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.

数值研究了两种形式的超声激发（单频和双频超声模式）下的惯性空化阈值。Gilmore-Akulichev 模型与 Zener 粘弹性模型相结合用于模拟气泡动力学。阈值压力由两个标准确定，一个基于气泡半径，另一个基于气泡破裂速度。针对不同的初始气泡大小、声信号模式、频率、组织粘度、组织弹性及其所有组合研究阈值行为。由于大量的参数及其多种组合（大约$1.5$每个阈值标准十亿），所有模拟都在图形处理单元上执行以加快计算速度。我们使用了我们自己用 C++ 和 CUDA C 语言编写的代码。获得的结果表明，使用双频信号模式有助于降低惯性空化阈值（与单频模式相比）。基于气泡大小的标准给出的阈值低于使用气泡破裂速度的标准。随着弹性的增加，阈值压力也增加，而与弹性不同，改变粘度对最佳阈值的影响非常小。对双频驱动信号的最佳超声频率的详细分析发现，对于粘度小于$0.02$帕$·$s，一般情况下，第一最优频率远小于第二最优频率，可以达到1MHz。然而，对于高粘度，两个最佳频率相似并且在范围内变化$0.01$–$0.05$ 兆赫。总体而言，本研究详细分析了双频信号激励下软组织中的惯性空化。这可能有助于进一步发展生物医学超声的不同应用。