Claudiu Schirda^{1}

The smoothly varying waveform and sampling that starts at k=0 and the innate property of rewinding periodically to k=0, makes the rosette trajectory achieve the same spatial resolution and spectral bandwidth as other trajectories (EPSI, SSI, CONCEPT) using less than twice gradient strength and slew rate. This makes it an ideal candidate for superresolution MRSI and ultra-high field SI acquisitions.

Interest
in achieving high resolution spectroscopic imaging (SI) is not necessarily new
and research in superresolution^{1} and ultra-high field (UHF, >=7T) MRSI seem
to have produced developments at an increased rate in recent years. Approaches to
high resolution MRSI include using readout gradients that simultaneously sample
the spectral information and one (echo planar EPSI^{2}) or two spatial dimensions
(spiral-SSI^{3}, rosette-RSI^{4}), concentric circles-CONCEPT^{5}), or conventional CSI
with very short TR^{6} and some form of sensitivity encoding. Among
mentioned trajectories, each has its appeal: EPSI samples data on a cartesian
grid with constant sampling uniformity (η=1)
and is the most established, SSI and RSI start acquisition at k=0, making them
more robust to motion^{7}, with SSI being able to achieve up to η=0.97 sampling uniformity, while CONCEPT allows
for easy design of the sampling density function, by choosing number of rings
accordingly^{8}.

Acquiring
data at high (3T) or UHF, is appealing for increasing the SNR. However, for gradient
readout trajectories, this setting brings the additional challenge of having to
reach an increased spectral bandwidth^{9} (SW), demanding the use of increased
gradient strength (Gmax) and slew-rate (SRmax) which, if not addressed, can
result in decreased data quality^{10}. Methods
such as SPICE^{11} (based on EPSI) or dual-density SSI acquisition^{12}, sample the
extended k-space to reach for an in-plane resolution (IPR) of 2.5-3 mm and,
using low-rank denoising, achieve super-resolution^{1}. However, this is done by
pushing the scanner gradient system close to its limits. Temporally interleaving
the trajectories can typically alleviate the hardware demands but results in a
proportional increase in total scan time and it may not always be an option. Thus, the question is, what acquisition trajectory would be more desirable for superresolution MRSI?

To demonstrate the rosette trajectory (k=kmax*sin(2π*f1*t)*exp(1i*2π*f2*t)) capabilities at high Nx, we use Hadamard-RSI^{13} to
scan a BRAINO phantom on a Siemens MR/PET scanner (2.9T) with a 20-channel head-neck
coil (12-channels used), with TR=1s, WET water suppression, 4-slices/averages,
10mm slice thickness, 2mm gap, TE=56.2/45/61.8/50.6ms (inferior to superior), FOV=200mm,
and Nx=100/80/40/20 for IPR=2/2.5/5/10 mm and SW=4.95ppm (610Hz), using Nsh=180/120/60/20
trajectories, rotated by 2π/Nsh to fully sample k-t space, with a maximum
gradient strength Gmax=11.2/9/4.5/5 mT/m and SRmax=30/25/15/25 mT/m/ms (Figure
1). A 1.6min 20x20x4 Hadamard-RSI
acquisition was first validated against 4 individual 20x20 CSI slices with
elliptical encoding at corresponding TEs, 4.2 min each: Bland-Altman 95%
confidence for the (RSI-CSI) difference was within 8.6% of mean. The Nx=100 acquisition
was reconstructed on a 128x128x4x512 matrix and processed with LCModel^{14} in the
4.2-0.2ppm range. For all data sets, the center k-space corresponding to Nx=20 (kmax=.5/cm)
was reconstructed on a 32x32x4x512 grid, and average Crammer-Rao
lower bounds (CRLB) for tNAA/tCr/tCho were compared, after being normalized for
acquisition time.

A single, fully sampled k-t space slice, FOV=240mm, acquisition matrix 96x96 reconstructed to 128x128, SW=575Hz (4.67ppm), TR=1.5s (matching the Nx, SW and TR of the dual-density SSI in Ref. 12) was also acquired in 3.75mins.

No eddy current or trajectory correction or low-rank denoising was used in processing any of the data.

CRLB maps for tNAA for the 12mins 100x100x4 acquisition are shown in Figure 2, with a sample spectrum in Figure 3. Average CRLBs for tNAA/tCr/tCho, were 8.3/9.4/10.2. While these results highlight the high SNR sensitivity of the RSI acquisition, obviously denoising would be needed for in-vivo acquisitions (because of much greater B0 inhomogeneities, etc). The time spent for Nx=100/80/40/20 in the Nx=20 center of k-space can be estimated by multiplying the total acquisition time by 2/π*asin(20/Nx) and is 13/16/33/100%, thus 1.5/1.3/1.3/1.3 mins. The average of the tNAA/tCr/tCho CRLBs normalized to time, relative to the Nx=20 acquisition are 1.06/1.0/0.98 for the Nx=100/80/40 acquisitions. Figure4 shows the common region used for comparison, with sample spectra in Figure5. While the normalized CRLBs show no difference down to IPR=2.5mm (up to Nx=80), the average 6% increase in CRLB for the IPR=2mm (Nx=100) acquisition, suggests the detrimental effect of increased gradient strength is starting to become observable.

The Nx=96, SW=575Hz was acquired with Gmax=8.5mT/m and
SRmax=25mT/m/ms in half the time of a dual-density SSI acquisition^{12}. These numbers are almost one third of the gradient strength of the 22.4mT/m and
one fifth of the slew-rate SRmax=125mT/m/ms used for SSI. While, as implemented, only 17% of the data is
collected in the Nx=16 center k-space, sampling uniformity is η=0.9 across the entire k-space and 100%
of data is used as opposed to having to discarding 41% of time for ramp-down and rewinding (23% SNR penalty).

1. Kasten et al JMR 2016

2. Posse S. et al Radiology 1994

3. Adalsteinsson E et al MRM 1995

4. Schirda et al JMRI 2009

5. Furuyama JK et al MRM 2012

6. Považan M et al Neuroimage 2015

7. Jackson JI et al MRM 1992

8. Hingerl L et al MRM 2018

9. EbelA and Maudsley AA. MRM 2005

10. Kim DH and Spielman DM. MRM 2006

11. F. Lam and Z-P Liang. MRM 2014

12.I. Bhattacharya and M. Jacob. MRM 2017

13. Schirda et al. ISMRM 2015

14. Provencher SW. NMR Biomed 2001

RosetteTrajectories segments for Nx=20/40/80/100 (blue/green/black/red) for one spectral dwell time (spDT=1640ms, corresponding to SW=610Hz)

tNAA CRLB maps for the 12 minute 100x100x4 acquisition, reconstructed to 128x128x4.

Sample spectrum from slice 1

Common region fro comparing the different Nx acquisitions.

Sample spectra for Nx=20/40/80/100 (blue/green/black/red) from the same location (shown in Figure 4, on slice 1)