Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation

TL;DR

This paper introduces a novel method for accurately estimating the 2D vector displacement field in quasistatic elastography by using sparse relaxation of the momentum equation, significantly improving displacement and strain estimates without prior material knowledge.

Contribution

The paper presents a new approach that leverages a special form of the momentum equations to filter ultrasound displacement data, enabling precise 2D displacement reconstruction with limited measurements and no prior material property knowledge.

Findings

Error in lateral displacement estimates reduced from 50% to 2%.

Strain error decreased from over 250% to below 2%.

Method validated on simulated, phantom, and in-vivo data.

Abstract

We consider the problem of estimating the $2D$ vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the $2D$ vector displacement field and very limited information of the second component, the method reconstructs the second component quite accurately. No a priori knowledge of the heterogeneous distribution of material properties is required. This method relies on using a special form of the momentum equations to filter ultrasound displacement measurements to produce more precise estimates. We verify the method with applications to simulated displacement data. We validate the method with applications to displacement data measured from a tissue mimicking phantom, and in-vivo data; significant improvements are noticed in the filtered displacements recovered from all the tests. In verification studies, error in lateral displacement estimates decreased from about $50\%$ to about $2\%$, and strain error decreased from more than $250\%$ to below $2\%$.