We present a reduced-order model (ROM) methodology for inverse scattering problems in which the ROMs are data-driven, i.e. they are constructed directly from data gathered by sensors. Moreover, the entries of the ROM contain localised information about the coefficients of the wave equation. We solve the inverse problem by embedding the ROM in physical space. Such an approach is also followed in the theory of ‘optimal grids,’ where the ROMs are interpreted as two-point finite-difference discretisations of an underlying set of equations of a first-order continuous system on this special grid. Here, we extend this line of work to wave equations and introduce a new embedding technique, which we call Krein embedding, since it is inspired by Krein’s seminal work on vibrations of a string. In this embedding approach, an adaptive grid and a set of medium parameters can be directly extracted from a ROM and we show that several limitations of optimal grid embeddings can be avoided. Furthermore, we show how Krein embedding is connected to classical optimal grid embedding and that convergence results for optimal grids can be extended to this novel embedding approach. Finally, we also briefly discuss Krein embedding for open domains, that is, semi-infinite domains that extend to infinity in one direction.

We present an improved multiplicative Contrast Source Inversion (CSI) approach for Electrical Properties Tomography (EPT). In EPT, the conductivity and permittivity profiles of a body part are reconstructed based on a known circularly polarized part of the magnetic field (the B_1^+-field) that has its support inside the body part of interest. The CSI method attempts to reconstruct these profiles in an iterative and alternating manner by first fixing the contrast and updating the contrast source (product of tissue contrast and electric field) and subsequently fixing the contrast source and updating the contrast. In this paper, regularization is included in a multiplicative way similar to the standard multiplicative CSI-EPT method. However, the regularized objective function is different and an update for the contrast is obtained through one-step Jacobi filtering of a least-squares reconstruction that is based on the updated contrast source. Two-dimensional numerical experiments for conductivity and permittivity tissue profiles of a female body model show that, for data with various noise levels, the proposed regularization approach generally provides improved tissue reconstructions compared with standard multiplicative CSI-EPT.

MRI systems have a thin conducting layer placed between the gradient and RF coils, this acts as a shield at the RF-frequency, minimizing noise coupled into the experiment, and decreasing the coupling between the RF and gradient coils. Ideally, this layer should be transparent to the gradient fields to reduce eddy currents. In this work the design of such a shield, specifically for low-field point-of-care Halbach based MRI devices, is discussed. A segmented double layer shield is designed and constructed based on eddy current simulations. Subsequently, the performance of the improved shield is compared to a reference shield by measuring the eddy current decay times as well as using noise measurements. A maximum reduction factor of 2.9 in the eddy current decay time is observed. The segmented shield couples in an equivalent amount of noise when compared to the unsegmented reference shield. Turbo spin echo images of a phantom and the brain of a healthy volunteer show improvements in terms of blurring using the segmented shield.

Objective: Low-cost low-field point-of-care MRI systems are used in many different applications. System design has correspondingly different requirements in terms of imaging field-of-view, spatial resolution and magnetic field strength. In this work an iterative framework has been created to design a cylindrical Halbach-based magnet along with integrated gradient and RF coils that most efficiently fulfil a set of user-specified imaging requirements. Methods: For efficient integration, target field methods are used for each of the main hardware components. These have not been used previously in magnet design, and a new mathematical model was derived accordingly. These methods result in a framework which can design an entire low-field MRI system within minutes using standard computing hardware. Results: Two distinct point-of-care systems are designed using the described framework, one for neuroimaging and the other for extremity imaging. Input parameters are taken from literature and the resulting systems are discussed in detail. Discussion: The framework allows the designer to optimize the different hardware components with respect to the desired imaging parameters taking into account the interdependencies between these components and thus give insight into the influence of the design choices.

Purpose: Concomitant gradient fields have been extensively studied at clinical field strengths. However, their effects have not yet been modeled for low-field point-of-care (POC) systems. The purpose of this work is to characterize the effects associated with concomitant fields for POC Halbach-array-based systems. Methods: The concomitant fields associated with a cylindrical gradient coils designed for a transverse (Formula presented.) and a signal model including the tilting effect of the effective magnetic field are derived. The formalism is used to simulate and predict concomitant field related distortions. A 46-mT Halbach-array-based system with a maximum gradient strength of 15 mT/m is used to verify the model using two-dimensional spin-echo sequences. Results: The simulations and experimental results are in good agreement with the derived equations. The fundamental characteristics of the concomitant field equations are different to conventional MRI systems: Image distortions occur primarily in the transverse directions and a cross-term only exists when applying transverse gradient pulses simultaneously. Conclusion: The level of image warping in the frequency encoding direction is insignificant for the POC systems discussed here. However, when trying to achieve short echo-times by using strong phase encoding and readout-dephasing gradients, the combination can result in image warping and blurring which should be accounted for in image interpretation.

