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.

Electromagnetic Properties and the Basis for CDI, MREIT, and EPT.

The electromagnetic properties of body tissues depend on numerous factors, the most important of which are ionic concentrations and, particularly in the low-frequency regime, membrane density and geometry. In this chapter, the characteristics of these properties and their spectra are introduced. The properties measured by different types of MR-based methods are described.

Modeling for Electromagnetic Characterization, Prediction, and Reconstruction.

Electromagnetic modeling is an essential and crucial element in MRI-based methods of characterizing electromagnetic properties or current flow. In its simplest form, modeling can be used to predict measurements of magnetic flux density (Bz in the case of MREIT or B1 fields in the case of EPT) based on realistic representations of the imaged object. Further, projected current density methods must refer to a uniform model of an imaged object in order to calculate the projected current density distribution. Modeling in this area is most commonly performed using finite element methods and often using commercial finite element software. While it is not necessary to know every feature of this type of software, understanding the basics of finite element methods will help in interpreting and examining the results and learning how to perform simulations efficiently. We describe aspects of the finite element approach and demonstrate models relevant to simulations performed in this area.

Magnetic Resonance Current Density Imaging (MR-CDI).

Current density imaging (CDI) was developed with the aim of determining the three-dimensional distribution of externally applied electric current pathways inside a conductive medium, using measurements of magnetic flux density [Formula: see text] data. While the B field may be measurable using instruments such as a magnetometer, in magnetic resonance current density imaging (MR-CDI), an MRI scanner is used to measure the magnetic flux density data induced by current flow. In MR-CDI, the object must be rotated inside the MRI machine to find all three components of the B-field, as only the component of B parallel to the magnet main magnetic field can be measured. In principle, once the all three components of the B field have been obtained from an MR imaging experiment, the current density distribution [Formula: see text] can be reconstructed from Ampere's law [Formula: see text]. However, the need to rotate the object within the MRI scanner limits the usability of this technique. To overcome this problem, researchers have investigated the current density reconstruction problem using only one component of the magnetic flux density Bq, where q = x, y, z. In this chapter, we discuss numerical algorithms developed to reconstruct the distribution of J information from the measured B-field.

Phantom Construction and Equipment Configurations for Characterizing Electrical Properties Using MRI.

Phantom objects are commonly employed in MRI systems as stable substitutes for biological tissues to ensure systems for measuring images are operating correctly and safely. For magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance electrical property tomography (MREPT), conductivity or permittivity phantoms play an important role in checking MRI pulse sequences, MREIT equipment performance, and algorithm validation. The construction of these phantoms is explained in this chapter. In the first part, materials used for phantom construction are introduced. Ingredients for modifying the electromagnetic properties and relaxation times are presented, and the advantages and disadvantages of aqueous, gel, and hybrid conductivity phantoms are explained. The devices and methods used to confirm phantom electromagnetic properties are explained. Next, different types of MREIT electrode materials and the constant current sources used for MREIT studies are discussed. In the last section, we present the results of previous MREIT and MREPT studies.

MR Current Density and MREIT Data Acquisition.

Magnetic resonance electrical impedance tomography (MREIT) can provide internal conductivity distributions at low frequency (below 1 kHz) induced by an external injecting current. In MREIT, we inject current I using at least one pair of electrodes into an object to produce internal current density J = (Jx, Jy, Jz) and magnetic flux density B = (Bx, By, Bz) in the object. An MRI scanner with its main magnetic field pointing the z direction is used to measure the induced magnetic flux density (Bz) caused by external current injection. To avoid the interaction of external current injection with MRI acquisitions, it is important to synchronize the current injection with MRI sequence. In the first part of this chapter, we will discuss the practical aspects of a successful MREIT experiment. Following a brief introduction to the experiment setup, we will then summarize various MRI sequences used for MREIT, magnetic flux density measurement, and image reconstructions for MREIT experiments.

Magnetic Resonance Electrical Impedance Tomography.

Magnetic Resonance Electrical Impedance Tomography (MREIT) is a high-resolution bioimpedance imaging technique that has developed over a period beginning in the early 1990s to measure low-frequency (<1 kHz) tissue electrical properties. Low-frequency electrical properties are particularly important because they provide valuable information on cell structures and ionic composition of tissues, which may be very useful for diagnostic purposes. MREIT uses one component of the magnetic flux density data induced due to an exogenous-current administration, measured using an MRI machine, to reconstruct isotropic or anisotropic electrical property distributions. The MREIT technique typically requires two linearly independent current administrations to reconstruct conductivity uniquely. Since its invention, researchers have explored its potential for measuring electrical conductivity in regions such as the brain and muscle tissue. It has also been investigated in disease models, for example, cerebral ischemia and early tumor detection. In this chapter, we aim to provide a solid foundation of the different MREIT image reconstruction algorithms, including both isotropic and anisotropic conductivity reconstruction approaches. We will also explore the newly developed diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) method, a practical method for anisotropic tissue property imaging, at the end of the chapter.

