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

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 /ω _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.