# Low-Frequency Magnetic Field Exposure System for Cells Electromagnetic Biocompatibility Studies
## 3 Numerical Simulations of Exposure System  
Simulations are performed using two commercially available simulation software--CST Studio Suite and COMSOL Multiphysics to compare the results of numerical simulations of the identical model concerning the B-field distribution and its homogeneity in the AOI [38]. Each AOI is in real experiments Erlenmeyer flask filled with yeast extract-peptone-dextrose (YPD) medium with beer yeast cells Saccharomyces Cerevisiae. Within the simulations, the AOI is represented by a cylinder with dimensions of 68 mm in width, 40 mm in height, and a volume of 145 cm\({}^{3}\) and is filled with distilled water, Figure 2. Considering the percentage of distilled water in the YPD medium--95%, its substitution for distilled water, in terms of dielectric material properties, in the simulations, is permissible. Primary numerical simulations were realized to adjust the appropriate parameters of the system, where it was investigated how the input parameters influence the magnetic flux density distribution and its homogeneity [39]. The model includes two identical applicators--the exposed one and the control one, shielding between the coils, a metal incubator and ten samples representing the AOI, all depicted in Figure 2. The shielding with dimensions 1000 \(\times\) 160 mm\({}^{2}\) (height \(\times\) width) is placed exactly in the middle between the coils. The distance between the edges of coils is 174 mm. The internal walls of the incubator Q-cell 240 are made from plastic. It is not known which kind of material is behind the internal plastic wall, so the simulations are made for the worst situation. Thus, the case behind the internal plastic wall is made from iron. The incubator manufacturer did not provide a technical drawing of the internal composition of  
Figure 2: Components included in the numerical model. the incubator with a description of the material used. Therefore, the incubator is represented as a container with dimensions 1315 \(\times\) 504 \(\times\) 320 mm\({}^{3}\) (height \(\times\) width \(\times\) depth) in the numerical simulation. The walls of the incubator are modelled by a metal sheet with a thickness of 2 mm; the shielding is created from a metal sheet with a thickness of 3 mm. The electromagnetic parameters of the metal sheets at a frequency of 50 Hz are the ones from the simulation software library:  
* \(\varepsilon_{\text{r}}=1\)
* \(\mu_{\text{r}}=1000\)
* \(\sigma=1.04\times 10^{7}\) S-m\({}^{-1}\). This type of metal sheet is usually used in the manufacturing of refrigerators. Ninety evaluation points, nine in each AOI, are considered for calculating the homogeneity of B-field (HBF). The B-field as RMS is calculated at these evaluation points and based on these values the HBF is calculated in the exposure coil for each sample separately:  
\[\text{HBF}=\frac{B}{B_{\text{C4}}}\times 100\ [\%] \tag{1}\]  
where \(B_{\text{C4}}\) is the value of B-field exactly in the middle of the coil, sample C, point 4 (p4), Figure 2, since the reference value \(B_{\text{C4}}\) also represents the highest value of the B-field from all evaluation points, the value of \(B\) is substituted by the minimum value within a particular sample, so HBF represents the worst case of each sample's homogeneity. The whole numerical space is discretized using a tetrahedral mesh in the CST Studio, and the low-frequency domain solver employing a magnetoquasistatic equation is applied. Built-in function Symmetry Planes cannot be applied; the boundary condition in XY, YZ, and YX planes are set to the open ones. For this reason and due to available computing capacity, the simulations are performed with the accuracy of \(10^{-3}\). However, simulation complexity and computational capacity limit the simulation accuracy. In COMSOL, the model is created in a 3D spatial layout discretized using an automatic generated tetrahedral fine mesh. Then, the multiphysical interface electromagnetic heating and the frequency-transient study are applied.