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

• Published in: The Journal of the Acoustical Society of America Vol. 131; no. 6; pp. 4324 - 4336
• Main Authors: Treeby, Bradley E., Jaros, Jiri, Rendell, Alistair P., Cox, B. T.
• Format: Journal Article
• Language: English
• Published: Melville, NY Acoustical Society of America 01.06.2012; American Institute of Physics
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Nonlinear acoustics, macrosonics; Physics; Spectral method; Power law; Modeling; Non linear acoustics
• ISSN: 0001-4966; 1520-8524; 1520-8524
• DOI: 10.1121/1.4712021

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.