Simulation of Acoustic Propagation in 3D Viscoelastic Inhomogeneous Media with Application to Medical Shear Wave Elastography

Abstract

This paper proposes a new numerical framework to simulate ultrasound wave propagation in 3D viscoelastic heterogeneous media based on the elastodynamic wave equation including a 3D second-order time-domain perfectly matched layer formulation. A finite difference discretization of this formulation is presented, along with a stability analysis. The resulting model is capable of simulating 3D shear and longitudinal acoustic waves for arbitrary source geometries and excitations, together with arbitrary initial and boundary conditions. A simulation example is provided to show the application of our proposed method for tissue elastography imaging. Specifically, the propagation of shear waves from a localized lesion to the surrounding normal tissue is examined.