## 3 Results  
### Acoustic Field and Energy Dissipation  
This section addresses the acoustic characteristics induced by LIFU in a model excluding the SCC structure and examines the acoustic dissipation calculated in the model that includes the SCC. The first step in the analysis of acoustic streaming is to observe the changes in acoustic pressure distribution due to variations in transducer frequency. However, when the SCC is present, it can distort the pressure profile in the propagation path. To avoid this distortion, we first calculated the focal characteristics of LIFU without the SCC in the water domain. All calculations were performed using a transducer designed with a focal distance of 42 mm at frequencies of 400, 600, and 800 kHz, and both axial and lateral directions were analyzed using normalized intensity. The normalization was applied based on the intensity result at 800 kHz, which had the highest intensity. For the axial direction (Figure 4a), normalization was applied using the maximum intensity of 38.21 W/cm\({}^{2}\) at 800 kHz. The results showed that as the frequency increased, the focal distance became longer. The focal distance for the 400 kHz transducer was the shortest, measuring 40.616 mm with an intensity of 9.82 W/cm\({}^{2}\). The 600 kHz transducer had a focal distance of 41.383 mm with an intensity of 21.66 W/cm\({}^{2}\), while the 800 kHz transducer had a focal distance of 41.619 mm. As the frequency increased, the focal length became closer to the designed geometric focal distance of 42 mm. This result was due to the effect of diffraction reduction caused by the increased frequency. Generally, higher ultrasound frequencies lead to shorter focal distances due to greater attenuation at higher frequencies [55]. However, this result is based on findings in the water domain, where the attenuation coefficient is low [41]. Additionally, since we used lower frequency bands in ultrasound, the overall impact of diffraction reduction, particularly for higher Fresnel numbers, is more pronounced [56]. The reduction in diffraction improves the directivity of acoustic wave propagation, indicating that higher frequencies bring the focal point closer to the geometric focal distance. Although higher frequencies increase the precision of the focus, in the field of transcranial ultrasound, the frequency cannot be arbitrarily increased [33; 34; 35]; thus, the analysis was conducted using the currently designed transducer. The lateral direction results were calculated along the line defined by y = 0, corresponding to the z-value where the intensity was maximum in the axial direction (Figure 4b). Normalization was applied using the maximum intensity value (38.21 W/cm\({}^{2}\)) at each frequency to determine the full width at half maximum (FWHM). As the frequency increased, the FWHM narrowed, measuring 2.54 mm at 400 kHz, 1.72 mm at 600 kHz, and 1.30 mm at  
Figure 3: Comparison between the 2D axisymmetric model and the FEM-BEM combined model. The result compares the total acoustic pressure along the axial distance and shows similar trends with minimal error. 800 kHz. These results indicate that as the frequency increases, the ultrasound becomes more focused with a smaller focal volume. Since the model without the SCC treats all domains as water, phenomena such as reflection or refraction at material boundaries do not need to be considered; as a result, a clean intensity profile is observed. However, in models with the FEM domain, the ultrasound passing through water and temporal bone can distort the wavefront due to the wave propagation phenomena. These phenomena are also present at the boundary between the temporal bone and the SCC. Taking these factors into account, the model calculated the total acoustic dissipation in the SCC and temporal bone, which is particularly important for determining the streaming velocity of the endolymph and concurrent temperature rise. As the area where streaming velocity occurs increases, the displacement of the copula also increases.