Morphology-, noise-, and resolution-robust ultrasound elasticity imaging with Fourier neural operator

Quasi-static strain elastography is a non-invasive technique for estimating tissue stiffness fields from displacement fields obtained by comparing ultrasound signals before and after compression. While recent deep learning approaches have enabled faster and more accurate elasticity estimation compared to traditional methods, several challenges remain for clinical translation. In this study, we employed finite element simulations of free-hand palpation to investigate the applicability of the Fourier neural operator (FNO) for mapping displacement fields to elasticity fields in quasi-static strain elastography. Four practical scenarios were investigated: (1) prediction across diverse lesion morphologies, (2) generalization to cases with lesion counts differing from those in the training data and to lesion morphologies not seen during training, including adaptation through few-shot fine-tuning, (3) robustness to noise in measured displacement fields, and (4) resilience to variations in ultrasound device resolution. FNO achieved competitive predictive accuracy across lesion types and consistently outperformed DeepONet, although U-Net yielded lower errors in several cases involving multiple lesions or sharp modulus discontinuities. In contrast, FNO showed markedly stronger robustness to noisy displacement inputs than U-Net and maintained reliable performance under moderate resolution mismatch, with degradation observed under more aggressive downsampling. For unseen realistic tumor morphologies, few-shot fine-tuning substantially improved prediction accuracy. Finally, we performed a qualitative zero-shot evaluation on a public experimental phantom dataset using axial displacement fields estimated from pre- and post-compression radio-frequency (RF) data. The simulation-trained FNO localized inclusion-like regions without additional fine-tuning, although quantitative contrast agreement remained limited because pixelwise modulus ground truth was unavailable. These results suggest that FNO is a promising operator-learning framework for axial displacement-to-modulus mapping in quasi-static strain elastography, while explicit simulation of raw ultrasound signal formation and displacement estimation from pre- and post-compression RF/in-phase quadrature (IQ) data remains outside the scope of the present study.