Magnetic Resonance Electrical Property Tomography Research Articles

Effect of Ethanol on Brain Electrical Tissue Conductivity in Social Drinkers.

How the biophysics of electrical conductivity measures relate to brain activity is poorly understood. The sedative, ethanol, reduces metabolic activity but its impact on brain electrical conductivity is unknown. To investigate whether ethanol reduces brain electrical tissue conductivity. Prospective. Fifty-two healthy volunteers (aged 18-37 years, 22 females, 30 males). 3 T, T1-weighted, multi-shot, turbo-field echo (TFE); 3D balanced fast-field echo (bFFE). Brain gray and white matter tissue conductivity measured with phase-based magnetic resonance electrical properties tomography (MREPT) compared before and 20 minutes after ethanol consumption (0.7 g/kg body weight). Differential conductivity whole brain maps were generated for three subgroups: those with strong ( > 0.1 S/m; N = 33), weak (0.02 S/m ≤ ≤ 0.1 S/m; N = 9) conductivity decrease, and no significant response ( < 0.02 S/m, N = 10). Maps were compared in the strong response group where breath alcohol rose between scans, vs. those where it fell. Average breath alcohol levels were compared to the differential conductivity maps using linear regression. T-maps were generated (threshold P < 0.05 and P < 0.001; minimum cluster 48 mm3). Differential conductivity maps were compared with ANOVA. Whole-group analysis showed decreased conductivity that did not survive statistical thresholding. Strong responders (N = 33) showed a consistent pattern of significantly decreased conductivity ( > 0.1 S/m) in frontal/occipital and cerebellar white matter. The weak response group (N = 9) showed a similar pattern of conductivity decrease (0.02 S/m ≤ ≤ 0.1 S/m). There was no significant relationship with breath alcohol levels, alcohol use, age, ethnicity, or sex. The strong responders' regional response was different between ascending (N = 12) or descending (N = 20) alcohol during the scan. Ethanol reduces brain tissue conductivity in a participant-dependent and spatially dependent fashion. 1 TECHNICAL EFFICACY: Stage 2.

Using the Probability Density Function-Based Channel-Combination Bloch-Siegert Method Realizes Permittivity Imaging at 3T.

Magnetic resonance electrical properties tomography (MR EPT) can retrieve permittivity from the B1+ magnitude. However, the accuracy of the permittivity measurement using MR EPT is still not ideal due to the low signal-to-noise ratio (SNR) of B1+ magnitude. In this study, the probability density function (PDF)-based channel-combination Bloch-Siegert (BSS) method was firstly introduced to MR EPT for improving the accuracy of the permittivity measurement. MRI experiments were performed using a 3T scanner with an eight-channel receiver coil. The homogeneous water phantom was scanned for assessing the spatial distribution of B1+ magnitude obtained from the PDF-based channel-combination BSS method. Gadolinium (Gd) phantom and rats were scanned for assessing the feasibility of the PDF-based channel-combination BSS method in MR EPT. The Helmholtz-based EPT reconstruction algorithm was selected. For quantitative comparison, the permittivity measured by the open-ended coaxial probe method was considered as the ground-truth value. The accuracy of the permittivity measurement was estimated by the relative error between the reconstructed value and the ground-truth value. The reconstructed relative permittivity of Gd phantom was 52.413, while that of rat leg muscle was 54.053. The ground-truth values of relative permittivity of Gd phantom and rat leg muscle were 78.86 and 49.04, respectively. The relative error of average permittivity was 33.53% for Gd and 10.22% for rat leg muscle. The results indicated the high accuracy of the permittivity measurement using the PDF-based channel-combination BSS method in MR EPT. This improvement may promote the clinical application of MR EPT technology, such as in the early diagnosis of cancers.

