## 3 Results  
### Necessity of TI Stimulation Optimization  
Figure 3 suggests the importance of optimizing the TI stimulation parameters. We arranged 24 electrodes in two rows as shown in Figure 3a and numbered the electrodes in the counterclockwise direction according to the position of the reference electrode. To understand the electrode arrangement, the slices of the 1 st layer and 2 nd layer are displayed on the right side of Figure 3a. In the 1 st layer, the electrode at the same position as the reference electrode is designated as No. 1, and the number of electrodes in all layers is 12. Electrodes numbered 13 to 24 are present in the 2 nd layer. The reference electrodes are placed for individual E-field formation.  
In this section, electrode pairs are formed with electrodes in the same position on the first and second layers. Since the two electrode pairs that form the electric fields E1 and E2 are in a parallel relationship, this was named a parallel electrode pair. All models were evaluated for the lowest and highest PR values in the case where only parallel electrode pairs were allowed. Figure 3b shows the concept for all parallel electrode pair evaluations. The red and blue dots indicate the positions of the electrode pairs, and it can be confirmed that the electrode pairs do not cross and have a parallel relationship. The purple dot indicates the area where energy is concentrated when TI stimulation is applied using the two electrode pairs. The focused area changed depending on the location of the electrode, and the conditions of the electrode location where energy was concentrated in the target area were investigated.  
The left side of Figure 3c compares the E-field slice distribution results of the worst-case and parallel optimizations. The setting that was optimized for parallel pairs was called parallel optimization TI. The right side of Figure 3c shows the comparison of the difference in PR values of the worst TI and parallel opt TI for all models. To visualize the difference between the PR values of the two groups, the PR value of the worst TI for each subject was set at 0, the reference point, and the difference between the PR values of the parallel opt TI and worst TI is displayed on the right side. For the worst TI, the PR value was 0.0389 \(\pm\) 0.0231 (mean \(\pm\) standard deviation). For the parallel opt TI, the PR value was 3.3957 \(\pm\) 0.8553. \(E_{total}\) was the average value of the electric fields in the entire area, including areas not activated by stimulation, whereas \(E_{target}\) was the average of electric fields induced in the only target nerve. We calculated the ratio of the average value of the  
Figure 3: Comparison of TI stimulation results in the worst case and parallel electrode pair optimization. (**a**) Example of an electrode arrangement for TI stimulation (**b**) Concept of an unoptimized electrode setting and optimized electrode setting. (**c**) Comparison of worst TI and parallel opt TI results, \({}^{*}p<0.001\).  
electric field of the entire area and the target area as the PR value to prevent numerical errors. As the targeting ability improves, the energy is concentrated in the targeted area while minimizing the energy in the unwanted background area. Therefore, the average value of the energy in the target area is much higher than the average value of the energy in the entire background area, which may result in higher PR values than in studies using previous PR values.  
To confirm the significance of the average difference in PR values, a paired _t_-test was performed. Purple dots represent raw data. The mean and standard deviation of the changes are shown in black. The PR value of the parallel opt TI was 87 times higher than that of the worst TI (_p_ < 0.001).