Benedikt A Poser^{1}, Berkin Bilgic^{2}, Borjan A. Gagoski^{3,4}, Kâmil Uludağ^{1}, V Andrew Stenger^{5}, Lawrence L Wald^{2,6,7}, and Kawin Setsompop^{2,6}

wave-CAIPI allows for high undersampling factors and hence acquisition speed-up in anatomical imagines sequences including 3D GRE, 2D SMS-TSE and MP-RAGE (3D TFL). The coil array’s full 3D sensitivity encoding is exploited, resulting in negligible g-factor penalties even in highly accelerated scans. Echo-planar imaging (EPI) sequences, both 2D and 3D EPI with Cartesian blipped-CAIPI have recently brought tremendous speed-up to BOLD and diffusion imaging in the neurosciences. We here explore the potential of going beyond blipped-CAIPI EPI by incorporating sinusoidal z- and y- gradient wave perturbations into the EPI readout. Initial results are shown for 3D wave-CAIPI EPI at 7T.

**Introduction**

*Wave-CAIPI EPI sequence: *Three considerations complicate the implementation: (1)
typical readout duration (echo spacing) is below 1ms (depending on spatial
resolution and matrix size); this imposes significant time and slew-rate
constraints on the waves (number of wave cycles, wave amplitude); (2) The
alternating readout gradient requires a polarity reversal of the cosine wave (an
even function) for alternate echoes; (3)
The regular uni-directional EPI phase encoding blips must be accommodated, most
economically into the ramp-up/ramp-down of the alternating cosine wave. The
waves were incorporated into an in-house 3D CAIPI EPI sequence [8,13] shown in Figure
1.

*Data acquisition:* Phantoms and N=3 human volunteers were scanned on a Siemens Magnetom 7T (32ch head coil, 70/200 body
gradient). All
imaging and CAIPI parameters are summarized in Figure 2.

*Wave-CAIPI reconstruction: *is extended to allow
different point spread functions (psfs) for even and odd k-lines and to enable
N/2 ghost correction. This will help address differences in corkscrew
trajectory due to polarity reversal between alternating lines. The reconstruction then solves the system,

(see Fig 3)

where ρ is the unknown image, *k _{e}*
and

Both the ghost term and even/odd psfs are estimated from the undersampled data without calibration measurement. This is achieved by a model reduction that summarizes the ghost model in 2, and psfs in 4 coefficients per y and z gradient axis, thus requiring estimation of only 10 numbers. These unknowns can then be simultaneously optimized with the parallel imaging reconstruction as per [14].

**Results and Discussion**

Successful wave-CAIPI
reconstructions were achieved for the 4x2 and 4x4 accelerated data, shown in
Figure 4. No CAIPI shift was used in this case. Improved reconstruction can be
noted in the 4x4 case, where in the central regions the wave sampling results
in lower residual artifact. This agrees with expectations, since the wave
gradients reduce the g-factor penalty by spreading the alias across the FoV
(Figure 5). Introducing CAIPI blips in addition to the waves will result
in further improvement.

As g-factor reduces with larger wave gradient moments, the application of stronger wave gradients will further improve the reconstruction. In particular, the use of head gradient systems will allow for a more significant sine/cosine perturbation during the short EPI readout (c.f. Fig 2).

wave-CAIPI EPI was here showcased for 3D EPI, but is directly applicable to 2D SMS EPI, owing to the direct 3D k-space analogy between the two [15,16]; SMS EPI will be explored next.

1. Bilgic B, Gagoski BA, Cauley SF, Fan AP, Polimeni JR, Grant PE, Wald LL, Setsompop K; Wave-Caipi for Highly Accelerated 3D Imaging; Mag Res Med, 2015; 73(6):2152-2162

2. Gagoski BA, Bilgic B, Eichner C, Bhat H, Grant PE, Wald LL, Setsompop K; RARE/Turbo Spin Echo Imaging with Simultaneous MultiSlice Wave-CAIPI; Mag Res Med, 2015; 73(3):929-38;

3. Polak D, Setsompop K, Cauley SF, Gagoski B.A, Bhat H, Maier F, Bachert P, Wald LL, Bilgic B; Wave-CAIPI for Highly Accelerated MP-RAGE Imaging; ISMRM 2017, submitted.

4. Breuer FA, Blaimer M, Heidemann RM, Mueller MF, Griswold MA, Jakob PM. Controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) for multi-slice imaging. Magn Reson Med; 2005;53 (3):684–691.

5. Breuer F, Blaimer M, Mueller MF, Seiberlich N, Heidemann RM, Griswold MA, Jakob PM. Controlled aliasing in volumetric parallel imaging (2D CAIPIRINHA). Magn. Reson. Med. 2006;55.3:549–556.

6. Breuer F, Moriguchi H, Seiberlich N, Blaimer M, Jakob PM, Duerk JL, Griswold MA. Zigzag sampling for improved parallel imaging. Magn. Reson. Med. 2008;60.2:474–478.