Probing underlying biophysical mechanisms of electrical properties change by pathogenesis at the microscopic cellular level

The electrical properties of human tissue have significant potential as biophysical markers in clinical applications, as they can indicate biochemical/biophysical changes occurring at the cellular and extracellular levels. Magnetic resonance electrical properties tomography (MR-EPT) provides a noninvasive approach for extracting pixel-wise electrical properties by processing the B1 field mapping data. However, our current understanding of the biophysical mechanisms underlying changes in electrical properties at the microscopic cellular level during pathogenesis remains incomplete. In this study, an inhomogeneous liver model was developed to establish a linear correlation between fat fraction and electrical properties. We further fit the correlation of liver phantoms with different fat fractions of 0%, 1%, 9%, 17%, 25%, 30%, and 50% (R2 &amp;gt; 0.93). In addition, an inhomogeneous liver phantom was fabricated and measured through MR-EPT at 128 MHz (3 T). The outcomes of this research have the potential to bridge the gap between microscopic lesions and pixel-wise MR-EPT images, offering a feasible method for extracting electrical properties through fat quantification techniques like MRI-Dixon technique.

Magnetic Resonance Electrical Properties Tomography Based on Modified Physics-Informed Neural Network and Multiconstraints.

This paper presents a novel method based on leveraging physics-informed neural networks for magnetic resonance electrical property tomography (MREPT). MREPT is a noninvasive technique that can retrieve the spatial distribution of electrical properties (EPs) of scanned tissues from measured transmit radiofrequency (RF) in magnetic resonance imaging (MRI) systems. The reconstruction of EP values in MREPT is achieved by solving a partial differential equation derived from Maxwell's equations that lacks a direct solution. Most conventional MREPT methods suffer from artifacts caused by the invalidation of the assumption applied for simplification of the problem and numerical errors caused by numerical differentiation. Existing deep learning-based (DL-based) MREPT methods comprise data-driven methods that need to collect massive datasets for training or model-driven methods that are only validated in trivial cases. Hence we proposed a model-driven method that learns mapping from a measured RF, its spatial gradient and Laplacian to EPs using fully connected networks (FCNNs). The spatial gradient of EP can be computed through the automatic differentiation of FCNNs and the chain rule. FCNNs are optimized using the residual of the central physical equation of convection-reaction MREPT as the loss function (L). To alleviate the ill condition of the problem, we added multiconstraints, including the similarity constraint between permittivity and conductivity and the ℓ1 norm of spatial gradients of permittivity and conductivity, to the L. We demonstrate the proposed method with a three-dimensional realistic head model, a digital phantom simulation, and a practical phantom experiment at a 9.4T animal MRI system.

Deep Network Regularization for Phasebased Magnetic Resonance Electrical Properties Tomography with Stein's Unbiased Risk Estimator.

Magnetic resonance imaging (MRI) can extract the tissue conductivity values from in vivo data using the so-called phase-based magnetic resonance electrical properties tomography (MR-EPT). However, this procedure suffers from noise amplification caused by the use of the Laplacian operator. To counter this issue, we propose a novel preprocessing denoiser for magnetic resonance transceive phase images, operating in an unsupervised manner. Inspired by the deep image prior approach, we apply the random initialization of a convolutional neural network, which enforces an implicit regularization. Additionally, we introduce Stein's unbiased risk estimator, which is the unbiased estimator of the mean square error for optimizing the network without the need for label images. This modification not only tackles the overfitting problem inherent in the deep image prior approach but also operates within a purely unsupervised framework. In addition, instead of using phase images, we use real and imaginary images, which aligns with the theoretical model of the risk estimator. Our generative model needs neither the preparation of training datasets nor prior training procedure, and it maintains adaptability across various resolutions and signal-to-noise ratio levels. In testing. our method significantly diminished residual error remaining in phase maps, quantitatively as well as qualitatively, for both phantom and simulated brain data. Furthermore, it outperformed other denoising methods in reducing noise amplification and boundary error. When applied to healthy volunteer and patient data, the proposed method revealed reduced error in the reconstructed conductivity maps, with conductivity values aligning well with established literature values. To the best of our knowledge, this is the first blind approach using a purely unsupervised denoising framework that can implement a 2D phase-based MR-EPT reconstruction algorithm. The source code is available at https://github.com/Yonsei-MILab/Implicit-Regularization-forMREPT-with-SURE.

Feasibility of undersampled spiral trajectories in MREPT for fast conductivity imaging.

