Dual-time-scale method for modeling of the nonlinear amplitude-modulated ultrasound fields

Abstract

This study focuses on modeling of the nonlinear acoustic wave propagation in situations when the amplitude of the focused ultrasound field is modulated by a low-frequency signal. This problem is relevant to both ultrasound imaging applications entailing the use of the acoustic radiation force, and treatment applications such as histotripsy. The difficulty of predicting the pressure wavefield lies in a fact that the excessive length of the low-frequency modulated signal may significantly increase the computational effort. To tackle the problem, this study utilizes the dual-time-scale approach, where two temporal variables are introduced to distinguish between ultrasound-scale and modulation-scale variations. In this case, the Westervelt-type equation can be effectively solved using hybrid time-frequency algorithm for any transient (sufficiently smooth) modulation envelope. To validate the proposed approach, the Khokhlov-Zabolotskaya-Kuznetsov equation was solved in the time domain for an example pressure profile on the boundary. A comparison between the time-domain and hybrid calculations demonstrates that the latter are notably faster, require significantly less memory, and have satisfactory accuracy for the ratios between the modulation and carrier ultrasound frequencies below 0.1.