Magnetic Resonance Electrical Impedance Tomography Research Articles

Simulation of a synchronized methodology for MR-based electromechanical property imaging during transcranial electrical stimulation

Introduction: Recent investigations into the biomechanics of the brain have unveiled alteration in tissue stiffness triggered by external stimuli. For instance, visual stimulation effects can be measured in elasticity images of the cortex generated by functional magnetic resonance elastography (MRE). Such a mechanical characterization method combined with non-invasive brain stimulation (NIBS), a technique that seeks to selectively modulate particular parts of the brain using weak electrical currents, has the potential to influence research on various neurological disorders. In this in silico study, we aimed to elucidate individual and interdependent aspects related to a synchronized biomechanical imaging and non-invasive brain stimulation methodology. Magnetic resonance electrical impedance tomography (MREIT) was incorporated to the pipeline, providing a promising way of evaluating NIBS-induced electrical current patterns in the brain while leveraging MRE and transcranial alternating current stimulation (tACS) experimental settings.Methods: A mouse head model was assembled using open-access atlases to include five anatomical structures: skin/subcutaneous tissue, skull, cerebrospinal fluid (CSF), brain white and grey matters. MRE, tACS, and MREIT experiments were simulated using Comsol Multiphysics with Matlab Livelink. Synthetic MRE and MREIT data were processed using the subzone non-linear inversion and harmonic Bz algorithm, respectively, to reconstruct images of the distributed complex shear modulus and electrical conductivity.Results and Discussion: Lorentz body forces arising from simultaneous MRE and tACS elicited elastic waves of negligible amplitude compared with the extrinsic actuation levels reported in the literature, which allowed accurate reconstructions of the complex shear modulus. Qualitative electrical conductivity maps retrieved by MREIT accurately delineated anatomical regions of the brain model and could be used to recover reasonably accurate distributions of tACS-induced currents. This multi-physics approach has potential for translation to human brain imaging, and may provide more possibilities for the characterization of brain function together than in isolation.

Imaging of bronchopulmonary dysplasia

Bronchopulmonary dysplasia (BPD) is a multifactorial disease with many associated co-morbidities, responsible for most cases of chronic lung disease in childhood. The use of imaging exams is pivotal for the clinical care of BPD and the identification of candidates for experimental therapies and a closer follow-up. Imaging is also useful to improve communication with the family and objectively evaluate the clinical evolution of the patient's disease. BPD imaging has been classically performed using only chest X-rays, but several modern techniques are currently available, such as lung ultrasound, thoracic tomography, magnetic resonance imaging and electrical impedance tomography. These techniques are more accurate and provide clinically meaningful information. We reviewed the most recent evidence published in the last five years regarding these techniques and analyzed their advantages and disadvantages.

A Fast Magnetic Flux Density Measurement Method With Skip-Echo Acquired Turbo Spin Echo (SATE).

The measurements of magnetic flux density ( Bz) needed in magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance current density imaging (MRCDI) techniques often utilize spin echo (SE)-based sequences for data acquisition. The low imaging speed of SE-based methods significantly hampers the clinical applications of MREIT and MRCDI. Here, we propose a new sequence for substantially accelerating the acquisition of Bz measurements. A skip-echo acquired turbo spin echo (SATE) imaging sequence based on the conventional turbo spin echo (TSE) technique was proposed by adding a skip-echo module in front of the TSE acquisition module. The skip-echo module consisted of a series of refocusing pulses without acquisition. In SATE, amplitude-modulated crusher gradients were used to remove the stimulated echo pathways, and the radiofrequency (RF) pulse shape was specially selected to preserve more signals. In efficiency evaluation experiments performed on a spherical gel phantom, we demonstrated that SATE had improved measurement efficiency compared to the conventional TSE sequence via skipping one echo before acquiring signals. The accuracy of the Bz measurements by SATE was validated against those by the multi-echo injection current nonlinear encoding (ME-ICNE) method, while SATE was able to accelerate the data acquisition up to 10-fold. Volumetric coverage of Bz maps obtained in the phantom, pork, and human calf illustrated that SATE can reliably measure volumetric Bz distributions within clinically acceptable time. The proposed SATE sequence provides a fast and effective approach for volumetric coverage of Bz measurements, greatly facilitating the clinical applications of MREIT and MRCDI techniques.

QUANTITATIVE ANALYSIS OF ELECTRICAL CURRENT EFFECT ON MAGNETIC RESONANCE IMAGE TISSUE INTENSITY

Recent studies in magnetic resonance imaging (MRI) aim to improve image quality while reducing scan time. Electrical current injection in the form of magnetic resonance electrical impedance tomography (MREIT) is believed to be affecting image quality and scan time thus can improve the possibility of becoming a non-chemical contrast agent in MRI. This study will observe and analyze the effect of electrical current injection on a phantom object to determine whether there is a different tissue image intensity.  A thigh of lamb was used as a biological tissue phantom. The scan was performed on both T1and T2-weighted without and with an electrical current injection of 0.5 mA Electrical current injection decreased mean of tissue image intensity on T1-weighted images on both muscle (1759 vs 794) and bone (2752 vs 1550) (p<0.05). On the other hand, the electrical current increased mean of tissue image intensity on T2-weighted images on both muscle (303 vs 897) and bone (579 vs 1499) (p<0.05). There is also a difference in tissue image intensity on both T1 and T2-weighted images with and without electrical current injection on bone and muscle. The implication of this difference in image quality is a subject for further study.

