A hybrid CNN-adjoint optimization framework for reconstruction of viscoelastic tissue properties in magnetic resonance elastography

2026-10-01

AI Summary

This study addresses the ill-posed inverse problem of reconstructing the complex shear modulus from displacement fields in magnetic resonance elastography (MRE), which is inherently susceptible to noise interference and boundary excitation limitations. To overcome these challenges, this work proposes a novel hybrid framework integrating data-driven learning with physics-based constraints. Specifically, a convolutional neural network (CNN) is employed to provide high-quality initial estimates, which are subsequently refined through partial differential equation (PDE)-constrained optimization utilizing a modified Stokes forward model, the adjoint method, and a nonlinear conjugate gradient algorithm. By synergizing the strong generalization capability of CNNs with the precision of physics-informed optimization, the proposed framework effectively mitigates the limitations of conventional approaches, significantly enhancing both the convergence speed and reconstruction accuracy of viscoelastic parameter estimation in MRE.

Abstract

Magnetic resonance elastography (MRE) is a noninvasive imaging modality for quantifying the viscoelastic properties of soft tissues from shear wave propagation. Recovering the complex-valued shear modulus from measured displacement fields leads to a severely ill-posed inverse problem, particularly in the presence of noise and limited boundary excitations. We investigate adjoint-based optimization, convolutional neural network (CNN) reconstruction, and a hybrid framework combining both approaches. The forward model is based on a scalar form of the modified stationary Stokes system with a complex shear modulus. We establish well-posedness of the forward problem, existence of minimizers, and first-order optimality conditions for the adjoint-based formulation, and implement a nonlinear conjugate-gradient method with Armijo line search. While PDE-constrained optimization can accurately refine coefficient reconstructions, its performance depends strongly on initialization. We therefore construct a two-dimensional CNN that maps complex-valued displacement measurements to spatially varying complex shear modulus fields and provides rapid, informative initial reconstructions. The proposed hybrid method uses the CNN reconstruction to initialize the adjoint-based optimization, yielding faster convergence and improved accuracy. The CNN is trained on coefficient fields containing individual perturbations and tested on both individual and previously unseen combined configurations. Numerical experiments demonstrate that the CNN generalizes to these more challenging configurations, while subsequent PDE-constrained optimization further refines the reconstructed coefficient. These results demonstrate the potential of combining data-driven initialization with physics-based optimization for efficient and accurate MRE reconstruction.

Problem

• magnetic resonance elastography
• inverse problem
• viscoelastic properties
• shear modulus reconstruction
• ill-posed

Innovation

• Magnetic Resonance Elastography
• Hybrid CNN-Adjoint Optimization
• Viscoelastic Property Reconstruction
• PDE-Constrained Optimization
• Data-Driven Initialization