Viscoelastic modulus reconstruction using time harmonic vibrations

TL;DR

This paper introduces an iterative method for high-resolution viscoelastic tissue imaging using internal displacement measurements, leveraging Fréchet derivatives to improve reconstruction quality without data differentiation.

Contribution

The paper develops a novel adjoint-based iterative reconstruction method that avoids data differentiation, enhancing viscoelastic imaging accuracy with a good initial guess.

Findings

Method improves image quality in numerical experiments

No differentiation of displacement data needed

Requires a well-matched initial guess

Abstract

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.