Iterative Image Reconstruction for PROPELLER-MRI: Through-plane Motion Considerations

Introduction: The PROPELLER family of sequences is characterized by low sensitivity to motion. In PROPELLER, k-space data are acquired in sets of parallel lines that form blades, and each blade is corrected for in-plane motion. Also, “quality” weights are assigned to blades during image reconstruction in order to reduce the effects of k-space errors and through-plane motion on the final image. Recently, an iterative reconstruction method using NUFFT was introduced for PROPELLER MRI, since it is well-known that iterative image reconstruction methods mitigate artifacts that arise from data inconsistencies and minimize image noise by use of regularization strategies. “Quality” weights similar to those used in conventional gridding can also be incorporated in this iterative image reconstruction approach in order to reduce the effects of through-plane motion. The goal of this study was to assess the performance of iterative PROPELLER image reconstruction based on un-weighted and weighted least squares cost functions in the presence of through-plane motion, and compare it to that of conventional gridding. Methods: PROPELLER k-space data acquisitions were simulated using the Shepp-Logan phantom, since its k-space image is known analytically. The simulated k-space sampling pattern contained 32 blades, 20 lines per blade, and 128 samples per line. The simulated field of view in image space was 24cm x 24cm, and an image matrix of 256x256 was selected. The Shepp-Logan phantom is composed of 10 different ellipses. Through-plane motion was simulated by increasing the size of one ellipse for 10 randomly selected blades. Zero mean Gaussian noise was added to the real and imaginary parts of the k-space data to achieve an SNR≅20 inside one of the unaffected ellipses in the image reconstructed with gridding. Images were reconstructed with Quadratic Penalized Least Squares (QPLS) and Quadratic Penalized Weighted Least Squares (QPWLS) iterative reconstruction, and also with gridding. The sampling density compensation function combined with the “quality” weights was used in both gridding and QPWLS reconstruction. Penalty values of {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9} and {1, 2, 3, 4, 5, 6, 7, 8, 9} were used for QPWLS and QPLS iterative reconstruction, respectively. The full-width at half max (FWHM) of the point spread function (PSF) was estimated for gridding, QPWLS and QPLS with each penalty value. The process described above was repeated 100 times. For each reconstruction approach, maps of the difference between the mean of the 100 reconstructed images and the ideal Shepp-Logan phantom were generated, and the mean error per voxel was estimated. Graphs of the mean error per voxel and FWHM of the PSF as a function of the penalty value were produced for both iterative reconstruction techniques, with and without through-plane motion. In addition, PROPELLER k-space data from a healthy human brain were acquired on a 3T GE MRI scanner (Waukesha, WI) using the acquisition parameters mentioned above. In order to simulate through-plane motion, ten randomly selected blades from one slice were replaced with k-space blades from an adjacent slice. The same process was repeated 100 times. Images were reconstructed from the resulting datasets using gridding, as well as QPWLS and QPLS iterative reconstruction. Standard deviation maps were generated and the mean standard deviation over the whole slice was estimated for all reconstruction approaches. Results & Discussion: In the presence of through-plane motion, the mean error per voxel for gridding and QPWLS reconstruction with any penalty value was comparable to the mean error per voxel when no motion was added (Fig.1A). In contrast, the mean error per voxel for QPLS reconstruction significantly increased when through-plane motion was simulated (Fig.1B). Furthermore, when using QPWLS and penalty = 0.2, the mean error per voxel was lower (Fig.1A) and the SNR was approximately 20% higher (Fig.2A,C,D,F) compared to gridding, for only a small increase in FWHM of the PSF (from 2.5mm for gridding to 3.18mm for QPWLS) (Fig.1A). For QPLS with penalty=3, the mean error per voxel was minimum, and lower than that of gridding when no motion was simulated. However, in the presence of through-plane motion the mean error per voxel for QPLS with any penalty value became higher than that of gridding. For both QPWLS and QPLS, the increases in mean error per voxel for very low and very high penalty values were due to Gibbs ringing and excessive smoothing, respectively (Fig.1). Artifacts induced by through-plane motion were visible only in images reconstructed using QPLS (Fig 2). However, the SNR in the selected region of interest was higher when using QPLS compared to gridding or QPWLS. Standard deviation maps of the human brain images reconstructed with the 3 methods showed regions with increased standard deviation when using QPLS (Fig.3). The lowest mean standard deviation across the human brain slice was achieved for QPWLS with a penalty value of 0.2 (Fig.3). In summary, iterative PROPELLER reconstruction with QPWLS minimizes image artifacts due to through-plain motion. It also provides a significant increase in SNR compared to conventional gridding, for only a small reduction in spatial resolution. In contrast, iterative reconstruction with QPLS improves SNR compared to gridding, but does not address the effects of through-plane motion. In conclusion, iterative image reconstruction using NUFFT and QPWLS maintains the low sensitivity to motion of the PROPELLER family of sequences and provides higher SNR than conventional gridding for approximately the same spatial resolution. References: 1) Pipe JG, et al., MRM 2006;55:380-385. 2) Fessler JA, et al., IEEE Trans Signal Proc 2003;51:560-574. 3) Tamhane AA, et al., ISMRM 2007 p.7. GRIDDING QPLS QPWLS