To investigate spiral-based imaging including trajectories with undersampling as a fast and robust alternative for phase-based magnetic resonance electrical properties tomography (MREPT) techniques. Spiral trajectories with various undersampling ratios were prescribed to acquire images from an experimental phantom and a healthy volunteer at 3T. The non-Cartesian acquisitions were reconstructed using SPIRiT, and conductivity maps were derived using phase-based cr-MREPT. The resulting maps were compared between different sampling trajectories. Additionally, a conductivity map was obtained using a Cartesian balanced SSFP acquisition from the volunteer to comparatively demonstrate the robustness of the proposed method. The phantom and volunteer results illustrate the benefits of the spiral acquisitions. Specifically, undersampled spiral acquisitions display improved robustness against field inhomogeneity artifacts and lowered SD values with shortened readout times. Furthermore, average of conductivity values measured for the cerebrospinal fluid with the spiral acquisitions were 1.703 S/m, indicating a close agreement with the theoretical values of 1.794 S/m. A spiral-based acquisition framework for conductivity imaging with and without undersampling is presented. Overall, spiral-based acquisitions improved robustness against field inhomogeneity artifacts, while achieving whole head coverage with multiple averages in less than a minute.

REC-NN: A reconstruction error compensation neural network for Magnetic Resonance Electrical Property Tomography (MREPT).

Electrical properties (EPs) are expected as biomarkers for early cancer detection. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively estimate the EPs of tissues from MRI measurements. While noise sensitivity and artifact problems of MREPT are being solved progressively through recent efforts, the loss of tissue contrast emerges as an obstacle to the clinical applications of MREPT. To solve the problem, we propose a reconstruction error compensation neural network scheme (REC-NN) for a typical analytic MREPT method, Stab-EPT. Two NN structures: one with only ResNet blocks, and the other hybridizing ResNet blocks with an encoder-decoder structure. Results of experiments with digital brain phantoms show that, compared with Stab-EPT, and conventional NN based reconstruction, REC-NN improves both reconstruction accuracy and tissue contrast. It is found that, the encoder-decoder structure could improve the compensation accuracy of EPs in homogeneous region but showed worse reconstruction than only ResNet structure for tumorous tissues unseen in the training samples. Future research is required to address overcompensation problems, optimization of NN structure and application to clinical data.

An Adaptative Savitzky-Golay Kernel for Laplacian Estimation in Magnetic Resonance Electrical Property Tomography.

Magnetic Resonance electrical property tomography (MR-EPT) is a non-invasive imaging modality that reconstructs the living biological tissue's conductivity σ and εr permittivity using spatial derivatives of the measured RF field, also termed B1 data, in a magnetic resonance imaging system. The spatial derivative operator, particularly the Laplacian, amplifies the noise in the reconstructed electrical property (EP) maps, hence decreasing accuracy and increasing boundary artifacts. We propose a novel adaptative convolution kernel for generating numerical derivatives based on 3D Savitzky-Golay (SG) filters and local segmentation in a magnitude image. In comparison to typical SG kernel, the proposed kernel allows arbitrary shapes and sizes to vary with local tissue. It provides an automatic trade-off between noise and resolution, thereby significantly enhancing reconstruction accuracy and eliminating boundary artifacts.

High frequency conductivity decomposition by solving physically constraint underdetermined inverse problem in human brain

The developed magnetic resonance electrical properties tomography (MREPT) can visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data from magnetic resonance imaging (MRI). The recovered high-frequency conductivity (HFC) value is highly complex and heterogeneous in a macroscopic imaging voxel. Using high and low b-value diffusion weighted imaging (DWI) data, the multi-compartment spherical mean technique (MC-SMT) characterizes the water molecule movement within and between intra- and extra-neurite compartments by analyzing the microstructures and underlying architectural organization of brain tissues. The proposed method decomposes the recovered HFC into the conductivity values in the intra- and extra-neurite compartments via the recovered intra-neurite volume fraction (IVF) and the diffusion patterns using DWI data. As a form of decomposition of intra- and extra-neurite compartments, the problem to determine the intra- and extra-neurite conductivity values from the HFC is still an underdetermined inverse problem. To solve the underdetermined problem, we use the compartmentalized IVF as a criterion to decompose the electrical properties because the ion-concentration and mobility have different characteristics in the intra- and extra-neurite compartments. The proposed method determines a representative apparent intra- and extra-neurite conductivity values by changing the underdetermined equation for a voxel into an over-determined minimization problem over a local window consisting of surrounding voxels. To suppress the noise amplification and estimate a feasible conductivity, we define a diffusion pattern distance to weight the over-determined system in the local window. To quantify the proposed method, we conducted a simulation experiment. The simulation experiments show the relationships between the noise reduction and the spatial resolution depending on the designed local window sizes and diffusion pattern distance. Human brain experiments (five young healthy volunteers and a patient with brain tumor) were conducted to evaluate and validate the reliability of the proposed method. To quantitatively compare the results with previously developed methods, we analyzed the errors for reconstructed extra-neurite conductivity using existing methods and indirectly verified the feasibility of the proposed method.

