Reconstruct Lame parameters of linear isotropic elasticity system

TL;DR

This paper presents a method to uniquely and stably reconstruct the Lamé parameters of a linear isotropic elasticity system from tissue displacement data, using complex geometrical optics solutions for boundary conditions.

Contribution

It introduces a novel approach to reconstruct Lamé parameters in elasticity systems from displacement measurements with stability guarantees.

Findings

Unique reconstruction of Lamé parameters established.

Stable reconstruction demonstrated under certain boundary conditions.

Characterization of boundary conditions via complex geometrical optics solutions.

Abstract

Transient Elastography enables detection and characterization of tissue abnormalities. In this paper we assume that the displacements are modeled by linear isotropic elasticity system and the tissue displacement has been obtained by the first step in hybrid methods. Then we reconstruct the Lam\'e parameters of this system from knowledge of tissue displacement. We show that for a sufficiently large number of solutions of the elasticity system and for an open set of the well-chosen boundary conditions, $(\lambda,\mu)$ can be uniquely and stably reconstructed. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics solutions.