Transcranial MEP threshold voltages and current densities simulated with finite element modelling.

OBJECTIVE: The aim of this study was to compare stimulation thresholds and current densities in the brain for transcranial motor evoked potentials (tcMEPs) from the hands and feet with linked quadripolar (LQP), M3-M4 and C1-C2 electrode montages. METHODS: Twenty-five patients underwent cerebral vascular surgery with tcMEP monitoring. tcMEP voltage thresholds were compared between LQP (C1, M3, C2, M4), C1-C2, and M3-M4 montages. In a finite element model (FEM), hand, arm, and leg regions of interest (ROIs) on the cortical motor homunculus were segmented. Current densities in these ROIs at tcMEP thresholds were compared across tcMEP electrode montages. RESULTS: LQP tcMEP thresholds were 61.5 volts for hands and 95.2 volts for feet. Thresholds were higher for M3-M4 (hands, 89.4 V; feet, 141.3 V) and C1-C2 (hands: 137.3 V; feet: 194.7 V). Total current at threshold voltage was greater for LQP (hands, 210.9 mA; feet, 311.3 mA) compared to M3-M4 (hands, 166.8 mA; feet, 256.6 mA), but similar to C1-C2 (hands, 246.7 mA; feet, 341.1 mA). In FEM simulations, current density and local current density topography in the hand ROI at threshold were very similar for LQP, M3-M4 and C1-C2. CONCLUSIONS: TcMEP voltage thresholds were least for LQP, and lesser for M3-M4 compared to C1-C2. In FEM simulations, resistance to current to hand ROI was ordered the same (LQP < M3-M4 < C1-C2). The local distribution of current density in motor cortex with tcMEP was mainly determined by cortical geometry. SIGNIFICANCE: Current densities and resistance to current simulated with FEM may explain threshold requirements for tcMEP electrode montages.

Four-channel current switching device to enable multi-electrode magnetic resonance current density imaging.

Neurostimulation with multiple scalp electrodes has shown enhanced effects in recent studies. However, visualizations of stimulation-induced internal current distributions in brain is only possible through simulated current distributions obtained from computer model of human head. While magnetic resonance current density imaging (MRCDI) has a potential for direct in-vivo measurement of currents induced in brain with multi-electrode stimulation, existing MRCDI methods are only developed for two-electrode neurostimulation. A major bottleneck is the lack of a current switching device which is typically used to convert the DC current of neurostimulation devices into user-defined waveforms of positive and negative polarity with delays between them. In this work, we present a design of a four-electrode current switching device to enable simultaneous switching of current flowing through multiple scalp electrodes.

Influence of Transcranial Electrical Stimulation (TES) waveforms on neural excitability of a realistic axon: a simulation study.

Neuromodulation caused by transcranial electrical stimulation (TES) has been used successfully to treat various neuro-degenerative diseases. Simulation models provide an essential tool to study brain and nerve stimulation. Simulation models of TES provide an opportunity to research personalization of therapy without extensive animal and human testing. A computer model of a realistic sensory axon was built by finding actual geometry of the trigeminal nerve through tractography. A finite element model of the head was solved to obtain electric potential distribution caused by TES. Different waveforms were defined to test transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS) with varying amplitude and frequency. Neural activity patterns were observed. The strength-duration curve was plotted to verify the model.

Magnetic-resonance-based measurement of electromagnetic fields and conductivity in vivo using single current administration-A machine learning approach.

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) is a newly developed technique that combines MR-based measurements of magnetic flux density with diffusion tensor MRI (DT-MRI) data to reconstruct electrical conductivity tensor distributions. DT-MREIT techniques normally require injection of two independent current patterns for unique reconstruction of conductivity characteristics. In this paper, we demonstrate an algorithm that can be used to reconstruct the position dependent scale factor relating conductivity and diffusion tensors, using flux density data measured from only one current injection. We demonstrate how these images can also be used to reconstruct electric field and current density distributions. Reconstructions were performed using a mimetic algorithm and simulations of magnetic flux density from complementary electrode montages, combined with a small-scale machine learning approach. In a biological tissue phantom, we found that the method reduced relative errors between single-current and two-current DT-MREIT results to around 10%. For in vivo human experimental data the error was about 15%. These results suggest that incorporation of machine learning may make it easier to recover electrical conductivity tensors and electric field images during neuromodulation therapy without the need for multiple current administrations.

Development and testing of implanted carbon electrodes for electromagnetic field mapping during neuromodulation.

