A Hybrid Volume-Surface Integral Equation Method for Rapid Electromagnetic Simulations in MRI.

OBJECTIVE: We developed a hybrid volume surface integral equation (VSIE) method based on domain decomposition to perform fast and accurate magnetic resonance imaging (MRI) simulations that include both remote and local conductive elements. METHODS: We separated the conductive surfaces present in MRI setups into two domains and optimized electromagnetic (EM) modeling for each case. Specifically, interactions between the body and EM waves originating from local radiofrequency (RF) coils were modeled with the precorrected fast Fourier transform, whereas the interactions with remote conductive surfaces (RF shield, scanner bore) were modeled with a novel cross tensor train-based algorithm. We compared the hybrid-VSIE with other VSIE methods for realistic MRI simulation setups. RESULTS: The hybrid-VSIE was the only practical method for simulation using 1 mm voxel isotropic resolution (VIR). For 2 mm VIR, our method could be solved at least 23 times faster and required 760 times lower memory than traditional VSIE methods. CONCLUSION: The hybrid-VSIE demonstrated a marked improvement in terms of convergence times of the numerical EM simulation compared to traditional approaches in multiple realistic MRI scenarios. SIGNIFICANCE: The efficiency of the novel hybrid-VSIE method could enable rapid simulations of complex and comprehensive MRI setups.

MARIE 2.0: A Perturbation Matrix Based Patient-Specific MRI Field Simulator.

High static field MR scanners can produce human tissue images of astounding clarity, but rely on high frequency electromagnetic radiation that generates complicated in-tissue field patterns that are patient-specific and potentially harmful. Many such scanners use parallel transmitters to better control field patterns, but then adjust the transmitters based on general guidelines rather than optimizing for the specific patient, mostly because computing patient-specific fields was presumed far too slow. It was recently demonstrated that the combination of fast low-resolution tissue mapping and fast voxel-based field simulation can be used to perform a patient-specific MR safety check in minutes. However, the field simulation required several of those minutes, making it too slow to perform the dozens of simulations that would be needed for patient-specific optimization. In this paper we describe a compressed-perturbation-matrix technique that nearly eliminates the computational cost of including complex coils (or coils and shields) in voxel-based field simulation of tissue, thereby reducing simulation time from minutes to seconds. The approach is demonstrated on a wide variety of head+coil and head+coil+shield configurations, using the implementation in MARIE 2.0, the latest version of the open-source MR field simulator MARIE.

Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications.

In this work, we propose a method for the compression of the coupling matrix in volume-surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic analysis in magnetic resonance imaging (MRI) applications, for which the coupling matrix models the interactions between the coil and the body. We showed that these effects can be represented as independent interactions between remote elements in 3D tensor formats, and subsequently decomposed with the Tucker model. Our method can work in tandem with the adaptive cross approximation technique to provide fast solutions of VSIE problems. We demonstrated that our compression approaches can enable the use of VSIE matrices of prohibitive memory requirements, by allowing the effective use of modern graphical processing units (GPUs) to accelerate the arising matrix-vector products. This is critical to enable numerical MRI simulations at clinical voxel resolutions in a feasible computation time. In this paper, we demonstrate that the VSIE matrix-vector products needed to calculate the electromagnetic field produced by an MRI coil inside a numerical body model with 1 mm3 voxel resolution, could be performed in ~ 33 seconds in a GPU, after compressing the associated coupling matrix from ~ 80 TB to ~ 43 MB.