Gradient Nonlinearity and B0-induced Distortion Corrections of Prospective Motion Correction Data at 7T MRI

Uten Yarach^{1}, Daniel Stucht^{1}, Hendrik Mattern^{1}, Frank Godenschweger^{1}, and Oliver Speck^{1}

** Data acquisition: **Experiments were performed on a 7T MR (Siemens)
equipped with a 32-channel head coil. The
application of the proposed method to real motion with PMC enabled was performed
using 3D MPRAGE with matrix; 256x256x176, voxel size; 1 mm3, TR/TE/TI;
1800/1.99/1050 ms, and BW; 200 Hz/pixel. After the first half of the
acquisition, the volunteer was instructed to perform a one-time head rotation
around the z-axis. The motion pattern from the tracking log file is shown in figure
1a. The field maps were also
measured before and after motion using dual-echo 3D FLASH with the same
resolution as 3D MPRAGE, TR/TE1/TE2; 10.00/3.06/5.84 ms, and BW; 250 Hz/pixel.

** Image
reconstruction:** We
aimed to obtain the distortion-free PMC MR images () by minimizing the residual sum of squares (Eq. 1) using the Conjugate Gradient (CG) method

$$min_v\left\{∑_{i,j}‖m^{i,j}−M^iFG^i_{reg2warp}C^{i,j}v‖_2^2+λ‖Lv‖_2^2\right\} ----(1)$$

where $$$m^{i,j}$$$ is MR measurement data at pose $$$i$$$ and coil $$$j$$$ which is aligned to a Cartesian grid by PMC. Coil
sensitivity ($$$C^{i,j}$$$) was estimated from the central 64x64x64
k-space data of 3D FLASH (TE1) acquired using a cosine tapper window^{4}, $$$M^i$$$ is a Cartesian undersampling mask
(1=sampled, 0=otherwise), $$$F$$$
is fast Fourier transform. $$$G^i_{reg2warp}$$$ is a 3D regular Cartesian to warped
coordinate operator transferring the image data from regular to warped
coordinate systems. Following the nonuniform FFT (NUFFT) algorithm^{5}, we
implemented the operator using a Kaiser-Bessel
interpolation with optional 2x oversampling. The warped coordinates corrupted
by *GNL* and *∆B _{0}* at any pose $$$i$$$ were prepared prior to solving Eq. 1
using the vendor-provided Spherical Harmonics expansion of the gradient
distortions and the dual-echo field map method

1. Zaitsev M, Dold C, Sakas G, Hennig J, Speck O. Magnetic resonance imaging of freely moving objects: prospective real-time motion correction using an external optical motion tracking system. NeuroImage. 2006; 31: 1038–1050.

2. Bammer R, Aksoy M, Liu C. Augmented generalized SENSE reconstruction to correct for rigid body motion. Magn Reson Med. 2007; 57: 90–102.

3. Pruessmann KP, Weiger M, Bornert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med. 2001; 46: 638–651.

4. Bernstein MA, King KE, Zhou XJ. Handbook of MRI pulse sequences, Elsevier Academic Press, Printed in USA, 2004; p 522–544.

5. Fessler J, Sutton B. Nonuniform fast Fourier transforms using min–max interpolation, IEEE Trans. Sig. 2003; 51: 560–574.

6. Jezzard P, and Balaban RS. Correction for geometric distortion in echo planar images from B0 field variations, Magn Reson Med. 1995; 34: 65–73

7. Hansen PC. Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion. Philadelphia: SIAM; 1998; 247 p.

8. Vogel CR. Non-convergence of the L-curve regularization parameter selection method. Inverse Prob. 1996; 12(4): 535–547.

9. Koch KM, Papademetris X, Rothman D, de Graaf RA. Rapid calculations of susceptibility-induced magnetostatic field perturbations for in vivo magnetic resonance. Phys Med Biol. 2006; 51: 6381–6402.

Fig.1.
(a) The
motion pattern during data acquisition.
(b) The 2x2 undersampled
k-space data reconstructed by the CG-SENSE and the proposed technique. The axial images in the
2nd and 3rd rows correspond to the white lines #1 and #2,
respectively. The sagittal images in the 4th row correspond to the
white lines #3.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

4301