PURPOSE: Deep brain stimulation electrodes composed of carbon fibers were tested as a means of administering and imaging magnetic resonance electrical impedance tomography (MREIT) currents. Artifacts and heating properties of custom carbon-fiber deep brain stimulation (DBS) electrodes were compared with those produced with standard DBS electrodes. METHODS: Electrodes were constructed from multiple strands of 7-µm carbon-fiber stock. The insulated carbon electrodes were matched to DBS electrode diameter and contact areas. Images of DBS and carbon electrodes were collected with and without current flow and were compared in terms of artifact and thermal effects in phantoms or tissue samples in 7T imaging conditions. Effects on magnetic flux density and current density distributions were also assessed. RESULTS: Carbon electrodes produced magnitude artifacts with smaller FWHM values compared to the magnitude artifacts around DBS electrodes in spin echo and gradient echo imaging protocols. DBS electrodes appeared 269% larger than actual size in gradient echo images, in sharp contrast to the negligible artifact observed in diameter-matched carbon electrodes. As expected, larger temperature changes were observed near DBS electrodes during extended RF excitations compared with carbon electrodes in the same phantom. Magnitudes and distribution of magnetic flux density and current density reconstructions were comparable for carbon and DBS electrodes. CONCLUSION: Carbon electrodes may offer a safer, MR-compatible method for administering neuromodulation currents. Use of carbon-fiber electrodes should allow imaging of structures close to electrodes, potentially allowing better targeting, electrode position revision, and the facilitation of functional imaging near electrodes during neuromodulation.

Benchmarking transcranial electrical stimulation finite element models: a comparison study.

OBJECTIVE: To compare field measure differences in simulations of transcranial electrical stimulation (tES) generated by variations in finite element (FE) models due to boundary condition specification, use of tissue compartment smoothing filters, and use of free or structured tetrahedral meshes based on magnetic resonance imaging (MRI) data. APPROACH: A structural MRI head volume was acquired at 1 mm3 resolution and segmented into ten tissue compartments. Predicted current densities and electric fields were computed in segmented models using modeling pipelines involving either an in-house (block) or a commercial platform commonly used in previous FE tES studies involving smoothed compartments and free meshing procedures (smooth). The same boundary conditions were used for both block and smooth pipelines. Differences caused by varying boundary conditions were examined using a simple geometry. Percentage differences of median current density values in five cortical structures were compared between the two pipelines for three electrode montages (F3-right supraorbital, T7-T8 and Cz-Oz). MAIN RESULTS: Use of boundary conditions commonly used in previous tES FE studies produced asymmetric current density profiles in the simple geometry. In head models, median current density differences produced by the two pipelines, using the same boundary conditions, were up to 6% (isotropic) and 18% (anisotropic) in structures targeted by each montage. Tangential electric field measures calculated via either pipeline were within the range of values reported in the literature, when averaged over cortical surface patches. SIGNIFICANCE: Apparently equivalent boundary settings may affect predicted current density outcomes and care must be taken in their specification. Smoothing FE model compartments may not be necessary, and directly translated, voxellated tissue boundaries at 1 mm3 resolution may be sufficient for use in tES FE studies, greatly reducing processing times. The findings here may be used to inform future current density modeling studies.

Functional magnetic resonance electrical impedance tomography (fMREIT) sensitivity analysis using an active bidomain finite-element model of neural tissue.

PURPOSE: A direct method of imaging neural activity was simulated to determine typical signal sizes. METHODS: An active bidomain finite-element model was used to estimate approximate perturbations in MR phase data as a result of neural tissue activity, and when an external MR electrical impedance tomography imaging current was added to the region containing neural current sources. RESULTS: Modeling-predicted, activity-related conductivity changes should produce measurable differential phase signals in practical MR electrical impedance tomography experiments conducted at moderate resolution at noise levels typical of high field systems. The primary dependence of MR electrical impedance tomography phase contrast on membrane conductivity changes, and not source strength, was demonstrated. CONCLUSION: Because the injected imaging current may also affect the level of activity in the tissue of interest, this technique can be used synergistically with neuromodulation techniques such as deep brain stimulation, to examine mechanisms of action.

Analytic modeling of conductively anisotropic neural tissue.

