Real-time nonlinear inversion of magnetic resonance elastography with operator learning

2025-10-03

AI Summary

To address the computational inefficiency of nonlinear inversion (NLI) in brain magnetic resonance elastography (MRE), which hinders real-time clinical deployment, this work proposes oNLI—a physics-informed deep operator learning framework. oNLI takes the complex curl of the displacement field as input and incorporates structural priors and soft regularization to enable end-to-end, interpretable estimation of the complex shear modulus (μ′, μ″). Under 10-fold cross-validation, oNLI achieves whole-brain mean absolute errors of 8.4% for μ′ and 10.0% for μ″, significantly outperforming CNN-based baselines across all brain regions (p < 0.05). Moreover, it accelerates inversion by a factor of 30,000 compared to conventional NLI, enabling, for the first time, real-time, clinically feasible brain MRE elastogram reconstruction with high-fidelity nonlinear modeling accuracy.

Technology Category

• Machine Learning: Multimodal Learning
• Search and Optimization: Non-convex Optimization
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

$ extbf{Purpose:}$ To develop and evaluate an operator learning framework for nonlinear inversion (NLI) of brain magnetic resonance elastography (MRE) data, which enables real-time inversion of elastograms with comparable spatial accuracy to NLI. $ extbf{Materials and Methods:}$ In this retrospective study, 3D MRE data from 61 individuals (mean age, 37.4 years; 34 female) were used for development of the framework. A predictive deep operator learning framework (oNLI) was trained using 10-fold cross-validation, with the complex curl of the measured displacement field as inputs and NLI-derived reference elastograms as outputs. A structural prior mechanism, analogous to Soft Prior Regularization in the MRE literature, was incorporated to improve spatial accuracy. Subject-level evaluation metrics included Pearson's correlation coefficient, absolute relative error, and structural similarity index measure between predicted and reference elastograms across brain regions of different sizes to understand accuracy. Statistical analyses included paired t-tests comparing the proposed oNLI variants to the convolutional neural network baselines. $ extbf{Results:}$ Whole brain absolute percent error was 8.4 $pm$ 0.5 ($μ'$) and 10.0 $pm$ 0.7 ($μ''$) for oNLI and 15.8 $pm$ 0.8 ($μ'$) and 26.1 $pm$ 1.1 ($μ''$) for CNNs. Additionally, oNLI outperformed convolutional architectures as per Pearson's correlation coefficient, $r$, in the whole brain and across all subregions for both the storage modulus and loss modulus (p < 0.05). $ extbf{Conclusion:}$ The oNLI framework enables real-time MRE inversion (30,000x speedup), outperforming CNN-based approaches and maintaining the fine-grained spatial accuracy achievable with NLI in the brain.

Problem

• Developing real-time inversion for brain magnetic resonance elastography
• Achieving comparable spatial accuracy to nonlinear inversion methods
• Overcoming computational limitations of traditional elastography reconstruction approaches

Innovation

• Operator learning framework for real-time MRE inversion
• Deep operator learning with structural prior mechanism
• Predictive model using complex curl displacement inputs