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 inhomogeneity
1. 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 other
2. 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 demonstrated
3. However, due to being based on the small-tip-angle
approximation
4, 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-trajectory
5, 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 measured
6 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 (=γ
B1/2π), 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 14PRE20380625References
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