Reference-Based Integral MR-EPT:Simulation and Experiment Studies on the 9.4T MRI

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.

Improving phase-based conductivity reconstruction by means of deep learning-based denoising of B 1 + phase data for 3T MRI

PURPOSE

To denoise B 1 + phase using a deep learning method for phase-based in vivo electrical conductivity reconstruction in a 3T MR system.

METHODS

For B 1 + phase deep-learning denoising, a convolutional neural network (U-net) was chosen. Training was performed on data sets from 10 healthy volunteers. Input data were the real and imaginary components of single averaged spin-echo data (SNR = 45), which was used to approximate the B 1 + phase. For label data, multiple signal-averaged spin-echo data (SNR = 128) were used. Testing was performed on in silico and in vivo data. Reconstructed conductivity maps were derived using phase-based conductivity reconstructions. Additionally, we investigated the usability of the network to various SNR levels, imaging contrasts, and anatomical sites (ie, T₁ , T₂ , and proton density-weighted brain images and proton density-weighted breast images. In addition, conductivity reconstructions from deep learning-based denoised data were compared with conventional image filters, which were used for data denoising in electrical properties tomography (ie, the Gaussian filtering and the Savitzky-Golay filtering).

RESULTS

The proposed deep learning-based denoising approach showed improvement for B 1 + phase for both in silico and in vivo experiments with reduced quantitative error measures compared with other methods. Subsequently, this resulted in an improvement of reconstructed conductivity maps from the denoised B 1 + phase with deep learning.

CONCLUSION

The results suggest that the proposed approach can be used as an alternative preprocessing method to denoise B 1 + maps for phase-based conductivity reconstruction without relying on image filters or signal averaging.

Electrical Properties Tomography: A Methodological Review

Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.

Magnetic resonance electrical property mapping at 21.1 T: a study of conductivity and permittivity in phantoms, ex vivo tissue and in vivo ischemia

Electrical properties (EP), namely conductivity and permittivity, can provide endogenous contrast for tissue characterization. Using electrical property tomography (EPT), maps of EP can be generated from conventional MRI data. This report investigates the feasibility and accuracy of EPT at 21.1 T for multiple RF coils and modes of operation using phantoms. Additionally, it demonstrates the EP of the in vivo rat brain with and without ischemia. Helmholtz-based EPT was implemented in its Full-form, which demands the complex [Formula: see text] field, and a simplified form requiring either just the [Formula: see text] field phase for conductivity or the [Formula: see text] field magnitude for permittivity. Experiments were conducted at 21.1 T using birdcage and saddle coils operated in linear or quadrature transceive mode, respectively. EPT approaches were evaluated using a phantom, ex and in vivo Sprague-Dawley rats under naïve conditions and ischemic stroke via transient middle cerebral artery occlusion. Different conductivity reconstruction approaches applied to the phantom displayed average errors of 12%-73% to the target acquired from dielectric probe measurements. Permittivity reconstructions showed higher agreement and an average 3%-8% error to the target depending on reconstruction approach. Conductivity and permittivity of ex and in vivo rodent brain were measured. Elevated EP in the ischemia region correlated with the increased sodium content and the influx of water intracellularly following ischemia in the lesion were detected. The Full-form technique generated from the linear birdcage provided the best accuracy for EP of the phantom. Phase-based conductivity and magnitude-based permittivity mapping provided reasonable estimates but also demonstrated the limitations of Helmholtz-based EPT at 21.1 T. Permittivity reconstruction was improved significantly over lower fields, suggesting a novel metric for in vivo brain studies. EPT applied to ischemic rat brain proved sensitivity to physiological changes, motivating the future application of more advanced reconstruction approaches.

Integral MR-EPT With the Calculation of Coil Current Distributions

Many integral equation (IE)-based magnetic resonance electrical property tomography (MR-EPT) methods use unloaded incident radio-frequency (RF) fields from simulations that may not fully reflect the real situation and thus lead to reconstruction errors. To improve the accuracy of IE-based MR-EPT methods, a novel approach that enables the calculation of loaded coil current distributions and avoids the explicit use of incident RF fields is presented in this paper. In the proposed method, a hybrid source composed of the current source from the coil and the contrast source from the subject are introduced in the integral equations. Because the loaded coil current distributions can be extracted from the reconstructed hybrid source, the simulated incident RF fields are eliminated from the problem formulations. To improve the convergence performance, a modified conjugate gradient (CG) scheme was used where the gradients of the current source and contrast source were balanced through using different weighting parameters. The proposed method was verified through full-wave simulations at 9.4 and 7 T involving a heterogeneous ball and an anatomical head phantom. The numerical results indicated that by using the proposed method, an accurate coil current distributions and EPs profiles can be reconstructed and the desirable robustness against noise can also be achieved.