High resolution 3D-RARE imaging at 9.4T can be very challenging due to increased artifacts caused by strong T2- and Gibbs ringing. In this work, we present the combination of two correction algorithms, local subvoxel-shift unringing and T2-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 train4. From this calibration data the mean T2-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 filter3 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 T2-compensation and no 3D-unringing, 2) no T2-compensation and 3D-unringing, T2-compensation and no 3D-unringing and 4) both T2-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.
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