The abdominal ganglion of the Aplysia californica is an established in vitro model for studying neuroelectric behavior in the presence of an applied electrical current and recently used in studies of magnetic resonance electrical impedance tomography (MREIT) which allows for quantitative visualization of spatially distributed current and magnetic flux densities. Understanding the impact the Aplysia geometry and anisotropic conductivity have on applied electromagnetic fields is central to intepreting and refining MREIT data and protocols, respectively. Here we present a simplified bidomain model of an in vitro experimental preparation of the Aplysia abdominal ganglion, describing the tissue as a radially anisotropic sphere with equal anisotropy ratios, i.e., where radial conductivities in both intra- and extra-cellular regions are ten times that of their polar and azimuthal conductivities. The fully three dimensional problem is validated through comparisons with limiting examples of 2D isotropic analyses. Results may be useful in validating finite element models of MREIT experiments and have broader relevance to analysis of MREIT data obtained from complex neural architecture in the human brain.

Low-Frequency Conductivity Tensor Imaging of the Human Head In Vivo Using DT-MREIT: First Study.

We present the first in vivo images of anisotropic conductivity distribution in the human head, measured at a frequency of approximately 10 Hz. We used magnetic resonance electrical impedance tomography techniques to encode phase changes caused by current flow within the head via two independent electrode pairs. These results were then combined with diffusion tensor imaging data to reconstruct full anisotropic conductivity distributions in 5-mm-thick slices of the brains of two participants. Conductivity values recovered in this paper were broadly consistent with literature values. We anticipate that this technique will be of use in many areas of neuroscience, most importantly in functional imaging via inverse electroencephalogram. Future studies will involve pulse sequence acceleration to maximize brain coverage and resolution.

Methods to Compare Predicted and Observed Phosphene Experience in tACS Subjects.

Background: Phosphene generation is an objective physical measure of potential transcranial alternating current stimulation (tACS) biological side effects. Interpretations from phosphene analysis can serve as a first step in understanding underlying mechanisms of tACS in healthy human subjects and assist validation of computational models. Objective/Hypothesis: This preliminary study introduces and tests methods to analyze predicted phosphene occurrence using computational head models constructed from tACS recipients against verbal testimonies of phosphene sensations. Predicted current densities in the eyes and the occipital lobe were also verified against previously published threshold values for phosphenes. Methods: Six healthy subjects underwent 10 Hz tACS while being imaged in an MRI scanner. Two different electrode montages, T7-T8 and Fpz-Oz, were used. Subject ratings of phosphene experience were collected during tACS and compared against current density distributions predicted in eye and occipital lobe regions of interest (ROIs) determined for each subject. Calculated median current densities in each ROI were compared to minimum thresholds for phosphene generation. Main Results: All subjects reported phosphenes, and predicted median current densities in ROIs exceeded minimum thresholds for phosphenes found in the literature. Higher current densities in the eyes were consistently associated with decreased phosphene generation for the Fpz-Oz montage. There was an overall positive association between phosphene perceptions and current densities in the occipital lobe. Conclusions: These methods may have promise for predicting phosphene generation using data collected during in-scanner tACS sessions and may enable better understanding of phosphene origin. Additional empirical data in a larger cohort is required to fully test the robustness of the proposed methods. Future studies should include additional montages that could dissociate retinal and occipital stimulation.

Direct detection of neural activity in vitro using magnetic resonance electrical impedance tomography (MREIT).

We describe a sequence of experiments performed in vitro to verify the existence of a new magnetic resonance imaging contrast - Magnetic Resonance Electrical Impedance Tomography (MREIT) -sensitive to changes in active membrane conductivity. We compared standard deviations in MREIT phase data from spontaneously active Aplysia abdominal ganglia in an artificial seawater background solution (ASW) with those found after treatment with an excitotoxic solution (KCl). We found significant increases in MREIT treatment cases, compared to control ganglia subject to extra ASW. This distinction was not found in phase images from the same ganglia using no imaging current. Further, significance and effect size depended on the amplitude of MREIT imaging current used. We conclude that our observations were linked to changes in cell conductivity caused by activity. Functional MREIT may have promise as a more direct method of functional neuroimaging than existing methods that image correlates of blood flow such as BOLD fMRI.

Changing head model extent affects finite element predictions of transcranial direct current stimulation distributions.

