A Bayesian model for highly accelerated phase-contrast MRI

Abstract

Purpose: Phase-contrast magnetic resonance imaging is a noninvasive tool to assess cardiovascular disease by quantifying blood flow; however, low data acquisition efficiency limits the spatial and temporal resolutions, real-time application, and extensions to four-dimensional flow imaging in clinical settings. We propose a new data processing approach called Reconstructing Velocity Encoded MRI with Approximate message passing aLgorithms (ReVEAL) that accelerates the acquisition by exploiting data structure unique to phase-contrast magnetic resonance imaging.

Theory and methods: The proposed approach models physical correlations across space, time, and velocity encodings. The proposed Bayesian approach exploits the relationships in both magnitude and phase among velocity encodings. A fast iterative recovery algorithm is introduced based on message passing. For validation, prospectively undersampled data are processed from a pulsatile flow phantom and five healthy volunteers.

Results: The proposed approach is in good agreement, quantified by peak velocity and stroke volume (SV), with reference data for acceleration rates R≤10. For SV, Pearson r≥0.99 for phantom imaging (n = 24) and r≥0.96 for prospectively accelerated in vivo imaging (n = 10) for R≤10.

Conclusion: The proposed approach enables accurate quantification of blood flow from highly undersampled data. The technique is extensible to four-dimensional flow imaging, where higher acceleration may be possible due to additional redundancy. Magn Reson Med 76:689-701, 2016. © 2015 Wiley Periodicals, Inc.

Keywords: Bayesian inference; approximate message passing; cardiac MRI; factor graph; flow imaging; minimum mean squared error estimation; peak blood flow; velocity.

Figure 1

A representative set of VISTA sampling patterns for ReVEAL at an acceleration rate of R = 10 with 108 phase encode lines and 20 frames. (a) The VISTA sampling pattern for the compensated data. (b) The VISTA sampling pattern for the encoded measurements. (c) The interleaved encoded and compensated sampling patterns.

Figure 2

The conditional prior distributions used by ReVEAL. (a) The conditional distribution for a velocity-encoded, complex-valued pixel given the corresponding velocity-compensated pixel for velocity-free regions. In this case, the magnitude and phase are constrained. (b) The conditional distribution for a velocity-encoded, complex-valued pixel given the corresponding compensated pixel for velocity-containing regions. Here, only the magnitude is constrained.

Figure 3

The factor graph representation of the joint posterior of PC-MRI data for the proposed model. Message passing on the graph, also known as belief propagation, is a metaphor for an iterative algorithm. By applying the sum-product rule, the update rules for the algorithm can be derived. Computation on the left and right loopy portions are accelerated via GAMP. The center potion of the graph is updated using standard belief propagation.

Figure 4

A summary of retrospectively accelerated in vivo data quality metrics. A fully sampled through-plane image of the ascending aorta was acquired and retrospectively accelerated for rates R = 2, 4, 6, 8, 10, 12, 14, and 16. ReVEAL, ReVEAL no mixture, and k-t SPARSE-SENSE are compared to fully sampled data. (a) The stroke volume in the ascending aorta versus acceleration rate. (b) The peak velocity in the ascending aorta versus acceleration rate. (c) The normalized mean squared error (NMSE) in dB versus acceleration rate. The images used to calculate NMSE were obtained by forming a complex number with magnitude equal to the compensated image magnitude, i.e. |x_b|, and phase equal to the velocity encoded phase, i.e. θ_υ. (d) The structural similarity index (SSIM) (42) for the velocity encoded phase image versus acceleration rate. The phase SSIM measurement was performed only on pixels within the top 95% of magnitude value in the reference image.

Figure 5

Retrospectively accelerated in vivo data reconstructed at R = 12. ReVEAL, ReVEAL no mixture, and k-t SPARSE-SENSE are compared to the fully sampled data for one representative frame. The first column was reconstructed from fully sampled data using the adaptive array combination method (36). The remaining columns were reconstructed from R = 12 accelerated data with ReVEAL, ReVEAL no mixture, and k-t SPARSE-SENSE. (a) The reconstructed, normalized magnitude images. (b) The absolute difference in magnitude between the accelerated images and the fully sampled image. (c) The velocity maps in cm/s. (d) The absolute difference between the fully sampled velocity map and the velocity map recovered from accelerated data. The difference was taken for pixels within the top 90% of magnitude in the reference image to avoid large differences due to low magnitude phase noise.

Figure 6

Representative velocity-time profiles from in vivo data. (a) The mean velocity in an ROI versus time in the descending aorta from retrospectively accelerated in vivo data at R = 10. ReVEAL, ReVEAL no mixture, and k-t SPARSE-SENSE are compared to fully sampled data. (b) The peak velocity in an ROI versus time in the descending aorta from retrospectively accelerated in vivo data. (c) The mean velocity in an ROI versus time in the ascending aorta from prospectively accelerated in vivo data at R = 10. ReVEAL, ReVEAL no mixture, and k-t SPARSE-SENSE are compared to GRAPPA at R = 1.74. (d) The peak velocity in an ROI versus time in the ascending aorta from prospectively accelerated in vivo data.

Figure 7

Prospectively accelerated in vivo data reconstructed at R = 10 and GRAPPA at R = 1.74. ReVEAL, ReVEAL no mixture, and k-t SPARSE-SENSE are compared for one representative frame. (a) The normalized magnitude image. (b) The velocity (phase) map in cm/s. (c) The posterior probability of velocity present in a voxel, in grayscale from 0 (black) to 1 (white). Only ReVEAL provides this time-resolved posterior estimate of velocity locations.