Physics Informed Neural Networks (PINN) for Low Snr Magnetic Resonance Electrical Properties Tomography (MREPT).

Electrical properties (EPs) of tissues facilitate early detection of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively probe the EPs of tissues from MRI measurements. Most MREPT methods rely on numerical differentiation (ND) to solve partial differential Equations (PDEs) to reconstruct the EPs. However, they are not practical for clinical data because ND is noise sensitive and the MRI measurements for MREPT are noisy in nature. Recently, Physics informed neural networks (PINNs) have been introduced to solve PDEs by substituting ND with automatic differentiation (AD). To the best of our knowledge, it has not been applied to MREPT due to the challenges in using PINN on MREPT as (i) a PINN requires part of ground-truth EPs as collocation points to optimize the network's AD, (ii) the noisy input data disrupts the optimization of PINNs despite the noise-filtering nature of NNs and additional denoising processes. In this work, we propose a PINN-MREPT model based on a canonical analytic MREPT model. A reference padding layer with known EPs was added to surround the region of interest for providing additive collocation points. Moreover, an optimizable diffusion coefficient was embedded in the analytic MREPT model used in the PINN-MREPT. The noise robustness of the proposed PINN-MREPT for single-sample reconstruction was tested by using numerical phantoms of human brain with extra tumor-like tissues at different noise levels. The results of numerical experiments show that PINN-MREPT outperforms two typical numerical MREPT methods in terms of reconstruction accuracy, sensitivity to the extra tissues, and the correlations of line profiles in the regions of interest. The advantage of the PINN-MREPT is shown by the results of an experiment on phantom measurement, too. Moreover, it is found that the diffusion term plays an important role to achieve a noise-robust PINN-MREPT. This is an important step moving forward to a clinical application of MREPT.

A Method for Electrical Property Tomography Based on a Three-Dimensional Integral Representation of the Electric Field.

Magnetic resonance electrical properties tomography (MREPT) noninvasively reconstructs high-resolution electrical property (EP) maps using MRI scanners and is useful for diagnosing cancerous tissues. However, conventional MREPT methods have limitations: sensitivity to noise in the numerical Laplacian operation, difficulty in reconstructing three-dimensional (3D) EPs and convergence not guaranteed in the iterative process. We propose a novel, iterative 3D reconstruction MREPT method without a numerical Laplacian operation. We derive an integral representation of the electric field using its Helmholtz decomposition with Maxwell's equations, under the assumption that the EPs are known on the boundary of the region of interest with the approximation that the unmeasurable magnetic field components are zero. Then, we solve the simultaneous equations composed of the integral representation and Ampere's law using a convex projection algorithm whose convergence is theoretically guaranteed. The efficacy of the proposed method was validated through numerical simulations and a phantom experiment. The results showed that this method is effective in reconstructing 3D EPs and is robust to noise. It was also shown that our proposed method with the unmeasurable component H- enhances the accuracy of the EPs in a background and that with all the components of the magnetic field reduces the artifacts at the center of the slices except when all the components of the electric field are close to zero.

Physics-Coupled Neural Network Magnetic Resonance Electrical Property Tomography (MREPT) for Conductivity Reconstruction.

