Three-dimensional finite difference models of shear wave propagation in isotropic, homogeneous soft tissue

Abstract

Shear wave elastography with ultrasound applies an acoustic radiation force to generate shear waves in viscoelastic soft tissue. To address the need for more effective simulation tools that model shear waves generated by an applied acoustic radiation force, three-dimensional (3D) finite difference programs that simulate propagation of shear waves in an isotropic, homogeneous medium have been created. These programs simulate shear wave propagation in elastic and viscoelastic soft tissue models. The 3D finite difference implementation combines an explicit time-stepping approach and a staggered spatial grid with an absorbing boundary condition that reduces boundary reflections. The acoustic radiation force in these simulations is quickly and accurately simulated in FOCUS (http://www.egr.msu.edu/ ~fultras-web) for a focused linear ultrasound array with an f/# of 2. The compressional wave speed is 1500 m/s and the shear wave speed is 1.5m/s in the elastic and viscoelastic tissue models, and the shear viscosity is 1 Pa·s in the viscoelastic model. The simulation completes 90,000 time steps of a 10 ms simulation in an 80 mm × 80 mm × 80 mm region with spatial sampling equal to the wavelength of compressional component in three days on a 3.4 MHz Intel i7 processor. [Supported in part by NIH Grants R01EB012079 and R01DK092255.]