## 3 Experiment and Analysis
### Imaging  
Figure 2a as a cross-sectional anatomy image provides a preliminary reference [51] for us to understand the human thigh structure. In order to build a simulation model with more details, the inner structure information of human thigh needs to be obtained by B-mode ultrasound imaging, especially the details of the tumor region.  
The B-mode ultrasound image of human thigh tissue has been constructed by the Delay and Sum (DAS) [52] algorithm, which is supported by the K-Wave simulation tool with ring ultrasound transducer array, as shown in Figure 2b. B-mode ultrasound image helps us to find the focus position for HIFU heating and provides us with the a priori information of the internal medium in SOS imaging. In the process of SOS image reconstruction, we first split up the human thigh model into seven parts including skin, subcutaneous fat, muscle, thigh bone, bone marrow, tumor and blood vessels with the boundary information from the B-mode ultrasound image. Due to the existence of thermal diffusion, the temperature  
Figure 4: Density map of human thigh model (Submerged in water). (**a**) Model A: radius of muscle is 55 mm, radius of tumor is 6.5 mm. (**b**) Model B: radius of muscle is 60 mm, radius of tumor is 6.5 mm. (**c**) Model C: radius of muscle is 65 mm, radius of tumor is 6.5 mm. (**d**) Model D: radius of muscle is 60 mm radius of tumor is 6 mm. (**e**) Model E: radius of muscle is 60 mm radius of tumor is 7 mm. (**f**) Model F: radius of muscle is 70 mm radius of tumor is 6.5 mm.  
gradually decreases along the direction of thermal diffusion with the focusing position as the center. Therefore, the SOS in each part is not consistent. The simplification model of SOS distribution reconstruction is established using the average value of each part in the actual SOS image as the value of the target SOS in the corresponding part. In the iterative estimation of SOS distribution with FWI method, the SOS in each part is unrelated with other parts and the initial SOS in each part refers to the acoustic properties of the corresponding human tissue. Furthermore, we set the SOS in thigh bone, bone marrow and blood vessels to the standard values (SOS values at room temperature) and keep the SOS in these regions constant. The reasons for the constant SOS in the above regions are as follows. Firstly, since the regions of bone and bone marrow are outside the effective heating area, HIFU heating almost has little influence in the two regions. Secondly, considering the size of vessel regions, the SOS change in the small region hardly contributes to the accuracy of the whole SOS iteration. Meanwhile, the SOS iteration in the small region is sensitive to noise which may lead to the wrong iteration direction of SOS, so it is necessary that SOS in vessel regions remains constant. These assumptions help us to improve the accuracy in estimating the SOS values and the reconstruction image of SOS is shown in Figure 2c. Since the accurate SOS in the tumor region is essential to the temperature-controlled hyperthermia, the SOS in the internal region of the tumor is averaged to improve the robustness and accuracy of SOS estimation. During the SOS imaging iteration, the averaged SOS value in tumor region is illustrated in Figure 5. From Figure 5b (a zooming curve of the black rectangle region in Figure 5a); we can discern that the SOS fluctuation in the tumor region can be limited to less than 0.2 m/s which in return can yield the temperature monitoring accuracy to 0.2 \({}^{\circ}\)C.