Current density imaging using directly measured harmonic Bz data in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) measures magnetic flux density signals through the use of a magnetic resonance imaging (MRI) in order to visualize the internal conductivity and/or current density. Understanding the reconstruction procedure for the internal current density, we directly measure the second derivative of Bz data from the measured k-space data, from which we can avoid a tedious phase unwrapping to obtain the phase signal of Bz . We determine optimal weighting factors to combine the derivatives of magnetic flux density data, [Symbol: see text](2) Bz , measured using the multi-echo train. The proposed method reconstructs the internal current density using the relationships between the induced internal current and the measured [Symbol: see text](2) Bz data. Results from a phantom experiment demonstrate that the proposed method reduces the scanning time and provides the internal current density, while suppressing the background field inhomogeneity. To implement the real experiment, we use a phantom with a saline solution including a balloon, which excludes other artifacts by any concentration gradient in the phantom.

Shear modulus decomposition algorithm in magnetic resonance elastography.

Magnetic resonance elastography (MRE) is an imaging modality capable of visualizing the elastic properties of an object using magnetic resonance imaging (MRI) measurements of transverse acoustic strain waves induced in the object by a harmonically oscillating mechanical vibration. Various algorithms have been designed to determine the mechanical properties of the object under the assumptions of linear elasticity, isotropic and local homogeneity. One of the challenging problems in MRE is to reduce the noise effects and to maintain contrast in the reconstructed shear modulus images. In this paper, we propose a new algorithm designed to reduce the degree of noise amplification in the reconstructed shear modulus images without the assumption of local homogeneity. Investigating the relation between the measured displacement data and the stress wave vector, the proposed algorithm uses an iterative reconstruction formula based on a decomposition of the stress wave vector. Numerical simulation experiments and real experiments with agarose gel phantoms and human liver data demonstrate that the proposed algorithm is more robust to noise compared to standard inversion algorithms and stably determines the shear modulus.

Non-iterative conductivity reconstruction algorithm using projected current density in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) is to visualize the current density and the conductivity distribution in an electrical object Omega using the measured magnetic flux data by an MRI scanner. MREIT uses only one component B(z) of the magnetic flux density B = (B(x), B(y), B(z)) generated by an injected electrical current into the object. In this paper, we propose a fast and direct non-iterative algorithm to reconstruct the internal conductivity distribution in Omega with the measured B(z) data. To develop the algorithm, we investigate the relation between the projected current density J(P), a uniquely determined component of J by the map from current J to measured B(z) data and the isotropic conductivity. Three-dimensional numerical simulations and phantom experiments are studied to show the feasibility of the proposed method by comparing with those using the conventional iterative harmonic B(z) algorithm.

In vivo electrical conductivity imaging of a canine brain using a 3 T MREIT system.

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.

Conductivity imaging with low level current injection using transversal J-substitution algorithm in MREIT.

An aim of magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and conductivity of the electrically imaged object by injecting current through electrodes attached to it. Due to a limited amount of injection current, one of the most important factors in MREIT is how to control the noise contained in the measured magnetic flux density data. This paper describes a new iterative algorithm called the transversal J-substitution algorithm which is robust to measured noise. As a result, the proposed transversal J-substitution algorithm considerably improves the quality of the reconstructed conductivity image under a low injection current. The relation between the reconstructed contrast of conductivity and the measured noise in the magnetic flux density is analyzed. We show that the contrast of first update of the conductivity with a homogeneous initial guess using the proposed algorithm has sufficient distinguishability to detect the anomaly. Results from numerical simulations demonstrate that the transversal J-substitution algorithm is robust to the noise. For practical implementations of MREIT, we tested real experiments in an agarose gel phantom using low current injection with amplitudes 1 mA and 5 mA to reconstruct the interior conductivity distribution.

Noise analysis and MR pulse sequence optimization in MREIT using an injected current nonlinear encoding (ICNE) method.

