane. Transfer impedance measurements were obtained during each seizure with a 57-electrode epicortical array by applying 50 μA current at 1.7 kHz to two electrodes and recording voltages from all remaining electrodes. Images were reconstructed from averaged SWD-related impedance traces obtained from EIT measurements in successive seizures. We report the occurrence of reproducible impedance changes during the initial spike phase, which had an early onset in the whisker barrel cortex and spread posteriorly, laterally and ventrally over 20 ms (p < 0.03125, N = 5). These findings, which confirm and extend knowledge of SWD initiation and expression, suggest that EIT is a valuable neuroimaging tool for improving understanding of neural circuits implicated in epileptic phenomena.

Multi-frequency electrical impedance tomography and neuroimaging data in stroke patients

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique, which has the potential to expedite the differentiation of ischaemic or haemorrhagic stroke, decreasing the time to treatment. Whilst demonstrated in simulation, there are currently no suitable imaging or classification methods which can be successfully applied to human stroke data. Development of these complex methods is hindered by a lack of quality Multi-Frequency EIT (MFEIT) data. To address this, MFEIT data were collected from 23 stroke patients, and 10 healthy volunteers, as part of a clinical trial in collaboration with the Hyper Acute Stroke Unit (HASU) at University College London Hospital (UCLH). Data were collected at 17 frequencies between 5 Hz and 2 kHz, with 31 current injections, yielding 930 measurements at each frequency. This dataset is the most comprehensive of its kind and enables combined analysis of MFEIT, Electroencephalography (EEG) and Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) data in stroke patients, which can form the basis of future research into stroke classification.

A Versatile and Reproducible Multi-Frequency Electrical Impedance Tomography System

A highly versatile Electrical Impedance Tomography (EIT) system, nicknamed the ScouseTom, has been developed. The system allows control over current amplitude, frequency, number of electrodes, injection protocol and data processing. Current is injected using a Keithley 6221 current source, and voltages are recorded with a 24-bit EEG system with minimum bandwidth of 3.2 kHz. Custom PCBs interface with a PC to control the measurement process, electrode addressing and triggering of external stimuli. The performance of the system was characterised using resistor phantoms to represent human scalp recordings, with an SNR of 77.5 dB, stable across a four hour recording and 20 Hz to 20 kHz. In studies of both haeomorrhage using scalp electrodes, and evoked activity using epicortical electrode mats in rats, it was possible to reconstruct images matching established literature at known areas of onset. Data collected using scalp electrode in humans matched known tissue impedance spectra and was stable over frequency. The experimental procedure is software controlled and is readily adaptable to new paradigms. Where possible, commercial or open-source components were used, to minimise the complexity in reproduction. The hardware designs and software for the system have been released under an open source licence, encouraging contributions and allowing for rapid replication.

Applications for Electrical Impedance Tomography (EIT) and Electrical Properties of the Human Body

Electrical Impedance Tomography (EIT) is a promising application that displays changes in conductivity within a body. The basic principle of the method is the repeated measurement of surface voltages of a body, which are a result of rolling injection of known and small-volume sinusoidal AC current to the body through the electrodes attached to its surface. This method finds application in biomedicine, biology and geology. The objective of this paper is to present the applications of Electrical Impedance Tomography, along with the method's capabilities and limitations due to the electrical properties of the human body. For this purpose, investigation of existing literature has been conducted, using electronic databases, PubMed, Google Scholar and IEEE Xplore. In addition, there was a secondary research phase, using paper citations found during the first research phase. It should be noted that Electrical Impedance Tomography finds use in a plethora of medical applications, as the different tissues of the body have different conductivities and dielectric constants. Main applications of EIT include imaging of lung function, diagnosis of pulmonary embolism, detection of tumors in the chest area and diagnosis and distinction of ischemic and hemorrhagic stroke. EIT advantages include portability, low cost and safety, which the method provide, since it is a noninvasive imaging method that does not cause damage to the body. The main disadvantage of the method, which blocks its wider spread, appears in the image composition from the voltage measurements, which are conducted by electrodes placed on the periphery of the body, because the injected currents are affected nonlinearly by the general distribution of the electrical properties of the body. Furthermore, the complex impedance of the skin-electrode interface can be modelled by using a capacitor and two resistor, as a result of skin properties. In conclusion, Electrical Impedance Tomography is a promising method for the development of noninvasive diagnostic medicine, since it is able to provide imaging of the interior of the human body in real time without causing harm or putting the human body in risk.

