Characterization of hemodynamics in the heart and great vessels is useful for quantification of cardiac function and evaluation of pathologies, such as valvular and congenital heart disease. Phase-contrast MRI (PC-MRI) provides volumetric, time resolved images of the hemodynamics within the heart and great vessels in a safe and noninvasive manner; however, clinical application of PC-MRI, when extended to multiple flow directions or volumetric coverage, is limited by long acquisition times¹.An empirical Bayes reconstruction technique is presented, extending through-plane velocity imaging presented previously². The data from all encodings and across all frames are jointly processed to recover a minimum mean squared error estimate of the three-directional velocity map. A mixture prior exploits the correlation across encodings: voxel values are similar across encodings in regions of zero velocity, whereas voxel values differ in phase at voxels with velocity. The Bayes processing provides automated scoring of probability of velocity, via a hidden indicator random variable, to apply this regularizing constraint. We model this velocity indicator variable as a Markov chain. Additional regularization is provided by a sparse prior on non-decimated spatio-temporal wavelet coefficients. VISTA sampling⁴ provides informative k-space samples that are incoherent across space, time, and encodings. Wavelet sub-band weights and Markov chain parameters are self-tuning via expectation-maximization^2,5,6. Belief propagation, accelerated by generalized approximate message passing³ yields fast computation (see Fig 1.).

Data were processed for a digital phantom and five healthy volunteers using ReVEAL; for comparison, the phantom data were also reconstructed using L1 SENSE that processed data from each encoding individually.

Simulation study: A dynamic 120x120 planar digital phantom with 48 temporal frames was simulated using Matlab. Circular receiver coils were simulated using the Biot-Savart law and estimated from the undersampled data. Three-directional flow in a small circular “vessel” was simulated by replicating the image four times and modulating the phase of three of these images, within the vessel, with three distinct time-velocity profiles. All four images contained a slowly, time-varying background phase. Data were simulated using referenced four point encoding and R=12 VISTA sampling. The k-space data were corrupted with complex-valued Gaussian noise. Five velocity time profiles, 12 or 16 coil acquisition, and two phantom configurations were used to create n=20 samples.

In vivo study: Planar images with three velocity encoded directions were similarly reconstructed in five healthy volunteers. Data were acquired using a Siemens Avanto 1.5T scanner with an 18 channel cardiac array and a prospective ECG triggered sequence using referenced 4 point encoding. Scan parameters were TE=2.7ms, TR=4.7ms, two lines per segment for a temporal resolution of 38ms, flip angle 15^o, FOV 320x320mm², matrix size 160x158. The imaging plane was placed above the aortic valve, and each acquisition was repeated 6 times per volunteer. The data were prospectively accelerated by R=8 using VISTA sampling patterns and acquired in 10 heartbeats during a single breath-hold. A 40 ms prescan provided an estimate of measurement noise power used in ReVEAL.

Stroke volume (SV) and peak velocity (PV) estimation errors are reported in Fig. 2 for the n=20 phantom trials. The table displays bias, standard deviation, and Pearson’s coefficient for the estimated flow parameters; also shown are normalized mean squared error on complex-valued images and the SSIM⁷ similarity metric computed on the magnitude and phase images. For both SV and PV, the ReVEAL reconstruction shows significant reduction in both bias and standard deviation, compared to L1-SENSE. Peak velocity correlation coefficient improves from 0.65 to 0.92. In vivo results in Fig. 3 explore repeatability of flow measurements from in vivo ReVEAL reconstructions across six acquisitions per healthy volunteer. Flow parameters were computed in the ascending aorta on a region of interest hand selected, frame by frame, by a board-certified cardiologist.L1 SENSE and ReVEAL utilize the same squared-error data fidelity penalty and spatio-temporal regularization using wavelets, and each method requires a single hand tuned regularization parameter. Both L1 SENSE and ReVEAL are enhanced by the use of optimized VISTA sampling patterns. However, ReVEAL jointly processes the data across the four encoded images to exploit correlations between them. The results shown here are for planar images. The extension to volumetric images, and thus 4D flow, is straightforward. We expect to achieve even higher acceleration rates for 4D flow imaging—potentially enabling 4D flow in a single breath-hold—due to increased spatial correlation and improved SNR in volumetric images.