## 2 Materials and Methods
### Validation of Numerical Methods: Acoustic Streaming, Heat Transfer, and FEM-BEM  
Since our model involves a variety of physical phenomena, including fluid flow and heat transfer induced by acoustics, each aspect of the physics was validated separately by comparing it with previous experimental or numerical results. Additionally, since the model includes an integrated system with both FEM and BEM domains, we compared the integrated model with a 2D axisymmetric FEM model, which is commonly used in finite element analysis. First, the fluid flow induced by acoustics was compared with experimental results on the streaming velocity in water caused by focused ultrasound [53]. For comparison, our model used a transducer with a frequency of 5.05 MHz, an acoustic pressure of 191 kPa at the source position, and a diameter of 10 mm. The result matched the experimental data well, particularly regarding the peak streaming velocity as the distance from the acoustic source increased (Figure 2a). Therefore, our acoustic streaming model was validated as a credible representation of the streaming effect triggered by focused ultrasound stimulation. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Study** & **Species** & **Rotation Condition** & **Displacement** & **Method** & **Reference** \\ \hline [PERSON] and [PERSON], 1979. & Bullfrog & Max. 200\({}^{\circ}\)/s rotation & 7–14 \(\mu\)m &
\begin{tabular}{c} Cinematographic \\ analysis \\ \end{tabular} & [48] \\ [PERSON] et al., 2009. & Oyster & Sinusoidal rotation & 53 nm per deg/s & Fluorescent microsphere & [49] \\ [PERSON] et al., 2019. & Human & Dix-Hallpike motion & Max. 44.2 \(\mu\)m & Finite element analysis & [28] \\ [PERSON] et al., 2020. & Human & 10\({}^{\circ}\)/s\({}^{2}\) & 1.3 \(\mu\)m & Finite element analysis & [52] \\ \hline \end{tabular}
\end{table} 
Table 2: Cupula displacement: experimental animal data and simulated human data. Second, we validated our model by comparing the results of heat generation in human tissue exposed to focused ultrasound [31]. When using tissue instead of bone, the following simulation settings were applied to verify whether similar results could be obtained as those found in the literature: frequency = 1 MHz, thermal conductivity = 0.59 W/(m\(\cdot\)K), specific heat = 3700 J/(kg\(\cdot\)K), density = 1045 kg/m\({}^{3}\), sound speed = 1550 m/s, and acoustic absorption coefficient = 10.1 Np/m. As in other studies [32; 43], the simulation was conducted using a 2D axisymmetric model, and ultrasound exposure was applied for 1 second. The comparison of temperature rises was conducted over a total duration of 5 seconds (Figure 2b). The result demonstrated good agreement between our simulation and the literature, although our results showed slightly lower temperature increases. Similarly, in this study, the ultrasound exposure duration was set to 1 second. This duration is commonly used in previous studies to evaluate temperature increases in biological tissues [43; 54]. The setting was also chosen to compare the resulting temperature increase with the U.S. Food and Drug Administration (FDA) guidelines for thermal safety and to provide a reproducible and clear standard for analysis. In finite element simulations related to ultrasound, 2D axisymmetric models are primarily used [32; 43]. This is because the small wavelength of ultrasound requires extremely small element sizes, which leads to an abnormal increase in computational costs [32]. However, since our model includes an asymmetric SCC, an axisymmetric model could not be used. Therefore, as an alternative, we constructed a 3D model that combines FEM and BEM. As mentioned earlier, the FEM model includes the endolymph, cupula of the SCC, and temporal bone, while the BEM covers the transducer and water domain. To verify the validity of this integrated model, we created a separate 2D axisymmetric model. The transducer used in our study followed the transducer parameters from [PERSON] et al., but with a modified focal length [31].