A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation

Abstract

Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.

Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams

“…The concept is illustrated here using the wellknown Navier-Stokes and a KZK models for focusing sound beams. Although the results presented here are not surprising-a common rule of thumb for the KZK equation is that it should not be considered accurate in configurations where acoustic waves approach the axis at angles of more than about 20 -they do demonstrate a particular application of the full-wave solver.…”

“…However, as computing technology has become increasingly powerful, there has been a renewed interest in solving full-wave models (e.g., Navier-Stokes or Westervelt equations). 7,[17][18][19][20][21][22][23][24] One reason for developing improved computational methodologies, therefore, is to enable the use of less restrictive HIFU models in practice. Moreover, the development of advanced computational algorithms is useful in the field of HIFU simulation as a whole.…”

Computation of nonlinear ultrasound fields using a linearized contrast source method

“…31,32,43 However, for stronger inhomogeneities the influences of these additional contrast sources need not be small, as opposed to the original nonlinear contrast source, and the Neumann iterative solution may become slowly convergent or even divergent. When this occurs, the solution of the integral equation by more advanced methods, [34][35][36]44 such as over-relaxation methods or Conjugate Gradient (CG) methods, becomes necessary.…”

“…Originally, the method could handle homogeneous nonlinear media with frequency power law attenuation. 28,30 Recently, the method has been extended to deal with media with spatially dependent nonlinearity and attenuation, 31,32 in which case its ability to deal with scattered wave fields becomes opportune.…”

Linearization strategies for the Iterative Nonlinear Contrast Source method for full-wave simulation of nonlinear ultrasound fields

“…At this stage, the remaining errors are the systematic errors introduced by the linearization around p (0) . After restart, the scheme reaches convergence again at j = 11, at which time it turns out that the systematic errors in the higher harmonics have effectively been eliminated by the linearization around p (7) . Of course, the same ¿nal result may be obtained by stopping the initial scheme earlier, i.e.…”