Reduced-order modeling of transient electromagnetic fields

Electrical Engineering, Mathematics and Computer Scienc

Low-frequency model-order reduction of electromagnetic fields without matrix factorization

Electrical Engineering, Mathematics and Computer Scienc

Learning a preconditioner to accelerate compressed sensing reconstructions in MRI

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.Circuits and System

Generalized Signal Models and Direct FID-Based Dielectric Parameter Retrieval in MRI

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. Accepted author manuscriptCircuits and System

Modal analysis of photonic and plasmonic resonators

Determining the electromagnetic field response of photonic and plasmonic resonators is a formidable task in general. Field expansions in terms of quasi-normal modes (QNMs) are often used, since only a few of these modes are typically required for an accurate field description. We show that by exploiting the structure of Maxwell’s equations, conjugate-symmetric frequency-domain field expansions can be efficiently computed via a Lanczos-type algorithm. Dominant QNMs can be identified a posteriori with error control and without a priori mode selection. Discrete QNM approximations of resonating nanostructures are presented and the spontaneous decay rate of a quantum emitter is also considered.Circuits and System

Limitations of 2-D Field Structure Assumptions in Electrical Properties Tomography and its 3-D CSI-EPT Solution

CSI-EPT is an Electrical Properties Tomography (EPT) reconstruction method that uses a Contrast Source Inversion (CSI) optimization approach to retrieve the conductivity and permittivity profiles of tissue based on -data. The method can handle variations in tissue profiles and was originally implemented for profile reconstructions in the midplane of a birdcage coil, where the RF field exhibits an E-polarized field structure [1]. Recently, CSI-EPT has been extended to a fully 3-D volumetric reconstruction method that is generally applicable (in- or outside the midplane) and no particular field structure or smoothness is assumed [2]. This is a major step towards turning CSI-EPT into a practical reconstruction method. Unfortunately, the computation times significantly increase (hours or even days, depending on the reconstruction domain of interest) and from this point of view a 2-D approach may be preferable. We show, however, that a 2-D approach is only warranted under very specific circumstances and having an E-polarized field structure is a necessary but not sufficient condition. In particular, we show that to obtain accurate tissue reconstructions based on 3-D -data, it is in general necessary to take all electromagnetic field components into account and a 2-D reconstruction approach will lead to reconstruction artefacts.Circuits and System

Characterization of concomitant gradient fields and their effects on image distortions using a low-field point-of-care Halbach-based MRI system

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.Signal Processing SystemsTera-Hertz Sensin

Radiofrequency safety of high permittivity pads in MRI—Impact of insulation material

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.Signal Processing System

Model-order reduction of electromagnetic fields in open domains

We have developed several Krylov projection-based model-order reduction techniques to simulate electromagnetic wave propagation and diffusion in unbounded domains. Such techniques can be used to efficiently approximate transfer function field responses between a given set of sources and receivers and allow for fast and memory-efficient computation of Jacobians, thereby lowering the computational burden associated with inverse scattering problems. We found how general wavefield principles such as reciprocity, passivity, and the Schwarz reflection principle translate from the analytical to the numerical domain and developed polynomial, extended, and rational Krylov model-order reduction techniques that preserve these structures. Furthermore, we found that the symmetry of the Maxwell equations allows for projection onto polynomial and extended Krylov subspaces without saving a complete basis. In particular, short-term recurrence relations can be used to construct reduced-order models that are as memory efficient as time-stepping algorithms. In addition, we evaluated the differences between Krylov reduced-order methods for the full wave and diffusive Maxwell equations and we developed numerical examples to highlight the advantages and disadvantages of the discussed methods.Circuits and System