7. Feinberg DA, Moeller S, Smith SM, Auerbach EJ, Ramanna S, Glasser MF, Miller KL, Ugurbil K, Yacoub E. Multiplexed Echo Planar Imaging for Sub-Second Whole Brain FMRI and Fast Diffusion Imaging. PLoS One. 2010; 5(12): e15710

8. Poser BA, Koopmans PJ, Witzel T, Wald LL, Barth M. Three dimensional echo-planar imaging at 7 Tesla. Neuroimage 2010;51:261-6.

9. Setsompop K, Gagoski B, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced gfactor penalty. Magn. Reson. Med. 2012;67:1210–1224.

10. Setsompop, K., Cohen-Adad, J., Gagoski, B. A., Raij, T., Yendiki, A., Keil, B., Wedeen, V.J., Wald, L. L. (2012). Improving diffusion MRI using simultaneous multi-slice echo planar imaging. NeuroImage, 63(1), 569-580.10.1016/j.neuroimage.2012.06.033

11. Ivanov, D., Poser, B. A., Huber, L., Pfeuffer, J., & Uludag, K. (2016). Optimization of simultaneous multislice EPI for concurrent functional perfusion and BOLD signal measurements at 7T. Magn Reson Med. 10.1002/mrm.26351

12. Huber, L., Ivanov, D., Guidi, M., Turner, R., Uludag, K., Moller, H. E., & Poser, B. A. (2016). Functional cerebral blood volume mapping with simultaneous multi-slice acquisition. NeuroImage, 125, 1159-1168. doi: 10.1016/j.neuroimage.2015.10.082

13. Poser AB, Ivanov D, Kemper VG, Kannengiesser SA, Uludag K, Barth M. CAIPIRINHA-accelerated 3D EPI for high temporal and/or spatial resolution EPI acquisitions. ESMRMB congress, Toulouse, 2013

14. Cauley, S. F., Setsompop, K., Bilgic, B., Bhat, H., Gagoski, B., & Wald, L. L. Autocalibrated wave-CAIPI reconstruction; Joint optimization of k-space trajectory and parallel imaging reconstruction. Magn Reson Med. 2016; DOI: 10.1002/mrm.26499

15. Zahneisen, B., Ernst, T., & Poser, B. A. (2015). SENSE and simultaneous multislice imaging. Magn Reson Med, 74(5), 1356-1362.

16. Zahneisen, B., Poser, B. A., Ernst, T. E., & Stenger, V. A. (2013). Three-dimensional Fourier Encoding of Simultaneously Excited Slices: Generalized Acquisition and Reconstruction Framework. Magn Reson Med, Magn Reson Med. 2014 Jun;71(6):2071-81

Wave-CAIPI
EPI with blip-2 CAIPI and 2 waves per readout. Top four plots: regular CAIPI
EPI sequence with readout, phase-encoding, and CAIPI blips on the partition encoding.
The plots below show the phase- and partition- encode after incorporating cosine and sine waves, respectively. If AfPe>AfPa, the PE-prewinder applies CAIPI ky-shifts, instead of kz blips. The zoom in (B) shows how PE-moments are realised by small ‘flat tops’ at either
end of the negative cosine wave: permissible Y-wave amplitudes are hence
coupled to the required PE-moment (FoV, AfPe), next to time and slew-rate constraints. Panel (C) shows a schematic wave-CAIPI
pattern.

Overview of the 7T CAIPI
and acquisition parameters used in the study. Conservative wave amplitude and
slew rate limits were set in the sequence, using 50mT/m respectively 170mT/m/ms
on the 7T scanner (SC72 body gradient); this corresponds to approximately 80% of the available gradient performance.

The system solved for the psf estimation, in the extension of the method to allow for N/2 ghost correction by separately solving for the psf on the odd and even readouts.

Top: Reconstruction
result of the 4x2 accelerated scan with 1.5mm isotropic
resolution, showing regular 4x2 undersampling, and the same scan protocol with 2-cycles
of cosine (Y-axis, 7.2/145) and sine (Z-axis, 8.5/170) waves applied during the
readout gradient. For detailed scan parameters see Fig.2.
Bottom: Reconstruction of the 4x4 accelerated scan with and without wave gradients. Application
of the wave gradients here leads to considerable improvement in the reconstruction
especially in the center of the brain, where the Cartesian 4x4 undersampling
results in considerable pile-up of aliasing signal and hence large g-factor
penalties (see Fig 5)

1/g-factor maps for the 4x4
undersampled scan without (top) and with (bottom) wave gradients. Average
g-factor for the regular undersampling is 2.68, and this reduces to 2.27 in the
presence of wave modulation to spread the alias along the readout. Shown on the
bottom right is the 1/g-factor
simulation for the case that the slew rate is doubled, which approximately
corresponds to utilizing 100% gradient performance on a head gradient set; here
the average g-factor is reduced to 1.8.