Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects.

We investigated how to construct low-order subspace basis sets to accurately represent electromagnetic fields generated within inhomogeneous arbitrary objects by radio-frequency sources external to a Huygen's surface. The basis generation relies on the singular value decomposition of Green's functions integro-differential operators which makes it feasible to derive a reduced-order yet stable model. We present a detailed study of the theoretical and numerical requisites for generating such basis, and show how it can be used to calculate performance limits in magnetic resonance imaging applications. Finally, we propose a novel numerical framework for the computation of characteristic modes of arbitrary inhomogeneous objects. We validated accuracy and convergence properties of the numerical basis against a complete analytical basis in the case of a uniform spherical object. We showed that the discretization of the Huygens's surface has a minimal effect on the accuracy of the calculations, which mainly depended on the electromagnetic solver resolution and order of approximation.

Maxwell parallel imaging.

PURPOSE: To develop a general framework for parallel imaging (PI) with the use of Maxwell regularization for the estimation of the sensitivity maps (SMs) and constrained optimization for the parameter-free image reconstruction. THEORY AND METHODS: Certain characteristics of both the SMs and the images are routinely used to regularize the otherwise ill-posed optimization-based joint reconstruction from highly accelerated PI data. In this paper, we rely on a fundamental property of SMs-they are solutions of Maxwell equations-we construct the subspace of all possible SM distributions supported in a given field-of-view, and we promote solutions of SMs that belong in this subspace. In addition, we propose a constrained optimization scheme for the image reconstruction, as a second step, once an accurate estimation of the SMs is available. The resulting method, dubbed Maxwell parallel imaging (MPI), works for both 2D and 3D, with Cartesian and radial trajectories, and minimal calibration signals. RESULTS: The effectiveness of MPI is illustrated for various undersampling schemes, including radial, variable-density Poisson-disc, and Cartesian, and is compared against the state-of-the-art PI methods. Finally, we include some numerical experiments that demonstrate the memory footprint reduction of the constructed Maxwell basis with the help of tensor decomposition, thus allowing the use of MPI for full 3D image reconstructions. CONCLUSION: The MPI framework provides a physics-inspired optimization method for the accurate and efficient image reconstruction from arbitrary accelerated scans.

Computation of ultimate SAR amplification factors for radiofrequency hyperthermia in non-uniform body models: impact of frequency and tumour location.

PURPOSE: We introduce a method for calculation of the ultimate specific absorption rate (SAR) amplification factors (uSAF) in non-uniform body models. The uSAF is the greatest possible SAF achievable by any hyperthermia (HT) phased array for a given frequency, body model and target heating volume. METHODS: First, we generate a basis-set of solutions to Maxwell's equations inside the body model. We place a large number of electric and magnetic dipoles around the body model and excite them with random amplitudes and phases. We then compute the electric fields created in the body model by these excitations using an ultra-fast volume integral solver called MARIE. We express the field pattern that maximises the SAF in the target tumour as a linear combination of these basis fields and optimise the combination weights so as to maximise SAF (concave problem). We compute the uSAFs in the Duke body models at 10 frequencies in the 20-900 MHz range and for twelve 3 cm-diameter tumours located at various depths in the head and neck. RESULTS: For both shallow and deep tumours, the frequency yielding the greatest uSAF was ∼900 MHz. Since this is the greatest frequency that we simulated, we hypothesise that the globally optimal frequency is actually greater. CONCLUSIONS: The uSAFs computed in this work are very large (40-100 for shallow tumours and 4-17 for deep tumours), indicating that there is a large room for improvement of the current state-of-the-art head and neck HT devices.

The ultimate signal-to-noise ratio in realistic body models.

PURPOSE: We compute the ultimate signal-to-noise ratio (uSNR) and G-factor (uGF) in a realistic head model from 0.5 to 21 Tesla. METHODS: We excite the head model and a uniform sphere with a large number of electric and magnetic dipoles placed at 3 cm from the object. The resulting electromagnetic fields are computed using an ultrafast volume integral solver, which are used as basis functions for the uSNR and uGF computations. RESULTS: Our generalized uSNR calculation shows good convergence in the sphere and the head and is in close agreement with the dyadic Green's function approach in the uniform sphere. In both models, the uSNR versus B0 trend was linear at shallow depths and supralinear at deeper locations. At equivalent positions, the rate of increase of the uSNR with B0 was greater in the sphere than in the head model. The uGFs were lower in the realistic head than in the sphere for acceleration in the anterior-posterior direction, but similar for the left-right direction. CONCLUSION: The uSNR and uGFs are computable in nonuniform body models and provide fundamental performance limits for human imaging with close-fitting MRI array coils. Magn Reson Med 78:1969-1980, 2017. © 2016 International Society for Magnetic Resonance in Medicine.