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Magnetic resonance electrical properties tomography (MREPT) aims to visualize the internal high-frequency conductivity distribution at Larmor frequency using the B1 transceive phase data. From the magnetic field perturbation by the electrical field associated with the radiofrequency (RF) magnetic field, the high-frequency conductivity and permittivity distributions inside the human brain have been reconstructed based on the Maxwell’s equation. Starting from the Maxwell’s equation, the complex permittivity can be described as a second order elliptic partial differential equation. The established reconstruction algorithms have focused on simplifying and/or regularizing the elliptic partial differential equation to reduce the noise artifact. Using the nonlinear relationship between the Maxwell’s equation, measured magnetic field, and conductivity distribution, we design a deep learning model to visualize the high-frequency conductivity in the brain, directly derived from measured magnetic flux density. The designed moving local window multi-layer perceptron (MLW-MLP) neural network by sliding local window consisting of neighboring voxels around each voxel predicts the high-frequency conductivity distribution in each local window. The designed MLW-MLP uses a family of multiple groups, consisting of the gradients and Laplacian of measured B1 phase data, as the input layer in a local window. The output layer of MLW-MLP returns the conductivity values in each local window. By taking a non-local mean filtering approach in the local window, we reconstruct a noise suppressed conductivity image while maintaining spatial resolution. To verify the proposed method, we used B1 phase datasets acquired from eight human subjects (five subjects for training procedure and three subjects for predicting the conductivity in the brain).

We introduce a new stable MINI-element pair for incompressible Stokes equations on quadrilateral meshes, which uses the smallest number of bubbles for the velocity. The pressure is discretized with the P 1 -midpoint-edge-continuous elements and each component of the velocity field is done with the standard Q 1 -conforming elements enriched by one bubble a quadrilateral. The superconvergence in the pressure of the proposed pair is analyzed on uniform rectangular meshes, and tested numerically on uniform and non-uniform meshes.

Background Multielectrode arrays (MEAs) have been used to understand electrophysiological network dynamics by recording real-time activity in groups of cells. The extent to which the collection of such data enables hypothesis testing on the level of circuits and networks depends largely on the sophistication of the analyses applied. New method We studied the systemic temporal variations of endogenous signaling within an organotypic hippocampal network following theta-burst stimulation (TBS) to the Schaffer collateral-commissural pathways. The recovered current source density (CSD) information from the raw grid of extracellular potentials by using a Gaussian interpolation method increases spatial resolution and avoids border artifacts by numerical differentials. Results We compared total sink and source currents in DG, CA3, and CA1; calculated accumulated correlation coefficients to compare pre- with post-stimulation CSD dynamics in each region; and reconstructed functional connectivity maps for regional cross-correlations with respect to temporal CSD variations. The functional connectivity maps for potential correlations pre- and post-TBS were compared to investigate the neural network as a whole, revealing differences post-TBS. Comparison with existing method(s) Previous MEA work on plasticity in hippocampal evoked potentials has focused on synchronicity across the hippocampus within isolated subregions. Such analyses ignore the complex relationships among diverse components of the hippocampal circuitry, thus failing to capture network-level behaviors integral to understanding hippocampal function. Conclusions The proposed method of recovering current source density to examine whole-hippocampal function is sensitive to experimental manipulation and is worth further examination in the context of network-level analyses of neural signaling.

Electrical brain stimulation (EBS) is an invasive electrotherapy and technique used in brain neurological disorders through direct or indirect stimulation using a small electric current. EBS has relied on computational modeling to achieve optimal stimulation effects and investigate the internal activations. Magnetic resonance diffusion weighted imaging (DWI) is commonly useful for diagnosis and investigation of tissue functions in various organs. The apparent diffusion coefficient (ADC) measures the intensity of water diffusion within biological tissues using DWI. By measuring trace ADC and magnetic flux density induced by the EBS, we propose a method to extract electrical properties including the effective extracellular ion-concentration (EEIC) and the apparent isotropic conductivity without any auxiliary additional current injection. First, the internal current density due to EBS is recovered using the measured one component of magnetic flux density. We update the EEIC by introducing a repetitive scheme called the diffusion weighting J-substitution algorithm using the recovered current density and the trace ADC. To verify the proposed method, we study an anesthetized canine brain to visualize electrical properties including electrical current density, effective extracellular ion-concentration, and effective isotropic conductivity by applying electrical stimulation of the brain.