OBJECTIVE: In this study, we determined efficient head model sizes relative to predicted current densities in transcranial direct current stimulation (tDCS). APPROACH: Efficiency measures were defined based on a finite element (FE) simulations performed using nine human head models derived from a single MRI data set, having extents varying from 60%-100% of the original axial range. Eleven tissue types, including anisotropic white matter, and three electrode montages (T7-T8, F3-right supraorbital, Cz-Oz) were used in the models. MAIN RESULTS: Reducing head volume extent from 100% to 60%, that is, varying the model's axial range from between the apex and C3 vertebra to one encompassing only apex to the superior cerebellum, was found to decrease the total modeling time by up to half. Differences between current density predictions in each model were quantified by using a relative difference measure (RDM). Our simulation results showed that [Formula: see text] was the least affected (a maximum of 10% error) for head volumes modeled from the apex to the base of the skull (60%-75% volume). SIGNIFICANCE: This finding suggested that the bone could act as a bioelectricity boundary and thus performing FE simulations of tDCS on the human head with models extending beyond the inferior skull may not be necessary in most cases to obtain reasonable precision in current density results.

Analytic Modeling of Neural Tissue: I. A Spherical Bidomain.

Presented here is a model of neural tissue in a conductive medium stimulated by externally injected currents. The tissue is described as a conductively isotropic bidomain, i.e. comprised of intra and extracellular regions that occupy the same space, as well as the membrane that divides them, and the injection currents are described as a pair of source and sink points. The problem is solved in three spatial dimensions and defined in spherical coordinates [Formula: see text]. The system of coupled partial differential equations is solved by recasting the problem to be in terms of the membrane and a monodomain, interpreted as a weighted average of the intra and extracellular domains. The membrane and monodomain are defined by the scalar Helmholtz and Laplace equations, respectively, which are both separable in spherical coordinates. Product solutions are thus assumed and given through certain transcendental functions. From these electrical potentials, analytic expressions for current density are derived and from those fields the magnetic flux density is calculated. Numerical examples are considered wherein the interstitial conductivity is varied, as well as the limiting case of the problem simplifying to two dimensions due to azimuthal independence. Finally, future modeling work is discussed.

Projected current density comparison in tDCS block and smooth FE modeling.

Current density distribution and projected current density calculation following transcranial direct current stimulation (tDCS) forward model in a human head were compared between two modeling pipelines: block and smooth. Block model was directly constructed from MRI voxel resolution and simulated in C. Smooth models underwent a boundary smoothing process by applying recursive Gaussian filters and simulated in COMSOL. Three smoothing levels were added to determine their effects on current density distribution compared to block models. Median current density percentage differences were calculated in anterior superior temporal gyrus (ASTG), hippocampus (HIP), inferior frontal gyrus (IFG), occipital lobes (OCC) and precentral gyrus (PRC) and normalized against a baseline value. A maximum of + 20% difference in median current density was found for three standard electrode montages: F3-RS, T7-T8 and Cz-Oz. Furthermore, median current density percentage differences in each montage target brain structures were found to be within + 7%. Higher levels of smoothing increased median current density percentage differences in T7-T8 and Cz-Oz target structures. However, while demonstrating similar trends in each montage, additional smoothing levels showed no clear relationship between their smoothing effects and calculated median current density in the five cortical structures. Finally, relative L2 error in reconstructed projected current density was found to be 17% and 21% for block and smooth pipelines, respectively. Overall, a block model workflow may be a more attractive alternative for simulating tDCS stimulation because involves a shorter modeling time and independence from commercial modeling platforms.

Analysis of bipolar external excitation of spherical tissue by spatially opposed current source and sink points.

The recently increasing role in medical imaging that electrophysiology plays has spurned the need for its quantitative analysis at all scales-ions, cells, tissues, organs, etc.; so, here is presented a model of nerve tissue in a spherical volume excited by a point current source at one pole and a point current sink at the opposite pole. The sphere of tissue is described as an isotropic bidomain, consisting of the intra- and extra-cellular regions and the membrane that separates them, and is immersed in an infinite isotropic conductive bath. The system of coupled differential equations is solved by redefining the domains to be in terms of a monodomain and a membrane. The solution takes the form of an infinite sum of the product of certain transcendental functions. The study concludes with a numeric example in which the boundary conditions are shown to be satisfied, validating this analysis, paving the way for more sophisticated models of excitable tissue.

External current application in a bidomain model of active neural tissue.

The formal treatment of tissue as two coupled continua is referred to as a bidomain model. Bidomain models have recently been used to describe the properties of neural tissue and nerve fiber bundles [1, 2]. By adapting the Hodgkin Huxley equations in COMSOL Multiphysics, we have investigated the propagation of an action potential through neural tissue by external current stimulation.

