In this work, a new numerical framework is proposed and implemented to simulate acoustic wave propagation in 3D viscoelastic heterogeneous media. The framework is based on the elastodynamic wave equation in which a 3D second-order time-domain perfectly matched layer (PML) formulation is developed to model unbounded media. The numerical framework is discretized by a finite difference formulation and its stability analysis is discussed.
The proposed numerical method is capable of simulating 3D shear and longitudinal acoustic waves for arbitrary source geometries and excitations, together with arbitrary initial and boundary conditions. After validation of the framework, it was used to simulate the propagation of ultrasound shear wave in high intensity focused ultrasound (HIFU) induced thermal lesions located within soft tissue. The parameters in these simulations were obtained from standard double-indentation measurements of the viscoelastic parameters of normal and thermally coagulated chicken breast tissue samples. A HIFU system was used to induce thermal lesions in tissue.
In this study, a new elastography procedure was also introduced to differentiate between the normal and HIFU induced thermal lesions. This method is based on time-frequency analysis of shear wave propagation within the tissue. In the proposed method, the Wigner-Ville distribution has been used as a time-frequency analytical technique to detect the location of shear wave propagating within the tissue, and to estimate the shear speed of the wave as well as its center frequency and attenuation coefficient. This method was applied to the acoustic wave propagation simulation results of the HIFU thermal lesion. It was finally used to estimate the local viscoelastic parameters of the medium. It was demonstrated that the proposed method is capable of differentiating the thermal lesions from the normal tissue based on their viscoelastic parameters.