Magnetic resonance electrical impedance tomography (MREIT) measures induced magnetic flux densities subject to externally injected currents in order to visualize conductivity distributions inside an electrically conducting object. Injection currents induce magnetic flux densities that appear in phase parts of acquired MR image data. In the conventional current injection method, we inject currents during the time segment between the end of the first RF pulse and the beginning of the reading gradient in order to ensure the gradient linearity. Noting that longer current injections can accumulate more phase changes, we propose a new pulse sequence called injection current nonlinear encoding (ICNE) where the duration of the injection current pulse is extended until the end of the reading gradient. Since the current injection during the reading gradient disturbs the gradient linearity, we first analyze the MR signal produced by the ICNE pulse sequence and suggest a novel algorithm to extract the induced magnetic flux density from the acquired MR signal. Numerical simulations and phantom experiments show that the new method is clearly advantageous in terms of the reduced noise level in measured magnetic flux density data. The amount of noise reduction depends on the choice of the data acquisition time and it was about 24% when we used a prolonged data acquisition time of 10.8 ms. The ICNE method will enhance the clinical applicability of the MREIT technique when it is combined with an appropriate phase artefact minimization method.

In MREIT (magnetic resonance electrical impedance tomography), we inject electrical current into a volume conductor to induce a distribution of a magnetic flux density. By measuring the internal magnetic flux density data using an MR scanner, we reconstruct images of cross-sectional conductivity and current density distributions. One of the most important technical problems in MREIT is to reduce the noise level in measured magnetic flux density data since it limits the reconstructed conductivity image quality. The noise level is inversely proportional to the current injection pulse width and the signal-to-noise ratio of MR magnitude images. Knowing that we cannot simultaneously increase both factors for a chosen echo time, we show that there is an optimal current injection pulse width minimizing the noise level. Experimental results demonstrate that the optimal current injection pulse width and appropriately chosen data acquisition time considerably reduce the noise standard deviation of measured magnetic flux density data. Even though there may occur undesirable side-effects with an increased data acquisition time, we found that the the pulse sequence with the optimal timing outperforms conventional method in terms of the noise level and conductivity image quality.

Cross-sectional conductivity imaging in magnetic resonance electrical impedance tomography (MREIT) requires the measurement of internal magnetic flux density using an MRI scanner. Current injection MRI techniques have been used to induce magnetic flux density distributions that appear in phase parts of the obtained MR signals. Since any phase error, as well as noise, deteriorates the quality of reconstructed conductivity images, we must minimize them during the data acquisition process. In this paper, we describe a new method to correct unavoidable phase errors to reduce artefacts in reconstructed conductivity images. From numerical simulations and phantom experiments, we found that the zeroth- and first-order phase errors can be effectively minimized to produce better conductivity images. The promising results suggest that this technique should be employed together with improved MREIT pulse sequences in future studies of high-resolution conductivity imaging.

In magnetic resonance electrical impedance tomography (MREIT), we measure the induced magnetic flux density inside an object subject to an externally injected current. This magnetic flux density is contaminated with noise, which ultimately limits the quality of reconstructed conductivity and current density images. By analysing and experimentally verifying the amount of noise in images gathered from two MREIT systems, we found that a carefully designed MREIT study will be able to reduce noise levels below 0.25 and 0.05 nT at main magnetic field strengths of 3 and 11 T, respectively, at a voxel size of 3 x 3 x 3 mm(3). Further noise level reductions can be achieved by optimizing MREIT pulse sequences and using signal averaging. We suggest two different methods to estimate magnetic flux noise levels, and the results are compared to validate the experimental setup of an MREIT system.

Magnetic resonance electrical impedance tomography (MREIT) is a new conductivity imaging modality that was motivated to deal with the well-known ill-posedness problem in electrical impedance tomography (EIT). In order to bypass this ill-posed nature, MREIT takes advantage of an MRI scanner as a tool to capture the z-component Bz of the induced internal magnetic flux density B = (Bx, By, Bz) due to an injection current. Here, z is the direction of the main magnetic field of the MRI scanner. In this work, we propose an enhanced version of the variational gradient Bz algorithm that benefits from a careful use of boundary conditions in a variational formulation of the Bz-based MREIT model. We found that the proposed algorithm is advantageous especially in dealing with conductivity images near the boundary of the subject. Improvements in reconstructed image quality are shown by numerical simulations.

