# Low-Frequency Magnetic Field Exposure System for Cells Electromagnetic Biocompatibility Studies
## 3 Numerical Simulations of Exposure System
The values of HBF calculated in CST Studio and COMSOL in the exposure coil are listed in Table 1. The results show that the applied B-field uniformity of the AOI of three middle samples B, C, and D in the exposure coil is better than 99.16%, in sample A is minimum homogeneity of 92.55%, in sample E is the homogeneity of 92.75%. Therefore, the three middle samples would be a suitable solution for the research focused on electromagnetic biocompatibility studies at a cellular level. The two edge samples should be considered in further experiments as the non-homogeneous application of B-field. However, the existence of two sets of samples--homogeneous and inhomogeneous--can offer interesting and important results, namely how the less homogeneity of the applied field affects cell growth. Since the control samples represent a state without intervention, the main objective for the control coil is to reach the magnitude of the B-field lower than the Earth's magnetic flux density value of 39 \(\pm\) 5 \(\mu\)T, measured at the original experimental sample's location. The geomagnetic field measurement is performed with a Vernier Labquest3 measuring instrument incorporating a Vernier MG-BTA probe. The maximal values of B-field RMS values obtained by simulation in CST and COMSOL are listed in Table 2. The highest value \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Sample/** & \multicolumn{2}{c}{**A**} & \multicolumn{2}{c}{**B**} & \multicolumn{2}{c}{**C**} & \multicolumn{2}{c}{**D**} & \multicolumn{2}{c}{**E**} \\ \cline{2-10}
**Software** & **CST** & **CM** & **CST** & **CM** & **CST** & **CM** & **CST** & **CM** & **CST** & **CM** \\ \hline \(B\) [mT] & 95.61 & 92.55 & 99.77 & 99.71 & 99.88 & 100 & 99.16 & 99.72 & 95.13 & 92.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The homogeneity of B-field at evaluation points in CST Studio and COMSOL in exposure coil. of the B-field appeared in sample A at the level of 11.16 \(\upmu\)T, which represents approximately 29% of the earth's magnetic field value. The results from both simulation programs are comparable in the center of the exposure coil and control coil, but values from the upper edge of the exposure coil differ significantly. The RMS values of the B-field obtained from both simulation programs differed in all evaluating points at most at 84 \(\upmu\)T (4.94%) in the exposure coil and 4 \(\upmu\)T (47.75%) in the control coil. The difference in the obtained values is acceptable and is caused by a different calculation method of the applied software programs, finite integration technique vs finite element method. The CST Studio is used for further verification of the EMF parameters of the exposure system. Figure 3 shows the variation of B-field distribution in the solenoid on the axis at the input current of 0.7 A versus distance of the sample's position in the coil cavity. The exposure coil meets the homogeneity criteria only in the three central samples, B, C, and D. The control coil meets the criteria of the maximum value of the B-field in all five samples. The variation of E-field distribution in the coil on the axis at the current input of 0.7 A versus distance of the sample's position in the coil cavity is shown in Figure 4. The \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample/Software**} & \multicolumn{2}{c}{**A**} & \multicolumn{2}{c}{**B**} & \multicolumn{2}{c}{**C**} & \multicolumn{2}{c}{**D**} & \multicolumn{2}{c}{**E**} \\ \cline{2-11}  & **CST** & **CM** & **CST** & **CM** & **CST** & **CM** & **CST** & **CM** & **CST** & **CM** \\ \hline \(B\) [mT] & 11.16 & 8.12 & 8.89 & 6.13 & 7.89 & 5.54 & 8.65 & 5.52 & 10.58 & 6.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The maximal value of B-field at evaluation points in CST and COMSOL in control coil. Figure 3: Magnetic flux density distribution along the axis for exposure and control coil, data from CST Studio Suite.