## 3 Result and Discussion
### Dynamic Sound Speed, Specific Heat Capacity, Thermal Conductivity, and Density  
Simulations are carried out using the dynamic sound speed, dynamic specific heat capacity, dynamic thermal conductivity, and dynamic density, respectively, and the HIFU irradiation time is 10 s. Figure 6 describes the axial profiles of dynamic sound speed, dynamic specific heat capacity, dynamic thermal conductivity, and dynamic density, which are affected only by the temperature in the vicinity of the ultrasonic focus. Figure 5: (**a**) The evolution of \((B/A)_{liver}\) at t = 2 s and 5 s. The effects of the dynamic non-linearity parameter on: (**b**) \(p\) and (**c**) \(T\) at the ultrasonic focus, and (**d**) the thermal damage zone at t = 5 s.  
Figure 7a shows that the axial profiles of the peak acoustic pressure for simulations with dynamic \(C_{\mathit{Liver}}\), dynamic \(K_{\mathit{Liver}}\), and dynamic \(\rho_{\mathit{Liver}}\) are almost the same as that for simulation with constant tissue properties. At ultrasonic focus, the peak acoustic pressure with dynamic \(c_{\mathit{Liver}}\) is a little greater than that with constant tissue properties, which is consistent with previously reported results [14]. Figure 7b demonstrates the evolutions of focal temperature with time for simulations using dynamic \(c_{\mathit{Liver}}\), dynamic \(C_{\mathit{Liver}}\), dynamic \(K_{\mathit{Liver}}\), dynamic \(\rho_{\mathit{Liver}}\), and constant tissue properties, respectively. Before t = 2 s, the rate of focal temperature rise is almost the same for simulations using dynamic \(c_{\mathit{Liver}}\), dynamic \(C_{\mathit{Liver}}\), dynamic \(K_{\mathit{Liver}}\), dynamic \(\rho_{\mathit{Liver}}\), and constant tissue properties. This may be due to the very small change in the tissue properties during the early HIFU irradiation stage, as shown in Figure 6. After t = 2 s, Figure 6 shows that the sound speed and density decrease with the increase of HIFU irradiation time, but the specific heat capacity and thermal conductivity have the opposite trend. According to Formula (5), the values of focal \(Q_{\mathit{ext}}\) for dynamic \(c_{\mathit{Liver}}\) and dynamic \(\rho_{\mathit{Liver}}\) are both greater than that for the constant tissue properties. Consequently, the rate of focal temperature rise for dynamic \(c_{\mathit{Liver}}\) and dynamic \(\rho_{\mathit{Liver}}\) is faster than that for constant tissue properties, as shown in Figure 7b. The rate of focal temperature rise for dynamic \(C_{\mathit{Liver}}\) is slower than that for constant tissue properties. This feature can be explained by the physical significance of specific heat capacity, which is defined as the amount of energy that is required to increase the temperature of a unit mass of tissue by 1 \({}^{\circ}\)C [27]. In other words, for the same amount of heat energy and mass, the larger the specific heat capacity, the smaller the temperature rise. The focal temperature for dynamic \(K_{\mathit{Liver}}\) rises slower than that for constant \(K_{\mathit{Liver}}\), and the focal temperature for dynamic \(K_{\mathit{Liver}}\) is 5.33 \({}^{\circ}\)C lower than that for the constant tissue properties at 10 s. This feature can be explained by the greater thermal conductivity meaning that more thermal energy is lost from the treated areas because of thermal diffusion [28]. Therefore, it can be concluded that greater thermal conductivity leads to a slower focal temperature rise, which is similar to [PERSON]'s result [9].