We present cross-sectional conductivity images of two biological tissue phantoms. Each of the cylindrical phantoms with both diameter and height of 140 mm contained chunks of biological tissues such as bovine tongue and liver, porcine muscle and chicken breast within a conductive agar gelatin as the background medium. We attached four recessed electrodes on the sides of the phantom with equal spacing among them. Injecting current pulses of 480 or 120 mA ms into the phantom along two different directions, we measured the z-component Bz of the induced magnetic flux density B = (Bx, By, Bz) with a magnetic resonance electrical impedance tomography (MREIT) system based on a 3.0 T MRI scanner. Using the harmonic Bz algorithm, we reconstructed cross-sectional conductivity images from the measured Bz data. Reconstructed images clearly distinguish different tissues in terms of both their shapes and conductivity values. In this paper, we experimentally demonstrate the feasibility of the MREIT technique in producing conductivity images of different biological soft tissues with a high spatial resolution and accuracy when we use a sufficient amount of the injection current.

This paper reviews the latest impedance imaging technique called Magnetic Resonance Electrical Impedance Tomography (MREIT) providing information on electrical conductivity and current density distributions inside an electrically conducting domain such as the human body. The motivation for this research is explained by discussing conductivity changes related with physiological and pathological events, electromagnetic source imaging and electromagnetic stimulations. We briefly summarize the related technique of Electrical Impedance Tomography (EIT) that deals with cross-sectional image reconstructions of conductivity distributions from boundary measurements of current-voltage data. Noting that EIT suffers from the ill-posed nature of the corresponding inverse problem, we introduce MREIT as a new conductivity imaging modality providing images with better spatial resolution and accuracy. MREIT utilizes internal information on the induced magnetic field in addition to the boundary current-voltage measurements to produce three-dimensional images of conductivity and current density distributions. Mathematical theory, algorithms, and experimental methods of current MREIT research are described. With numerous potential applications in mind, future research directions in MREIT are proposed.

We present a mathematical model to analyze transadmittance data for the detection of breast cancer using TransScan TS2000 commercial system. The model was constructed based on the assumption that a lesion exists near the surface of a breast region. The breast region that is considered as a background is assumed to be homogeneous at least near the surface where we attach a planar array of electrodes. Based on the model, we developed a lesion estimation algorithm utilizing single- or multifrequency transadmittance data. The approximate ratio of two conductivity values for the lesion and background needs to be known to estimate the size of the lesion even though the location estimate does not require this ratio. From the results of numerical simulations with added noise, we suggest better ways of interpreting TS2000 transadmittance images for the detection of breast cancer with improved accuracy. Since this study provides a rigorous mathematical modeling of TS2000 commercial system, it will be possible to apply the technique to lesion estimation problems based on more realistic models of breast regions in future studies.

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component B/sub z/ of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density B/sub z/. Based on the novel mathematical formulation, we propose the gradient B/sub z/ decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate B/sub z/ only once in contrast to the previously developed harmonic B/sub z/ algorithm where the numerical computation of /spl nabla//sup 2/B/sub z/ is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.

A new image reconstruction algorithm is proposed to visualize static conductivity images of a subject in magnetic resonance electrical impedance tomography (MREIT). Injecting electrical current into the subject through surface electrodes, we can measure the induced internal magnetic flux density B = (Bx, By, Bz) using an MRI scanner. In this paper, we assume that only the z-component Bz is measurable due to a practical limitation of the measurement technique in MREIT. Under this circumstance, a constructive MREIT imaging technique called the harmonic Bz algorithm was recently developed to produce high-resolution conductivity images. The algorithm is based on the relation between inverted delta2Bz and the conductivity requiring the computation of inverted delta2Bz. Since twice differentiations of noisy Bz data tend to amplify the noise, the performance of the harmonic Bz algorithm is deteriorated when the signal-to-noise ratio in measured Bz data is not high enough. Therefore, it is highly desirable to develop a new algorithm reducing the number of differentiations. In this work, we propose the variational gradient Bz algorithm where Bz is differentiated only once. Numerical simulations with added random noise confirmed its ability to reconstruct static conductivity images in MREIT. We also found that it outperforms the harmonic Bz algorithm in terms of noise tolerance. From a careful analysis of the performance of the variational gradient Bz algorithm, we suggest several methods to further improve the image quality including a better choice of basis functions, regularization technique and multilevel approach. The proposed variational framework utilizing only Bz will lead to different versions of improved algorithms.

We consider an inverse conductivity problem arising in anomaly detections with its mathematical model based on the T-Scan system (breast cancer detection system). In this model, we try to detect an anomaly D from one or two sets of measured data that are available only on a small portion $\Gamma$ of the boundary of the subject $\Omega$. In practice, $\Omega$ differs in each subject, so our detection algorithm should not depend much on the global geometry of $\Omega$. The purpose of this work is to provide a mathematical ground for the reconstruction of a rough feature of D which is stable against any measurement noise and any change of geometry $\partial\Omega$. Based on rigorous estimates with a simplified model, we found an approximation that gives a noniterative detection algorithm of finding a useful feature of anomaly. We also present a multifrequency approach to handling the case where the complex conductivity of the background is not homogeneous and is not known a priori.

