Wave Inversion for Magnetic Resonance Elastography Using Physics-Trained Neural Networks
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Two-dimensional wave inversion for reconstructing soft tissue biomechanical parameters, such as tissue stiffness, is a highly ill-posed problem, strongly affected by data quality and unknown boundary conditions. This is a key challenge in magnetic resonance elastography (MRE), a non-invasive imaging technique that probes the mechanical properties of soft biological tissues by acquiring the three-dimensional displacement wavefield generated by externally induced harmonic vibrations [1]. Spatially resolved tissue biomechanical properties, in particular the shear wave speed as a proxy for tissue stiffness, must then be accurately recovered from the wavefield under constraints of limited computational resources. Recently, machine learning approaches have emerged as promising tools to improve the robustness, efficiency, and quality of this reconstruction in MRE [2,3]. In this work, we leveraged physics-based synthetic data to generate the displacement wavefield within small 4×4 image patches, for known viscoelastic material properties, assuming local material homogeneity. Using these data, we trained a hierarchical vision transformer-based neural network (ElastoNet [3]), explicitly leveraging the multicomponent and multifrequency nature of MRE data within both the data generation and the network architecture. ElastoNet was designed to be independent of the image resolution and vibration frequencies and was applied iteratively over the full image during inference. We compared our method with both traditional (direct) and neural network-based inversion methods for MRE, and showed that it achieved a higher accuracy on abdominal in silico data. ElastoNet was also highly generalizable to abdominal in vivo data, with a focus on the liver, spleen, and kidneys, achieving high anatomical detail resolution and allowing for characterization of the frequency dispersion. Overall, this work contributes to advancing research in MRE toward more accurate and computationally efficient characterization of in vivo tissue biomechanics.
