## 3 Results
### Improvement of TI Stimulation Optimization with Free Pair Acceptance of Electrodes  
Electrodes were randomly chosen to validate the optimization of electrode pair combinations for the two most crucial factors in TI stimulation: (1) electrode pair combination and (2) difference in current adjustment. More electrode combinations were calculated by allowing a free selection of electrodes instead of selecting only parallel pairs. Accordingly, a combination of electrode pairs was made by selecting four possible electrodes, hence the total number of electrodes that could be selected was \({}_{24}\)C\({}_{4}\) = 10,626 electrodes. This is referred to as cross-optimization TI (Cross opt TI). Figure 4a shows the difference in electrode arrangement between parallel opt TI and cross opt TI.  
Figure 4: Comparison of TI stimulation results in parallel optimization and electrode-free optimization (**a**) Concept of electrode arrangement between parallel optimization and electrode-free settings. (**b**) Comparison of parallel opt TI and cross opt TI results, *_p_ < 0.005.  
The left of Figure 4b shows the slice distribution result of parallel optimization and electrode-free optimization. The right of Figure 4b shows the comparison of PR values of parallel optimization and electrode-free optimization and the difference in the PR values. For visualization purposes, the PR value of parallel opt TI for each subject was assigned to be 0 as the reference point, and the difference between the PR values of parallel opt TI and cross opt TI is displayed on the right side. As noted in the previous section, for the parallel opt TI, the PR value was 3.3957 \(\pm\) 0.8553, and for Cross opt TI, the PR value was 3.7876 \(\pm\) 0.9307. To confirm the significance of the average difference in PR values, a paired \(t\)-test was performed. The purple dots represent raw data. The mean and standard deviation of the changes are shown in black. The mean PR value of Cross opt TI was higher than that of parallel opt TI (+12%) (\(p<\) 0.005).  
Table 3 shows a comparison of optimal electrode pairings for parallel-opt TI and cross-opt TI across all models. Subject ID refers to the ID of the patient used in the experiment. Parallel opt TI Pair refers to the optimal pair of two electrodes obtained through simulation for the patient. Since electrode pairs form an electric field, and in this methodology, they form two electric fields, so we named them E1 and E2 in descending order according to the number of electrode pairs that make up each. In all E1 and E2, the electrodes shown on the front are positively charged, and the electrodes shown on the back are negatively charged. In certain models, cross-opt TI and parallel-opt TI showed the same optimal pair conditions, but for others, the electrode settings were changed. An analysis of the corresponding anatomical factors can be seen in Figure S2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subject ID** & **Parallel Opt TI Pair** & **Cross Opt TI Pair** \\ \hline  
61F9C73 & E1: 10, 22 & E2: 12, 24 & E1: 6, 13 & E2: 10, 23 \\ AFA8C6F48087 & E1: 10, 22 & E2: 12, 24 & E1: 5, 13 & E2: 10, 23 \\ BDBD4C7F4443 & E1: 11, 23 & E2: 12, 24 & E1: 10, 24 & E2: 10, 23 \\ EB27F9C7 CA47 & E1: 1, 13 & E2: 8, 20 & E1: 10, 21 & E2: 12, 24 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Electrode pair differences between parallel opt and cross opt-in all models.