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Velocity spectrum imaging using radial k-t SPIRiT
Journal of Cardiovascular Magnetic Resonance volume 14, Article number: W59 (2012)
Fourier velocity encoding (FVE) [P.R.Moran,MRI(1),1982] assesses the distribution of velocities within a voxel by acquiring a range of velocity encodes (kv) points. The ability to measure intra-voxel phase dispersion, however, comes at the expense of clinically infeasible scan times. We have recently extended [C.Santelli,ESMRMB(345),2011] the auto-calibrating parallel imaging technique SPIRiT [M.Lustig,MRM(64),2010] to exploit temporal correlations in dynamic k-t signal space and successfully applied it to radially undersampled FVE data. Prior assumption of Gaussian velocity spectra additionally allows undersampling along the velocity encoding dimensions [P.Dyverfeldt,MRM(56),2006]. In this work, a scheme is proposed to non-uniformly undersample the kv-axes in addition to undersampling k-t space for reconstructing mean and standard deviation (SD) of the velocity spectra for each voxel in aortic flow measurements.
2D radial (FOV=250mmx250mm) fully sampled cine FVE data of the aortic arch for 3 orthogonal velocity components was obtained from 5 healthy volunteers on a 3T Philips Achieva scanner (Philips Healthcare, Best, The Netherlands) using a 6 element receive array. Three different first gradient moments corresponding to encoding velocities of 25cm/s, 50cm/s and 200cm/s were applied along with a reference point (kv=0). Undersampled radial data sets were obtained by separately re-gridding these 4-point measurements onto Golden-angle profiles (Fig.1a).
The interpolation operator G, enforcing consistency between calibration data from a fully sampled centre of k-space and reconstructed Cartesian k-space points, x, is extended for dynamic MRI by including temporal correlations between adjacent data frames (Fig.1b). Data consistency is imposed using gridding-operator D (Fig.1a). Then, x is recovered by solving the minimization problem in Fig.1d). Reconstruction was performed for every kv-point separately using dedicated software implemented in Matlab (Natick,MA,USA). A 7x7x3 neighborhood in kx-ky-t space was chosen for the k-t space interpolation kernel. The weights were calculated from a 30x30x(nr cardiac phases) calibration area (Fig.1c). Mean and SD of velocity distributions were calculated for the resulting coil-combined images.
Fig.2a) compares the mean root-mean-square error (RMSE) of the reconstructed mean velocities and SDs in the aortic arch for different undersampling factors and for each flow direction (M-P-S). Fig.2b) shows in-plane streamlines reconstructed from the acquired mean velocities and turbulence intensity maps calculated from SD values.
A novel auto-calibrating reconstruction technique for dynamic radial imaging was successfully applied to undersampled 4-point FVE data from five healthy volunteers. Results show that up to 12-fold radial undersampling provides accurate quantification of mean velocities and turbulence intensities derived from velocity spectra.
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Santelli, C., Kozerke, S. & Schaeffter, T. Velocity spectrum imaging using radial k-t SPIRiT. J Cardiovasc Magn Reson 14, W59 (2012). https://doi.org/10.1186/1532-429X-14-S1-W59
- Aortic Arch
- Turbulence Intensity
- Temporal Correlation
- Velocity Spectrum
- Parallel Imaging Technique