Physics-Informed Deep Learning for Shear Wave Speed Estimation in MR Elastography.

Area of Science:

• Biomedical Imaging
• Medical Physics
• Machine Learning in Medicine

Background:

• Magnetic Resonance Elastography (MRE) is a key non-invasive technique for assessing in vivo tissue biomechanics, specifically shear wave speed (SWS).
• Traditional MRE faces challenges due to slow data acquisition and complex, ill-posed wave inversion processes.
• Existing methods often rely on handcrafted image priors, limiting robustness and efficiency.

Purpose of the Study:

• To develop a data-driven approach for robust SWS estimation from undersampled k-space data in MRE.
• To jointly optimize image reconstruction and MRE inversion using a physics-informed neural network framework.
• To enable accurate and accelerated stiffness mapping directly from k-space data.

Main Methods:

• A novel physics-informed reconstruction framework combining a neural network (NN)-regularized reconstruction module and a phase-gradient inversion (k-MDEV) module.
• An end-to-end trainable method that estimates SWS directly from measured k-space data.
• Evaluation on retrospectively highly undersampled brain MRE data, comparing against a total variation (TV) minimization approach, and testing on in vivo data.

Main Results:

• The proposed data-driven method achieved a 30% reduction in normalized root-mean-square error (NRMSE) compared to the TV minimization approach.
• End-to-end training demonstrated superior SWS estimation performance over separate image reconstruction and SWS calculation.
• Accurate SWS quantification was achieved even at high acceleration factors (up to 19).

Conclusions:

• The developed end-to-end trainable MRE reconstruction method enables accurate SWS mapping directly from k-space data.
• The NN-based reconstruction significantly outperforms traditional methods like TV minimization, highlighting the value of data-driven regularization.
• This approach shows potential for rapid stiffness mapping in dynamic studies, functional imaging, and real-time clinical applications, generalizing well to in vivo data.