## 3 Simulation Results
### Effect of Phase Angle Difference on Transient Cavitation Threshold  
The phase angle difference of the ultrasonic excitation signal has an influence on the distribution of sound pressure and the occurrence of bubble chaotic oscillation [43], and it also has an influence on the  
Figure 5: Pressure waveforms of different frequency combinations in liver: (**a**) 1.4 MHz; (**b**) 1.4 + 2.0 MHz; (**c**) 1.4 + 2.0 + 2.6 MHz.  
transient cavitation threshold in the medium. In order to study the influence of different phase angle differences of the multifrequency excitation signal on the transient cavitation threshold, taking the three different kinds of phase angle combinations of triple-frequency (\(2.6+2.0+1.4\) MHz) excitation as an example, the phase angle of 2.6 MHz excitation is set to 0, and that of 2.0 MHz and 1.4 MHz excitation are \(\alpha\) and \(\beta\), respectively, and the phase angles of 2.0 MHz and 1.4 MHz excitation are \(\alpha=\beta=0\), \(\alpha=2\pi/3\), \(\beta=\pi\) and \(\alpha=2\pi/3\), \(\beta=4\pi/3\), respectively. The phase angle difference between them is gradually increasing, and the phase angle differences are 0, \(\pi/2\), and \(2\pi/3\), respectively. Figure 6 shows the relationship between the transient cavitation threshold and the initial bubble radius under triple-frequency excitation with different phase angle differences in water, blood, brain, and liver.  
It can be seen from Figure 6 that when the initial bubble radius in water, blood, brain, and liver is small, the transient cavitation threshold excited by triple-frequency (\(2.6+2.0+1.4\) MHz) is almost not affected by the change of phase angle difference at first, which may be caused by the nonlinear decrease of bubble oscillation [44]. The amplitude of transient cavitation threshold in brain and liver fluctuates less than that in water and blood. When the bubble radius is larger, the corresponding transient cavitation threshold is more sensitive to the phase angle difference of the excitation, which is more obvious in water and blood. Specifically, when the initial bubble radius in water, blood, brain, and liver is greater than 5.8 \(\upmu\)m, 5.3 \(\upmu\)m, 4.2 \(\upmu\)m, and 4.1 \(\upmu\)m, respectively, the cavitation threshold of different phase angle differences is significantly different. Under the same larger initial bubble radius, when the phase angle is \(\alpha=\beta=0\), the phase angle difference of the triple-frequency excitation is 0, and the transient cavitation threshold is the lowest compared with other phase angle differences; when the phase angle is \(\alpha=2\pi/3\), \(\beta=4\pi/3\), the phase angle difference of the triple-frequency excitation is \(2\pi/3\), and the transient cavitation threshold of these four media is at the highest value compared  
Figure 6: Transient cavitation threshold of triple-frequency (2.6 + 2.0 + 1.4 MHz) excitation with different phase angle differences in different media: (**a**) water; (**b**) blood; (**c**) brain; (**d**) liver.  
with other phase angle differences. With the increase of the phase angle difference of triple-frequency excitation, the corresponding transient cavitation threshold of the triple-frequency excitation in the medium increases gradually. Therefore, the phase angle difference of the multifrequency excitation has an impact on the transient cavitation threshold in the medium. In the actual HIFU treatment process, the lower transient cavitation threshold can be obtained by selecting the appropriate phase angle difference of the multifrequency excitation.