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality providing high resolution conductivity images based on the current injection MRI technique. In contrast to electrical impedance tomography (EIT), the MREIT system utilizes the internal information of current density distribution which plays an important role in eliminating the ill-posedness of the inverse problem in EIT. It has been shown that the J-substitution algorithm in MREIT reconstructs conductivity images with higher spatial resolution. However, fundamental mathematical questions, including the uniqueness of the MREIT problem itself and the convergence of the algorithm, have not yet been answered. This paper provides a rigorous proof of the uniqueness of the MREIT problem and analyses the convergence behaviour of the J-substitution algorithm.

Magnetic resonance current density imaging (MRCDI) is to provide current density images of a subject using a magnetic resonance imaging (MRI) scanner with a current injection apparatus. The injection current generates a magnetic field that we can measure from MR phase images. We obtain internal current density images from the measured magnetic flux densities via Ampere's law. However, we must rotate the subject to acquire all of the three components of the induced magnetic flux density. This subject rotation is impractical in clinical MRI scanners when the subject is a human body. In this paper, we propose a way to eliminate the requirement of subject rotation by careful mathematical analysis of the MRCDI problem. In our new MRCDI technique, we need to measure only one component of the induced magnetic flux density and reconstruct both cross-sectional conductivity and current density images without any subject rotation.

In magnetic resonance electrical impedance tomography (MREIT) we inject currents through electrodes placed on the surface of a subject and try to reconstruct cross-sectional resistivity (or conductivity) images using internal magnetic flux density as well as boundary voltage measurements. In this paper we present a static resistivity image of a cubic saline phantom (50 x 50 x 50 mm3) containing a cylindrical sausage object with an average resistivity value of 123.7 ohms cm. Our current MREIT system is based on an experimental 0.3 T MRI scanner and a current injection apparatus. We captured MR phase images of the phantom while injecting currents of 28 mA through two pairs of surface electrodes. We computed current density images from magnetic flux density images that are proportional to the MR phase images. From the current density images and boundary voltage data we reconstructed a cross-sectional resistivity image within a central region of 38.5 x 38.5 mm2 at the middle of the phantom using the J-substitution algorithm. The spatial resolution of the reconstructed image was 64 x 64 and the reconstructed average resistivity of the sausage was 117.7 ohms cm. Even though the error in the reconstructed average resistivity value was small, the relative L2-error of the reconstructed image was 25.5% due to the noise in measured MR phase images. We expect improvements in the accuracy by utilizing an MRI scanner with higher SNR and increasing the size of voxels scarifying the spatial resolution.

We consider magnetic resonance electrical impedance tomography, which aims to reconstruct the conductivity distribution using the internal current density furnished by magnetic resonance imaging. We show the uniqueness of the conductivity reconstruction with one measurement imposing the Dirichlet boundary condition. We also propose a fast non-iterative numerical algorithm for the conductivity reconstruction using the internal current vector information. The algorithm is mainly based on efficient numerical construction of equipotential lines. The resulting numerical method is stable in the sense that the error of the computed conductivity is linearly proportional to the input noise level and the introduction of internal current data makes the impedance tomography problem well-posed. We present various numerical examples to show the feasibility of using our method.

Recently, a new static resistivity image reconstruction algorithm is proposed utilizing internal current density data obtained by magnetic resonance current density imaging technique. This new imaging method is called magnetic resonance electrical impedance tomography (MREIT). The derivation and performance of J-substitution algorithm in MREIT have been reported as a new accurate and high-resolution static impedance imaging technique via computer simulation methods. In this paper, we present experimental procedures, denoising techniques and image reconstructions using a 0.3-tesla (T) experimental MREIT system and saline phantoms. MREIT using J-substitution algorithm effectively utilizes the internal current density information resolving the problem inherent in a conventional EIT, that is, the low sensitivity of boundary measurements to any changes of internal tissue resistivity values. Resistivity images of saline phantoms show an accuracy of 6.8%-47.2% and spatial resolution of 64 /spl times/ 64. Both of them can be significantly improved by using an MRI system with a better signal-to-noise ratio.

