Gradient localized (GradLoc) parallel imaging using a 3-D magnetic encoding field
with a quadratic-phase RF pulse to precompensate for through-slice dephasing
Jason P. Stockmann1, Gigi Galiana2, and R. Todd Constable1,2
Yale University, Department of Biomedical Engineering1, Department of Diagnostic Radiology2, New Haven, Conn., USA
PHASE SCRAMBLING PULSES
Spatial encoding magnetic fields (SEMs) with quadratic or
hyperbolic shapes have been proposed for spatial encoding
schemes [1-5], spectral localization [6], and RF excitation of
curvilinear regions [7-9]. Quadratic SEMs have also been used in
Cartesian sequences to “phase scramble” the signal, permitting
unaliased reconstructions with variable fields-of-view (FOVs) using
the Fresnel transform [10-11].
More recently, second-order phase scrambling pulses have been
used to localize signals from a target region of interest (ROI) [12],
offering an alternative to selective RF pulses. Signals are dephased
when the nonlinear SEM applies an extra k-space shift vector to
spins lying outside the ROI, shifting their echo peak outside the
readout window. Gradient localization (GradLoc) has been
experimentally shown using xy and x2-y2 SEMs.
In the present work we extend GradLoc to the case of the “Z2”
spherical harmonic produced by an insert coil originally developed
for O-Space imaging [13] experiments. To achieve this, a quadratic
phase slice-select RF pulse is used to pre-compensate the
through-slice phase applied by the 3-D SEM while retaining the
desired in-plane phase scrambling.
Second, we show the feasibility of
the method using a high-strength
quadratic gradient insert on a 3T
MRI scanner. In previous work
using low-power quadratic shims,
achieving a large quadratic
gradient moment has required Fig. 1. Phase-scrambled
Figure 1. (a.) 12 cm dia. gradient insert coil used
to generate
Z2 field,
gradient
echo sequence
long slice
TE times
[2], [3].field at 1% of maximum strength, and
(b.)using
transverse
of quadratic
(c.) a hyperboloidal isocontour corresponding to γGZ2(x,y,z) = 0. An 8channel transmit-receive RF array nests inside the gradient coil.
Z2 GRADLOC WITH QUADRATIC PHASE
RF SLICE-SELECT PULSES
A quadratic-phase RF “chirp” pulse is designed using the low flip
angle approximation. The target slice profile is a rectangular slab
with quadratic phase equivalent to that applied by the phasescrambling SEM, but with opposite sign.
The Fourier transform is used to calculate an RF pulse that
produces approximately this desired slice profile. The profiles are
measured by playing a dephase-rephase gradient in the throughslice (z) direction following RF excitation and then Fourier
transforming the resulting signal.
Figure 3. Comparison of slice
profiles for a conventional
windowed sinc (left) and
quadratic phase RF pulse
(center). The phase of the
excitation pulse precompensates
the phase applied by the Z2
SEM. Example shown is a 3 mm
slice at z = 0.
PARALLEL IMAGING WITH GRADLOC
GradLoc k-space data can be undersampled just as they are in
Cartesian SENSE [15]. Images are reconstructed with coil profiles
obtained using the adaptive method in [16] from fully-sampled
GradLoc images of the same target ROI in the lower-right
quarter of the object.
SENSE GradLoc acquisition time is 1/(2R) as compared to a fullysampled full-FOV image with equivalent voxel size, where R is
the k-space undersampling factor.
Figure 5. RF coil profiles are
obtained from fully-sampled
GradLoc images in the 5 cm
target ROI of an orange
phantom.
Figure 6. Reference image of (a.)
an orange (256×256, 10 cm FOV)
and (b.) fully sampled GradLoc
image (128×128, 5 cm FOV).
SENSE parallel reconstructions of
under-sampled GradLoc image
are shown with (c.) R=2 and (d.)
R=4 images, for net acceleration
factors of 4 and 8, respectively.
Insufficient coil encoding exists
within the ROI in the R=4 case.
Acquired GradLoc images show the expected dephasing of spins
outside the target ROI. K-space data are filtered prior to Fourier
transformation to reduce artifacts caused by the imperfect
scrambling of spins outside the ROI. GradLoc images show unusual
contrast, since different parts of the image are refocused at
different TEs [12].
a
b
c
d
CONCLUSIONS
• Quandratic phase RF pulses can be used to precompensate
for through-slice dephasing applied by a 3-D SEM phase
scrambling pulse.
• GradLoc and SENSE parallel imaging are combined for an
accelerated acquisition of a target ROI.
THROUGH-SLICE DEPHASING
• For transverse slices, the Z2 SEM varies twice as strongly
through-slice than in-slice, causing severe signal loss [14],
particularly for thick and offset slices.
 Performance is limited by the number of spatiallyvarying RF receive coils in the ROI.
Future work:
• Slice phase can be pre-compensated by a quadratic phase
slice select RF pulse.
 Try using GRAPPA [17] to perform parallel image
reconstruction to avoid acquiring fully-sampled coil
profile images.
Figure 4. GradLoc images of a kiwi with a 4 mm slice thickness and
(a.) 7 cm FOV, (b.) 3.5 cm FOV with the same resolution acquired in half
the time, and (c.) an offset FOV.
 Test method on sagittal and coronal slices.
 Refine RF pulse design
REFERENCES
[1] Hennig J, MAGMA 2008. [2] Pipe J, MRM 1995. [3] Gallichan D, MRM 2011. [4] Stockmann, MRM 2010. [5] Assländer J, ISMRM 2011. [6] Pohmann R, JMR 1999.
[7] De Graaf R, ISMRM 2007. [8] Weber H, ISMRM 2011. [9] Schneider J, MRM 2011. [10] Ito S, MRM 2008. [11] Zaitsev M, ISMRM 2010. [12] Witschey WR, ISMRM
2011. [13] Stockmann J, ISMRM 2011. [14] Galiana G, MRM 2011. [15] Pruessmann K, MRM 1999. [16] Walsh D, MRM 2000. [17] Griswold, MRM 2001.
Figure 2. Signal level (left) degrades with slice offset and slice thickness
when Z2 SEM is used in GradLoc imaging (ROI = FOV/2). To recover the
full signal, a quadratic phase is applied to the slice during RF excitation
in a modified GradLoc gradient echo sequence (right). The GradLoc FOV
is shifted using extra lobes on the X and Y SEMs. For off-center slices, the
extra phase applied by the Z2 SEM is compensated with an adjustment
to the Z slice select SEM pulse.
ACKNOWLEDGEMENTS
The authors wish to thank W Witschey, D Gallichan, A Welz, G Schultz, S Littin, H Weber, C Cocosco, M Zaitsev, and J Hennig at Freiburg University for their insights on
nonlinear SEM encoding.
Grant support comes from NIH BRP R01 EB012289-02.
Correspondence:
jason.stockmann@yale.edu
Poster is available at:
http://jasonstockmann.com
Poster #2291