Computation of nonlinear ultrasound fields using a linearized contrast source method

• Published in: The Journal of the Acoustical Society of America Vol. 134; no. 2; pp. 1442 - 1453
• Main Authors: Verweij, Martin D, Demi, Libertario, van Dongen, Koen W A
• Format: Journal Article
• Language: English
• Published: United States 01-08-2013
• Subjects: Computer Simulation; Motion; Nonlinear Dynamics; Numerical Analysis, Computer-Assisted; Pressure; Sound; Time Factors; Ultrasonics - methods; Ultrasonography - methods
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.4812863

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.