This paper considers the fundamental questions, such as existence and uniqueness, of a mathematical model arising in the MREIT system, which is an electrical impedance tomography technique integrated with magnetic resonance imaging. The mathematical model for MREIT is the Neumann problem of a nonlinear elliptic partial differential equation $\nabla\cdot(\frac{a(x)}{|\nabla u(x)|}\nabla u(x))=0$. We show that this Neumann problem belongs to one of two cases: either infinitely many solutions exist or no solution exists. This explains rigorously the reason why we have used the modified model in [O. Kwon, E. J. Woo, J. R. Yoon, and J. K. Seo, IEEE Trans. Biomed. Engrg., 49 (2002), pp. 160--167], which is a system of the Neumann problem associated with two different Neumann data. For this modified system, we prove a uniqueness result on the edge detection of a piecewise continuous conductivity distribution.

This paper deals with the inverse problem of inferring the position of an electrically grounded conductor D from a single measurement of electric field (Cauchy data) on the boundary of a smooth domain \mbox{$\Omega \subset R^n,$ $n=2,3$,} that contains $\overline D$. We present new simple and real time algorithms for locating D with a rigorous mathematical verification. These location search techniques use a special property of the surface charge density of the electrically grounded conductor. The computations in these location search methods are very simple, so that the location of a moving grounded conductor can be detected in a instant even in three dimensions.

We consider the inverse scattering problem by plane screens with Robin type boundary condition. It is proved that the shape of screen located on the known plane and the constant impedance are uniquely determined with a single incident plane wave. We also concern Frechet derivative with respect to the impedance function. Numerical experiments are given.

We consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current-voltage observation. We develop a real time algorithm for determining the location of the anomaly. This new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage. Combined with the size estimation result, this algorithm gives a good initial guess for Newton-type schemes. We give the rigorous proof for the location search algorithm. Both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast, stable and efficient. © 2001 John Wiley & Sons, Inc.

We consider the inverse problem of determining multiple anomalies within a homogeneous medium occupied in a region Ω⊂n, n = 2 or 3 from the measurement of voltage response to an injected current on the boundary ∂Ω. We propose a new method of finding the total size of multiple anomalies from the boundary measurement. This algorithm works within a real time and gives a quite precise total size of the anomalies. Next, we present asymptotic formulae which are useful to develop a reconstruction algorithm. Numerical experiments based on the size estimation and asymptotic formulae indicate its efficiency.

We consider the inverse scattering problem for the Helmholtz equation determining the unknown sound-soft obstacle for a fixed wavenumber k >0. The far-field pattern for the translation of a connected bounded obstacle is represented for the one fixed reference obstacle. Using this representation, we establish Lipschitz stability of the recovery of the translated location from knowledge of the far-field pattern for one incident plane wave. Lipschitz stability estimates for balls in 3 are also obtained from two incident plane waves and far-field patterns.

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. Recentin vivoanimal and human MREIT studies have revealed unique conductivity contrasts related to different physiological and pathological conditions of tissues or organs. When performingin vivobrain 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.

Magnetic Resonance Electrical Impedance Tomography(MREIT) is a new medical imaging technique for the cross-sectional conductivity distribution of a human body using both EIT(Electrical Impedance Tomography) and MRI(Magnetic Resonance Imaging) system. MREIT system was designed to enhance EIT imaging system which has inherent low sensitivity of boundary measurements to any changes of internal tissue conductivity values. MREIT utilizes a recent CDI (Current Density Imaging) technique of measuring the internal current density by means of MRI technique. In this paper, a mathematical modeling for MREIT and image reconstruction method called the alternating J-substitution algorithm are presented. Computer simulations show that the alternating J-substitution algorithm provides accurate high-resolution conductivity images.

For an internal conductivity image, magnetic resonance electrical impedance tomography (MREIT) injects an electric current into an object and measures the induced magnetic flux density, which appears in the phase part of the acquired MR image data. To maximize signal intensity, the injected current nonlinear encoding (ICNE) method extends the duration of the current injection until the end of the MR data reading. It disturbs the usual linear encoding of the MRk-space data used in the inverse Fourier transform. In this study, we estimate the magnetic flux density, which is recoverable from nonlinearly encoded MRk-space data by applying a Newton method.

Magnetic resonance electrical impedance tomography (MREIT) aims at producing high-resolution cross-sectional conductivity images of an electrically conducting object such as the human body. Following numerous phantom imaging experiments, the most recent study demonstrated successful conductivity image reconstructions of postmortem canine brains using a 3 T MREIT system with 40 mA imaging currents. Here, we report the results of in vivo animal imaging experiments using 5 mA imaging currents. To investigate any change of electrical conductivity due to brain ischemia, canine brains having a regional ischemic model were scanned along with separate scans of canine brains having no disease model. Reconstructed multi-slice conductivity images of in vivo canine brains with a pixel size of 1.4 mm showed a clear contrast between white and gray matter and also between normal and ischemic regions. We found that the conductivity value of an ischemic region decreased by about 10-14%. In a postmortem brain, conductivity values of white and gray matter decreased by about 4-8% compared to those in a live brain. Accumulating more experience of in vivo animal imaging experiments, we plan to move to human experiments. One of the important goals of our future work is the reduction of the imaging current to a level that a human subject can tolerate. The ability to acquire high-resolution conductivity images will find numerous clinical applications not supported by other medical imaging modalities. Potential applications in biology, chemistry and material science are also expected.

