CSI-EPT in Presence of RF-Shield for MR-Coils

Repeatability and Reproducibility Uncertainty in Magnetic Resonance-Based Electric Properties Tomography of a Homogeneous Phantom

Uncertainty assessment is a fundamental step in quantitative magnetic resonance imaging because it makes comparable, in a strict metrological sense, the results of different scans, for example during a longitudinal study. Magnetic resonance-based electric properties tomography (EPT) is a quantitative imaging technique that retrieves, non-invasively, a map of the electric properties inside a human body. Although EPT has been used in some early clinical studies, a rigorous experimental assessment of the associated uncertainty has not yet been performed. This paper aims at evaluating the repeatability and reproducibility uncertainties in phase-based Helmholtz-EPT applied on homogeneous phantom data acquired with a clinical 3 T scanner. The law of propagation of uncertainty is used to evaluate the uncertainty in the estimated conductivity values starting from the uncertainty in the acquired scans, which is quantified through a robust James-Stein shrinkage estimator to deal with the dimensionality of the problem. Repeatable errors are detected in the estimated conductivity maps and are quantified for various values of the tunable parameters of the EPT implementation. The spatial dispersion of the estimated electric conductivity maps is found to be a good approximation of the reproducibility uncertainty, evaluated by changing the position of the phantom after each scan. The results underpin the use of the average conductivity (calculated by weighting the local conductivity values by their uncertainty and taking into account the spatial correlation) as an estimate of the conductivity of the homogeneous phantom.

A Novel Discretization Procedure in the CSI-FEM Algorithm for Brain Stroke Microwave Imaging

In this work, the contrast source inversion method is combined with a finite element method to solve microwave imaging problems. The paper's major contribution is the development of a novel contrast source variable discretization that leads to simplify the algorithm implementation and, at the same time, to improve the accuracy of the discretized quantities. Moreover, the imaging problem is recreated in a synthetic environment, where the antennas, and their corresponding coaxial port, are modeled. The implemented algorithm is applied to reconstruct the tissues' dielectric properties inside the head for brain stroke microwave imaging. The proposed implementation is compared with the standard one to evaluate the impact of the variables' discretization on the algorithm's accuracy. Furthermore, the paper shows the obtained performances with the proposed and the standard implementations of the contrast source inversion method in the same realistic 3D scenario. The exploited numerical example shows that the proposed discretization can reach a better focus on the stroke region in comparison with the standard one. However, the variation is within a limited range of permittivity values, which is reflected in similar averages.

Combining deep learning and 3D contrast source inversion in MR-based electrical properties tomography

Magnetic resonance electrical properties tomography (MR-EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements of the transmit magnetic field. Different reconstruction methods are available; however, all these methods present several limitations, which hamper the clinical applicability. Standard Helmholtz-based MR-EPT methods are severely affected by noise. Iterative reconstruction methods such as contrast source inversion electrical properties tomography (CSI-EPT) are typically time-consuming and are dependent on their initialization. Deep learning (DL) based methods require a large amount of training data before sufficient generalization can be achieved. Here, we investigate the benefits achievable using a hybrid approach, that is, using MR-EPT or DL-EPT as initialization guesses for standard 3D CSI-EPT. Using realistic electromagnetic simulations at 3 and 7 T, the accuracy and precision of hybrid CSI reconstructions are compared with those of standard 3D CSI-EPT reconstructions. Our results indicate that a hybrid method consisting of an initial DL-EPT reconstruction followed by a 3D CSI-EPT reconstruction would be beneficial. DL-EPT combined with standard 3D CSI-EPT exploits the power of data-driven DL-based EPT reconstructions, while the subsequent CSI-EPT facilitates a better generalization by providing data consistency.

Transceive phase corrected 2D contrast source inversion-electrical properties tomography

PURPOSE

To remove the necessity of the tranceive phase assumption for CSI-EPT and show electrical properties maps reconstructed from measured data obtained using a standard 3T birdcage body coil setup.

METHODS

The existing CSI-EPT algorithm is reformulated to use the transceive phase rather than relying on the transceive phase assumption. Furthermore, the radio frequency (RF)-shield is numerically implemented to accurately model the RF fields inside the MRI scanner. We verify that the reformulated two-dimensional (2D) CSI-EPT algorithm can reconstruct electrical properties maps given 2D electromagnetic simulations. Afterward, the algorithm is tested with three-dimensional (3D) FDTD simulations to investigate if the 2D CSI-EPT can retrieve the electrical properties for 3D RF fields. Finally, an MR experiment at 3T with a phantom is performed.

