## 2 Materials and Methods
### Simulation Model  
A two-dimensional axisymmetric simulation model of the HIFU ablation was established by using COMSOI 6.0, as shown in Figure 1. In this simulation, the curvature radius of the transducer was 150 mm and the aperture diameter was 95 mm. The excitation signal was a sine wave with a center frequency of 1.12 MHz. Assuming that tissue is a homogeneous medium, the thickness of the tissue for the simulation was 50 mm and the diameter 50 mm.  
The transducer size and ablation tissue used by [PERSON] et al. [12] in low-power cumulative HIFU were different from those in this study. When the acoustic power was 50 W (acoustic intensity at focus was 425 W/cm\({}^{2}\))--150 W (acoustic intensity at focus was 1250 W/cm\({}^{2}\)) in this study--the acoustic intensity was roughly equal to that of 110 W (acoustic intensity at focus was 423 W/cm\({}^{2}\)), while it would be 300 W (acoustic intensity at focus was 1150 W/cm\({}^{2}\)) in clinical treatment according to the numerical calculation.  
The perfectly matched layer (PML) was used for the boundary of the simulation area to absorb the acoustic waves propagating to the boundary of the solution area and to prevent the reflected waves from interfering with the acoustic field focus when the acoustic waves propagate to the boundary.  
The grid size used in the numerical calculation in this study was 0.1 mm \(\times\) 0.1 mm (\(<\)\(\lambda\)/10, \(\lambda\) is wavelength), which could meet the accuracy requirements for solving the acoustic and thermal fields. The initial temperature of the tissue in the simulation was 30 \({}^{\circ}\)C, consistent with the experimental ambient temperature.  
Table 1 shows the acoustic intensity at the focal point of the focusing transducer in water at different powers used in this experiment.  
Simulations were performed in phantom and bovine liver to explore the relationship between their BFRs and the AFR. The acoustic and thermal parameters of the two tissues are shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline
**Power** & **Intensity** \\
**[W]** & **[W/cm\({}^{2}\)]** \\ \hline
50 & 425 \\ \hline
75 & 624 \\ \hline
100 & 831 \\ \hline
125 & 1040 \\ \hline
150 & 1270 \\ \hline \end{tabular}
\end{table}
Table 1: Acoustic power and corresponding intensity at the focus.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Tissues** & **Acoustic Velocity** & **Attenuation Coefficient** & **Density** & **Heat Capacity** & **Thermal Conductivity** \\  & \(c\) **[m**\(\cdot\)**s\({}^{-1}\)]** & \(\alpha\) **[Np**\(\cdot\)**m\({}^{-1}\)**\(\cdot\)**MHz\({}^{-1}\)]** & \(\rho\) **[kg**\(\cdot\)**m\({}^{-3}\)]** & \(C\) [J**\(\cdot\)**kg\({}^{-1}\)**\(\cdot\)**K\({}^{-1}\)]** & \(\kappa\) **[W**\(\cdot\)**m\({}^{-1}\)**\(\cdot\)**K\({}^{-1}\)]** \\ \hline Phantom & 1570 \({}^{\mathrm{a}}\) & 7.7 \({}^{\mathrm{a}}\) & 1060 \({}^{\mathrm{a}}\) & 3600 \({}^{\mathrm{a}}\) & 0.5 \({}^{\mathrm{a}}\) \\ Bovine liver & 1596 & 3.5 & 1036 & 3560 \({}^{\mathrm{b}}\) & 0.5 \({}^{\mathrm{b}}\) \\ \hline \end{tabular}
\end{table}
Table 2: Acoustic and thermal parameters of the two tissues.  
Figure 1: Schematic diagram of the model used in the simulation.