Impact of Curl Operation on Stiffness Estimation in Brain MR Elastography

Motivation: To improve the reliability of MRE in stiffness estimation. Goal(s): To assess how curl and gradient-based methods compare in estimating stiffness and preserving biological contrasts in MRE. Approach: Direct inversion (DI) and neural network inversion (NNI) methods were evaluated on simulated and in vivo data using both curl and gradient displacement field as input features. Results: Curl operator-based stiffness estimates were softer, consistent with more complete removal of the longitudinal wave. However, both curl-based and gradient-based methods captured biologically relevant contrasts. Impact: The findings provide insights for selecting MRE processing methods, indicating that while curl-based methods improve shear wave isolation, gradient-based approaches may serve as better training data for capturing stiffness variations in structurally complex, inhomogeneous tissues.