Simulation Study on the Dynamics of Cavitation Bubbles in Multi-Frequency Ultrasound

High-intensity focused ultrasound (HIFU) therapy is an effective minimally invasive treatment technique. This work aimed to present a theoretical foundation for transient cavitation control in HIFU treatment and investigate cavitation bubbles in multi-frequency ultrasound. In this theoretical study, the nonlinear vibrations of bubbles in different mediums (water, urine, kidney, and muscle) were simulated using Gilmore-Akulichev and modified Keller-Miksis equations. The dynamic changes of bubble radius during irradiation by multi-frequency combined ultrasound were analyzed, and the effects of multi-frequency ultrasound combinations and frequency differences on the maximum and minimum values of bubble expansion radius and bubble collapse time were investigated. At the same highest frequency, the triple-frequency produced the largest bubble expansion radius (Rmax) while the single-frequency resulted in the smallest bubble expansion radius (Rmin). At the same lowest frequency, the single-frequency had the biggest bubble expansion radius and the triple-frequency had the smallest bubble expansion radius. Compared to the combination with a large frequency difference at high frequency, the triple-frequency combination with a small frequency difference at low frequency exhibited a noticeably larger Rmax, but Rmin showed the opposite behavior. Rmax/Rmin decreased for the same ultrasonic combination when the medium viscosity increased. The bubble expansion radius ratio Rmax/Rmin was positively correlated with the bubble collapse time. There was a strong correlation between the frequency difference and the multi-frequency ultrasound combination and the maximum and minimum values of the cavitation bubble radius and the collapse time.