Use of an invertebrate animal model (Aplysia californica) to develop novel neural interfaces for neuromodulation.

New tools for monitoring and manipulating neural activity have been developed with steadily improving functionality, specificity, and reliability, which are critical both for mapping neural circuits and treating neurological diseases. This review focuses on the use of an invertebrate animal, the marine mollusk Aplysia californica, in the development of novel neurotechniques. We review the basic physiological properties of Aplysia neurons and discuss the specific aspects that make it advantageous for developing novel neural interfaces: First, Aplysia nerves consist only of unmyelinated axons with various diameters, providing a particularly useful model of the unmyelinated C fibers in vertebrates that are known to carry important sensory information, including those that signal pain. Second, Aplysia's neural tissues can last for a long period in an ex vivo experimental setup. This allows comprehensive tests such as the exploration of parameter space on the same nerve to avoid variability between animals and minimize animal use. Third, nerves in large Aplysia can be many centimeters in length, making it possible to easily discriminate axons with different diameters based on their conduction velocities. Aplysia nerves are a particularly good approximation of the unmyelinated C fibers, which are hard to stimulate, record, and differentiate from other nerve fibers in vertebrate animal models using epineural electrodes. Fourth, neurons in Aplysia are large, uniquely identifiable, and electrically compact. For decades, researchers have used Aplysia for the development of many novel neurotechnologies. Examples include high-frequency alternating current (HFAC), focused ultrasound (FUS), optical neural stimulation, recording, and inhibition, microelectrode arrays, diamond electrodes, carbon fiber microelectrodes, microscopic magnetic stimulation and magnetic resonance electrical impedance tomography (MREIT). We also review a specific example that illustrates the power of Aplysia for accelerating technology development: selective infrared neural inhibition of small-diameter unmyelinated axons, which may lead to a translationally useful treatment in the future. Generally, Aplysia is suitable for testing modalities whose mechanism involves basic biophysics that is likely to be similar across species. As a tractable experimental system, Aplysia californica can help the rapid development of novel neuromodulation technologies.

PEF treatment effect on plant tissues of heterogeneous structure no longer an enigma: MRI insights beyond the naked eye

Alteration of cell membrane permeability by exposure of plant tissues to pulsed electric fields (PEF) is associated with physical changes in cellular and subcellular structures. The aim of our study was to investigate the possible non-uniform effect of PEF treatment due to the structural heterogeneity of plant tissues commonly used in industrial PEF applications: apple fruits, potato tubers, and carrot taproots. Spatial distribution of T2 relaxation times was measured using magnetic resonance imaging in relation to local electric field established during PEF treatment and measured by magnetic resonance electrical impedance tomography. The results showed an increasingly inhomogeneous distribution of T2 relaxation times with increasing complexity of the structure (carrot > potato > apple). Feasibility and considerable potential for the use of the T2 mapping technique in the analysis of the effects of PEF on plant tissue structures was demonstrated.

Analytic modeling of neural tissue: II. Nonlinear membrane dynamics.

Computational modeling of neuroactivity plays a central role in our effort to understand brain dynamics in the advancements of neural engineering such as deep brain stimulation, neuroprosthetics, and magnetic resonance electrical impedance tomography. However, analytic solutions do not capture the fundamental nonlinear behavior of an action potential. What is needed is a method that is not constrained to only linearized models of neural tissue. Therefore, the objective of this study is to establish a robust, straightforward process for modeling neurodynamic phenomena, which preserves their nonlinear features. To address this, we turn to decomposition methods from homotopy analysis, which have emerged in recent decades as powerful tools for solving nonlinear differential equations. We solve the nonlinear ordinary differential equations of three landmark models of neural conduction-Ermentrout-Kopell, FitzHugh-Nagumo, and Hindmarsh-Rose models-using George Adomian's decomposition method. For each variable, we construct a power series solution equivalent to a generalized Taylor series expanded about a function. The first term of the decomposition series comes from the models' initial conditions. All subsequent terms are recursively determined from the first. We show rapid convergence, achieving a maximal error of with only eight terms. We extend the region of convergence with one-step analytic continuation so that our complete solutions are decomposition splines. We show that this process can yield solutions for single- and multi-variable models and can characterize a single action potential or complex bursting patterns. Finally, we show that the accuracy of this decomposition approach favorably compares to an established polynomial method, B-spline collocation. The strength of this method, besides its stability and ease of computation, is that, unlike perturbation, we make no changes to the models' equations; thus, our solutions are to the problems at hand, not simplified versions. This work validates decomposition as a viable technique for advanced neural engineering studies.

