Optimizing high permittivity materials for SAR minimization in transmit arrays: influence of the phase distribution of the excitation profile
Gillian G Haemer1,2,3, Manushka V Vaidya1,2,3, Daniel K Sodickson1,2,3, Graham C Wiggins1,2, and Riccardo Lattanzi1,2,3

1The Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University School of Medicine, New York, NY, United States, 2The Bernard and Irene Schwartz Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, United States, 3The Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, NY, United States

Synopsis

Appropriate high-permittivity, low-conductivity materials placed between the RF coil and the sample can provide performance improvement in both transmission and reception. We employed a simulation framework based on dyadic Green’s functions for multi-layered spherical geometries to analyze how HPMs affect the tradeoff between excitation homogeneity and global Specific Absorption Rate (SAR) for RF shimming at 7T using an L-curves analysis. Three target excitation profiles were analyzed, with uniform amplitude and varied phase, to determine the influence that target phase distribution has on the optimal relative permittivity results.

Purpose

Placing high permittivity, low conductivity materials (HPM) between the radiofrequency (RF) coil and the sample has been proposed as a method for reshaping B1+ fields, independent of RF shimming or parallel transmission1,2,3. HPMs have also been shown to improve both receive sensitivity2,4 and transmit efficiency2,5,6 of RF coils. L-curves analysis has been employed to optimize the relative permittivity of an encircling layer of HPM surrounding the imaging sample7. Specifically, the optimal tradeoff between global SAR and profile fidelity was investigated for different HPMs using Ultimate Intrinsic SAR (UISAR) as a performance reference for a SAR-minimizing RF shimming algorithm8. However, the algorithm constrains the target excitation profile to have flat amplitude and phase throughout the excitation plane, whereas phase-relaxed RF shimming approaches are much more common, and can allow for larger SAR reduction. Relaxing the phase constraint in the algorithm would make SAR minimization a non-convex optimization. Therefore, to investigate the effects that the phase of the target excitation profile has on the optimal relative permittivity of the HPM, we generated L-curves for realistic phase distributions.

Methods

Simulations for a closely-packed 48-coil array geometry9 were performed with a full-wave simulation tool based on dyadic Green’s functions10. The array elements were placed at a 1 cm distance from a uniform spherical phantom (radiussphere = 8.4cm) (Figure 1) with electrical properties of average brain tissue11R = 63, σ = 0.46S/m) at 7 Tesla. The space between the coil and the phantom was filled with HPM, for which conductivity was kept to zero and relative permittivity was varied between 1 and 300. UISAR and global SAR of the array were calculated for three target excitation profiles with uniform amplitude and: flat phase, Gaussian phase, and a CP-like phase (Figure 2). The Gaussian phase distribution was chosen to match a low-field phase profile, while the CP-like phase distribution was chosen to match phase-unconstrained excitation profiles12. All excitations were for a transverse plane through the center of the sphere. The SAR of the array was normalized by the UISAR and plotted as a function of the root mean square error (RMSE) of the achieved excitation profile for various degrees of regularization (i.e., L-curve plots). For each case, the optimal relative permittivity for the HPM layer was chosen based on the proximity of the corresponding L-curve to the origin, and results were compared to the case without HPM.

Results

UISAR for a near perfect excitation (RMSE < .001) was constant for the three phase profiles. UISAR values varied for different phase profiles only for large RMSE (Figure 3). The phase distribution of the target excitation profile did not affect the optimal relative permittivity for the HPM layer, which was εR = 100 for the cases of Gaussian, CP-like, and flat phase (Figure 4). L-curves for optimal HPM show similar performance benefits when compared to the case without HPM for all three phase distributions (Figure 5).

Discussion and Conclusions

Similar coil performance was found for the realistic profile phase distributions and the original flat-phase excitation. Some performance benefit was seen under a case of poor excitation uniformity for the Gaussian phase distribution, similar to what may be expected at lower field strength. However, performance loss was seen under the same conditions for the CP-like phase distribution, which may be explained by a misalignment of the CP-like phase profile with the coil geometry. This and previous work7 suggest that, for a given field strength, the optimal relative permittivity depends mainly on the array geometry. However, since previous work has shown that lower global SAR can be achieved by relaxing the phase constraint13, another explanation could be that the spatial distribution of the phase in a target excitation profile has a smaller effect on coil performance than the constraint of the phase in the RF shimming algorithm. In all cases the target profile amplitude was uniform to investigate the effect of the phases. Future work will include combining realistic phase with smoother distributions of the profile amplitude, which are known to improve coil performance8, and could result in different optimal HPM properties. In addition, to confirm that the choice of the target profile has a minor effect, phase-unconstrained RF shimming optimization will be explored in future work.

Acknowledgements

The Center for Advanced Imaging Innovation and Research (CAI2R, www.cai2r.net) at New York University School of Medicine is supported by NIH/NIBIB grant number P41 EB017183.

References

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[3] Yang QX, Wang J, Wang J, et al. Reducing SAR and Enhancing Cerebral Signal-to-Noise Ration with High Permittivity Padding at 3T. MRM 2011; 65(2): 358-62.

[4] Lattanzi R, Vaidya MV, Carluccio G, et al. Effects of high-permittivity materials on absolute RF coil performance as a function of B0 and object size. ISMRM 2014, Milan, Italy, p4818.

[5] Brink WM, van der Jagt AM, Versluis M, et al. High Permittivity Dielectric Pads Improve High Spatial Resolution Magnetic Resonance Imaging of the Inner Ear at 7 T. MRM 2014; 49(5): 271-7.

[6] Collins CM, Carluccio G, Vaidya MV, et al. High-permittivity Materials can Improve Global Performance and Safety of Close-Fitting Arrays. ISMRM 2014, Milan, Italy, p0404.

[7] Haemer G, Vaidya MV, Collins CM, et al. SAR Reduction in RF Shimming through the use of High Permittivity Materials: approach towards the Ultimate Intrinsic SAR. ISMRM 2015, Toronto, ON, p3105.

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Figures

Figure 1: Excitation geometry, including the coil-only case and the case with HPM. 48 coil geometry packing depicted in relation to the ultimate basis set of currents.

Figure 2: Three target excitation profiles were simulated. The amplitude was constant and equal for all of them. Three phase distributions were implemented: flat, Gaussian, and CP-like.

Figure 3: Ultimate Intrinsic SAR vs. profile fidelity for the three target excitations under RF shimming conditions.

Figure 4: L-curves comparing the flat-phase target excitation (solid lines) to the case (dashed lines) with Gaussian (A) and CP-like (B) phase distributions. Colored lines differentiate relative permittivities of the HPM layer, with values indicated in the legend. The optimal relative permittivity for a given excitation corresponds to the curve most closely approaching the origin.

Figure 5: L-curves for all three excitation profiles, for the cases of εR = 1 (no HPM, or Air) and εR = 100, which is the optimal relative permittivity for all cases (see Figure 4). Results suggest that the phase of the profile has a minor effect on performance.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
3541