## 3 Simulation Results
### Influence of Multifrequency Ultrasonic Combination on Transient Cavitation Threshold
In Figure 1, the triple-frequency combination with high frequency corresponding to the transient cavitation threshold from low to high are \(1.4+1.41+1.42\) MHz, \(1.4+1.5+1.6\) MHz, and \(1.4+2.0+2.6\) MHz, but the triple-frequency combination with low frequency corresponding to the transient cavitation threshold from low to high are \(0.7+0.71+0.72\) MHz, \(0.7+0.8+0.9\) MHz, and \(0.7+1.3+1.9\) MHz. When the lowest frequency of the triple-frequency combination is the same, the larger the frequency difference is, the higher the corresponding transient cavitation threshold is. When the initial bubble radius is small, the influence of frequency difference on the transient cavitation threshold of different triple-frequency combinations is not obvious. With the increase of initial bubble radius, the influence of frequency difference on the transient cavitation threshold of the high-frequency triple-frequency combination is more obvious, but the influence on the transient cavitation threshold of the low-frequency triple-frequency combination is not obvious. Figure 2 shows the relationship between the transient cavitation threshold and the initial bubble radius in water, blood, brain, and liver under the combination of single-frequency (2.6 MHz), dual-frequency (2.6 + 2.0 MHz), and triple-frequency (2.6 + 2.0 + 1.4 MHz). For these four different media, under the same initial bubble radius, the transient cavitation threshold of the dual-frequency combination is lower than that of the single-frequency ultrasound, and the transient cavitation threshold of the triple-frequency combination is lower than that of the dual-frequency combination. With the increase of the initial bubble radius, the difference between the transient cavitation threshold of the dual-frequency and triple-frequency combination and that of the single-frequency ultrasound gradually increases, but the difference between the transient cavitation threshold of the dual-frequency and triple-frequency combination is not significant. The results show that when the highest frequency of the multifrequency combination is the same as that of the single-frequency ultrasound, the transient cavitation threshold of the multifrequency combination is lower than that of the single-frequency ultrasound. Compared with the single-frequency ultrasound, the smaller the initial bubble radius, the smaller the effect of the multifrequency combination on reducing the transient cavitation threshold. The larger the initial bubble radius is, the better the effect of the multifrequency combination to reduce the transient cavitation threshold is. It is generally believed that if the ultrasound with lower frequency is introduced into the multifrequency combination, the transient cavitation threshold will be reduced [10; 16; 27; 36]. The simulation results are consistent with the experimental results of [PERSON] et al. [15], who used multifrequency irradiation to enhance cavitation: compared with the single frequency ultrasound, the dual-frequency combination can significantly enhance the cavitation effect, while the triple-frequency combination can further enhance the cavitation effect. Figure 3 shows the relationship between the transient cavitation threshold and the initial bubble radius in water, blood, brain, and liver under the combination of single-frequency (1.4 MHz), dual-frequency (1.4 + 2.0 MHz), and triple-frequency (1.4 + 2.0 + 2.6 MHz). Compared with Figure 2, the single-frequency in Figure 3 is reduced, and the dual-frequency and triple-frequency are combined in the way of increasing frequency. For these four different media, under the same initial bubble radius, the transient cavitation threshold of the dual-frequency combination is higher than that of the single-frequency ultrasound, and the transient cavitation threshold of the triple-frequency combination is higher than that of the dual-frequency combination.