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On the minimum phase control required for B1 shimming
Steven M. Wright1

1Electrical and Computer Engineering, Texas A&M University, College Station, TX, United States

Synopsis

Phase only B1 shimming is a cost-effective and simple approach to improving RF field homogeneity for high field MRI. Without a multiple channel transmitter, this is implemented by switching transmission lines or possibly lumped element phase shift networks. This abstract investigates the minimum phase shift required in a potential multi-bit electronic phase shifter. For practical shimming solutions, those not requiring significant increases in power to achieve a 90 degree tip angle as compared to ‘birdcage’ or conjugate phase currents, it is concluded that 45 degrees may be a sufficient resolution for such a phase shifter.

Introduction

Many approaches to the mitigation of B1 inhomogeneity at high fields have been investigated, including the use Transmit SENSE1-4, B1 shimming using either amplitude and phase or just phase control5,6, dielectric inserts7, and time sequencing of coils8,9. Phase only shimming can be very effective, but is not trivial to implement at high powers without multiple transmitters. We are implementing an electronically controlled phase shifter10 to potentially enable dynamic B1 shimming on systems without multiple channel transmitters. Here we investigate the minimum phase control bit required for a switchable phase shifter to be used for B1 shimming.

Methods

Multi-bit phase shifters can be implemented by switching transmission lines or lumped-element phase delay networks. As each ‘bit’ of phase control adds insertion loss and complexity, it is desirable to use as few bits as possible. We simulated the effectiveness of B1 shimming solutions as a function of the minimum phase control bit employed, φmin. Two models were simulated using in-house developed full-wave FDTD software and optimization programs. One, a 37x26 cm uniform phantom inside a 12 rung volume array, was used for comparison and validation6. The other was a human model exported from a commercial FDTD program. Reference shim solutions in each case used ‘conjugate phase’, where the phases of each rung are adjusted to be in-phase at the center of the optimization region. Phase only optimizations were performed for tip angle homogeneity, with a 90 degree tip at the center of the region of interest (ROI), over different ROIs, with and without constraints on maximum local SAR. For each optimization case examined, the standard deviation (STD) of the tip angle over the ROI, maximum local SAR, and “power factor”, defined as the ratio of the power required to generate a 90 degree tip in the homogeneity region to the power required for the reference conjugate phase currents. Finally, for each case the sensitivity to minimum phase control bit was studied as follows. For each value of minimum phase control bit φmin, a different random phase of +/- φmin/2 was introduced to each rung in the array. 10000 simulations were rung for each value of φmin, and the worst case of tip homogeneity (standard deviation), maximum SAR and power factor were recorded.

Results

Figure 1 compares the tip angle map from the reference conjugate phase determined currents to those obtained from a phase only optimization for homogeneity only, and another solution placing equal “weight” on constraining maximum local SAR. Both provide significant improvement over the reference phases, but removing the constraint on SAR increases the power to achieve a 90 degree pulse by a factor of nearly 30. Adding a constraint on SAR improves the situation dramatically, as seen in Fig. 1c. Figure 2 compares the results of adding 10000 random phase variations for each value of minimum phase control.. As can be seen, the constrained optimization is relatively insensitive to the phase error, while the unconstrained optimization is highly sensitive. Figures 3 and 4 repeat this analysis for another case, optimizing the B1 shim over a 6 x 6 cm circular ROI including the prostate. Figure 3a shows the tip angle map from the reference solution, Fig. 3b the map for a phase only optimization with no constraint on SAR, and Fig. 3c the corresponding map with a weight on SAR minimization. Note that the scale on Fig. 3b has been chosen to highlight the ROI. Figures 4a and 4b repeat the random phase error analysis of Fig. 2 for this model. The dashed lines indicate the tip angle homogeneity (STD) and max local SAR from the reference solution. Again, the unconstrained optimization, aside from being unacceptable due to high power requirements, is highly sensitive to phase error, while the constrained optimization is much less sensitive. Additionally the constrained optimization improves both max local SAR and homogeneity over the region of interest while requiring only 64% more power.