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.

Low frequency conductivity reconstruction based on a single current injection via MREIT.

Conventional magnetic resonance electrical impedance tomography (MREIT) reconstruction methods require administration of two linearly independent currents via at least two electrode pairs. This requires long scanning times and inhibits coordination of MREIT measurements with electrical neuromodulation strategies. We sought to develop an isotropic conductivity reconstruction algorithm in MREIT based on a single current injection, both to decrease scanning time by a factor of two and enable MREIT measurements to be conveniently adapted to general transcranial- or implanted-electrode neurostimulation protocols. In this work, we propose and demonstrate an iterative algorithm that extends previously published MREIT work using two-current administration approaches. The proposed algorithm is a single-current adaptation of the harmonic B z algorithm. Forward modeling of electric potentials is used to capture changes of conductivity along current directions that would normally be invisible using data from a single-current administration. Computational and experimental results show that the reconstruction algorithm is capable of reconstructing isotropic conductivity images that agree well in terms of L 2 error and structural similarity with exact conductivity distributions or two-current-based MREIT reconstructions. We conclude that it is possible to reconstruct high quality electrical conductivity images using MREIT techniques and one current injection only.

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.

Evaluation of magnetohydrodynamic effects in magnetic resonance electrical impedance tomography at ultra-high magnetic fields.

PURPOSE: Artifacts observed in experimental magnetic resonance electrical impedance tomography images were hypothesized to be because of magnetohydrodynamic (MHD) effects. THEORY AND METHODS: Simulations of MREIT acquisition in the presence of MHD and electrical current flow were performed to confirm findings. Laminar flow and (electrostatic) electrical conduction equations were bidirectionally coupled via Lorentz force equations, and finite element simulations were performed to predict flow velocity as a function of time. Gradient sequences used in spin-echo and gradient echo acquisitions were used to calculate overall effects on MR phase images for different electrical current application or phase-encoding directions. RESULTS: Calculated and experimental phase images agreed relatively well, both qualitatively and quantitatively, with some exceptions. Refocusing pulses in spin echo sequences did not appear to affect experimental phase images. CONCLUSION: MHD effects were confirmed as the cause of observed experimental phase changes in MREIT images obtained at high fields. These findings may have implications for quantitative measurement of viscosity using MRI techniques. Methods developed here may be also important in studies of safety and in vivo artifacts observed in high field MRI systems.

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.

Accelerating acquisition strategies for low-frequency conductivity imaging using MREIT.

We sought to improve efficiency of magnetic resonance electrical impedance tomography data acquisition so that fast conductivity changes or electric field variations could be monitored. Undersampling of k-space was used to decrease acquisition times in spin-echo-based sequences by a factor of two. Full MREIT data were reconstructed using continuity assumptions and preliminary scans gathered without current. We found that phase data were reconstructed faithfully from undersampled data. Conductivity reconstructions of phantom data were also possible. Therefore, undersampled k-space methods can potentially be used to accelerate MREIT acquisition. This method could be an advantage in imaging real-time conductivity changes with MREIT.

The effect of potassium chloride on Aplysia Californica abdominal ganglion activity.

OBJECTIVE: Spontaneous activity in the abdominal ganglion of Aplysia can be used as a convenient bioelectricity source in tests of novel MRI-based functional imaging methods, such as functional Magnetic Resonance Electrical Impedance Tomography (fMREIT). In these tests, it is necessary to find a consistent treatment that modulates neural activity, so that these results can be compared with control data. Effects of MREIT imaging currents combined with treatment were also of interest. APPROACH: Potassium chloride (KCl) was employed as a rhythm modulator. In a series of experiments, effects of adding different volumes of KCl solution were tested and compared with experiments on control groups that had artificial sea water administered. In all cases, neuronal activity was measured with micro electrode arrays. MAIN RESULTS: It was possible to reversibly stop spontaneous activity in ganglia by increasing the extracellular potassium chloride concentration to 89 mM. There was no effect on experimental outcomes when current was administered to the sample chamber between recordings. SIGNIFICANCE: KCl can be used as a reversible neural modulator for testing neural detection methods.