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Physics-Informed Compressed Sensing for PC-MRI: An Inverse Navier-Stokes Problem.

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    Physics-informed compressed sensing (PICS) reconstructs velocity fields from low-quality MRI data. This method accurately segments flow fields and estimates pressure and stress, even with sparse signals.

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    Area of Science:

    • Medical Imaging
    • Fluid Dynamics
    • Computational Science

    Background:

    • Phase-contrast magnetic resonance imaging (PC-MRI) is crucial for non-invasive blood flow quantification.
    • Reconstructing velocity fields from sparse and noisy PC-MRI data presents significant challenges.
    • Accurate estimation of hydrodynamic pressure and wall shear stress requires high-fidelity velocity field data.

    Purpose of the Study:

    • To develop a novel physics-informed compressed sensing (PICS) method for velocity field reconstruction from undersampled PC-MRI signals.
    • To enable joint reconstruction and segmentation of velocity fields.
    • To infer hidden hemodynamic parameters like pressure and wall shear stress.

    Main Methods:

    • Formulation of a physics-informed compressed sensing (PICS) approach.
    • Solving an inverse Navier-Stokes boundary value problem.
    • Employing a Bayesian framework with Gaussian random fields for regularization.
    • Updating prior information using Navier-Stokes equations, an energy-based segmentation functional, and k-space signal consistency.

    Main Results:

    • Successful reconstruction and segmentation of velocity fields from highly undersampled (15% k-space coverage) and low signal-to-noise ratio (SNR ~10) PC-MRI data.
    • Demonstrated capability to infer hydrodynamic pressure and wall shear stress.
    • Reconstructed velocity fields showed excellent agreement with those from fully-sampled (100% k-space coverage) high SNR (>40) data.

    Conclusions:

    • The PICS method offers a robust solution for reconstructing and segmenting velocity fields from challenging PC-MRI data.
    • This approach significantly enhances the utility of sparse and noisy MRI data for hemodynamic analysis.
    • PICS holds promise for improved non-invasive cardiovascular flow assessment and disease diagnosis.