Designing 2D and 3D selective adiabatic pulses
Albert Jang1,2 and Michael Garwood1

1Center for Magnetic Resonance Research and Department of Radiology, University of Minnesota, Minneapolis, MN, United States, 2Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, United States

Synopsis

Two-dimensional (2D) adiabatic pulses based on sampling k-space have previously been developed using amplitude modulation in one orthogonal direction and frequency modulation in the other2. Here, a new method for designing two and three-dimensional adiabatic pulses using a sub-pulse approach is introduced. Namely, a parent adiabatic pulse is divided into sub-pulse elements, each of which is a 2D selective pulse. Using this approach, selective excitation is achieved through the 2D pulse while being adiabatically driven by the parent adiabatic pulse. This can be extended to three-dimensions by applying blips along the remaining direction between sub-pulses. Simulation and experimental results are presented, confirming the validity of this approach.

Introduction

Frequency modulated (FM) pulses have certain benefits over amplitude modulated (AM) pulses, including broadband excitation with low peak power and uniform rotation of magnetization in the presence of extreme B1 inhomogeneity1. A two-dimensional (2D) adiabatic pulse was previously demonstrated in which k-space was sampled using amplitude modulation in one orthogonal direction and frequency modulation in the other2. It was further shown that the quadratic phase of FM pulses such as the chirp and hyperbolic secant (HS1) can be extended to two dimensions by exploiting radial symmetry when sampling k-space. Exploiting the spatiotemporal nature of phase coherence, B1+ compensation was demonstrated3. However, due to being based on the small-tip-angle approximation4, the linear relation between peak B1 and flip angle was limited to within 20°. In this work, we introduce a new method of designing adiabatic pulses in both two- and three-dimensions.

Principle

The design approach utilizes a parent adiabatic pulse that is divided into sub-pulse elements, each of which is a 2D spatially selective pulse. Specifically, an adiabatic pulse, such as an HS1, is discretized and sufficiently oversampled. These sampled elements are then binned into sub-pulse elements. The B1 amplitudes of consecutive pulse elements are modulated by the HS1 amplitude function, whereas the phase of these elements are given by the sum of the 2D pulse and HS1 pulse phases. Between sub-pulses, a blip is inserted to nullify the area accrued under the gradients to re-center k-space for the subsequent sub-pulse element. In the case of using a 2D pulse weighted by a jinc function along a 2D spiral k-trajectory5, the resulting pulse is shown in FIG 1. By selectively exciting using the 2D pulse while driving it adiabatically through the parent adiabatic HS1 pulse, an infinitely long cylinder can be excited to any flip angle until inversion, where it becomes adiabatic. This 2D adiabatic pulse can be extended to three-dimensions by applying blips in the remaining direction between sub-pulses, as will be shown below.

Methods

A 2D HS1 pulse (Tp = 33.28 ms and R = 20) was designed using the method described above. Spiral gradients were time warped to meet slew rate constraints. Bloch simulations were performed to confirm selective excitation and adiabatic inversion. Phantom experiments were carried out on a 90 cm 4T scanner (Varian). Gradients were measured6 and calibrated, followed by modification of the RF pulse based on these measurements for high fidelity. The signals obtained from two gradient echo (GRE) acquisitions, one with the 2D inversion pulse used as a preparation pulse and one without, were subtracted to extract the inversion profile. Finally, in-vivo experiments were carried out on human brain.

Results and Discussion

The cylindrical excitation profile of the 2D HS1 pulse at adiabatic inversion, along with the linear projection of Mz along the middle of the cylinder as a function of resonance offset (Ω) and RF amplitude ω1 (=γB1/2π), both obtained from Bloch simulations, are shown in FIG 2. Similar to the 1D case, the 2D HS1 exhibits both a linear regime and an adiabatic regime. Comparing the phantom images acquired from GRE (FIG 3A) with the inversion profile obtained as described above (FIG 3B), it is apparent uniform selective cylindrical inversion is achieved. The inversion profile obtained by sweeping RF amplitude ω1 and taking a linear projection through the center of the cylindrical inversion (FIG 3C), shows adiabatic property. FIG 4 is a human brain image with 2D HS1 applied prior to slice select in the GRE sequence. As indicated by the black ring, which is the location where Mz is 0 along the wall of the inversion profile, inversion is accomplished. Last, excitation profile of a 3D HS1 pulse along the x-y plane (FIG 5A), x-z plane (FIG 5B), and y-z plane (FIG 5C) obtained using simulations, demonstrates excitation of a finite height cylinder while maintaining adiabatic inversion. To address the long pulse duration inherent to multi-dimensional pulses, we have confirmed through simulations that this can be shortened by segmenting the pulse and using multi-shot excitation.

Conclusion

A new method of designing two- and three-dimensional adiabatic pulses has been introduced. Through simulations, it was shown that using a 2D HS1 pulse, cylindrical selective excitation is achieved with adiabatic inversion. This was further verified through phantom and in-vivo experiments. A 3D HS1 pulse was also demonstrated through simulations in which a cylinder of finite height was inverted with adiabaticity. These pulses have potential applications for use in inner-volume selection, navigation techniques, and for inverting magnetization with inhomogeneous B1.

Acknowledgements

P41 EB015894, S10 RR023730, S10 RR027290, R24 MH105998, AHA 14PRE20380625

References

[1] Garwood M, DelaBarre L. The return of the frequency sweep: designing adiabatic pulses for contemporary NMR. J Magn Reson 2001;153:155–177.

[2] Conolly S, Pauly J, Nishimura D, Macovski A. Two-dimensional selective adiabatic pulses. Magn Reson Med 1992;24:302–313.

[3] Jang A, Kobayashi N, Moeller S, Vaughan J. Thomas, Zhang J, Garwood M. 2D pulses using spatially dependent frequency sweeping. Magn Reson Med 2015, accepted.

[4] Pauly J, Nishimura D, Macovski A. A k-space analysis of small-tip- angle excitation. J Magn Reson 1989;81:43–56.

[5] Pauly J. Stanford University Radiological Sciences Laboratory RF Pulse Design Software. http://rsl.stanford.edu/research/software.html. Published March 1, 2003. Updated April 19, 2015. Accessed April 2, 2015.

[6] Duyn J, Yang Y, Frank J, van der Veen JW. Simple correction method for k-space trajectory deviations in MRI. J Magn Reson 1998;132:150–153.

Figures

FIG 1A: Two-dimensional excitation pulse that employs 2D jinc sub-pulses to selectively excite and a HS1 parent pulse to drive adiabaticity. Magnification of the sub-pulse elements in the dashed box is shown in B. The gradient blips in between sub-pulses used to re-center k-space are indicated by the arrows.

FIG 2A: Adiabatic inversion profile obtained from Bloch simulation shows cylindrical spatial selectivity. B: Sweeping RF amplitude (ω1) and plotting the linear projection through the center of Mz for various offset frequencies along the x-direction (Ωx) exhibit both a linear and adiabatic region.

FIG 3. Comparing GRE image of phantom (A) with inversion profile generated by the 2D HS1 pulse (B) demonstrates selective adiabatic inversion. C: Inversion profile through center of the cylindrical inversion for various RF amplitudes ω1 shows adiabatic property.

FIG 4. In-vivo brain image with pulse applied prior to GRE slice select. The black ring indicates where Mz is 0 along the wall of the inversion profile.

FIG 5. Excitation profile of a 3D HS1 pulse along the x-y plane (A), x-z plane (B), and y-z plane (C) obtained using simulations, demonstrates excitation of a cylinder with finite height while maintaining adiabatic inversion.



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