Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging

TL;DR

This paper introduces a momentum-equation-based regularization method for 2D ultrasound elastography image registration, demonstrating superior accuracy and robustness over traditional strain-based methods through extensive simulation and phantom experiments.

Contribution

The study reformulates a momentum-based post-processing method as a regularization term within a variational framework, improving elastography image registration accuracy and robustness.

Findings

Momentum-based regularization achieved lowest strain errors.

Plane stress assumption regularization yielded highest strain contrast.

Method outperformed strain magnitude regularization in noisy and model-mismatch scenarios.

Abstract

Objective: Evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. Methods:We reformulate a previously proposed momentum-equation-based post-processing method (SPREME) as a regularization term directly integrated into an image registration energy functional. Four regularization types are implemented and compared: a strain magnitude ($\R_\epsilon$), a strain magnitude with incompressibility constraint ($R_{\epsilon i}$), and a momentum-based regularization under plane strain ($R_{P\epsilon}$) and plane stress ($R_{P\sigma}$) assumptions. Each is evaluated in a variational framework solved via Gauss-Newton optimization. Data:Registration performance is assessed using synthetic ultrasound image sequences generated from 2D and 3D finite element simulations, as well as experimental phantom data. Comparisons are based on displacement and strain field errors, strain contrast, and contrast-to-noise ratio (CNR). Results: Momentum-based regularization, particularly under plane stress assumptions ($R_{P\sigma}$), achieved the lowest strain errors and highest strain contrast across both single-frame and accumulated measurements, even when the underlying tissue deformation violated 2D assumptions. In contrast, strain magnitude regularization with an incompressibility constraint ($R_{\epsilon i}$) produced unstable results in 3D and accumulated displacement scenarios. Conclusions: Mechanics-based regularization that incorporates momentum conservation outperforms strain-based techniques in elastographic image registration, particularly when applied directly in the optimization framework. This approach improves robustness to noise and model mismatch, offering a promising direction for future displacement-based inverse imaging methods.