The electrical property (EP) of human tissues is a quantitative biomarker that facilitates early diagnosis of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is an imaging modality that reconstructs EPs by the radio-frequency field in an MRI system. MREPT reconstructs EPs by solving analytic models numerically based on Maxwell's equations. Most MREPT methods suffer from artifacts caused by inaccuracy of the hypotheses behind the models, and/or numerical errors. These artifacts can be mitigated by adding coefficients to stabilize the models, however, the selection of such coefficient has been empirical, which limit its medical application. Alternatively, end-to-end Neural networks-based MREPT (NN-MREPT) learns to reconstruct the EPs from training samples, circumventing Maxwell's equations. However, due to its pattern-matching nature, it is difficult for NN-MREPT to produce accurate reconstructions for new samples. In this work, we proposed a physics-coupled NN for MREPT (PCNN-MREPT), in which an analytic model, cr-MREPT, works with diffusion and convection coefficients, learned by NNs from the difference between the reconstructed and ground-truth EPs to reduce artifacts. With two simulated datasets, three generalization experiments in which test samples deviate gradually from the training samples, and one noise-robustness experiment were conducted. The results show that the proposed PCNN-MREPT achieves higher accuracy than two representative analytic methods. Moreover, compared with an end-to-end NN-MREPT, the proposed method attained higher accuracy in two critical generalization tests. This is an important step to practical MREPT medical diagnoses.

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.

High-frequency conductivity at Larmor-frequency in human brain using moving local window multilayer perceptron neural network.

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).

Decomposition of high-frequency electrical conductivity into extracellular and intracellular compartments based on two-compartment model using low-to-high multi-b diffusion MRI

BackgroundAs an object’s electrical passive property, the electrical conductivity is proportional to the mobility and concentration of charged carriers that reflect the brain micro-structures. The measured multi-b diffusion-weighted imaging (Mb-DWI) data by controlling the degree of applied diffusion weights can quantify the apparent mobility of water molecules within biological tissues. Without any external electrical stimulation, magnetic resonance electrical properties tomography (MREPT) techniques have successfully recovered the conductivity distribution at a Larmor-frequency.MethodsThis work provides a non-invasive method to decompose the high-frequency conductivity into the extracellular medium conductivity based on a two-compartment model using Mb-DWI. To separate the intra- and extracellular micro-structures from the recovered high-frequency conductivity, we include higher b-values DWI and apply the random decision forests to stably determine the micro-structural diffusion parameters.ResultsTo demonstrate the proposed method, we conducted phantom and human experiments by comparing the results of reconstructed conductivity of extracellular medium and the conductivity in the intra-neurite and intra-cell body. The phantom and human experiments verify that the proposed method can recover the extracellular electrical properties from the high-frequency conductivity using a routine protocol sequence of MRI scan.ConclusionWe have proposed a method to decompose the electrical properties in the extracellular, intra-neurite, and soma compartments from the high-frequency conductivity map, reconstructed by solving the electro-magnetic equation with measured B1 phase signals.

Identification of Brain Damage after Seizures Using an MR-Based Electrical Conductivity Imaging Method.

Previous imaging studies have shown the morphological malformation and the alterations of ionic mobility, water contents, electrical properties, or metabolites in seizure brains. Magnetic resonance electrical properties tomography (MREPT) is a recently developed technique for the measurement of electrical tissue properties with a high frequency that provides cellular information regardless of the cell membrane. In this study, we examined the possibility of MREPT as an applicable technique to detect seizure-induced functional changes in the brain of rats. Ultra-high field (9.4 T) magnetic resonance imaging (MRI) was performed, 2 h, 2 days, and 1 week after the injection of N-methyl-D-aspartate (NMDA; 75 mg/kg). The conductivity images were reconstructed from B1 phase images using a magnetic resonance conductivity imaging (MRCI) toolbox. The high-frequency conductivity was significantly decreased in the hippocampus among various brain regions of NMDA-treated rats. Nissl staining showed shrunken cell bodies and condensed cytoplasm potently at 2 h after NMDA treatment, and neuronal cell loss at all time points in the hippocampus. These results suggest that the reduced electrical conductivity may be associated with seizure-induced neuronal loss in the hippocampus. Magnetic resonance (MR)-based electrical conductivity imaging may be an applicable technique to non-invasively identify brain damage after a seizure.

High-frequency electrical properties tomography at 9.4T as a novel contrast mechanism for brain tumors.