SNR-Enhanced, Rapid Electrical Conductivity Mapping Using Echo-Shifted MRI.

Magnetic resonance electrical impedance tomography (MREIT) permits high-spatial resolution electrical conductivity mapping of biological tissues, and its quantification accuracy hinges on the signal-to-noise ratio (SNR) of the current-induced magnetic flux density (Bz). The purpose of this work was to achieve Bz SNR-enhanced rapid conductivity imaging by developing an echo-shifted steady-state incoherent imaging-based MREIT technique. In the proposed pulse sequence, the free-induction-decay signal is shifted in time over multiple imaging slices, and as a result is exposed to a plurality of injecting current pulses before forming an echo. Thus, the proposed multi-slice echo-shifting strategy allows a high SNR for Bz for a given number of current injections. However, with increasing the time of echo formation, the Bz SNR will also be compromised by T2*-related signal loss. Hence, numerical simulations were performed to evaluate the relationship between the echo-shifting and the Bz SNR, and subsequently to determine the optimal imaging parameters. Experimental studies were conducted to evaluate the effectiveness of the proposed method over conventional spin-echo-based MREIT. Compared with the reference spin-echo MREIT, the proposed echo-shifting-based method improves the efficiency in both data acquisition and current injection while retaining the accuracy of conductivity quantification. The results suggest the feasibility of the proposed MREIT method as a practical means for conductivity mapping.

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.

Magnetic Resonance Electrical Properties Tomography (MREPT).

This chapter explains the magnetic resonance electrical impedance tomography (MREPT) technique used to image electrical properties at high frequencies. The chapter describes the MREPT data acquisition methods, current state-of-the-art image reconstruction algorithms, and experiments with phantoms, animals, and humans.

Numerical conductivity reconstruction from partial interior current density information in three dimensions

This paper focuses on conductivity imaging of a three dimensional object using interior current density information (ICDI). Applications include the emerging hybrid tomographic methods known as magnetic resonance electrical impedance tomography and current density impedance imaging, which potentially have both high contrast and high resolution. For all possible forms of ICDI data, the Fréchet derivative of the map between conductivity and ICDI is derived. Then, an iterative reconstruction method is formulated based on the Newton scheme. The method is implemented numerically and its properties are investigated on simulated data obtained from two different phantoms. The method is also benchmarked against the J-substitution method. We systematically study the possibilities, challenges, shortcomings, and artifacts due the different forms of full and partial ICDI data and one or several boundary conditions. The results establish that at least two components of two non-parallel interior current densities are required to obtain good reconstructions; this is an important outcome for conductivity imaging methods which use only one component of the magnetic field. The results hold promise for the near real-time and high resolution conductivity reconstruction in practical applications.

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.

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. 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. 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. 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.

Fast evaluation of the Biot-Savart integral using FFT for electrical conductivity imaging

Magnetic resonance electrical impedance tomography (MREIT) and current density imaging (MRCDI) are emerging as new methods to non-invasively assess the electric conductivity of and current density distributions within biological tissue in vivo. The accurate and fast computation of magnetic fields caused by low frequency electrical currents is a central component of the development, evaluation and application of reconstruction methods that underlie the estimations of the conductivity and current density, respectively, from the measured MR data. However, methods for performing these computations have not been well established in the literature. In the current work, we describe a fast and efficient technique to evaluate the Biot-Savart integral based on the fast Fourier transform (FFT), and evaluate its convergence. We show that the method can calculate magnetic fields in realistic human head models in one minute on a standard computer, while keeping error below 2%.

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

Artifacts observed in experimental magnetic resonance electrical impedance tomography images were hypothesized to be because of magnetohydrodynamic (MHD) effects. 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. 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. 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.

Induced Current Magnetic Resonance Electrical Conductivity Imaging With Oscillating Gradients.

In this paper, induced current magnetic resonance electrical impedance tomography (ICMREIT) by means of current induction due to time-varying gradient fields of magnetic resonance imaging (MRI) systems is proposed. Eddy current and secondary magnetic flux density distributions are calculated for a numerical model composed of a z-gradient coil and a cylindrical conductor. An MRI pulse sequence is developed for the experimental evaluation of ICMREIT on a 3T MRI scanner. A relationship between the secondary magnetic flux density and the low-frequency (LF) MR phase is formulated. Characteristics of the LF phase, the eddy current, and the reconstructed conductivity distributions based on the simulated and the physical measurements are in agreement. Geometric shifts, which may contaminate the LF phase measurements, are not observed in the MR magnitude images. Low sensitivity of the LF phase measurements is a major limitation of ICMREIT towards clinical applications. The reconstructed conductivity images are rough estimates of true conductivity distribution of the experimental phantoms. Although the experimental results show that ICMREIT is safe and potentially applicable, its measurement sensitivity and reconstruction accuracy need to be optimized in order to improve the technique towards clinical applications.