Multifrequency neural network-based wave inversion in MR elastography with uncertainty quantification

Magnetic Resonance Elastography (MRE) enables non-invasive characterization of in vivo soft tissue stiffness by solving a wave inversion reconstruction problem. Multifrequency MRE has been used to stabilize the reconstruction and characterize the frequency dispersion of tissue in both classical and neural network-based approaches. However, existing techniques, including the neural network-based MRE wave inversion method ElastoNet, perform single-frequency inversions and aggregate the results, underutilizing the potential of multifrequency MRE data. Therefore, we propose a multifrequency neural network-based wave inversion for MRE (MF-ElastoNet). A hierarchical vision transformer was trained on small patches of synthetically generated data, assuming a generalized viscoelastic material model spanning the full spectrum from ideal elastic to ideal viscous frequency-dispersion behavior. Our model was designed to support data at any resolution and vibration frequencies, and to provide uncertainty quantification of its predictions using evidential deep learning. MF-ElastoNet was evaluated in finite element simulations of abdominal MRE, phantoms, and in vivo multifrequency MRE of the liver, spleen, and kidneys of 37 healthy volunteers, covering acquisitions from 20 to 100 Hz. MF-ElastoNet achieved higher accuracy than single-frequency approaches in reconstructing compounded shear wave speed maps, as a proxy for tissue stiffness, and recovering frequency-dependent dispersion, enabling accurate characterization of tissue behavior across the elastic-to-viscoelastic spectrum. Stability analysis of model predictions revealed that as few as 3 independent input frequencies were sufficient to achieve consistency in all cases. The proposed multifrequency inversion method advances neural network-based reconstructions in MRE towards accurate and trustworthy wideband tissue characterization in research and clinical applications.