GPU-accelerated study of the inertial cavitation threshold in viscoelastic soft tissue using a dual-frequency driving signal

Inertial cavitation thresholds under two forms of ultrasonic excitation (the single-and dual-frequency ultrasound modes) are studied numerically. The Gilmore-Akulichev model coupled with the Zener viscoelastic model is used to model the bubble dynamics. The threshold pressures are determined with two criteria, one based on the bubble radius and the other on the bubble collapse speed. The threshold behavior is investigated for different initial bubble sizes, acoustic signal modes, frequencies, tissue viscosities, tissue elasticities, and all their combinations. Due to the large number of parameters and their many combinations (around 1.5 billion for each threshold criterion), all simulations were executed on graphics processing units to speed up the calculations. We used our own code written in the C++ and CUDA C languages. The results obtained demonstrate that using the dual-frequency signal mode can help to reduce the inertial cavitation threshold (in comparison to the single frequency mode). The criterion based on the bubble size gives a lower threshold than the criterion using the bubble collapse speed. With an increase of the elasticity, the threshold pressure also increases, whereas changing the viscosity has a very small impact on the optimal threshold, unlike the elasticity. A detailed analysis of the optimal ultrasound frequencies for a dual-frequency driving signal found that for viscosities less than 0.02 Pa.s, the first optimal frequency, in general, is much smaller than the second optimal frequency, which can reach 1 MHz. However, for high viscosities, both optimal frequencies are similar and varied in the range 0.01-0.05 MHz. Overall, this study presents a detailed analysis of inertial cavitation in soft tissue under dual-frequency signal excitation. It may be helpful for the further development of different applications of biomedical ultrasound.