Magnetic resonance current density imaging (MRCDI) is to provide a current density imaging by measuring the induced magnetic flux density within the subject using an magnetic resonance imaging (MRI) scanner. The analysis of the map T from current density vector fields to one component of the magnetic flux density clarifies a limitation of reconstruction of the current and is essential to develop efficient reconstruction algorithms for conductivity and current density imaging.

Magnetic resonance electrical impedance tomography (MREIT) has been developed as a new medical imaging modality providing high-resolution conductivity and current density images. This paper is about MREIT of the breast. To show the feasibility of breast MREIT, we carried numerical simulations and breast phantom experiments. We found that an anomaly with 4 mm diameter can be visualized in a reconstructed conductivity image using 5 mA injection current if the SNR of the corresponding MR magnitude image is at least 150. We propose a desirable electrode configuration and show our first experimental results of the breast MREIT. Developing an RF coil for the breast MREIT, we plan to conduct various experimental studies including tissue phantoms.

Recent progress in magnetic resonance electrical impedance tomography (MREIT) research has shown that conductivity images with higher spatial resolution and accuracy are achievable. One of the most important remaining problems to be solved in MREIT before we can apply the technique to human subjects is how to reduce the amount of injection current. Since we use an MRI scanner to measure the induced magnetic flux density data subject to an injection current, the data is contaminated with random noise. In order to obtain enough signal-to-noise ratio (SNR), we need to inject a large amount of current into the subject. However, it is obvious that we must comply with the electrical safety regulations and this means that we should deal with noisy data having a low SNR due to the limited amount of injection current. Furthermore, in the developed reconstruction algorithms, the required numerical differentiations of the noisy data may result in deterioration of the reconstructed conductivity image leading to a loss of important information. We propose a PDE-based denoising technique that diminishes the degradation of reconstructed conductivity images due to the noise in measured data. The proposed PDE-based technique is advantageous in reducing the random noise while preserving useful features in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, B/sub z/, of the induced magnetic flux density B = (B/sub x/,B/sub y/,B/sub z/). In MREIT, accurate measurements of B/sub z/ are essential in producing correct conductivity images. However, the measured B/sub z/ data may contain fundamental defects in local regions where MR magnitude image data are small. These defective B/sub z/ data result in completely wrong conductivity values there and also affect the overall accuracy of reconstructed conductivity images. Hence, these defects should be appropriately recovered in order to carry out any MREIT image reconstruction algorithm. This paper proposes a new method of recovering B/sub z/ data in defective regions based on its physical properties and neighboring information of B/sub z/. The technique will be indispensable for conductivity imaging in MREIT from animal or human subjects including defective regions such as lungs, bones, and any gas-filled internal organs.

We present a new medical imaging technique for breast imaging, breast MREIT, in which magnetic resonance electrical impedance tomography (MREIT) is utilized to get high-resolution conductivity and current density images of the breast. In this work, we introduce the basic imaging setup of the breast MREIT technique with an investigation of four different imaging configurations of current-injection electrode positions and pathways through computer simulation studies. Utilizing the preliminary findings of a best breast MREIT configuration, additional numerical simulation studies have been carried out to validate breast MREIT at different levels of SNR. Finally, we have performed an experimental validation with a breast phantom on a 3.0 T MREIT system. The presented results strongly suggest that breast MREIT with careful imaging setups could be a potential imaging technique for human breast which may lead to early detection of breast cancer via improved differentiation of cancerous tissues in high-resolution conductivity images.

Recent progress in magnetic resonance electrical impedance tomography (MREIT) research via simulation and biological tissue phantom studies have shown that conductivity images with higher spatial resolution and accuracy are achievable. In order to apply MREIT to human subjects, one of the important remaining problems to be solved is to reduce the amount of the injection current such that it meets the electrical safety regulations. However, by limiting the amount of the injection current according to the safety regulations, the measured MR data such as the z-component of magnetic flux density B/sub z/ in MREIT tend to have low SNR and get usually degraded in their accuracy due to the nonideal data acquisition system of an MR scanner. Furthermore, numerical differentiations of the measured B/sub z/ required by the conductivity image reconstruction algorithms tend to further deteriorate the quality and accuracy of the reconstructed conductivity images. In this paper, we propose a denoising technique that incorporates a harmonic decomposition. The harmonic decomposition is especially suitable for MREIT due to the physical characteristics of B/sub z/. It effectively removes systematic and random noises, while preserving important key features in the MR measurements, so that improved conductivity images can be obtained. The simulation and experimental results demonstrate that the proposed denoising technique is effective for MREIT, producing significantly improved quality of conductivity images. The denoising technique will be a valuable tool in MREIT to reduce the amount of the injection current when it is combined with an improved MREIT pulse sequence.

