Computation of nonlinear ultrasound fields using a linearized contrast source method

Abstract

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

Comparison of Fractional Wave Equations for Power Law Attenuation in Ultrasound and Elastography

“…( 29) is related to the wave equation ( 1) in Verweij et al (2013) (see also the references therein). These two wave equations are mathematically similar if nonlinear terms are disregarded, and if m(t) in Verweij et al (2013) is identified as m(t) = ρ 0 c 2 0 κ(t). Related similarity is observed between Eq.…”

Simulation of Ultrasonic Beam Propagation From Phased Arrays in Anisotropic Media Using Linearly Phased Multi-Gaussian Beams

“…These numerical methods can be used for all complex interfaces and for anisotropic materials, but they become computationally very expensive, especially in the case where 3-D models are required. Some other methods for beam modeling, such as applying the full-wave methods by Green's solution to the dispersive wave equation [11], using nonlinear acoustics [12]- [17], etc., have been explored for isotropic homogeneous and inhomogeneous media, but have yet to be applied to layered anisotropic media. An alternative method which is based on paraxial approximation is to model the radiation as a superposition of Gaussian beams.…”

Simulation of Ultrasound Fields

“…It has been formulated in its original form by Huijssen (2008) and Huijssen and Verweij (2010), and later, extensions have been described by Demi et al (2011), Demi (2013, and Verweij et al (2013). The method is based on the IE for a nonlinear contrast source problem.…”