Martin Krämer^{1}, Karl-Heinz Herrmann^{1}, Silvio Schmidt^{2}, Otto W Witte^{2}, and Jürgen R Reichenbach^{1,3,4,5}

High
resolution 3D-RARE imaging at 9.4T can be very challenging due to
increased artifacts caused by strong T_{2}-
and Gibbs ringing. In this work, we present the combination of two
correction algorithms, local subvoxel-shift unringing and
T_{2}-compensation,
to reduce effectively both types of artifacts. For this purpose, the
local subvoxel-shift algorithm has been extended to the third spatial
dimension and evaluated in healthy mice.

A
vendor supplied 3D-RARE imaging sequence with 3D-slab selective
excitation and linear ordering of the phase encoding was used as the
basis. The sequence was modified to include a short calibration scan
at the beginning of each measurement with all encoding gradients
turned off, thus essentially sampling the central k-space
line of the whole 3D-slab over the 180° readout train^{4}.
From this calibration data the mean T_{2}-decay
was fitted with an exponential function and used to correct k-space
steps in phase encoding direction in the measured data. In the third
3D-encoding direction no correction was necessary as the RARE module
was only applied in phase encoding direction.

The
algorithm introduced by Keller et
al.^{3}
uses subvoxel-shifts to sample and re-interpolate the Gibbs ringing
pattern at the zero crossings of the oscillating sinc-function.
For application to 2D-data a weighting filter function with a
saddle-like structure in k-space
was introduced which enhances the ringing in the direction in which
unringing is performed, ultimately allowing to perform 1D-unringing
separately in each direction. To apply the algorithm also to 3D-data
the previously presented 2D-k-space weighting filter^{3}
was extended in the third direction:

$$G_x=\frac{1+\cos k_y}{(1 + \cos k_y) + (1 + \cos k_x)} + \frac{1+\cos k_z}{(1 + \cos k_z) + (1 + \cos k_x)}\\G_y=\frac{1+\cos k_x}{(1 + \cos k_y) + (1 + \cos k_x)} + \frac{1+\cos k_z}{(1 + \cos k_z) + (1 + \cos k_y)}\\G_z=\frac{1+\cos k_y}{(1 + \cos k_y) + (1 + \cos k_z)} + \frac{1+\cos k_x}{(1 + \cos k_z) + (1 + \cos k_x)}$$

to reconstruct three modified versions of the original 3D dataset I, in each of which the ringing is enhanced in one of the three spatial dimensions:

$$I_x=FFT^{-1}\{ FFT\{I \} \cdot G_x \}\\I_y=FFT^{-1}\{ FFT\{I \} \cdot G_y \}\\I_z=FFT^{-1}\{ FFT\{I \} \cdot G_z \}$$

After
applying the 1D-unringing described by Keller et
al.
in *x*,
*y*
and *z*
direction the final image is reconstructed by averaging the three
unringed versions of the original image $$$I_{Final}=(I_x+I_y+I_z)/3$$$.
Healthy
mouse brains (male, C57BL/6J, 6 months old) were measured with the
modified 3D-RARE imaging sequence with the following parameters:
240x180x160 encoding matrix, 24x18x6mm FOV, 1600ms TR, 5.3ms echo
spacing, 150kHz acquisition bandwidth and RARE-factor of 20. The
resulting isotropic image resolution was 100µm with TA of 40 minutes
and an effective k-zero
TE of 53ms. Image reconstruction was performed offline with four
different settings: 1) no T_{2}-compensation
and no 3D-unringing, 2) no T_{2}-compensation
and 3D-unringing, T_{2}-compensation
and no 3D-unringing and 4) both T_{2}-compensation
and 3D-unringing. All measurements were performed on a 9.4T Bruker
BioSpec USR-94/20 MR scanner using a 2-channel quadrature cryoprobe.

1. Hennig J, Nauerth A, Friedburg H. RARE imaging: A fast imaging method for clinical MR. Magn Reson Med. 1986;3:823–833

2. de Graaf RA, Brown PB, McIntyre S, Nixon TW, Behar KL, Rothman DL. High magnetic field water and metabolite proton t1 and t2 relaxation in rat brain in vivo. Magn Reson Med. 2006;56:386–394.

3. Kellner E, Dhital B, Kiselev VG, Reisert M. Gibbs-ringing artifact removal based on local sub-voxel-shifts. Magn Reson Med. 2016;76:1574–1581.

4. Zhou X, Liang ZP, Cofer GP, Beaulieu CF, Suddarth SA, Johnson GA. Reduction of ringing and blurring artifacts in fast spin-echo imaging. J Magn Reson Imaging. 1993;3:803–807.

5. JP Mugler III. Optimized Three-Dimensional Fast-Spin-Echo MRI. J Magn Reson Imaging. 2015;39:745-767

Mean
T_{2}
decay obtained from the T_{2}
calibration data (blue) and fit result (red) which was used for
correction of the measured image data.

Coronal
(top row) and transverse (bottom row) slices of the acquired 3D
volume together with zoomed-in portions of the images showing the
original data and the results after applying only unringing or
T_{2}-compensation
as well as applying both together (left to right).