## 3 Experiment and Analysis
### Simulation Setup  
Our simulation is performed in a three-dimensional space supported by K-Wave. 3D simulation space is defined as \(N_{x}\times N_{y}\times N_{z}\) (\(490\times 490\times 40\)) in grid size, in which the spacing of each grid point is about 0.449 mm. The actual physical size of the simulation model is 220 \(\times\) 220 \(\times\) 18 mm. By observing Figure 2a, we can find that the internal structures of the human thigh including: skin, subcutaneous fat, muscle, thigh bone, bone marrow, tumor and blood vessels. All the tissues are defined respectively with reference to the properties such as size, SOS, density, attenuation coefficient, thermal conductivity and heat capacity in Table 1[49]. In addition, the blood perfusion rate is set to 0.01 s\({}^{-1}\). In our study, we assume the human thigh is placed in the ring ultrasound transducer array with 256 elements (with 100 mm radius and 9 mm height) as shown in Figure 1. The whole thigh is immersed in water at a constant temperature of 30 \({}^{\circ}\)C. All the ultrasound elements transmit pulse signals with five cycles. In addition, the center frequency of the transmitted signals is 1.5 Mhz whereas the sampling frequency is 12 MHz. Therefore, the wavelength is approximately 1 mm calculated from the center frequency and SOS. Considering that the height of the ring ultrasound transducer array is 9 mm, the focal shape should be a linear acoustic source composed of nine elements instead of one single acoustic source. Figure 3a illustrates the focus of ultrasound signals emitted by three of the 256 elements. The gray level represents the intensity of sound pressure and the focus spot is in black. It is illustrated that the profiles of ultrasound signals generated by 2 of 256 elements in Figure 3b. Figure 3c shows the pressure field in Pa generated by the ring ultrasound transducer array with 256 elements. To confirm the universality of the simulation, we set three human thigh models with different muscle radius including 55.00 mm, 60.00 mm and 65.00 mm. Furthermore, we change the position of the tumor according to the growth characteristic that tumors may grow close to blood vessels because they rely on vessels to provide a lot of oxygen and nutrients [50]. The multiple models of human thigh referring to Figure 2a are given in Figure 4, which displays the density maps of different human thigh models. Figure 2: (**a**) Cross-sectional anatomy image of human thigh tissue. (**b**) B-mode ultrasound imaging of human thigh tissue provided by K-Wave simulation tool with ring ultrasound transducer array. (**c**) Reconstruction image of SOS imaging (unit: m/s). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Medium** & **Size (mm)** & **SOS (m/s)** & **Density** & **Attenuation** & **Thermal** & **Specific Heat** \\  & & **(kg/m\({}^{3}\))** & **Coefficient** & **Conductivity** & **Capacity** \\  & & & **(NP/Mhz-m)** & **(W/m\({}^{\circ}\)C)** & **(J/kg.\({}^{\circ}\)C)** \\ \hline Water & 220 \(\times\) 220 \(\times\) 18 & 1482 & 1000 & 0.025 & 0.60 & 4178 \\ \hline Skin & 1.70 (Thickness) & 1595 & 1109 & 21.158 & 0.37 & 3391 \\ \hline Fat & 10.00 (Radius) & 1430 & 911 & 4.358 & 0.21 & 2348 \\ \hline Muscle & 60.00 (Radius) & 1580 & 1090 & 7.109 & 0.49 & 3421 \\ \hline Bone & 5.80 (Radius) & 2198 & 1178 & 47.000 & 0.32 & 1313 \\ \hline Bone Marrow & 6.70 (Radius) & 1372 & 980 & 4.358 & 0.20 & 2065 \\ \hline Tumor & 6.50 (Radius) & 1450 & 1050 & 5.650 & 0.51 & 3540 \\ \hline Blood Vessel Wall & 0.50 (Thickness) & 1570 & 1100 & 7.020 & 0.46 & 3306 \\ \hline Big Vessel (Blood) & 2.90 (Radius) & 1550 & 1060 & 2.368 & 0.52 & 3617 \\ \hline small Vessel (Blood) & 0.65 (Radius) & 1550 & 1060 & 2.368 & 0.52 & 3617 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of medium_Size describes the internal structure in the simulation model we used. SOS, Density and Attenuation Coefficients were used to calculate the acoustic field, and Thermal Conductivity and Specific Heat Capacity were used to calculate the biological heat transfer.