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Rapid whole-brain imaging with sub-mm resolution using sampling on tilted hexagonal grids (t-Hex)
Maria Engel1, Lars Kasper1, Franz Patzig1, Bertram Wilm1,2, Benjamin Dietrich1, Laetitia Vionnet1, and Klaas Paul Pruessmann1
1Institute for Biomedical Engineering, ETH Zurich and University of Zurich, Zurich, Switzerland, 2Skope Magnetic Resonance Technologies, Zurich, Switzerland

Synopsis

In this work, we show high-resolution stacks of spirals on a tilted hexagonal grid. The new scheme provides flexibility in balancing readout and scan time, thereby allowing for high-quality images in a temporal resolution regime suitable for fMRI. 0.6 mm whole-brain coverage is achieved in below 5.

Introduction

Rapid MR scanning of 3D volumes is aimed at in applications like fMRI with high spatial and temporal resolution (1). 3D Fourier encoding lends itself to this task: it provides high SNR due to data acquisition from the entire volume, while being amenable to undersampling by optimal parallel imaging acceleration in all three dimensions.
The most widespread and obvious encoding strategies used for this purpose include stacks of EPIs and spirals(2). Each k-space plane is covered by one shot of such a 2D trajectory. However, just like in the 2D case, when aiming for high spatial resolutions, it is not praticable to cover the entire k-space plane within a single shot. For such a long readout train, local field inhomogeneity would introduce severe distortions and blurring in the image. Additionally, the broadening of the PSF due to T2* decay renders the resolution gain more and more inefficient(3).
This challenge is typically met by covering each k-space plane by multiple interleaved shots. However, the overhead for other sequence modules such as RF excitation and spoiling has to be repeated for every shot and makes multiplication in the number of shots unattractive since it entails an increase in the total scan time. This effect is highly undesirable for time-resolved applications such as fMRI.
In this work, we propose to balance readout length and scan-time more flexibly than possible so far, relying on a tilted hexagonal grid (t-Hex) for fast k-space sampling (4,5). We show 0.6mm resolved in-vivo whole-brain images using t-Hex spirals.

Methods

T-Hex: The tilting of the hexagonal grid (6,7) underlying a stack of spirals is shown in Figure 1. Each point with coordinates [f,g] in the oblique coordinate system corresponds to one possibility of tilting the grid. Its distance to the origin determines the TAQ per shot.
Hardware:
  • Philips 7T Achieva system
  • 32 channel head array (Nova Medical)
  • Field camera consisting of an array of 16 1H-based NMR field probes and a dedicated MR acquisition system (8)
Sequence: Spiral k-space trajectories were designed for 0.6x0.6x2 mm3 resolution and whole-brain coverage (FOV= 24x24x12cm3), leading to 86 shots, each of which being 38ms long (Figure 2). A GRE sequence with two different T2*-contrasts was implemented:
  1. TE = 15 ms, TR = 56 ms, Total scan time = 4.8s
  2. TE = 25 ms, TR = 66 ms, Total scan time = 5.7s
Image reconstruction was performed by an iterative cg-SENSE reconstruction (9) extended to 3D, including multi-frequency-interpolation (10,11) for static off-resonance correction and based on the pre-monitored trajectories (12). Off-resonance and coil sensitivity maps were computed from a 3D multi-echo, spin-warp pre-scan (6 echoes, TE 2-7 ms, 2x2x2mm3 resolution).

Results

In Figure 3, scan time is plotted against TAQ per shot. Ideally one would aim for moving towards the lower left corner. Spirals stacked such that forming a hexagonal grid in the cross-section outperform in all resolution regimes conventional stacks (Cartesian grid). T-Hex provides additional flexibility in balancing total scan time and TAQ per shot. Figure 4 and 5 show in-vivo results.

Discussion

The T-Hex spiral for rapid 3D imaging introduced in this work is tailored to sampling less k-space volume than one k-space plane per shot. Just like its kindred t-Hex trajectories (7,4,5) which sample more k-space volume than one k-space plane per shot, it comprises a uniform undersampling, smooth T2* weighting and high average k-space speed. However unlike them, it does not need time-consuming blips and is attractive for the contiguous high-resolution domain. Its main benefit is to gain flexibility, when balancing readout and scan duration. This is especially true for a regime, where few shots per plane are suitable. Beyond that, an integer number of shots per plane is increasingly flexible on its own
To achieve appealing image quality, the reconstruction was based on the expanded signal model described above. Only dephasing in the ear canals and lower brain regions compromises those partially. This effect is mitigated for the shorter TE of 15ms.
The proposed t-Hex trajectory is equally applicable to different sampling schemes such as EPI or spiral-in. It may furthermore prove useful for multiband imaging.

