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

Magnetic Resonance Elastography (MRE) is a non-invasive imaging technique for mapping biomechanical properties of in vivo tissue, including shear wave speed (SWS), but involves intrinsically slow data acquisition and an ill-posed wave inversion. Instead of relying on handcrafted image priors, we propose a data-driven approach jointly combining image reconstruction and MRE inversion for robust SWS estimation from undersampled k-space data.

Our physics-informed reconstruction framework comprises two blocks: a model-based neural network (NN)-regularized reconstruction module and a phase-gradient inversion (k-MDEV) calculating SWS from the reconstructed images. Concatenating both blocks yields an end-to-end trainable method to estimate SWS directly from measured k-space data. We evaluated the method on retrospectively highly undersampled brain MRE data and compared it to a total variation (TV) minimization-based approach. We assessed the impact of end-to-end training (qualitative images and SWS maps as targets) versus pre-training (qualitative images as targets) and applied the method also to in vivo data.

Our approach significantly reduces NRMSE by 30% compared to TV. End-to-end training improves SWS estimation over separate image reconstruction and SWS calculation.

Accurate SWS quantification is possible at acceleration factors up to 19. Our method significantly outperforms TV, highlighting the need for data-driven regularization in this challenging MR problem. Further, our approach successfully generalizes to in vivo data.

We present the first end-to-end trainable MRE reconstruction method for estimating SWS maps directly from k-space. NN-based reconstruction can enable rapid stiffness mapping for dynamic studies, functional imaging, and real-time clinical feedback.