RESULTS

From the results of the 2D simulations, it is seen that CSI-EPT can reconstruct the electrical properties using MRI accessible quantities. For 3D simulations, it is observed that the electrical properties are underestimated, nonetheless, CSI-EPT has a lower standard deviation than the standard Helmholtz based methods. Finally, the first CSI-EPT reconstructions based on measured data are presented showing comparable accuracy and precision to reconstructions based on simulated data, and demonstrating the feasibility of CSI-EPT.

CONCLUSIONS

The CSI-EPT algorithm was rewritten to use MRI accessible quantities. This allows for CSI-EPT to fully exploit the benefits of the higher static magnetic field strengths with a standard quadrature birdcage coil setup.

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.

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.

Developments in Electrical-Property Tomography Based on the Contrast-Source Inversion Method

The main objective of electrical-property tomography (EPT) is to retrieve dielectric tissue parameters from B ^ 1 + data as measured by a magnetic-resonance (MR) scanner. This is a so-called hybrid inverse problem in which data are defined inside the reconstruction domain of interest. In this paper, we discuss recent and new developments in EPT based on the contrast-source inversion (CSI) method. After a short review of the basics of this method, two- and three-dimensional implementations of CSI-EPT are presented along with a very efficient variant of 2D CSI-EPT called first-order induced current EPT (foIC-EPT). Practical implementation issues that arise when applying the method to measured data are addressed as well, and the limitations of a two-dimensional approach are extensively discussed. Tissue-parameter reconstructions of an anatomically correct male head model illustrate the performance of two- and three-dimensional CSI-EPT. We show that 2D implementation only produces reliable reconstructions under very special circumstances, while accurate reconstructions can be obtained with 3D CSI-EPT.

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

Current integral-equation (IE) based MR electrical properties tomography (EPT) methods utilize simulated incident radio-frequency (RF) fields, which are inaccurate and lead to reconstruction errors. To improve the accuracy and practicability of IE-based MR-EPT methods, a new approach is presented that obtains the incident fields using reference subjects and RF field mapping techniques. The Incident field approximation (IFA) is first demonstrated in this paper. This approximation assumes that two imaged subjects with similar coil/subject interactions will have similar incident RF fields, thus one can feed the estimation of the incident fields within the imaged subject into the calculation of those within a homogeneous subject (reference subject). This is done by measuring the total RF fields ( field) of the reference using field mapping techniques, using the known EPs of the reference subject and by rearranging Ampere's Law and the integral equations. The calculated incident RF fields are then used to reconstruct the EPs' distribution with a three-dimensional (3D) integral-based MR-EPT method. Numerical simulation results indicated that the incident RF fields obtained from the reference subject provide accurate 3D reconstruction of EPs with less than 16% root mean square error (RMSE) in noise-free scenario while the conventional IE method had more than 28% RMSE. The phantom-based experiments at 9.4T MRI system have also been conducted to evaluate the performance of the proposed method and the results indicated that the proposed method achieved desirable robustness against the noise in practical scenario with less than 21% RMSE while the conventional differential equation-based method showed worse than 37% RMSE.

3-D Contrast Source Inversion-Electrical Properties Tomography

Contrast source inversion-electrical properties tomography (CSI-EPT) is an iterative reconstruction method to retrieve the electrical properties (EPs) of tissues from magnetic resonance data. The method is based on integral representations of the electromagnetic field and has been shown to allow EP reconstructions of small structures as well as tissue boundaries with compelling accuracy. However, to date, the CSI-EPT has been implemented for 2-D configurations only, which limits its applicability. In this paper, a full 3-D extension of the CSI-EPT method is presented, to enable CSI-EPT to be applied to realistic 3-D scenarios. Here, we demonstrate a proof-of-principle of 3-D CSI-EPT and present the reconstructions of a 3-D abdominal body section and a 3-D head model using different settings of the transmit coil. Numerical results show that the full 3-D approach yields accurate reconstructions of the EPs, even at tissue boundaries and is most accurate in regions where the absolute value of the electric field is highest.