Correction of electrode modelling errors in multi-frequency EIT imaging

The differentiation of haemorrhagic from ischaemic stroke using electrical impedance tomography (EIT) requires measurements at multiple frequencies, since the general lack of healthy measurements on the same patient excludes time-difference imaging methods. It has previously been shown that the inaccurate modelling of electrodes constitutes one of the largest sources of image artefacts in non-linear multi-frequency EIT applications. To address this issue, we augmented the conductivity Jacobian matrix with a Jacobian matrix with respect to electrode movement. Using this new algorithm, simulated ischaemic and haemorrhagic strokes in a realistic head model were reconstructed for varying degrees of electrode position errors. The simultaneous recovery of conductivity spectra and electrode positions removed most artefacts caused by inaccurately modelled electrodes. Reconstructions were stable for electrode position errors of up to 1.5 mm standard deviation along both surface dimensions. We conclude that this method can be used for electrode model correction in multi-frequency EIT.

Determination of head conductivity frequency response in vivo with optimized EIT-EEG

Electroencephalography (EEG) benefits from accurate head models. Dipole source modelling errors can be reduced from over 1cm to a few millimetres by replacing generic head geometry and conductivity with tailored ones. When adequate head geometry is available, electrical impedance tomography (EIT) can be used to infer the conductivities of head tissues. In this study, the boundary element method (BEM) is applied with three-compartment (scalp, skull and brain) subject-specific head models. The optimal injection of small currents to the head with a modular EIT current injector, and voltage measurement by an EEG amplifier is first sought by simulations. The measurement with a 64-electrode EEG layout is studied with respect to three noise sources affecting EIT: background EEG, deviations from the fitting assumption of equal scalp and brain conductivities, and smooth model geometry deviations from the true head geometry. The noise source effects were investigated depending on the positioning of the injection and extraction electrode and the number of their combinations used sequentially. The deviation from equal scalp and brain conductivities produces rather deterministic errors in the three conductivities irrespective of the current injection locations. With a realistic measurement of around 2 min and around 8 distant distinct current injection pairs, the error from the other noise sources is reduced to around 10% or less in the skull conductivity. The analysis of subsequent real measurements, however, suggests that there could be subject-specific local thinnings in the skull, which could amplify the conductivity fitting errors. With proper analysis of multiplexed sinusoidal EIT current injections, the measurements on average yielded conductivities of 340 mS/m (scalp and brain) and 6.6 mS/m (skull) at 2 Hz. From 11 to 127 Hz, the conductivities increased by 1.6% (scalp and brain) and 6.7% (skull) on the average. The proper analysis was ensured by using recombination of the current injections into virtual ones, avoiding problems in location-specific skull morphology variations. The observed large intersubject variations support the need for in vivo measurement of skull conductivity, resulting in calibrated subject-specific head models.

Correcting electrode modelling errors in EIT on realistic 3D head models

Electrical impedance tomography (EIT) is a promising medical imaging technique which could aid differentiation of haemorrhagic from ischaemic stroke in an ambulance. One challenge in EIT is the ill-posed nature of the image reconstruction, i.e., that small measurement or modelling errors can result in large image artefacts. It is therefore important that reconstruction algorithms are improved with regard to stability to modelling errors. We identify that wrongly modelled electrode positions constitute one of the biggest sources of image artefacts in head EIT. Therefore, the use of the Fréchet derivative on the electrode boundaries in a realistic three-dimensional head model is investigated, in order to reconstruct electrode movements simultaneously to conductivity changes. We show a fast implementation and analyse the performance of electrode position reconstructions in time-difference and absolute imaging for simulated and experimental voltages. Reconstructing the electrode positions and conductivities simultaneously increased the image quality significantly in the presence of electrode movement.

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.

A Reconstruction-Classification Method for Multifrequency Electrical Impedance Tomography

Multifrequency Electrical Impedance Tomography is an imaging technique which distinguishes biological tissues by their unique conductivity spectrum. Recent results suggest that the use of spectral constraints can significantly improve image quality. We present a combined reconstruction-classification method for estimating the spectra of individual tissues, whilst simultaneously reconstructing the conductivity. The advantage of this method is that a priori knowledge of the spectra is not required to be exact in that the constraints are updated at each step of the reconstruction. In this paper, we investigate the robustness of the proposed method to errors in the initial guess of the tissue spectra, and look at the effect of introducing spatial smoothing. We formalize and validate a frequency-difference variant of reconstruction-classification, and compare the use of absolute and frequency-difference data in the case of a phantom experiment.