## 4 Evaluation
### Method for Evaluating Simulation Results  
In this subsection, firstly, the default output style of SimNIBS simulation is described, along with the method for transforming the output value of the simulation in order to be able to perform the evaluation. In the default output style of SimNIBS, the electric field transition on the specific tissues is described visually. As described in Section 4.1, the human tissues are divided into tiny elements by means of FEM using SimNIBS. Therefore, the default value of the electric field is assigned to one tiny element as a simulation result. The simulation results are represented as changes in the color of the electric field on the surface of the eyeball, which is composed of tiny triangles. This output style makes it easy to observe the stimulated area in a specific tissue. However, it is difficult to compare the spatial information numerically. Therefore, it is necessary to employ a method that makes it easy to perform numerical comparisons. In this study, the eyeball surface is transformed into a plane surface in order to be able to compare the stimulated area on the eyeball surface numerically. We employed a method in which the spherical eyeball is output as a plane, similar to the Mercator projection of the globe. In SimNIBS, each of the many tiny triangles dividing the surface of the tissues has a single electric field value, and these triangles are not always equilateral triangles. It is challenging to transform the eyeball surface formed by this set of triangles into a plane. Therefore, as shown in the first step in Figure 6, an electric field value is assigned to a single point at the center of gravity of the triangle, in order to be able to handle it easily. As a result of this, only a single coordinate value is processed for each electric field value. Regarding the electric field values obtained by the simulation, the range of electric field values is normalized in order to be able to compare them with the results obtained using other electrode placements. The maximum electric field value is converted to 1, and the minimum electric value is converted to 0 in the second step of Figure 6. After dividing the electric field value data obtained with both eyes into data for each eye, as shown in the third step shown in Figure 6, in the fourth step, the rectangular coordinates of each element's center of gravity on the eyeball surface are converted into the polar coordinates. This conversion is a preliminary step for the transformation of the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Electrode**} & **Anode’s Coordinate** & **Cathode’s Coordinate** & **Electrode** & **Anode’s Coordinate** & **Cathode’s Coordinate** \\  & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** \\ \hline
1 & (63.36, 59.78, \(-\)24.16) & (18.1, 78.77, \(-\)95.18) & 4 & (\(-\)38.82, 78.54, \(-\)27.97) & (\(-\)37.49, 65.82, \(-\)93.9) \\
2 & (\(-\)67.2, 59.45, \(-\)24.09) & (\(-\)27.79, 75.21, \(-\)97.31) & 5 & (\(-\)1.03, 99.96, \(-\)23.91) & (18.1, 78.77, \(-\)95.18) \\
3 & (34.79, 78.28, \(-\)27.44) & (36.84, 60.07, \(-\)94.86) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coordinates of each stimulus electrode on the human face. Figure 5: The origin of the coordinate set in the head mesh model; figures were produced by the authors in SimNIBS (1 November 2021). eyballs into a plane, in a similar manner to the Mercator projection. In the 3D conversion of the polar coordinates, the provided coordinates correspond to the radius of the eyeball, the degrees of longitude, and the height in the eyeball. Therefore, the vertical axis of the transformed plane shown in the final step of Figure 6 represents the height coordinate in the eyeball, while the horizontal axis of the plane corresponds to the angular coordinates of the eyeball. The range of values on the vertical axis reflects the radius of the eyeball, and the range of values on the horizontal axis is approximate \(-\pi\) to \(\pi\).