Conclusion

Simulations indicate that a three bit phase shifter with phase bits of 45, 90 and 180 degrees, providing a maximum phase error of +/- 22.5 degrees on any rung, should be sufficient for practical B1 shimming solutions. This may be insufficient for unconstrained optimizations, which would require more accurate phase control. However, unconstrained solutions are likely not practical for high field body MR, the target of this investigation, due to very high power multipliers that result.

Acknowledgements

Support from the Cancer Prevention and Research Institute of Texas through research grant RP160847 is gratefully acknowledged.

References

1. Snyder, C.J., et al., Comparison between eight‐ and sixteen‐channel TEM transceive arrays for body imaging at 7 T. Magnetic Resonance in Medicine, 2012. 67(4): p. 954-964.

2. Hollingsworth, N., et al. An eight channel transmit system for Transmit SENSE at 3T. in Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on. 2011.

3. Zhang, Z., et al., Reduction of transmitter B1 inhomogeneity with transmit SENSE slice‐select pulses. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 2007. 57(5): p. 842-847.

4. Katscher, U., et al., Transmit sense. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 2003. 49(1): p. 144-150.

5. Metzger, G., et al. Local B1 shimming for imaging the prostate at 7 Tesla. in Proc 15th Annual Meeting ISMRM. 2007.

6. van den Berg, B., et al., 7 T body MRI: B 1 shimming with simultaneous SAR reduction. Physics in Medicine and Biology, 2007. 52(17): p. 5429.

7. Haines, K., N. Smith, and A. Webb, New high dielectric constant materials for tailoring the B1+ distribution at high magnetic fields. Journal of magnetic resonance, 2010. 203(2): p. 323-327.

8. Orzada, S., et al., RF excitation using time interleaved acquisition of modes (TIAMO) to address B1 inhomogeneity in high-field MRI. Magnetic Resonance in Medicine, 2010. 64(2): p. 327-333.

9. Thulborn, K.R., et al., SERIAL transmit–parallel receive (STxPRx) MR imaging produces acceptable proton image uniformity without compromising field of view or SAR guidelines for human neuroimaging at 9.4 Tesla. Journal of Magnetic Resonance, 2018. 293: p. 145-153.

10. Sun, C., et al., Digitally Controlled High-Power Phase Shifter for B1 Shimming at 7T. Proc. Intl. Soc. Mag. Reson. Med., 2019, submitted.

Figures

Figure 1. Comparison between optimized and reference currents for a 12 rung array and a 36x27 cm uniform phantom. a) Tip angle (α) map obtained by setting phase of the current on each rung to add in phase at center of region of interest (ROI), denoted by circle. b) Results with phase only optimization, no constraint on SAR. Power requirements increase by a factor of nearly 30 over reference case. c) Results with phase only optimization but with constraint on local SAR. Power requirements increase by 2.4, standard deviation in the ROI is 37% of reference, SARmax increased by 1.6.

Figure 2. Maximum tip angle (α), standard deviation (STD), local SAR­max, and power factor (compared to reference phases) vs. the value of the minimum phase control bit, φmin in a multi-bit phase shifter. For each value of φmin, 10000 simulations were run with a random phase error between +/- φmin/2 applied to each rung. For each φmin, the worst case STD, SARmax and power factor were recorded. For the constrained case the homogeneity remains improved over the reference case (18.6o) even with a φmin of 45o. The unconstrained case requires tight phase control, but is impractical due to power requirements.

Figure 3. Comparison between optimized and reference currents for an eight rung array. a) Tip angle map obtained by setting phase of the current on each rung to add in phase at center of region of interest (ROI), denoted by circle covering the prostate. b) Results with phase only optimization, no constraint on SAR. Power requirements increase by a factor of nearly 24 over reference case. c) Results with phase only optimization but with constraint on local SAR. Power requirements increase by only 1.64, standard deviation in the ROI is 70% of reference, and SARmax is actually decreased by 20%.

Figure 4. Worst case tip angle (α) standard deviation, local SAR­max, and power ratio (compared to reference case) vs. the value of the minimum phase control bit, φmin, for the case shown in Fig. 3. In this case, for the unconstrained optimization, the homogeneity quickly degrades with even a 10 degree minimum phase shift bit for the unconstrained case, but unconstrained optimization is impractical because of the high power required. For the constrained case the homogeneity and the SARmax remains significantly improved over the conjugate phase case even for a minimum phase control bit, φmin, of 45 degrees.

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