Dual-time approach to the numerical simulation of modulated nonlinear ultrasound fields

Egor V. Donsov, Bojan B Guzina

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 ωm and carrier ultrasound frequency ωu, as suggested by theoretical predictions. In particular, it is found that the solution error is on the order of few percent when ωmu = 1/20, and decreases thereon with diminishing ωm. The effectiveness of the dualtime 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 highintensity ultrasound fields in soft tissues, that are increasingly used for diagnostic purposes via applications of thus generated acoustic radiation force.

Original languageEnglish (US)
Pages (from-to)777-791
Number of pages15
JournalActa Acustica united with Acustica
Issue number5
StatePublished - Sep 1 2013


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