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Dual-Time Approach to the Numerical Simulation of Modulated Nonlinear Ultrasound Fields

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This study establishes a dual-time computational platform for solving the nonlinear parabolic wave equation in situations when the prescribed ultrasound excitation is modulated by a “low”-frequency envelope. The key advantage of the dual-time approach lies in the fact that the nonlinear solution is approximated, for an arbitrary modulation envelope, using a set of precomputed steady-state solutions. This makes the method computationally inexpensive, and allows for the fast simulation of long excitation signals for which the time-domain simulations are inherently fruitless. To study the applicability of the dual-time method a sample problem, which models the axisymmetric nonlinear wave propagation in soft tissues, is solved using both the dual-time approach and its conventional time-domain counterpart. The results demonstrate that the accuracy of the proposed approximation is proportional to the ratio between the (dominant) modulation frequency ω m and carrier ultrasound frequency ω u, as suggested by theoretical predictions. In particular, it is found that the solution error is on the order of few percent when ω m u = 1/20, and decreases thereon with diminishing ω m. The effectiveness of the dual-time simulations in terms of both memory and computational cost makes them particularly advantageous for more demanding problems, such as those entailing three-dimensional propagation of modulated nonlinear sound fields. One immediate application of the proposed computational platform resides in the simulation of high-intensity ultrasound fields in soft tissues, that are increasingly used for diagnostic purposes via applications of thus generated acoustic radiation force.
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Document Type: Research Article

Publication date: September 1, 2013

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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