We describe a new resistivity image reconstruction algorithm called J-substitution algorithm. It utilizes internal current density data measured by MRI technique with current injection. Computer simulations show that Magnetic Resonance Electrical Impedance Tomography (MREIT) system using J-substitution algorithm can produce high-resolution static resistivity images of a subject.

Current density imaging (CDI) is able to visualize a three-dimensional current density distribution J inside an electrically conducting subject caused by an externally applied current. CDI may use a magnetic resonance imaging (MRI) scanner to measure the induced magnetic flux density B and compute J via the Ampere law [Formula: see text]. However, measuring all three components of B = (B(x), B(y), B(z)) has a technical difficulty due to the requirement of orthogonal rotations of the subject inside the MRI scanner. In this work, we propose a new method of reconstructing a current density image using only B(z) data so that we can avoid the subject rotation procedure. The method utilizes an auxiliary injection current to compensate the missing information of B(x) and B(y). The major advantage of the method is its applicability to a subject with an anisotropic conductivity distribution. Numerical experiments show the feasibility of the new technique.

We present cross-sectional conductivity images of a biological tissue phantom obtained by using a 3.0 Tesla magnetic resonance electrical impedance tomography (MREIT) system. Inside the cylindrical phantom with 140 mm diameter and 140 mm height, biological tissues such as bovine tongue and liver, porcine muscle, and chicken breast were placed within an agar gelatin. Injecting current of 480 mA/spl middot/ms into the tissue phantom, we measured the z-component B/sub z/ of the induced magnetic flux density B=(B/sub x/, B/sub y/, B/sub z/). Using the harmonic B/sub z/ algorithm, we reconstructed cross-sectional conductivity images from the measured B/sub z/ data. Reconstructed images clearly distinguish different tissues in terms of both their shapes and conductivity values.

In Magnetic Resonance Electrical Impedance Tomography (MREIT), we measure the induced magnetic flux density inside an imaging object subject to an external injection current. The magnetic flux density is contaminated with noise and this ultimately limits the quality of reconstructed conductivity and current density images. By using two methods to analyze amounts of noise in 3T and 11T MREIT systems, we found that a carefully designed MREIT study will be able to reduce the noise level below 0.1 nT.

We describe a novel method of reconstructing images of an anisotropic conductivity tensor distribution inside an electrically conducting subject in magnetic resonance electrical impedance tomography (MREIT). MREIT is a recent medical imaging technique combining electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) to produce conductivity images with improved spatial resolution and accuracy. In MREIT, we inject electrical current into the subject through surface electrodes and measure the z-component Bz of the induced magnetic flux density using an MRI scanner. Here, we assume that z is the direction of the main magnetic field of the MRI scanner. Considering the fact that most biological tissues are known to have anisotropic conductivity values, the primary goal of MREIT should be the imaging of an anisotropic conductivity tensor distribution. However, up to now, all MREIT techniques have assumed an isotropic conductivity distribution in the image reconstruction problem to simplify the underlying mathematical theory. In this paper, we firstly formulate a new image reconstruction method of an anisotropic conductivity tensor distribution. We use the relationship between multiple injection currents and the corresponding induced Bz data. Simulation results show that the algorithm can successfully reconstruct images of anisotropic conductivity tensor distributions. While the results show the feasibility of the method, they also suggest a more careful design of data collection methods and data processing techniques compared with isotropic conductivity imaging.

This paper presents cross-sectional conductivity and current density images of an inhomogeneous saline phantom. Using a 0.3 Tesla MRI scanner with its main magnetic field in the z-direction, we measured the z-component of the induced magnetic flux density B/sub z/, due to multiple injection currents. Four recessed electrodes are used to inject six different currents without producing artifacts near the boundary of the imaging subject. We used an image reconstruction algorithm called/spl Delta//sup 2/B/sub z/, algorithm to reconstruct images with a spatial resolution of 82/spl times/82 pixels (0.6/spl times/0.6 mm/sup 2//pixel). The accuracy of the reconstructed image was estimated as 13.8 to 21.5% in terms of the relative L/sup 2/-error over all pixels.

