Shortening nonlinear phase multiband refocusing pulses with VERSE
Naoharu Kobayashi1, Kamil Ugurbil1, and Xiaoping Wu1

1CMRR, Radiology, University of Minnesota, Minneapolis, MN, United States

Synopsis

Current high resolution, whole brain diffusion MRI protocol at 7T for the Human Connectome Project uses linear phase multiband (MB) refocusing pulses that have duration longer than 10 ms. Recent studies show that shorter duration can be obtained by designing nonlinear phase MB refocusing pulses. In this study, we designed root-flipped MB and hyperbolic secant (HS1) based MB refocusing pulses and investigated how the variable rate selective excitation (VERSE) principle can be used to further reduce the pulse duration. Our results suggest that both root-flipped and HS1 based MB refocusing pulses can be shortened by VERSE.

Purpose

To investigate how the variable rate selective excitation (VERSE) principle1 can be used to further shorten the nonlinear phase multiband (MB) refocusing pulses designed with the root-flipped method2 or using hyperbolic secant (HS1) pulses3.

Methods

We started by designing root-flipped MB refocusing pulses for a peak transmit B1 (B1+) constraint of 13 µT. This was done by using the design tools published by Sharma et al2, and specifying design parameters relevant to 7T high resolution whole brain dMRI acquisitions: MB factor = 3 (MB3), slice thickness = 1 mm, and inter-slice distance = 33 mm (assuming a 108-mm field of view (FOV) covering a medium-sized human brain in an oblique slice direction). The designed MB3 pulse was 8.9 ms in length with a time bandwidth product (TB) of 6 for each single-band pulse component. We then designed two other MB3 refocusing pulses for same slice specifications, but using HS1 pulses3 as single-band components. The first MB3 HS1 pulse was generated to have the same TB of 6 (HS1 TB=6) as the root-flipped pulse, whereas the second MB3 HS1 pulse was designed for a higher TB of 12 (HS1 TB=12). Both MB pulses were formed by adding three 7-ms single-band HS1 pulses and introducing a 0.95-ms time shift in between4 to reduce the otherwise too high peak RF magnitude, resulting in pulse duration of 8.9 ms. All three MB3 pulses were subsequently reshaped by using VERSE1. In our VERSE implementation the time envelope of the input pulse was extracted to modulate the gradient so as to minimize the pulse duration under gradient hardware limitations (maximum amplitude of 70 mT/m and max slew rate of 200 T/m/s) and the peak B1+ constraint. The final pulse duration was 7.4, 4.8 and 8.2 ms for root flipped, HS1 TB=6, and HS1 TB=12 pulses, respectively. The slice profile of each pulse within a 10-cm FOV was simulated assuming uniform initial Mxy and considering crusher gradients. The sensitivity of these post-VERSE pulses was also investigated by imposing a 300 Hz off resonance in the simulation.

Results

While satisfying peak B1+ constraint, all three post-VERSE pulses presented a flatter envelop and shorter duration than their pre-VERSE counterpart (Fig. 1). The VERSE procedure reduced the pulse duration by 17%, 46% and 8% for root flipped, HS1 TB=6 and HS1 TB=12 pulse designs, respectively, with the shortest duration achieved with the HS1 TB=6 pulse design. All three MB3 pulses successfully refocused three 1-mm thick slices at the desired locations (Fig. 2). The slice profile however exhibited different characteristics, with the HS1 TB=6 pulse having least slice sharpness. The HS1 TB=12 pulse design resulted in a sharper slice profile comparable to that of the root flipped pulse. In the presence of off resonance, distortion in slice profile was observed for all three post-VERSE pulses (Fig. 2), with the HS1 TB=12 pulse having less distortion in its slice profile relative to HS1 TB=6 because of its higher bandwidth.

Discussion

We have demonstrated the effectiveness of VERSE in further reducing the duration of nonlinear phase MB refocusing pulses. With a comparable slice profile, the post-VERSE root flipped MB3 pulse was slightly shorter than the HS1 TB=12 pulse (7.4 vs 8.2 ms); this was mostly due to the fact that an effective ripple of 0.01 was allowed in both passband and stopband of the slice profile. Designing another root flipped pulse with no ripples resulted in an increased pulse duration comparable to that of the HS1 TB=12 pulse. The initially designed MB3 pulses exhibit high frequency oscillations (Fig. 1) due to the thin slice thickness and large inter-slice distance specified. Following conventional VERSE approaches by modulating gradient based on each time point of the input pulse requires additional computation time to be spent on smoothing the otherwise too rapidly changing gradient waveform so as to not exceed the maximum slew rate. To overcome this issue, we have decided to reshape the gradient based on the envelope of the input RF pulse. Our results suggest that this VERSE implementation represents an effective while efficient approach to reshaping MB pulses.

Conclusion

The VERSE principle can be applied to further reduce the duration for nonlinear phase MB refocusing pulses designed with the root flipped or HS1 pulse design method while satisfying certain peak RF power constraint.

Acknowledgements

This work is supported by NIH­ grant P41 EB015894.

References

1. Conolly S, Nishimura D, Macowski A. Variable-rate selective excitation. J Magn Reson 1988;78:440-458.

2. Sharma A, Lustig M, Grissom WA. Root-flipped multiband refocusing pulses. Magnetic Resonance in Medicine 2015. DOI:10.1002/mrm.25629.

3. Garwood M, DelaBarre L. The return of the frequency sweep: designing adiabatic pulses for contemporary NMR. Journal of magnetic resonance (San Diego, Calif: 1997) 2001;153(2):155-177.

4. Auerbach EJ, Xu J, Yacoub E, Moeller S, Ugurbil K. Multiband accelerated spin-echo echo planar imaging with reduced peak RF power using time-shifted RF pulses. Magn Reson Med 2013;69(5):1261-1267.


Figures

Fig. 1. Pulse shape of pre-VERSE (top row) and post-VERSE (middle row) nonlinear phase MB3 refocusing pulses, designed with root-flipped (left), HS1 TB=6 (center) and HS1 TB=6 (right) methods. The corresponding reshaped gradient waveforms are shown in the bottom row with the red line being the original constant gradient.

Fig. 2. Slice profile of post-VERSE nonlinear phase MB3 refocusing pulses without (top row) and with (bottom row) off resonance, designed with root-flipped (red), HS1 TB=6 (green) and HS1 TB=12 (blue) methods. Note that the use of a higher vs. lower TB value in HS1 pulse design resulted in sharper slice profile and less slice displacement in the presence of off resonance.



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