Magnetic resonance current density imaging (MRCDI) and magnetic resonance electrical impedance tomography (MREIT) visualize an internal distribution of current density and/or conductivity by injecting current into an electrically conductive object such as the human body using an MRI scanner. MREIT measures the induced magnetic flux density which appears in the phase part of the acquired MR image data. Recently, the injected current nonlinear encoding (ICNE) method in MREIT extended the duration of the current injection until the end of a reading gradient to maximize the signal intensity of the magnetic flux density. In this paper, we investigate the signal-to-noise ratio (SNR) of the magnetic flux density measured by the ICNE method in the presence of a zero-mean Gaussian random noise in measured k-space MR data. Based on the analysis of the noise standard deviation s(B(z)) of the magnetic flux density, we determine an optimal combination between the current injection pulse width T(c) and data acquisition time T(s) which minimize the noise level of the measured magnetic flux density for a given echo time T(E). On one hand, theoretically, the proposed ICNE MR pulse sequence using the optimal data acquisition time T(s)* reduces the noise level of the measured magnetic flux density by about 42.3% compared with the optimal data acquisition time of the conventional MREIT pulse sequence. On the other hand, practically, the prolonged T(s)* may result in undesirable artifacts including blurring, chemical shift and phase error along the phase encoding direction. We observe that the noise level is a function of the data acquisition time T(s) and the rate of change in the noise level is slow near T(s)=T(s)*. Numerical phantom experiments show that a compromised T(s) between the ordinary data acquisition time and the optimal T(s)* reduces a relatively large amount of undesirable artifacts and almost maintains the optimized noise level of the measured magnetic flux density.

Analysis of recoverable current from one component of magnetic flux density in MREIT and MRCDI.

Magnetic resonance current density imaging (MRCDI) provides a current density image by measuring the induced magnetic flux density within the subject with a magnetic resonance imaging (MRI) scanner. Magnetic resonance electrical impedance tomography (MREIT) has been focused on extracting some useful information of the current density and conductivity distribution in the subject Omega using measured B(z), one component of the magnetic flux density B. In this paper, we analyze the map Tau from current density vector field J to one component of magnetic flux density B(z) without any assumption on the conductivity. The map Tau provides an orthogonal decomposition J = J(P) + J(N) of the current J where J(N) belongs to the null space of the map Tau. We explicitly describe the projected current density J(P) from measured B(z). Based on the decomposition, we prove that B(z) data due to one injection current guarantee a unique determination of the isotropic conductivity under assumptions that the current is two-dimensional and the conductivity value on the surface is known. For a two-dimensional dominating current case, the projected current density J(P) provides a good approximation of the true current J without accumulating noise effects. Numerical simulations show that J(P) from measured B(z) is quite similar to the target J. Biological tissue phantom experiments compare J(P) with the reconstructed J via the reconstructed isotropic conductivity using the harmonic B(z) algorithm.

Measurement of induced magnetic flux density using injection current nonlinear encoding (ICNE) in MREIT.

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.

Optimization of current injection pulse width in MREIT.

In magnetic resonance electrical impedance tomography (MREIT), we inject electrical current into a volume conductor to induce a distribution of magnetic flux density. By measuring the internal magnetic flux density 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 the measured magnetic flux density data since it limits the quality of reconstructed images. The noise level is inversely proportional to the current injection pulse width and signal-to-noise ratio (SNR) 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 level. We suggest future works to reduce undesirable side effects due to an increased data acquisition time.

Phase artefact reduction in magnetic resonance electrical impedance tomography (MREIT).

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.

Conductivity image reconstruction from defective data in MREIT: numerical simulation and animal experiment.

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, Bz, of the induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements of Bz are essential in producing correct conductivity images. However, the measured Bz data may contain fundamental defects in local regions where MR magnitude image data are small. These defective Bz 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 Bz data in defective regions based on its physical properties and neighboring information of Bz. 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.

Noise analysis in magnetic resonance electrical impedance tomography at 3 and 11 T field strengths.

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.

Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study.

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.

Static conductivity imaging using variational gradient Bz algorithm in magnetic resonance electrical impedance tomography.

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.

Electrical conductivity imaging using gradient B, decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT).

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.