Acknowledgements

No acknowledgement found.

References

1. Feinberg DA, Moeller S, Smith SM, et al. Multiplexed Echo Planar Imaging for Sub-Second Whole Brain FMRI and Fast Diffusion Imaging Valdes-Sosa PA, editor. PLoS ONE 2010;5:e15710 doi: 10.1371/journal.pone.0015710.

2. Poser BA, Koopmans PJ, Witzel T, Wald LL, Barth M. Three dimensional echo-planar imaging at 7 Tesla. NeuroImage 2010;51:261–266 doi: 10.1016/j.neuroimage.2010.01.108.

3. Engel M, Kasper L, Barmet C, et al. Single-shot spiral imaging at 7 T. Magn. Reson. Med. 2018;80:1836–1846 doi: 10.1002/mrm.27176.

4. Engel M, Kasper L, Barmet C, Schmid T, Pruessmann KP. A rapid 3D spiral readout with uniform sampling density and smooth T2* weighting. In: Proceedings of the ISMRM 2018.

5. Engel M, Kasper L, Wilm B, Dietrich BE, Vionnet L, Pruessmann KP. T-Hex: Spiral sampling on a tilted hexagonal grid. In: Proceedings of the ISMRM 2019. ; 2019.

6. Mersereau RM. The Processing of Hexagonally Sampled Two-Dimensional Signals. Proc. IEEE 1979;67:930–949.

7. Engel M, Kasper L, Pruessmann KP. Rapid 3D imaging with multiplanar spirals. Proc. ISMRM 2017.

8. Dietrich BE, Brunner DO, Wilm BJ, et al. A field camera for MR sequence monitoring and system analysis. Magn. Reson. Med. 2016;75:1831–1840 doi: 10.1002/mrm.25770.

9. Pruessmann KP, Weiger M, Börnert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn. Reson. Med. 2001;46:638–651 doi: 10.1002/mrm.1241.

10. Man L-C, Pauly JM, Macovski A. Multifrequency interpolation for fast off-resonance correction. Magn. Reson. Med. 1997;37:785–792 doi: 10.1002/mrm.1910370523.

11. Barmet C, Tsao J, Pruessmann KP. Sensitivity encoding and B0 inhomogeneity – A simultaneous reconstruction approach. In: Proceedings of the ISMRM. ; 2005. p. 682.

12. Barmet C, Wilm BJ, Pavan M, et al. Concurrent higher-order field monitoring for routine head MRI: an integrated heteronuclear setup. In: Proceedings of the 18th Annual Meeting of ISMRM, Stockholm, Sweden. ; 2010. p. 216

Figures

a)Conventional stack of spirals b)Gray dots depict part of the hex. grid – transverse section of stack (box in a)). Green dots mark the revolutions acquired within 1 shot for 1, 2 & 3 shots being used per kspace plane. c)The hex. grid is described by oblique coord. f & g. All existing distances between grid points are represented in distances of the origin to points in 1 duodecant (yellow wedge) including its edges. Green rings mark dist. reflected in b), the red one highlights a dist. not covered by these. It is used when tilting the grid as show in d) with respect to the rotational axis of the stack.

A) T-Hex stack of spirals cut open. The uppermost shot is marked in dark green. The hexagonal grid shows the tilt as visualized in Fig. 1d). B) Cross-section corresponding to stack in A), colour-coded is the acquisition time point, indicating a smooth T2* filter. Owing to the cross-sectional depiction, “holes” appear on the central k-space axis. In fact, this region is equally uniformly sampled, since all spirals start from the rotational axis of the cylinder.

For three in-plane resolutions, the acquisition time for different stacks of spirals was computed and plotted against their total scan time. The latter comprises an overhead of 13ms per shot, accounting for typical slab excitation, fat suppression and spoiling modules. Cartesian and hexagonal grids were chosen such that they correspond to the same ellipsoid FOV in image domain.

Images acquired with t-Hex spiral-out as depicted in Fig.2. The whole brain is covered with 0.6x0.6x2mm3 resolution in 4.8s, TE = 15ms. Red lines mark theposition of the shown slices.

Images acquired with t-Hex spiral-out as depicted in Fig.2. The whole brain is covered with 0.6x0.6x2mm3 resolution in 5.7s, TE = 25ms. The upper row shows magnitude images of thre selected slices, the bottom row the corresponding phase images.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)
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