Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a <i>k</i>-space pseudospectral method

TLDR

Simulating nonlinear ultrasound propagation in realistic tissue media is widely applicable but computationally challenging due to the large domain size relative to the acoustic wavelength, and the governing equations derive from fluid mechanics incorporating nonlinearity, power‑law absorption, and heterogeneities. The study applies a k‑space pseudospectral method to reduce the number of grid points per wavelength for accurate nonlinear ultrasound simulations. The model uses coupled first‑order acoustic equations with convective nonlinearity and power‑law absorption expressed as spatial gradients, discretized via a k‑space pseudospectral technique that computes gradients with a Fourier‑collocation method. The method improves gradient accuracy, allowing sparser grids than finite difference approaches, and its accuracy and utility are shown in numerical experiments, including a 3‑D simulation of a clinical ultrasound probe’s beam pattern.

Abstract

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.