Deep learning-driven inversion framework for shear modulus estimation in magnetic resonance elastography

The multimodal direct inversion (MMDI) algorithm is widely used in magnetic resonance elastography (MRE) to estimate tissue shear stiffness but relies on the Helmholtz equation, which assumes a uniform, homogeneous, and infinite medium. Its use of the Laplacian operator also makes it highly sensitive to noise. This study proposes a deep-learning-driven inversion framework for shear modulus estimation in MRE (DIME) to improve the robustness and accuracy of inversion.

DIME was trained on displacement-stiffness pairs generated through finite element modeling (FEM), using small image patches to capture local wave behavior and enhance robustness to global variations. Validation was performed on homogeneous and heterogeneous FEM-simulated datasets. The method was further evaluated using an anatomy-informed simulated liver dataset with known ground truth (GT) and directly compared with MMDI. Finally, DIME was tested on in vivo liver MRE data from eight healthy and seven fibrotic subjects.

In FEM simulations, DIME produced stiffness maps with low inter-pixel variability, accurate boundary delineation, and higher correlation with GT than MMDI. In anatomy-informed liver simulations, DIME reproduced stiffness patterns with high fidelity (r = 0.99, R² = 0.98), while MMDI showed greater underestimation. In in vivo liver data, DIME preserved physiologically consistent stiffness patterns and closely matched MMDI, while MMDI demonstrated systematic over- or underestimation depending on the acquisition and filtering configuration.

DIME demonstrated higher correlation with ground truth in simulations and visually similar stiffness maps in vivo, while MMDI displayed a larger bias that may be attributed to directional filtering. These results highlight the feasibility of DIME for clinical MRE applications.