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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. Correspondence: jason.stockmann@yale.edu Poster is available at: http://jasonstockmann.com Gradient localized (GradLoc) parallel imaging using a 3-D magnetic encoding field with a quadratic-phase RF pulse to precompensate for through-slice dephasing 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 x 2 -y 2 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. THROUGH-SLICE DEPHASING Jason P. Stockmann 1, Gigi Galiana 2, and R. Todd Constable 1,2 Yale University, Department of Biomedical Engineering 1, Department of Diagnostic Radiology 2, New Haven, Conn., USA 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 phase- scrambling 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 through- slice (z) direction following RF excitation and then Fourier transforming the resulting signal. 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]. 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 fully- sampled full-FOV image with equivalent voxel size, where R is the k-space undersampling factor. CONCLUSIONS 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 using long TE times [2], [3]. Fig. 1. Phase-scrambled gradient echo sequence Poster #2291 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. 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. 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. 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. Figure 1. (a.) 12 cm dia. gradient insert coil used to generate Z2 field, (b.) transverse slice of quadratic field at 1% of maximum strength, and (c.) a hyperboloidal isocontour corresponding to γG Z2 (x,y,z) = 0. An 8- channel transmit-receive RF array nests inside the gradient coil. ab c d Figure 5. RF coil profiles are obtained from fully-sampled GradLoc images in the 5 cm target ROI of an orange phantom. 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. Performance is limited by the number of spatially- varying RF receive coils in the ROI. Future work: Try using GRAPPA [17] to perform parallel image reconstruction to avoid acquiring fully-sampled coil profile images. Test method on sagittal and coronal slices. Refine RF pulse design 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. Slice phase can be pre-compensated by a quadratic phase slice select RF pulse. 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.

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