# Stimulation Montage Achieves Balanced Focality and Intensity
## 2 Materials and Methods
### Experiment Design  
To test the performance of the proposed algorithm SBFI, and compare it to the conventional two-electrode system and some available algorithms mentioned, we designed various stimulation cases based on different clinical applications. First, the simplest test is to stimulate a single target containing only one voxel in the motor cortex with a desired intensity of 0.3 V/m (Figure 1), i.e., \(n_{tar}=11\), \(\mathbf{e}_{0}\) has a dimension of \(3\times 1\), and \(C\) has a dimension of \(3\times m\); this scenario mimics common clinical use. The second test is to stimulate multiple targets derived from synthetic data [15]. As indicated in Figure 2, the stimulation targets contain three brain regions with a maximum electric field of 0.3727 V/m in the left frontal lobe (region 1), 0.3522 V/m in the left occipital lobe (region 2), and 0.2841 V/m in the left temporal lobe (region 3). In this case, target voxels refer to those with an electric field intensity larger than 0.05 V/m. Therefore, \(n_{tar}=111\), \(\mathbf{e}_{0}\) has a dimension of \(333\times 1\), and \(C\) has a dimension of \(333\times m\). Our third test measures how each algorithm performs with real EEG data from a seizure patient. The target regions are identified by EEG source localization [15; 36]. In addition to examining SBFI performance on multiple targets in real seizure data, this study also demonstrates the applicability of our method to EEG-guided brain stimulation. Similar to the synthetic case, there are three target areas in the EEG-guided case, shown in Figure 3. One is in the occipital cortex (region 1) with maximum electric field of 0.1107 V/m, while the other two are on the left and right prefrontal lobe (region 2 and 3) with intensities of 0.0702 V/m and 0.0844 V/m, respectively. Due to the infeasibility of a conventional two-electrode system to target multiple areas, it is excluded in the performance comparison study of optimization algorithms for multiple targets. The comparison is therefore between SBFI, CLS, and MI. Figure 1: Results for the single target protocol. (**A**) Desired electric field and result of conventional montage. (**B**) Results of different optimization algorithms. The color scale represents intensity of the electric field, in V/m. (Note: Results are shown at the same scale [0, 0.3] V/m for various algorithms except CLS. The intensity above 0.3 V/m is saturated for visualization.) (**C**) The electrode configurations calculated by different algorithms. The Conventional montage and MI methods produce spread-out electric field distributions with a small number of electrodes. The CLS method can achieve focal stimulation, but the intensity is too weak. In addition, it requires the utilization of 80 electrodes, which is another drawback compared to the others. Both LCMV and SBFI successfully achieve focusing stimulation with sufficient intensity. SBFI is slightly better than LCMV in terms of intensity, target error, and focality. Figure 2: Results for the synthetic multiple targets protocol. (**A**) Results of different optimization algorithms for the synthetic multiple targets protocol. The color scale represents intensity of the electric field, in V/m. (Note: Results are shown at the same scale [0, 0.3727] V/m for various algorithms except for CLS. The intensity above 0.3727 V/m is saturated for visualization.) As before, the intensity of the CLS method is too weak, while the MI method appears to activate the whole left hemisphere. Only SBFI provides a good balance between stimulation intensity, precision, and accuracy. The LCMV was unable to find a valid solution for the multi-target case. (**B**) The electric field distribution pattern of SBFI using a single \(\lambda\) targeting synthetic multiple brain regions. (**C**) The electric field distribution pattern of SBFI using different \(\lambda\).