## 2 Methods
### Finite Element Discretization and Simulation  
After attaining the dielectric properties of each anatomical layer and neuromodulator settings, the cochlea model with an electrode array embedded and was meshed using tetrahedral finite elements for numerical solutions of partial differential equations in COMSOL. The ST and the tissue layers near the ST were meshed finely to obtain sufficient accuracy while reducing excessive computation time. Mesh settings for the electrode model were adaptively adjusted to different sizes and growth rates in different models. Since the outermost layer (bone) was far from the region of interest, the discretization element size was selected to be larger (i.e., known as the normal tetrahedral setting) than the cochlea \begin{table}
\begin{tabular}{l c} \hline \hline
**Anatomical Layers** & **Conductivity (S/m)** \\ \hline Scalas & 1.43 \\ \hline Basilar membrane & 0.0125 \\ \hline Spiral ligament & 1.67 \\ \hline Cochlea wall & 0.3 \\ \hline Sony layer & 0.0156 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Standard conductivity values for cochlea layers. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Anatomical Layers** & **Conductivity (\(\sigma\))** & **Relative Permittivity (\(\epsilon_{p}\))** \\ \hline Scalas & 1.789–2.46 & 16.6–68.4 \\ \hline Basilar membrane & 2.02 \(\times\) 10\({}^{-1}\)–9.78 \(\times\) 10\({}^{-1}\) & 2.57 \(\times\) 10\({}^{7}\)–5.48 \(\times\) 10\({}^{1}\) \\ \hline Spiral ligament & 2.51 \(\times\) 10\({}^{-1}\)–7.6 \(\times\) 10\({}^{-1}\) & 1.99 \(\times\) 10\({}^{7}\)–4.56 \(\times\) 10\({}^{1}\) \\ \hline Cochlea wall & 4.08 \(\times\) 10\({}^{-2}\)–3.12 \(\times\) 10\({}^{-1}\) & 3 \(\times\) 10\({}^{4}\)–6.2 \\ \hline Bony layer & 2.04 \(\times\) 10\({}^{-2}\)–1.56 \(\times\) 10\({}^{-1}\) & 5.22 \(\times\) 10\({}^{2}\)–1.24 \(\times\) 10\({}^{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Approximate values for the electrical properties of anatomical layers of the cochlea based on the frequency spectrum (10 Hz–100 MHz). layers. The meshing sizes were modified manually if the warnings were received from the software. The total number of the meshing elements varied between 0.1 million (M) to 0.2 M, depending on the model. Any surface that does not have a set value for potential or current has its current density set to zero to confine the current within the model. To calculate the electric potential variation based on the QS, the cochlea was assumed to be electrically passive, with each anatomical structure having an isotropic specific conductivity, as shown in Table 2. The electrical potential was governed by [PERSON]'s equation Equation (1). To measure the capacitive impact of the tissue on the induced electrical potential, the TS of Maxwell equation Equation (2) was used. \[\
abla\cdot(\sigma\
abla\
abla)=0 \tag{1}\]  
\[\
abla\cdot\left(\sigma\
abla\
abla-\varepsilon_{0}\varepsilon_{\mathrm{r}} \
abla\frac{\partial\
abla}{\partial t}\right)=0 \tag{2}\]  
where \(\sigma\) is the tissue conductivity, \(V\) is the measured electrical potential within the domains, \(\varepsilon_{0}\) is the permittivity of free space, and \(\varepsilon_{\mathrm{r}}\) is relative permittivity. \(\
abla\) is the Hamiltonian operator. After defining the solution method, an isotropic and homogeneous dielectric property of each tissue based on different frequency samples was assigned to each sub-domain of each cochlea model, as shown in Table 3. The wave propagation and inductive effects were assumed to be negligible. The charge-balanced on a fully differential rectangular waveform based on the desired frequency sample was applied to each electrode to obtain the results, as shown in Figure 4.  
Figure 4: Simulation of the anatomical layers by inserting current via electrode contact. The applied current pulse is shown in (**A**). The electrical potential (EP) variation distributions within the anatomical layers are shown in (**B**). The recorded EP based on the specified frequency level is shown in (**C**).