Parameter estimation in fluid flow models from undersampled frequency space data

TL;DR

The paper addresses the challenge of long 4D Flow MRI acquisitions by estimating boundary-condition parameters directly from undersampled k-space data. It introduces a Reduced-Order Unscented Kalman Filter (ROUKF) framework with a k-space data fidelity term to perform sequential, PDE-based parameter estimation, avoiding artifacts from CS reconstructions. Across synthetic aorta and carotid phantom experiments, frequency-space estimation yields higher accuracy than velocity reconstructions, with Gaussian sampling masks generally outperforming spiral masks and the method showing robustness to venc and magnitude assumptions. The work suggests that optimized k-space sampling and direct parameter inference can enable faster, noninvasive, patient-specific hemodynamics with reduced reconstruction bias.

Abstract

4D Flow MRI is the state of the art technique for measuring blood flow, and it provides valuable information for inverse problems in the cardiovascular system. However, 4D Flow MRI has a very long acquisition time, straining healthcare resources and inconveniencing patients. Due to this, usually only a part of the frequency space is acquired, where then further assumptions need to be made in order to obtain an image. Inverse problems from 4D Flow MRI data have the potential to compute clinically relevant quantities without the need for invasive procedures, and/or expanding the set of biomarkers for a more accurate diagnosis. However, reconstructing MRI measurements with Compressed Sensing techniques introduces artifacts and inaccuracies, which can compromise the results of the inverse problems. Additionally, there is a high number of different sampling patterns available, and it is often unclear which of them is preferable. Here, we present a parameter estimation problem directly using highly undersampled frequency space measurements. This problem is numerically solved by a Reduced-Order Unscented Kalman Filter (ROUKF). We show that this results in more accurate parameter estimation for boundary conditions in a synthetic aortic blood flow than using measurements reconstructed with Compressed Sensing. We also compare different sampling patterns, demonstrating how the quality of the parameter estimation depends on the choice of the sampling pattern. The results show a considerably higher accuracy than an inverse problem using velocity measurements reconstructed via compressed sensing. Finally, we confirm these findings on real MRI data from a mechanical phantom.

Figures (19)

• Figure 1: 3D aortic model geometry
• Figure 2: Sampling masks
• Figure 3: Examples of simulated measurements, taken at a slice in the $z$-direction.
• Figure 4: Examples of velocities reconstructed with BART using different masks and acceleration factors. Depending on the sampling mask, different kinds of artifacts appear in the reconstructed velocity.
• Figure 5: Examples of the phantom measurements. Reconstructed magnitudes of the magnetization of different coils show the different coil sensitivities.