Purpose: High permittivity dielectric pads are known to be effective for tailoring the RF field and improving image quality in high field MRI. Despite a number of studies reporting benign specific absorption rate (SAR) effects, their “universal” safety remains an open concern. In this work, we evaluate the impact of the insulation material in between the pad and the body, using both RF simulations as well as phantom experiments. Methods: A 3T configuration with high permittivity material was simulated and characterized experimentally in terms of B₁⁺ fields and RF power absorption, both with and without electrical insulation in between the high permittivity material and the sample. Different insulation conditions were compared, and electromagnetic analyses on the induced current density were performed to elucidate the effect. Results: Increases in RF heating of up to 49% were observed experimentally in a tissue-mimicking phantom after removing the material insulation. The B₁⁺ magnitude and RF transceive phase were not affected. Simulations indicated that an insulation thickness of 0.5–2 mm should be accounted for in numerical models in order to ensure reliable results. Conclusion: A reliable RF safety assessment of high permittivity dielectric pads requires accounting for the insulating properties of the plastic encasing. Ignoring the electrical insulation can lead to erroneous results with substantial increases in local SAR at the interface. Conversely, the material insulation does not need to be modeled to predict the B₁⁺ effects during the design of the pad geometry.

In this article, we present full-wave signal models for magnetic and electric field measurements in magnetic resonance imaging (MRI). Our analysis is based on a scattering formalism in which the presence of an object or body is taken into account via an electric scattering source. We show that these signal models can be evaluated, provided that Green's tensors of the background field are known along with the dielectric parameters of the object and the magnetization within the excited part of the object. Furthermore, explicit signal expressions are derived in the case of a small homogeneous ball that is embedded in free space and for which the quasi-static Born approximation can be applied. The conductivity and permittivity of the ball appear as explicit parameters in the resulting signal models and allow us to study the sensitivity of the measured signals with respect to these dielectric parameters. Moreover, for free induction decay signals, we show through simulations that, under certain conditions, it is possible to retrieve the dielectric parameters of the ball from noise-contaminated induction decay signals that are based on electric or magnetic field measurements.

Purpose: Parallel RF transmission (PTx) is one of the key technologies enabling high quality imaging at ultra-high fields (≥7T). Compliance with regulatory limits on the local specific absorption rate (SAR) typically involves over-conservative safety margins to account for intersubject variability, which negatively affect the utilization of ultra-high field MR. In this work, we present a method to generate a subject-specific body model from a single T1-weighted dataset for personalized local SAR prediction in PTx neuroimaging at 7T. Methods: Multi-contrast data were acquired at 7T (N = 10) to establish ground truth segmentations in eight tissue types. A 2.5D convolutional neural network was trained using the T1-weighted data as input in a leave-one-out cross-validation study. The segmentation accuracy was evaluated through local SAR simulations in a quadrature birdcage as well as a PTx coil model. Results: The network-generated segmentations reached Dice coefficients of 86.7% ± 6.7% (mean ± SD) and showed to successfully address the severe intensity bias and contrast variations typical to 7T. Errors in peak local SAR obtained were below 3.0% in the quadrature birdcage. Results obtained in the PTx configuration indicated that a safety margin of 6.3% ensures conservative local SAR estimates in 95% of the random RF shims, compared to an average overestimation of 34% in the generic “one-size-fits-all” approach. Conclusion: A subject-specific body model can be automatically generated from a single T1-weighted dataset by means of deep learning, providing the necessary inputs for accurate and personalized local SAR predictions in PTx neuroimaging at 7T.

Low-field MRI scanners are significantly less expensive than their high-field counterparts, which gives them the potential to make MRI technology more accessible all around the world. In general, images acquired using low-field MRI scanners tend to be of a relatively low resolution, as signal-to-noise ratios are lower. The aim of this work is to improve the resolution of these images. To this end, we present a deep learning-based approach to transform low-resolution low-field MR images into high-resolution ones. A convolutional neural network was trained to carry out single image super-resolution reconstruction using pairs of noisy low-resolution images and their noise-free high-resolution counterparts, which were obtained from the publicly available NYU fastMRI database. This network was subsequently applied to noisy images acquired using a low-field MRI scanner. The trained convolutional network yielded sharp super-resolution images in which most of the high-frequency components were recovered. In conclusion, we showed that a deep learning-based approach has great potential when it comes to increasing the resolution of low-field MR images.

In this paper we discuss an imaging method when the object has known support and its spatial Fourier transform is only known on a certain k-space undersampled pattern. The simple conjugate gradient least squares algorithm applied to the corresponding truncated Fourier transform equation produces reconstructions that are basically of a similar quality as reconstructions obtained by solving a standard compressed sensing problem in which support information is not taken into account. Connections with previous one-dimensional approaches are highlighted and the performance of the method for two-and three-dimensional simulated and measured incomplete spectral data sets is illustrated. Possible extensions of the method are also briefly discussed.