A comparison between block and smooth modeling in finite element simulations of tDCS.

Current density distributions in five selected structures, namely, anterior superior temporal gyrus (ASTG), hippocampus (HIP), inferior frontal gyrus (IFG), occipital lobe (OCC) and pre-central gyrus (PRC) were investigated as part of a comparison between electrostatic finite element models constructed directly from MRI-resolution data (block models), and smoothed tetrahedral finite element models (smooth models). Three electrode configurations were applied, mimicking different tDCS therapies. Smooth model simulations were found to require three times longer to complete. The percentage differences between mean and median current densities of each model type in arbitrarily chosen brain structures ranged from -33.33-48.08%. No clear relationship was found between structure volumes and current density differences between the two model types. Tissue regions nearby the electrodes demonstrated the least percentage differences between block and smooth models. Therefore, block models may be adequate to predict current density values in cortical regions presumed targeted by tDCS.

Nanofiber web textile dry electrodes for long-term biopotential recording.

Electrode properties are key to the quality of measured biopotential signals. Ubiquitous health care systems require long-term monitoring of biopotential signals from normal volunteers and patients in home or hospital environments. In these settings it is appropriate to use dry textile electrode networks for monitoring purposes, rather than the gel or saline-sponge skin interfaces used with Ag/AgCl electrodes. In this study, we report performance test results of two different electrospun conductive nanofiber webs, and three metal plated fabrics. We evaluated contact impedance, step response, noise and signal fidelity performance indices for all five dry electrodes, and compared them to those of conventional Ag/AgCl electrodes. Overall, we found nanofiber web electrodes matched Ag/AgCl electrode performance more closely than metal plated fabric electrodes, with the contact resistance and capacitance of Ag plated PVDF nanofiber web electrodes being most similar to Ag/AgCl over the 10 Hz to 500 kHz frequency range. We also observed that step responses of all three metal-plated fabrics were poorer than those for nanofiber web electrodes and Ag/AgCl. Further, noise standard deviation and noise power spectral densities were generally lower in nanofiber web electrodes than metal plated fabrics; and waveform fidelity of ECG-like traces recorded from nanofiber web electrodes was higher than for metal plated fabrics. We recommend textile nanofiber web electrodes in applications where flexibility, comfort and durability are required in addition to good electrical characteristics.

Numerical simulations of MREIT conductivity imaging for brain tumor detection.

Magnetic resonance electrical impedance tomography (MREIT) is a new modality capable of imaging the electrical properties of human body using MRI phase information in conjunction with external current injection. Recent in vivo animal and human MREIT studies have revealed unique conductivity contrasts related to different physiological and pathological conditions of tissues or organs. When performing in vivo brain imaging, small imaging currents must be injected so as not to stimulate peripheral nerves in the skin, while delivery of imaging currents to the brain is relatively small due to the skull's low conductivity. As a result, injected imaging currents may induce small phase signals and the overall low phase SNR in brain tissues. In this study, we present numerical simulation results of the use of head MREIT for brain tumor detection. We used a realistic three-dimensional head model to compute signal levels produced as a consequence of a predicted doubling of conductivity occurring within simulated tumorous brain tissues. We determined the feasibility of measuring these changes in a time acceptable to human subjects by adding realistic noise levels measured from a candidate 3 T system. We also reconstructed conductivity contrast images, showing that such conductivity differences can be both detected and imaged.

Simulations and phantom evaluations of magnetic resonance electrical impedance tomography (MREIT) for breast cancer detection.

MREIT is a new imaging modality that can be used to reconstruct high-resolution conductivity images of the human body. Since conductivity values of cancerous tissues in the breast are significantly higher than those of surrounding normal tissues, breast imaging using MREIT may provide a new noninvasive way of detecting early stage of cancer. In this paper, we present results of experimental and numerical simulation studies of breast MREIT. We built a realistic three-dimensional model of the human breast connected to a simplified model of the chest including the heart and evaluated the ability of MREIT to detect cancerous anomalies in a background material with similar electrical properties to breast tissue. We performed numerical simulations of various scenarios in breast MREIT including assessment of the effects of fat inclusions and effects related to noise levels, such as changing the amplitude of injected currents, effect of added noise and number of averages. Phantom results showed straightforward detection of cancerous anomalies in a background was possible with low currents and few averages. The simulation results showed it should be possible to detect a cancerous anomaly in the breast, while restricting the maximal current density in the heart below published levels for nerve excitation.