# Stimulation Montage Achieves Balanced Focality and Intensity
## 3 Results
### Study with Multiple Targets  
When stimulating disjointed target regions, the conventional two-electrode montage is no longer feasible, and using a multiple-electrode system is the only reasonable approach. Thus, the multiple-target studies exclude the conventional system, and comparisons are made only between different optimization methods. It is worth pointing out that LCMV performs reasonably in the single target case, but due to the hard constraint, the LCMV method has no feasible solution set for multiple target cases tested in our study. Therefore, we were not able to compare the performance of LCMV with all the other methods. The failure to have a feasible solution is the key drawback of the LCMV method, and this motivates us to propose the SBFI model. Desired electric field distribution of synthetic multiple targets is shown in Figure 2A. Similar to the results of the single target study, CLS can mimic the electric field distribution pattern of the desired result, except the intensities of all three regions are almost an order of magnitude smaller than the desired value. The effectiveness of stimulation is questionable at such low intensities. On the contrary, the MI method produces high enough stimulation intensity in those three areas but sacrifices the focality. From the distribution figure, it is hard to recognize three discrete areas; the MI method appears to activate the whole left hemisphere. In the case of the proposed SBFI method, effective and precise stimulation can be achieved simultaneously with \(\lambda=diag(0.5885,\ 0.247,\ 0.247)\). The intensity of all three regions is higher than 0.1 V/m, which is enough to induce cortical changes as shown in the literature [20; 40; 41]. Although the focality values of the three regions are relatively higher than in CLS, the energy outside the target region is actually lower than the threshold, which in turn will not be able to activate neurons. Thus, it is an acceptable tradeoff to see this small increase in focality value. Overall, the proposed SBFI method provides a good balance between stimulation intensity, precision, and accuracy. It not only can provide sufficient stimulation intensity as performed in the MI method, but also is able to minimize target error and focality simultaneously. Figure 2B shows the results of SBFI using a scalar \(\lambda\). It is clear that the scalar \(\lambda\) fails to balance the three target regions. The desired intensity of all three target regions is similar, but the result intensity at the motor cortex region is much lower than the other two  
regions. It appears the system does not favor the targets on the motor cortex region. One possible explanation could be the size of the target region. Intuitively, it is easier for the system to stimulate a large region than a tiny region because fewer electrodes are needed to minimize the intensity at the surrounding non-target region. If the target size is defined as the maximal distance between the target voxels and target mass center, the size of the motor cortex target is 12.9444 mm, which is the smallest among the three, compared to 13.6425 mm on the occipital lobe and 17.7783 mm on the temporal lobe. Thus, in order to compensate this unbalanced distribution of size, we have to assign different \(\lambda_{i}\) for different target regions. The results in Figure 2A clearly show that the proposed SBFI method can achieve reasonable balance between the intensity and locality by fine-tuning the optimization parameter \(\lambda=diag\Big{(}\lambda_{motor},\,\lambda_{occipital},\,\lambda_{temporal} \Big{)}\). This flexibility allows the system to achieve different optimal results tailored to various applications. Decreasing the values of \(\lambda\) will increase the weight of the first term \(\parallel\mathbf{Ds}\parallel^{2}\), which controls focality. The result will always have better focality and lower target error but with relatively lower intensity. For example, when \(\lambda\) is chosen to be \(diag(0.1085,\,0.055,\,0.055)\), the algorithm favors focality.