## Materials and Methods
### Electro-Quasistatic Boundary Value Problem  
In general, the macroscopic behavior of electromagnetic fields is described by [PERSON]'s equations. Assuming negligible magnetic inductive effects and propagation in the low-frequency regime (\(f=20\,\text{Hz}\)) as is commonly valid for bioelectric phenomena, [PERSON]'s equations can be simplified and the so-called electro-quasistatic approximation can be applied. In this case, the time-harmonic electric field is uniquely defined by the complex scalar potential \(\underline{\varphi}\) with \(\mathbf{E}=-\
abla\underline{\varphi}\). Assuming no impressed currents, this leads to  
\[\
abla\cdot\left(\left[j\omega\varepsilon_{0}\varepsilon_{r}(\mathbf{r}, \omega)+\sigma(\mathbf{r},\omega)\right]\
abla\underline{\varphi}(\mathbf{r}) \right)=0\,, \tag{4}\]  
with the imaginary unit \(j\), the angular frequency \(\omega\), the permittivity of free space \(\varepsilon_{0}\), the relative permittivity \(\varepsilon_{r}(\mathbf{r},\omega)\), and the electric conductivity \(\sigma(\mathbf{r},\omega)\). Details on the derivation can be retraced in, e.g., [58; 59; 60].  
We apply terminals with Dirichlet boundary conditions at the electrodes, with ground potential (\(\varphi=0\,\text{V}\)) at the surface of the posterior electrode and the stimulation potential to be optimized \(\varphi_{\text{stim}}\
eq 0\,\text{V}\) at the surface of the anterior electrode (Figure 3). Homogeneous Neumann boundary conditions are applied to the surface of the skin domain representing the insulating air.  
Figure 2: Equivalent circuit model for the electrode–tissue interface.  
The mesh tray introduced in Section 2.1 serves as an additional stabilization for the bone but also has an impact on the resulting electric field distribution. To reduce the complexity of the model and computation time, the mesh tray has not been modelled explicitly, but only been regarded as a floating potential boundary condition at the lateral and lower boarder of the defect region (Figure 3). The floating potential boundary condition  
\[\underline{\varphi}=\underline{\varphi}_{0}\,,\quad\int_{\partial\Omega}- \mathbf{n}\cdot\mathbf{J}dS=I_{0}=0\,\mathrm{A} \tag{5}\]  
applies a constant potential \(\varphi_{0}\) on the chosen surfaces, implying that the tangential electric field is zero and the electric field is perpendicular to the boundary. The value of the resulting potential depends on the integral source current \(I_{0}\). In our study, we regard \(I_{0}=0\,\mathrm{A}\), implying that the boundary will act as an unconnected perfect conductor. As the conductivity of the mesh tray is several orders of magnitude higher than that of the surrounding tissue, this is a valid approximation. Comparative simulations in a simplified model setup showed that the error in the electric field norm compared to a fully modelled mesh tray is less than 3% but the reduction in CPU time is 45%.  
Considering the mentioned boundary conditions summarized in Figure 3, Equation (4) is solved for the complex electric potential \(\underline{\varphi}(\mathbf{r})\). From this quantity, the complex amplitude of the electric field strength \(\underline{\mathbf{E}}=-\
abla\underline{\varphi}\) can be derived. Finally, the electric field norm \(|\underline{\mathbf{E}}|\) is computed that is used to rate the stimulation impact.