## 4 Evaluation
### Simulation Condition for Evaluation  
In this subsection, we firstly describe the simulation method used to verify the hypothesis. Then, we describe the simulation conditions. There are various types of electric field analysis methods that can be used in the human body, including FDTD (finite difference time domain method) [18] and FEM (finite element method) [19]. FDTD is a method that divides a finite region into cubic cells and obtains an electromagnetic field value for each cell on the basis of Maxwell's equations. It is possible to handle complicated objects by setting a medium for each cell. However, the FDTD method is time consuming. This is because FDTD requires an enormous number of iterations to perform the calculations for the low frequency band [20]. Although solutions have been investigated to overcome the problem of time consumption for FDTD in the low frequency band, most existing studies focus on frequency ranges of more than 100 Hz [20; 21]. Since the frequency range of the stimulation used in this study is supposed to be 10 Hz, based on our previous studies [11; 22], it is difficult to perform FDTD under our simulation conditions. An addition problem is that the staircase approximation is required for objects that have many curved surfaces, causing large errors. Therefore, FDTD is not suitable for the analysis of more complex tissues such as the human brain. FEM is a method that decomposes an object into small elements and finds electromagnetic fields inside each element. Although it is computationally expensive, it is suitable for performing electromagnetic field analysis on small objects such as the human body. Moreover, FEM can be performed even in the low frequency band. Therefore, we also used electric field analysis using the FEM method in our previous studies [11; 22]. SimNIBS is a free software package that supports the use of FEM to perform electric field simulations for Non-Invasive Brain Stimulation (NIBS) [23; 24; 25; 26]. SimNIBS was also been used in the previous studies, and divides the human body, which is the object of analysis, into tetrahedrons for simulation. Any model can be used as the human body model for the purposes of analysis using SimNIBS, but [PERSON] is given as an example. [PERSON] is a young and healthy man. His head model was created by applying the average facial data from five subjects, thus concealing his face. Informed consent was given in writing to disclose MR (magnetic resonance) data, and the data were completely anonymized following confirmation by the radiologist. High-resolution T1- and T2-weighted images and diffusion MR images were used for [PERSON]'s dataset. [PERSON]'s is a highly detailed dataset, with voxel sizes of \(1\times 1\times 1\) mm\({}^{3}\) for the T1- and T2-weighted images and \(2\times 2\times 2\) mm\({}^{3}\) for the diffusion MR images. SimNIBS is able to simulate stimulation using TMS and tDCS (transcranial direct current stimulation) as the initial setting, and the simulation result of tDCS can be used for the use of tACS in the low-frequency band. Since the frequency value in this study is supposed to be 10 Hz, as previously mentioned in this subsection, the tDCS simulation can be used to perform the evaluation. The simulation of tDCS in SimNIBS follows Laplace's equation to find the potential. \[\
abla\cdot(\sigma\
abla\varphi)=0\ \ \ \ \ (in\ \Omega), \tag{1}\]  
\[\mathbb{E}=-\
abla\varphi\ \ \ \ \ (in\ \Omega), \tag{2}\]  
\(\Omega\) is the range covered by the numerical calculations. In Equation (1), \(\sigma\) is the conductivity and \(\varphi\) is the potential caused by an external stimulus. \(\mathbb{E}\) in Equation (2) represents the electric field and is obtained by the gradient of the potential. In FEM, it is necessary toestablish a partial differential equation, as shown in Equation (1), within the range of all regions \(\Omega\). In SimNIBS, the weak form of the partial differential equation is derived, and the desired potential is obtained using the Galerkin method.