# Low-Frequency Magnetic Field Exposure System for Cells Electromagnetic Biocompatibility Studies
## 3 Numerical Simulations of Exposure System
E-field induced by the magnetic field (MF) generated by the exposure coil is of the order of \(10^{-4}\) V\(\cdot\)m\({}^{-1}\) in both coils. In the peripheral parts of the samples, there is a sharp increase and decrease in the monitored parameter due to the induced eddy currents in the samples, Figure 5.  
The E-field induced in the cell culture medium by the MF generated by the developed coil is in the order of \(10^{-4}\) V\(\cdot\)m\({}^{-1}\). The reported threshold for an E-field to elicit a biological effect is estimated to be around \(10^{-4}\) V\(\cdot\)m\({}^{-1}\) for neutrophil cells [8] and used in research into umbilical cord blood lymphocytes [40]. Thus, it is questionable if the EF generated by the new exposure system can be neglected, and the results obtained for biocompatibility studies can be referred to be caused by the MF. On the other hand, the E-field in the presented exposure system is 10-11 orders of magnitude lower than the E-field across a 7.5 nm thick cell membrane [41] with a typical transmembrane potential of 50-120 mV, which turns out to be 6.67 MV\(\cdot\)m\({}^{-1}\). Therefore, for the E-field calculation, the yeast cell is considered as a spherical capacitor according to:  
\[\mathrm{E}=U\frac{R_{2}}{R_{1}}\frac{1}{R_{2}-R_{1}} \tag{2}\]  
where \(U\) is the transmembrane potential, considered as 50 mV, \(R_{2}\) is the external diameter of the cell representing the external electrode, and \(R_{1}\) is the internal diameter of the cell representing the internal electrode. The \(R_{1}\) value is calculated as a difference between \(R_{2}\) and the thickness of the yeast cell membrane with a value of 7.5 nm. According to the calculation described above, the E-field induced by the new exposure system in the cell culture medium should not affect the processes in the cell membrane. Figure 4: Electric field distribution in exposure and control coil, data from CST Studio Suite. In the next step of simulations, the frequency change's effect on the of the B-field's homogeneity is verified. Eight frequencies are used: 50, 100, 500, 1000, 1500, 2000, 2500, 3000 Hz. The results show that the change in frequency does not affect the homogeneity of the B-field. The temperature field distribution is evaluated using COMSOL in the samples after two, four, six, and eight hours from the start of the experiment, while the initial temperature is set to 30 \({}^{\circ}\)C. A graphical representation of the spatial temperature distribution in the AOI after eight hours of irradiation is shown in Figure 6. Any temperature variation and notable temperature differences between exposure and control AOIs are observed at a current of 0.7 A and a magnetic flux density of maximal value of 2.4 mT for the eight hours duration of the experiment. The temperature distribution is uniform. The exposure coil does not cause temperature increase due to Joule heating of the content in the samples. The proposed exposure system is suitable for cell electromagnetic biocompatibility research studies. The crucial findings from the simulations are that there is a negligible influence of the iron shielding and of the incubator's iron walls on the exposure level or homogeneity. Figure 5: Total current density in exposure and control coil, data from CST Studio Suite.