## 3 Simulation Results
### Effect of Peak Negative Pressure and Its Duration on Transient Cavitation Threshold  
For a single spherical bubble in the medium, the dynamic response of the bubble can be evaluated by the initial bubble radius, the peak negative pressure of the ultrasound, and its duration. When the maximum radius of the bubble is \(R_{\text{max}}=2R_{0}\), the corresponding transient cavitation threshold is closely related to the peak negative pressure and its duration [39; 40]. Taking Figure 2d as an example, Figure 4 theoretically analyzes the reason for the difference of transient cavitation threshold of liver under the combined irradiation of 2.6 MHz, 2.6 + 2.0 MHz, and 2.6 + 2.0 + 1.4 MHz. The initial bubble radius is 5 \(\upmu\)m and the initial pressure is 0.101 MPa under the combination of three different frequencies of ultrasonic irradiation in Figure 4. It can be found from Figure 4 that from the single-frequency ultrasound to the triple-frequency combination, their peak negative pressure gradually increases, and the peak negative pressure values of the single-frequency (2.6 MHz), dual-frequency (2.6 + 2.0 MHz), and triple-frequency (2.6 + 2.0 + 1.4 MHz) combinations are \(-\)0.1005 MPa, \(-\)126 MPa, and \(-\)0.1685 MPa, respectively. In general, under the same ultrasound power, the peak negative pressure corresponding to the triple-frequency and dual-frequency combinations is greater than that corresponding to the single-frequency [13]. At the same time, the peak negative pressure duration of the single-frequency, dual-frequency, and triple-frequency combinations are 0.2 \(\upmu\)s, 0.23 \(\upmu\)s, and 0.24 \(\upmu\)s, respectively. It can be seen from Figure 4 that the duration of peak negative pressure of the three different combined frequencies of ultrasound is relatively small, but the difference of peak negative pressure is relatively large. The peak negative pressure of the triple-frequency combination is the largest while that of the single-frequency ultrasound is the smallest. The increase of peak negative pressure reduces the cavitation threshold of the medium, and the probability and intensity of cavitation are also greater [41]. It is concluded that when the peak negative pressure of the triple-frequency combination is the largest and the peak negative pressure of the single-frequency ultrasound is the  
Figure 4: Pressure waveforms of different frequency combinations in liver: (**a**) 2.6 MHz; (**b**) 2.6 + 2.0 MHz; (**c**) 2.6 + 2.0 + 1.4 MHz. smallest, the transient cavitation threshold of the triple-frequency combination is the lowest, and the transient cavitation threshold of the single-frequency ultrasound is the highest. In the same way, taking Figure 3d as an example, Figure 5 theoretically analyzes the reason for the difference of transient cavitation threshold of liver under the combined irradiation of 1.4 MHz, 1.4 + 2.0 MHz, and 1.4 + 2.0 + 2.6 MHz. In Figure 5, the initial bubble radius is 5 \(\upmu\)m and the initial pressure is 0.101 MPa under three different frequencies combined ultrasonic irradiation. From Figure 5, it can be found that the peak negative pressures of the single-frequency (1.4 MHz), dual-frequency (1.4 + 2.0 MHz), and triple-frequency (1.4 + 2.0 + 2.6 MHz) combined ultrasound are \(-\)0.1009 MPa, \(-\)0.1266 MPa, and \(-\)0.1685 MPa, respectively. At the same time, the peak negative pressure durations of the single-frequency, dual-frequency, and triple-frequency ultrasound are 0.37 \(\upmu\)s, 0.29 \(\upmu\)s, and 0.24 \(\upmu\)s, respectively. Under the ultrasonic irradiation of three different combined frequencies, the peak negative pressure of the corresponding ultrasound is \(\sim\)0.1 MPa, and the difference is not very large. However, their peak negative pressure duration is quite different. The longer the peak negative pressure duration is in a certain time range, the stronger the cavitation intensity is [42].