## 3 Result and Discussion
### Considering All Dynamic Tissue Properties  
In the above research results, the individual influence of each tissue property on HIFU hyperthermia was studied independently. Therefore, in this section, it is necessary to perform the simulation using all of the dynamic tissue properties to explore the joint influence on HIFU hyperthermia by comparing them with simulations using dynamic \(\alpha_{{\it liver}}\) and constant tissue properties. Note that we assume that the non-linearity parameter above 75 \({}^{\circ}\)C is replaced by that at 75 \({}^{\circ}\)C to simplify the physical model owing to (i) the dynamic non-linear parameter being found to have little effect on the acoustic pressure, temperature, and thermal damage zone in our calculation (Figure 5b-d); and (ii) above 75 \({}^{\circ}\)C, biological tissue having been coagulated. To ensure that all of the dynamic tissue properties are valid within their respective temperature ranges, the HIFU irradiation time is set to  
Figure 8: (**a**) Dynamic blood perfusion change with time. (**b**) Axial profile of dynamic blood perfusion at t = 2 s and 10 s. The effects of dynamic blood perfusion on: (**c**) \(p\) and (**d**) \(T\) at the ultrasonic focus and (**e**) thermal damage zone; (**f**) \(Q_{43}\) at t = 10 s.  
3 s. At time t = 3 s, Figure 9a shows that the peak acoustic pressure for simulation using all of the dynamic tissue properties is larger than that using dynamic \(\alpha_{\mathit{liver}}\) and constant tissue properties due to the influence of dynamic sound velocity, and the peak acoustic pressures are almost the same between the dynamic \(\alpha_{\mathit{liver}}\) and constant tissue properties. In Figure 9b, the peak value of \(Q_{\mathit{ext}}\) is the greatest for simulation using all of the dynamic tissue properties, followed by that for simulation using dynamic \(\alpha_{\mathit{liver}}\), and the smallest for simulation using constant tissue properties. In Figure 9c, before t = 1 s, the focal temperature is almost the same for simulation using dynamic \(\alpha_{\mathit{liver}}\) across all of the dynamic tissue properties and constant tissue properties; after t = 1 s, the rate of focal temperature rise is fastest for simulation using dynamic \(\alpha_{\mathit{liver}}\), followed by that for simulation using all of the dynamic tissue properties, and slowest for simulation using constant tissue properties. The maximum focal temperature for all of the dynamic tissue properties, dynamic \(\alpha_{\mathit{liver}}\), and constant tissue properties are 81.56 \({}^{\circ}\)C, 85.53 \({}^{\circ}\)C, and 65.94 \({}^{\circ}\)C, respectively, indicating that the maximum focal temperature for all of the dynamic tissue properties is lower than that for dynamic \(\alpha_{\mathit{liver}}\), although the peak value of \(Q_{\mathit{ext}}\) for all of the dynamic tissue properties is greater than that for dynamic \(\alpha_{\mathit{liver}}\). Based on the above research, this is mainly due to the influence of the comprehensive factors such as dynamic \(C_{\mathit{liver}}\), dynamic \(K_{\mathit{liver}}\), and dynamic \(W_{\mathit{b,liver}}\) on focal temperature, especially the influence of dynamic \(K_{\mathit{liver}}\). In Figure 9d, the thermal damage zone is an ellipse of 0.57 cm \(\times\) 0.16 cm size for all of the dynamic tissue properties, an ellipse of 0.6 cm \(\times\) 0.16 cm size for dynamic \(\alpha_{\mathit{liver}}\), and an ellipse of 0.51 cm \(\times\) 0.12 cm size for constant tissue properties, respectively. Consequently, it is can be concluded that the simulation using constant tissue properties significantly underestimates the focal temperature and thermal damage zone compared with the simulation using all of the dynamic tissue properties or dynamic \(\alpha_{\mathit{liver}}\). Meanwhile, although the dynamic acoustic absorption coefficient plays the most important role in relation to the focal temperature and thermal damage zone, other dynamic tissue properties ought to be considered.