# Numerical Study on the Application of Near-Infrared Temperature Distribution Measurement of HIFU
## 3 Results
### Nonlinear Effect  
When ultrasound propagates in biological tissues, its amplitude is sufficient to generate higher-order harmonics. Under the influence of strong ultrasound fields, non-linear effects have an important impact on the temperature field. As the energy increases, the non-linear effects excite higher-order harmonics. As the number of harmonics increases, the ultrasound pressure in the ultrasound field also increases. In this study, the non-linear components of the second order and above were ignored. The focus was on studying the non-linear characteristics, including the second harmonic. Figure 5 shows the comparison results of the ultrasound and thermal fields between the non-linear model and the linear model under different input powers.  
The following conclusion can be drawn by comparing the calculation results of the linear and non-linear models. With the increase in power, the maximum axial sound pressure shows an upward trend in both models. However, considering the non-linear effect, the increase in ultrasound pressure is more significant. The ultrasound pressure value calculated using the non-linear model is higher for a given power. Since the thermal field is calculated based on the ultrasound field, the significant enhancement of non-linear effects on the ultrasound pressure means that the trend of the temperature rise is also  
Figure 4: Simulation results of ultrasound and thermal fields corresponding to 100 W under linear conditions: (**a**) depicts the ultrasound field distribution of ultrasound; (**b**) shows the temperature distribution; (**c**) illustrates the ultrasound pressure distribution along the ultrasound axis; (**d**) shows the highest temperature rise after 5 s of ultrasound application.  
Figure 5: Comparison results of ultrasound and thermal fields between non-linear and linear models under different input powers.  
more pronounced. These results indicate that non-linear effects significantly impact the ultrasound and temperature fields of HIFU, especially in high-power situations. Under the action of 100 W sound power, the non-linear maximum ultrasound pressure is 38% higher than the linear one, and the maximum temperature is 13% higher.  
There is a slight deviation of 0.07 mm at the highest point of ultrasound pressure in both the linear and non-linear models. However, the highest point of temperature shifted by 0.9 mm away from the direction of the transducer. The influence of the non-linear effects on the propagation characteristics of the ultrasound waves can explain this offset. The non-linear effect enhances the focusing of the ultrasound energy, allowing the ultrasound waves to be more concentrated and converted into thermal energy, resulting in the corresponding movement of the highest temperature point away from the transducer. This result is of great significance for the application of HIFU technology. Understanding the influence of non-linear effects on ultrasound focusing and temperature distribution enables us to optimize and regulate HIFU device parameters effectively. It ensures the maximum focus on the ultrasound energy and the accurate positioning of the temperature, thereby achieving more effective treatment effects and ensuring patient safety.