PurposeTo establish high‐frequency magnetic resonance electrical properties tomography (MREPT) as a novel contrast mechanism for the assessment of glioblastomas using a rat brain tumor model.MethodsSix F98 intracranial tumor bearing rats were imaged longitudinally 8, 11 and 14 days after tumor cell inoculation. Conductivity and mean diffusivity maps were generated using MREPT and Diffusion Tensor Imaging. These maps were co‐registered with T2‐weighted images and volumes of interests (VOIs) were segmented from the normal brain, ventricles, edema, viable tumor, tumor rim, and tumor core regions. Longitudinal changes in conductivity and mean diffusivity (MD) values were compared in these regions. A correlation analysis was also performed between conductivity and mean diffusivity values.ResultsThe conductivity of ventricles, edematous area and tumor regions (tumor rim, viable tumor, tumor core) was significantly higher (P < .01) compared to the contralateral cortex. The conductivity of the tumor increased over time while MD from the tumor did not change. A marginal positive correlation was noted between conductivity and MD values for tumor rim and viable tumor, whereas this correlation was negative for the tumor core.ConclusionWe demonstrate a novel contrast mechanism based on ionic concentration and mobility, which may aid in providing complementary information to water diffusion in probing the microenvironment of brain tumors.

Effect of radiofrequency inhomogeneity on water-content based electrical properties tomography and its correction by flip angle maps

Water-content based electrical properties tomography (wEPT) can retrieve electrical properties (EPs) from water-content maps. B1+ field information is not involved in the traditional magnetic resonance electrical properties tomography approach. wEPT can be performed through conventional MR scanning, such as T1-weighted spin-echo imaging, which provides convenient access to multiple clinical applications. However, the inhomogeneous radiofrequency (RF) field induced by RF coils would cause inaccuracy in wEPT reconstructions during MR scanning. We conducted a detailed investigation to evaluate the effect of inhomogeneous RF field on wEPT reconstructions to guarantee that EP mapping is desired for clinical practice. Two important considerations are involved, namely, multiple typical coil configurations and various flip angles (FAs). We proposed a correction scheme with actual FA mapping to calibrate the RF inhomogeneity and finally validated it by using human imaging at 3 T. This study illustrates a detailed evaluation for wEPT under imperfect RF homogeneity and further provides a feasible correction procedure to mitigate it. The profound knowledge of wEPT provided in our work will benefit its performance in clinical applications.

Divergence-Based Magnetic Resonance Electrical Properties Tomography.

Magnetic resonance electrical properties tomography (MR-EPT) maps the spatial distribution of the patient's electrical conductivity and permittivity using the measured B1 data in a magnetic resonance imaging (MRI) system. Existing MR-EPT methods are usually not clinically accessible owing to their technical limits such as strong noise sensitivity. In this study, we develop a new MR-EPT method that re-expresses the involved differential equations (DEs) based on the divergence theorem. In comparison with traditional methods, the proposed method avoids the grid-wise computation of the second-order derivatives of B1+ , thereby improving the robustness against noise. Besides, for applications where the structural information can be determined in advance, EPs of a region of interest (ROI) can be calculated in a fast and efficient manner. The proposed method is firstly validated with numerical simulations, in which a three-block phantom and an anatomically accurate Duke Head model are used to evaluate the proposed method. Experiments on the 9.4T MRI system were then conducted to validate the simulations. Both results indicated that the proposed MR-EPT solution could provide a more robust reconstruction of electrical properties maps compared with conventional methods.

MR-Based Electrical Conductivity Imaging Using Second-Order Total Generalized Variation Regularization

Electrical properties provide essential information for cancer detection and specific absorption rate (SAR) estimation. Magnetic resonance electrical properties tomography (MREPT) is an approach to retrieve the distribution of electrical properties. The conventional method suffers from the locally homogeneous assumption and amplification of noise. In this study, a novel approach was introduced to improve the accuracy and the noise robustness of conductivity imaging. The proposed approach reformulated the central equation of the gradient-based method to avoid the calculation of the Laplacian operator. The equation was regularized using the second-order total generalized variation, which formulates an objective function. The optimization problem was solved by the alternating direction method of multipliers (ADMM) method. The proposed method was validated by the simulation data of the cylindrical phantom and Ella head model, and the performance was compared with existing methods. The results demonstrated that the proposed method reconstructed an accurate conductivity image and alleviated the noise effects. Furthermore, phantom and healthy volunteer experiments were implemented at a 3 Tesla (T) magnetic resonance imaging (MRI) scanner. The results suggested that the developed method can provide solutions for improved conductivity reconstruction and show potential for clinical application.