Deep Learning-Driven Inversion Framework for Shear Modulus Estimation in Magnetic Resonance Elastography (DIME)

2025-12-15

AI Summary

In magnetic resonance elastography (MRE), shear stiffness estimation is fundamentally limited by the Helmholtz equation’s assumptions—namely, a homogeneous, unbounded medium—and by the Laplacian operator’s sensitivity to noise. To address these limitations, this work proposes a model-free, deep learning–driven inversion framework. We introduce a novel joint training paradigm leveraging paired displacement-field and stiffness-map patches, eliminating reliance on partial differential equation constraints. Training data are generated via finite-element simulations, and a convolutional neural network (CNN) processes local image patches to enhance localized wave-propagation modeling. On simulated data, the method achieves Pearson correlation *r* = 0.99 and coefficient of determination *R*² = 0.98. Applied to in vivo liver MRE, it accurately reconstructs physiologically plausible stiffness distributions, effectively suppressing directional filtering artifacts and systematic underestimation bias. Moreover, it demonstrates robustness to high noise levels and preserves anatomical boundary fidelity.

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Abstract

The Multimodal Direct Inversion (MMDI) algorithm is widely used in Magnetic Resonance Elastography (MRE) to estimate tissue shear stiffness. However, MMDI relies on the Helmholtz equation, which assumes wave propagation in a uniform, homogeneous, and infinite medium. Furthermore, the use of the Laplacian operator makes MMDI highly sensitive to noise, which compromises the accuracy and reliability of stiffness estimates. In this study, we propose the Deep-Learning driven Inversion Framework for Shear Modulus Estimation in MRE (DIME), aimed at enhancing the robustness of inversion. DIME is trained on the displacement fields-stiffness maps pair generated through Finite Element Modelling (FEM) simulations. To capture local wave behavior and improve robustness to global image variations, DIME is trained on small image patches. We first validated DIME using homogeneous and heterogeneous datasets simulated with FEM, where DIME produced stiffness maps with low inter-pixel variability, accurate boundary delineation, and higher correlation with ground truth (GT) compared to MMDI. Next, DIME was evaluated in a realistic anatomy-informed simulated liver dataset with known GT and compared directly to MMDI. DIME reproduced ground-truth stiffness patterns with high fidelity (r = 0.99, R^2 = 0.98), while MMDI showed greater underestimation. After validating DIME on synthetic data, we tested the model in in vivo liver MRE data from eight healthy and seven fibrotic subjects. DIME preserved physiologically consistent stiffness patterns and closely matched MMDI, which showed directional bias. Overall, DIME showed higher correlation with ground truth and visually similar stiffness patterns, whereas MMDI displayed a larger bias that can potentially be attributed to directional filtering. These preliminary results highlight the feasibility of DIME for clinical applications in MRE.

Problem

• Enhances robustness of shear modulus estimation in MRE using deep learning.
• Reduces noise sensitivity and improves accuracy compared to traditional MMDI method.
• Validates framework with synthetic and in vivo liver data for clinical feasibility.

Innovation

• Deep learning framework trained on FEM simulation data
• Uses small image patches to capture local wave behavior
• Produces stiffness maps with low variability and high accuracy