Interior elastodynamics inverse problems: shear wave speed reconstruction in transient elastography

Abstract

We review and present new results on the transient elastography problem, where the goal is to reconstruct shear stiffness properties using interior time and space dependent displacement measurements. We present the unique identifiability of two parameters for this inverse problem, establish that a Lipschitz continuous arrival time satisfies the eikonal equation, and present two numerical algorithms, simulation results, and a reconstruction example using a phantom experiment accomplished by Mathias Fink's group (the Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII). One numerical algorithm uses a geometrical optics expansion and the other utilizes the arrival time surface.