Magnetic resonance electrical impedance tomography (MREIT) is a recently developed imaging technique that combines MRI and electrical impedance tomography (EIT). In MREIT, cross-sectional electrical conductivity images are reconstructed from the internal magnetic field density data produced inside an electrically conducting object when an electrical current is injected into the object. In this work we present the results of electrical conductivity imaging experiments, and performance evaluations of MREIT in terms of noise characteristics and spatial resolution. The MREIT experiment was performed with a 3.0 Tesla MRI system on a phantom with an inhomogeneous conductivity distribution. We reconstructed the conductivity images in a 128 × 128 matrix format by applying the harmonic Bz algorithm to the z-component of the internal magnetic field density data. Since the harmonic Bz algorithm uses only a single component of the internal magnetic field data, it was not necessary to rotate the object in the MRI scan. The root mean squared (RMS) errors of the reconstructed images were between 11% and 35% when the injection current was 24 mA. Magn Reson Med 51:1292–1296, 2004. © 2004 Wiley-Liss, Inc.

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of (inverted delta)2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.

Magnetic resonance electrical impedance tomography (MREIT) is to provide cross-sectional images of the conductivity distribution sigma of a subject. While injecting current into the subject, we measure one component Bz of the induced magnetic flux density B = (Bx, By, Bz) using an MRI scanner. Based on the relation between (inverted delta)2 Bz and inverted delta sigma, the harmonic Bz algorithm reconstructs an image of sigma using the measured Bz data from multiple imaging slices. After we obtain sigma, we can reconstruct images of current density distributions for any given current injection method. Following the description of the harmonic Bz algorithm, this paper presents reconstructed conductivity and current density images from computer simulations and phantom experiments using four recessed electrodes injecting six different currents of 26 mA. For experimental results, we used a three-dimensional saline phantom with two polyacrylamide objects inside. We used our 0.3 T (tesla) experimental MRI scanner to measure the induced Bz. Using the harmonic Bz algorithm, we could reconstruct conductivity and current density images with 82 x 82 pixels. The pixel size was 0.6 x 0.6 mm2. The relative L2 errors of the reconstructed images were between 13.8 and 21.5% when the signal-to-noise ratio (SNR) of the corresponding MR magnitude images was about 30. The results suggest that in vitro and in vivo experimental studies with animal subjects are feasible. Further studies are requested to reduce the amount of injection current down to less than 1 mA for human subjects.

In magnetic resonance electrical impedance tomography (MREIT), we try to reconstruct a cross-sectional resistivity (or conductivity) image of a subject. When we inject a current through surface electrodes, it generates a magnetic field. Using a magnetic resonance imaging (MRI) scanner, we can obtain the induced magnetic flux density from MR phase images of the subject. We use recessed electrodes to avoid undesirable artefacts near electrodes in measuring magnetic flux densities. An MREIT image reconstruction algorithm produces cross-sectional resistivity images utilizing the measured internal magnetic flux density in addition to boundary voltage data. In order to develop such an image reconstruction algorithm, we need a three-dimensional forward solver. Given injection currents as boundary conditions, the forward solver described in this paper computes voltage and current density distributions using the finite element method (FEM). Then, it calculates the magnetic flux density within the subject using the Biot-Savart law and FEM. The performance of the forward solver is analysed and found to be enough for use in MREIT for resistivity image reconstructions and also experimental designs and validations. The forward solver may find other applications where one needs to compute voltage, current density and magnetic flux density distributions all within a volume conductor.

Lately, a new static resistivity image reconstruction algorithm is proposed utilizing internal current density data obtained by the magnetic resonance current density imaging (MRCDI) technique. This new imaging method is called magnetic resonance electrical impedance tomography (MREIT). In this paper, we present experimental procedures, denoising techniques, and image reconstructions using a 0.3 Tesla experimental MREIT system and saline phantoms. MREIT using J-substitution algorithm effectively utilizes the internal current density information resolving the problem inherent in a conventional EIT, that is, the low sensitivity of boundary measurements to any changes of internal tissue resistivity values.

In MREIT, we reconstruct cross-sectional resistivity images of a subject. Injecting currents through surface electrodes, we measure internal magnetic flux density using MRCDI technique. Current density can be obtained from the magnetic flux density data. For resistivity image reconstruction algorithms, we need a three-dimensional forward solver computing voltage, current density, and magnetic flux density within the subject. Given injection currents as boundary conditions, the three-dimensional forward solver described in this paper calculates voltage and current density using FEM. Then, it computes the induced magnetic flux density within the subject using the Biot-Savart law.