Rapid Electrodynamic/Analytic Simulations for Coil Design Optimization
Riccardo Lattanzi1

1Center for Advanced Imaging Innovation and Research (CAI2R) and Bernard and Irene Schwartz Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine

Synopsis

Ultimate intrinsic SNR, SAR and TXE can be computed analytically in simple anatomy-mimicking geometries by using a complete set of surface current modes. The performance of RF coil designs with respect to the corresponding ultimate limits can be rapidly calculated within the same analytical simulation framework. Ideal current patterns associated with optimal performance can be also derived and can provide fundamental physical insight into what features are most important in constructing the best possible coil for magnetic resonance.

Target Audience

MR engineers and scientists looking for physical insight into the design of optimal radiofrequency (RF) coil arrays that can approach ultimate intrinsic performance limits.

Outcome/Objectives

This educational talk will review analytical approaches for rapid simulations of RF coil designs. Attendees will learn how the ultimate intrinsic signal-to-noise ratio (SNR), specific absorption rate (SAR) and Transmit Efficiency (TXE) are calculated. They will also learn how to use these absolute metrics for the rational design and assessment of RF coils.

Purpose

Coil optimization has remained a largely empirical process, in part because the complexity of Maxwell’s equations makes it challenging to gain clear intuition about what might constitute a truly task-optimal coil performance. Since time, cost and complexity limit the practicalnumber of prototype arraysthat can be built, simulations are a feasible alternativeapproach to investigate the effect of increasingthe number of coil elements on imaging performance. Nowadays it is common practice to include simulations of the SNR, gfactor, TXE and SAR in the design process.Although effective in improving existing array configurations,this approach does not necessarily aid in developing innovativedesigns and, furthermore, it gives no indication of how well agiven design performs in comparison to the maximumachievable performance.Ultimate performance limits [1-8], independent of the particular coil geometry,are absolute metrics that enable us to predict coil performance in simulation [9,10] or to rigorously assess the performance of actual coil prototypes [11]. Ideal current patterns associated with the best possible performance can be used as a visual guide for high-performance coil design [12,13].

Methods

Numerical simulations with techniques such as the finite difference time domain technique are time consuming and their numerical complexity grows rapidly as the number of modeled coils increases. The duration of these simulations also restricts the number of different coil-sample configurations that can be realistically explored. There is therefore a valuable role for rapid but rigorous electrodynamic simulation approaches that use comparatively simple geometrical models to provide insight into the fundamental dependency of coil performance upon geometrical and physical factors, such as shape and dimensions of the object and the conductors, or electrical properties of the tissues. In this educational talk we will describe a full-wave electrodynamic simulation framework based on dyadic Green’s functions (DGF), which enables to characterize the electromagnetic field in tissue-mimicking dielectric spheres and cylinders [9-12]. The performance of RF coil designs with respect to the corresponding ultimate limits can be rapidly calculated using this DGF approach. Ideal current patterns associated with optimal performance can be also derived within the same simulation framework and used to guide coil design.

Results/Discussion

Approaching ultimate intrinsic performance limits with finite arrays

The SNR of finite arrays in the center of a head-mimicking sphere rapidly approaches the UISNR with increasing number of coils. Array encoding efficiency in terms of gfactor increases with field strength and the number of coils in the array. A 96-element array was found to be almost as efficient as an array with an infinite number of coils in performing 4-fold linear accelerations at 7 T [9]. In the case of a body-mimicking uniform cylinder, at 1.5T and 3T it is possible to approach the ultimate intrinsic SNR for interior regions of the body with finite arrays of loop coils encircling the sample, whereas performance is considerably lower at UHF for the same configuration. Electric dipole can improve performance at UHF, where as few 16 dipoles can outperform 128 loops for a voxel at the center of a body-like object [10]. SNR efficiency at UHF could be improved for both superficial and deep regions by combining loops and dipoles in the same array [10,14].In the case of parallel transmission, global SAR can be maintained within one order of magnitude of the theoretical lower bound using transmit arrays with at least 12 coils. Global SAR for a finite array approaches the ultimate intrinsic limit faster for smaller values of B0. At 3T the SAR resulting from parallel excitation with an 8-element array is already only approximately three times larger than the corresponding ultimate intrinsic SAR and monotonically decreases with the number of transmit coils [5]. Ultimate intrinsic TXE can also be approached more closely by increasing the number of array elements. For example, it was shown that at 7 T a 16-channel transmit array could achieve only 40% of the ultimate intrinsic TXE, whereas the performance with 24 transmit elements was 70% [15].

Physical insight into the fundamental determinants of coil performance

The rate and extent at which the UISNR is approached for a particular geometry and field strength depends less on the number of elements than on its ability to mimic the ideal current patterns. The recently introduced “Optimality Principle” [16] has provided physical intuition about the shapes of ideal patterns, which otherwise arise out of a numerical optimization process. It has been shown that signal contributions from electric dipoles do not “emerge” at UHF strength, but they are always present, at least in cylindrical geometries. However, at low field strength they are masked by noise-optimizing dark modes, which creates closed loops configurations, such as birdcage structures or surface loops, to minimize the electric field. These dark modes become ineffective for deep-lying regions of body-mimicking cylinders at high frequency, for which the non-closed current patterns dominate. The Optimality Principle theory also explained that ideal current patterns are proportional to tangential electric fields, and therefore depend more on the current-carrying surface geometry than on body shape or composition [16].

Conclusion

Ultimate intrinsic SNR, SAR and TXE can be computed analytically in simple geometries by using a complete set of surface current modes, and the corresponding ideal surface current patterns can be derived. The existence of an upper bound, independent of coil array design, on MRI performance may be very useful for coil optimization. The comparison of the ultimate performance with that of a coil array under development, for example, can indicate whether there is room for further improvement and can help in selection of the best design for given field strengths and sample properties. Ideal current patterns can guide the design of RF coils. The complexity and variability of ideal current patterns at high frequency suggest that innovative coil designs may be needed to approach the optimal performance at UHF. The Optimality Principle can explain the shape of ideal current patterns and provide quantitative targets for rational coil design. At the same time, it yields fundamental physical insight into what features are most important in constructing the best possible coil for magnetic resonance.

Acknowledgements

This work was supported in part by NIH R01 EB024536, NSF 1453675, and it was performed under the rubric of the Center for Advanced Imaging Innovation and Research (CAI2R, www.cai2r.net), a NIBIB Biomedical Technology Resource Center (NIH P41 EB017183).

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