Neural Fields for Highly Accelerated 2D Cine Phase Contrast MRI

TL;DR

This work tackles the slow acquisition in 2D cine phase-contrast MRI by proposing implicit neural representations (neural fields) that jointly model magnitude $r$ and velocity-encoding phases $\varphi^0,\varphi^1$ for two velocity-encoded echoes. The neural field provides a continuous spatiotemporal parametrization $\Phi_{\theta}$ that reconstructs $u^0$ and $u^1$, enforcing echo coupling and phase consistency within a single variational objective; a voxel-based postprocessing step with regularization $\lambda_{\text{Hyb}}$ mitigates oversmoothing while preserving temporal coherence. The method is validated on Cartesian and radial k-space data across high and low temporal resolutions, achieving accurate reconstructions at up to $64\times$ undersampling for high temporal resolution and $16\times$ for low temporal resolution, consistently outperforming locally low-rank voxel-based baselines in flow and anatomy depiction. These results suggest substantial potential for reducing scan times in CPC MRI while maintaining reliable velocity estimation, with extensions to non-gated and 4D CPC MRI on the horizon.

Abstract

2D cine phase contrast (CPC) MRI provides quantitative information on blood velocity and flow within the human vasculature. However, data acquisition is time-consuming, motivating the reconstruction of the velocity field from undersampled measurements to reduce scan times. In this work, neural fields are proposed as a continuous spatiotemporal parametrization of complex-valued images, jointly modeling magnitude and phase across multiple echoes to enable velocity estimation, and leveraging their inductive bias for the reconstruction of the velocity data. Additionally, to compensate for the oversmoothing tendency observed in neural-field reconstructions under severe undersampling, a simple voxel-based postprocessing step is introduced. The method is validated numerically in Cartesian and radial k-space with both high and low temporal resolution data. This approach achieves accurate reconstructions at high acceleration factors, with low errors even at 32$\times$ and 64$\times$ undersampling for the high temporal resolution data, and 16$\times$ for the low temporal resolution data, and consistently outperforms classical locally low-rank regularized voxel-based methods in both flow estimates and anatomical depiction.

Figures (13)

• Figure 1: Retrospective variable-density and radial undersampling at factor 16$\times$. K-space lines are shown for two echoes at two different frames. The schemes ensure that different frequencies are sampled per echo at the same frame.
• Figure 2: Reconstruction results on Experiment 1 at an acceleration factor of 32$\times$. Images are zoomed in on the region of interest. Frame 30 is displayed for the $xy$ view. This is the frame where the neural field cannot capture the negative peak in the mean velocity. PSNR for the zoomed-in spatiotemporal scene and 2-norm relative error of the flow are also shown. Velocity maps are masked to the aorta region.
• Figure 3: Flow relative errors Experiment 1 (Section \ref{['sec:high res Cartesian']}). Left: 2-norm relative error, center: $\infty$-norm relative error, right: overall relative error. Note the stable performance of the neural field approach across acceleration factors, reflecting its inductive bias toward smooth flow fields.
• Figure 4: Top: reference flow (black) against predicted flow for neural field, hybrid, and LLR methods at different acceleration factors. The neural field struggles to capture the negative peak at frame 30, while the hybrid method does capture it except for factor $64\times$. Bottom: time-wise error of flow for neural field, hybrid, and LLR methods. The neural field presents its largest error at the negative peak in frame 30.
• Figure 5: Reconstruction results on Experiment 2 for patient P001 at an acceleration factor 16$\times$. PSNR for the zoomed-in spatiotemporal scene and 2-norm relative error of the flow are also shown. Velocity maps are masked to the aorta region.