Low-field permanent magnet-based MRI systems are finding increasing use in portable, sustainable and point-of-care applications. In order to maximize performance while minimizing cost many components of such a system should ideally be designed specifically for low frequency operation. In this paper we describe recent developments in constructing and characterising a low-field portable MRI system for in vivo imaging at 50 mT. These developments include the design of i) high-linearity gradient coils using a modified volume-based target field approach, ii) phased-array receive coils, and iii) a battery-operated three-axis gradient amplifier for improved portability and sustainability. In addition, we report performance characterisation of the RF amplifier, the gradient amplifier, eddy currents from the gradient coils, and describe a quality control protocol for the overall system.

Three-dimensional contrast source inversion-electrical properties tomography (3-D CSI-EPT) is an iterative reconstruction method that estimates the electrical properties of tissue from transmit field magnetic resonance data. However, in order to bring 3-D CSI-EPT into practice for complex tissue structures and to understand the origin and effect of errors, insight in the sensitivities of reconstruction accuracy to the major error-sources is necessary. In this paper, different strategies for implementing 3-D CSI-EPT, including their iterative structure, are presented, of which the regularized implementation shows the most potential to be used in practice. Moreover, the influence of initialization, noise, stopping criteria, incident fields, B1-maps, transceive phase and domain truncation are discussed. We show that of all these different error-sources, initialization, accurate coil models and domain truncation have the most dramatic effect on electrical properties reconstructions in practice.

In an earlier paper, we generalized the CGME (Conjugate Gradient Minimal Error) algorithm to the ℓ₂-regularized weighted least-squares problem. Here, we use this Generalized CGME method to reconstruct images from actual signals measured using a low-field MRI scanner. We analyze the convergence of both GCGME and the classical Generalized Conjugate Gradient Least Squares (GCGLS) method for the simple case when a Laplace operator is used as a regularizer and indicate when GCGME is to be preferred in terms of convergence speed. We also consider a more complicated ℓ₁-penalty in a compressed sensing framework.

In this paper we present a magnetic resonance imaging (MRI) technique that is based on multiplicative regularization. Instead of adding a regularizing objective function to a data fidelity term, we multiply by such a regularizing function. By following this approach, no regularization parameter needs to be determined for each new data set that is acquired. Reconstructions are obtained by iteratively updating the images using short-term conjugate gradient-type update formulas and Polak-Ribière update directions. We show that the algorithm can be used as an image reconstruction algorithm and as a denoising algorithm. We illustrate the performance of the algorithm on two-dimensional simulated low-field MR data that is corrupted by noise and on three-dimensional measured data obtained from a low-field MR scanner. Our reconstruction results show that the algorithm effectively suppresses noise and produces accurate reconstructions even for low-field MR signals with a low signal-to-noise ratio.

A new local method for magnetic resonance electrical properties tomography (EPT), dubbed transverse-EPT (T-EPT), is introduced. This approach iteratively optimizes the dielectric properties (conductivity and permittivity) and the z-component of the electric field strength, exploiting the locally E-polarized field structure typically present in the midplane of a birdcage radiofrequency (RF) coil. In contrast to conventional Helmholtz-based EPT, T-EPT does not impose homogeneity assumptions on the object and requires only first order differentiation operators, which makes the method more accurate near tissue boundaries and more noise robust. Additionally, in contrast to integral equation-based approaches, estimation of the incident fields is not required. The EPT approach is derived from Maxwell’s equations and evaluated on simulated data of a realistic tuned RF coil model to demonstrate its potential.

Purpose: To learn a preconditioner that accelerates parallel imaging (PI) and compressed sensing (CS) reconstructions. Methods: A convolutional neural network (CNN) with residual connections was used to train a preconditioning operator. Training and validation data were simulated using 50% brain images and 50% white Gaussian noise images. Each multichannel training example contains a simulated sampling mask, complex coil sensitivity maps, and two regularization parameter maps. The trained model was integrated in the preconditioned conjugate gradient (PCG) method as part of the split Bregman CS method. The acceleration performance was compared with that of a circulant PI-CS preconditioner for varying undersampling factors, number of coil elements and anatomies. Results: The learned preconditioner reduces the number of PCG iterations by a factor of 4, yielding a similar acceleration as an efficient circulant preconditioner. The method generalizes well to different sampling schemes, coil configurations and anatomies. Conclusion: It is possible to learn adaptable preconditioners for PI and CS reconstructions that meet the performance of state-of-the-art preconditioners. Further acceleration could be achieved by optimizing the network architecture and the training set. Such a preconditioner could also be integrated in fully learned reconstruction methods to accelerate the training process of unrolled networks.

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.