The developed model was tested and compared to another head model (the IT'IS head model, namely, MIDA model [23]), by simulating transcranial Direct Current Stimulation (tDCS), which is a form of electrical neurostimulation that uses direct electric current from a pair of electrodes placed on the head. MIDA model is a highly detailed human head and neck model with isotropic spatial resolution of 0.5 mm (the same as Menelik) and contains 115 different anatomical structures. The model was obtained from IT'IS free of charge (from IT'IS website).

For tDCS simulation, we considered two electrodes of size 5X7 cm^2 that consist of layers of 6 mm thick saline soaked sponge (conductivity 1.6 S/m) and 1 mm thick metallic sheet. The cathode electrode was placed above the right supraorbital region and the anode above the hand knob region of the left primary motor cortex as shown in fig. 6. The electric scalar potential distribution in the models was computed numerically by solving the charge continuity equation. The electric field strength was computed from the electric scalar potential gradient. The computation was performed using the stationary current solver of CST Studio by maintaining a potential difference of 0.5 V between the metallic layers of the anode and cathode. The low frequency tissue conductivity provided on the IT'IS database was used for the electromagnetic material properties of the different anatomical structures of the models.

The tDCS was simulated using three head models (the Menelik voxel model, Menelik surface mesh model, and MIDA voxel model) by employing two types of volumetric meshes (tetrahedral and hexahedral meshes). The computation domain of the Menelik voxel model was sampled to 278,476,016 hexahedral meshes. Similarly, the computation domain of the MIDA voxel model was sampled to 280,713,600 hexahedral meshes. The Menelik surface mesh model was sampled in both hexahedral and tetrahedral volumetric meshes. The surface mesh model enables computation at much finer hexahedral meshes since the model is not limited by the minimum voxel resolution (which is, 0.5 mm). Consequently, the computation domain for the Menelik surface mesh model was sampled at higher resolution of 542,138,912 hexahedral meshes. Moreover, for the FEM based computation, the Menelik surface mesh model was meshed to 38,791,002 tetrahedrons as shown in fig. 6. Given the complexity of the Menelik head model, the generation of the tetrahedral meshes took 3 days and 8 hours running on a workstation with 12 CPUs and 215 GB of RAM. Due to the limitations of the built-in CST Studio mesh generation algorithm, only one CPU was used that resulted in a much longer completion time.

As shown in fig. 7, the electric field distributions for the three models are similar. This is expected since the number and locations of the electrical materials (materials with unique conductivity) in the three models are similar. Even though the MIDA model contains large number of anatomical structures, the electrical conductivities of some of the structures are similar. For example, 30 anatomical structures are muscular tissues, 17 are nerves, 11 are cortical bones, and 9 are air cavities. Consequently, all the anatomical structures in the MIDA model were assigned 21 unique conductivity values, which is equivalent to the 22 unique conductivity values assigned for the structures in the Menelik model. Despite the similarity in the electric field distribution, there are differences in the computed electrode current. The computed electric current for the Menelik voxel model is 1.228 mA, for the Menelik surface mesh model (hexahedral) 1.613 mA, for the Menelik surface mesh model (tetrahedral) 1.414 mA, and for the MIDA voxel model 2.532 mA. The electric current difference between the Menelik voxel and surface mesh model is attributed to the difference in the resolution of the computation domain sampling. The computation domain for Menelik surface mesh model was sampled at higher resolution that included features with dimension smaller than the resolution of the voxel model (0.5 mm); thus, the electric current value for the Menelik surface mesh is more accurate. Moreover, the small difference in the current values of the Menelik surface mesh in tetrahedral and hexahedral volumetric mesh is due to the type of solvers used and the difference in volumetric mesh type. The Menelik model has more fat and thicker cranium than that of the MIDA model (see next section), which accounts for the higher impedance; consequently, the electric current is smaller for the Menelik model.

It is a common practice to test the numerical accuracy of a computational model by computation of the specific absorption rate (SAR) in radio frequency (RF) MRI transmit coil. SAR is a measure of the rate at which RF electromagnetic energy is absorbed by the human body. SAR is defined as the absorbed (dissipated) RF power per unit mass of tissue. As a testing and validation tool, SAR is utilized to check for errors or `flaws' in the model, which are manifested by very sharp SAR peaks. The cause of the errors could be artefacts, such as, isolated pieces of anatomical structures in wrong locations, sharp edges, and gaps between boundaries.

MRI birdcage coils loaded with the Menelik and MIDA voxel model were simulated using the high frequency time-domain solver of CST Studio. The birdcage coil has 16 rungs and two ends rings with capacitive elements (10.2 pF) tuned for resonance at 63.87 MHz; and it was driven with an input power of 2 W (see fig. 8). The computed local SAR of Menelik shows that there are no sharp peaks, which indicates the model has passed the basic validation test. Additionally, the model was also compared to the MIDA model based on the computed SAR and power loss in the tissues. Since SAR values from MRI are often presented in normalized form, the computed SAR was normalized for B+1 field at the coil center of 1 uT using the expression SAR^n=SAR /(B+1 / 1 u T)^2. Table 2 shows the normalized SAR values, the normalized maximum SAR averaged over 1 g and 10 g tissue weight, the total power loss in the tissues, weight and volume of the two models. It is striking to see that the power loss in the two models is nearly equal, which is about 3.1 mW. However, the total SAR for MIDA is slightly higher than Menelik due to the difference in weight. Additionally, the weight and power loss fraction of selected tissues, which comprise about 87% of the total weight and 85% of the power loss, are shown in table 2. The weight of fat and cortical bone is significantly higher in Menelik (2.2217 kg, 40.72%) than MIDA model (1.619 kg, 34.32%) whereas the weight of other tissues are virtually similar. The MIDA model includes the muscular tissues in the neck, which explains the equivalent muscle weight in the two models. Some anatomical structures in MIDA model (caudate nucleus, globus pallidus, hippocampus, mammillary body, nucleus accumbens, putamen, substantia nigra, and thalamus) were added to the grey matter since they have similar electrical and physical properties; thus, their total weight is equivalent to the grey matter of Menelik (where such structures were not segmented separately). Further analysis also shows that the highest power loss occurred in muscular tissue (21.03% in Menelik and 25.07% in MIDA model), which is expected since the muscle is soft tissue and has large volume. However, the power loss relative to tissue weight (SAR^n) is much higher in CSF and skin in the two head models, which is plausible since CSF has high conductivity and skin is the outermost tissue. Moreover, the SAR^n of the CSF (0.31 W/kg) and skin (0.29 W/kg) are equivalent for the two models, which can serve as another indicator to the high level of accuracy of Menelik model