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Fast field analysis for complex coils and metal implants in MARIE 2.0
Georgy D. Guryev1,2, Athanasios G. Polimeridis3, Elfar Adalsteinsson1,4,5, Lawrence L. Wald5,6,7, and Jacob K. White1

1Dept of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, United States, 2CDISE, Skolkovo Institute of Science and Technology, Moscow, Russian Federation, 3Q Bio, Redwood City, CA, United States, 4Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, United States, 5Harvard-MIT Division of Health Sciences Technology, Cambridge, MA, United States, 6Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Athinoula A. Martinos Center for Biomedical Imaging, Charlestown, MA, United States, 7Harvard Medical School, Boston, MA, United States

Synopsis

When multicoil transmit arrays are used in high field scanners, patient-specific optimization can improve image quality and increase safety margins, particularly for patients with implants. The feasibility of performing such optimizations in real-time was demonstrated recently[5], using a combination of fast tissue mapping and voxel-based field simulation[4], but only for a single-port coil and an implant-free patient. In this abstract we describe new techniques for simulating complex coils that accelerates MARIE simulation as much as an order of magnitude, and an efficient approach to including metal implants. We demonstrate field analysis in minutes using the open-source simulator MARIE2.0.

Introduction

When multi-coil transmit arrays are used in high field scanners, patient-specific optimization can improve image quality and increase safety margins, particularly for patients with implants. Such optimizations could become an important part of clinical practice, but only if they can be completed in a few minutes, and do not require the patient to spend much additional time in the scanner. The feasibility of several-minute patient-specific optimization was demonstrated recently, by combining a fast tissue mapping algorithm[5] with the voxel-based field simulator MARIE[4]. But the demonstration only considered a single-port coil and an implant-free patient, because otherwise, field simulation would have taken far too long. In this abstract, we present three new techniques that are part of MARIE2.0, two that reduce the cost of simulating complex coils by as much as an order of magnitude, and an approach to simulating metal implants that has only a marginal impact on simulation time.

Methods

One major computational bottleneck in MARIE is associated with its explicit representation of the interaction between the discretized elements of complex radio-frequency coils (thousands of elements) and the voxels in a realistic human body model (millions of voxels). The associated thousands by millions dense matrix is expensive to compute, difficult to store, and expensive to apply. In MARIE2.0, the coil-tissue coupling is represented implicitly, by first representing the coils with nearby voxels, and then using the FFT to compute the translation invariant interaction between voxels. More specifically, the implicit coupling approach consists of four main steps: 1) the projection of fine RF coil structures on the extended uniform gird (see Figure 1); 2) solve the coupled EM problem on a uniform voxelized grid; 3) precorrecting the volumetric solution with the directly evaluated components for near interactions and 4) project volumetric solution back to the coil structure.

Unnesting the Iteration

Another important aspect tightly connected to the previous problem is that the dense matrix-vector product with a coupling matrix becomes the most computationally demanding operation after the simulation setup is assembled. In modern software packages this issue is address by decomposing the full problem onto tissue and the coil-related ones, where for each outer coil iteration one had to solve the full body problem for a given coil excitation. This technique reduces the cost of the matrix-vector product (MVP) with a large dense coupling matrix by performing those on the outer iterations only. This approach dramatically increases the overall iteration count for the entire domain analysis, and leads to extended simulation times. Instead, the implicit representation of the coupling matrix is exploited, by unfold the nested iterations and solving for the fields in the coil and the body simultaneously without incurring penalties associated with a dense matrix. Thus, the unfolded iterations with appropriate preconditioning dramatically reduces the total number of iterations and in turn result in shorter simulation times.

Results

The comparison of the simulation times between MARIE and MARIE 2.0 are summarized in Figures 2-3, while the detailed runtime breakdown is provided in table 1. It is worth to note that the proposed framework is especially beneficial for bodies located reasonably close to the complex RF coil geometries. A careful consideration is required when using the framework with distant RF coils, since there appears a tradeoff between total iteration count and a cost per iteration due to increased FFT domain.The preliminary results of EM simulation with implants are show in Figure 5, note the impact of the metal implant. Simulation time differences with and without the implant are negligibly different.

Acknowledgements

The authors graciously acknowledge the support of the Skolkovo Institute of Technology Next Generation Program.

References

  1. J.R. Phillips et al.(1997)."A precorrected-FFT method for electrostatic analysis of complicated 3-D structures", IEEE TCAD, Vol.16:1059 - 1072
  2. Villena, Jorge Fernández, et al.(2016)."Fast electromagnetic analysis of MRI transmit RF coils based on accelerated integral equation methods." IEEE Trans. on Bio. Eng. 63.11 : 2250-2261.
  3. Bleszynski, E., et al.(1996)."AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems." Radio Science 31.5: 1225-1251.
  4. Villena, Jorge Fernandez, et al.( 2015.). "MARIE–a MATLAB-based open source software for the fast electromagnetic analysis of MRI systems." ISMRM Proceedings
  5. E. Milshteyn et al. (Abstract for ISMRM 2019). "Individualized SAR Calculations Using Computer-Vision-Based MR Segmentation and a Fast Electromagnetic Solver"

Figures

The figure depicts the uniform volumetric expansion basis for a given pair of triangles. The coupled system is solved for the interaction between the expansion basis and the body model

The MARIE2.0 speedup over MARIE achieved several RF coil geometries and body models. The largest speedup is achieved in the case a large body model and a refined coil discretization.

The breakdown of the simulation times for the 5mm Duke body model and the 16-Leg Birdcage RF coil. From the table follows that the coupling matrix assembly becomes the most time consuming part of simulation for large models.

The breakdown of the simulation times for the 4mm Billie body model and the 16-Leg Birdcage RF coil.

The preliminary results of implant simulation. The strait conducting strip is located inside a homogeneous sphere; the system is excited with a plane wave. The lower graphs depict Electric field distribution.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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