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. 2016 Jan:262:81-90.
doi: 10.1016/j.jmr.2015.11.010. Epub 2015 Dec 14.

Multiband RF pulses with improved performance via convex optimization

Hong Shang  1 , Peder E Z Larson  2 , Adam Kerr  3 , Galen Reed  4 , Subramaniam Sukumar  5 , Adam Elkhaled  2 , Jeremy W Gordon  5 , Michael A Ohliger  5 , John M Pauly  3 , Michael Lustig  6 , Daniel B Vigneron  2
Affiliations

Multiband RF pulses with improved performance via convex optimization

Hong Shang et al. J Magn Reson. 2016 Jan.

Abstract

Selective RF pulses are commonly designed with the desired profile as a low pass filter frequency response. However, for many MRI and NMR applications, the spectrum is sparse with signals existing at a few discrete resonant frequencies. By specifying a multiband profile and releasing the constraint on "don't-care" regions, the RF pulse performance can be improved to enable a shorter duration, sharper transition, or lower peak B1 amplitude. In this project, a framework for designing multiband RF pulses with improved performance was developed based on the Shinnar-Le Roux (SLR) algorithm and convex optimization. It can create several types of RF pulses with multiband magnitude profiles, arbitrary phase profiles and generalized flip angles. The advantage of this framework with a convex optimization approach is the flexible trade-off of different pulse characteristics. Designs for specialized selective RF pulses for balanced SSFP hyperpolarized (HP) (13)C MRI, a dualband saturation RF pulse for (1)H MR spectroscopy, and a pre-saturation pulse for HP (13)C study were developed and tested.

Keywords: Convex optimization; Generalized flip angle; Improved pulse performance; Multiband; RF pulse design; Shinnar–Le Roux algorithm.

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Figures

Figure 1
Figure 1
(double column) Diagram of the design procedure. The example is of a pulse design for application 1, to design a multiband RF pulse with shortest duration used in bSSFP sequence.
Figure 2
Figure 2
(1.5 column) (A) Multiband arbitrary-phase lactate-only RF pulse (mb-ap-SLR) for bSSFP 13C sequence at 14T with shortest duration is compared to a standard single-band minimum-phase SLR pulse (sb-mp-SLR) (C). For both pulses, Bloch simulations are shown for the magnitude excitation profile in logarithmic scale (B), and linear scale (D). The specification of multiband profile is highlighted in black in (B).
Figure 3
Figure 3
(1.5 column) (A) A multiband arbitrary-phase urea-only RF pulse (mb-ap-SLR) for bSSFP 13C sequence at 14T with shortest duration, is compared to a multiband linear-phase SLR pulse (mb-lp-SLR) (C). For both pulses, Bloch simulations are shown for the magnitude excitation profile (B) and the phase profile adjusted for the linear phase component (D). The specification of the multiband profile is highlighted in black in (B). The arbitrary-phase pulse has peak B1 value of 0.477 Gauss (510 Hz), while the linear-phase pulse has peak B1 value of 1.831 Gauss (1961 Hz).
Figure 4
Figure 4
(1.5 column) (A) Simulated and measured excitation profile of the pyruvate-only pulse plotted with the profile specifications (black lines). For the 3D bSSFP imaging with selective RF pulses on HP 13C phantom at 14T, urea / lactate / pyruvate images are shown after injecting HP urea (B). The same sequence but injecting HP pyruvate is shown in C. One central axial slice of the 3D images is displayed in B and C.
Figure 5
Figure 5
(1.5 column) bSSFP lactate-only RF pulse design with different end-spike (peak amplitude) constraint (A), and the corresponding simulated profiles (B). The pulse in blue is the same as the multiband pulse in Figure 2(A).
Figure 6
Figure 6
(Double column) Dualband saturation pulse for suppression of both water (90°) and glutamine/glutamate/NAA (120°) for 1H MRS at 3T. Pulse waveform (A). Bloch simulation of the saturation profile (B), with the predefined specification highlighted in black. Zoomed in plots of each band (D, E, F). The measured profile agrees well with the simulated result (C).
Figure 7
Figure 7
(1.5 column) (A) Saturation RF pulse with extremely low stopband ripple (mb-ap-SLR) used in HP 13C Lactate study with repetitive pre-saturation pulse, was compared to a standard maximum-phase SLR pulse (sb-mp-SLR) (C). For both pulses, Bloch simulations of the saturation profile are shown for passband (B) and stopband (D). The specification of the multiband profile is highlighted in black in (B, D).
Figure 8
Figure 8
(1.5 column) Bloch simulation of 13C saturation RF pulse profile with non-ideal B1 transmit field calibration. Each profile corresponds to a scaled RF pulse. The profile of optimized pulse with reduced stopband ripple is shown in (A, B), while the maximum-phase SLR pulse profile is shown in (C, D). The passband is visualized in (A, C) with linear scale while the stopband is visualized in (B, D) with log scale. The specification of the multiband profile is highlighted in black.
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