## 2 Materials and Methods  
The research on interactions between the human body and the electromagnetic waves requires the utilization of an appropriate numerical method and numerical body models. For the purpose of this research, the Remcom XFdtd computer program was applied [18; 19]. It implements the FDTD numerical method that is widely used for electromagnetic simulations of microwave structures fabricated with dielectric materials of complex properties [20; 21]. It is especially useful for simulating biological effects from electromagnetic radiation [15]. This method is very efficient in providing accurate results of the field penetration into biological tissues [22; 23]. Computer simulation of energy absorbed by body tissues with the FDTD method and numerical model of body is a well established methodology for studying the thermal effect of the interaction of the human body with electromagnetic waves. In [24], the predicted values of absorbed energy were compared to data obtained from an empirical experiment based on measurements with infrared thermography. Comparison between numerical solutions (FDTD) and empirical data showed good agreement. That is why I used this method in further research. In computer programs that utilize FDTD, models of simulated objects have to be divided into cuboidal elementary cells (voxels) with a side-length not larger than one-tenth of the wavelength in the simulated object. Often, in the case of heterogeneous body models, much smaller voxels are used, which results from the need to reproduce small body structures such as, for example, thin blood vessels or small bones. The simulation of the entire body with these models requires the use of many elementary cells, and hence the significant hardware resources of the computer, in the memory of which the model is stored and values of wave parameters calculated for all voxels. Heterogeneous anthropomorphic models, especially, when used to simulate interaction with very short waves, require time-consuming computer simulations and may require the use of significant hardware resources (in particular, computer memory). To reduce the simulation time, for this investigation only the model of the human head was used, which is presented in Figure 1. It is a model that was elaborated based on body scans using the magnetic resonance technique at the Hershey Institute [25; 26]. The model is provided by the Remcom company to be used with XFdtd software (software: XFdtd version 7.8.1 manufacturer: Remcom, 315 South Allen Street, Suite 416 State College, PA, USA). In this model, tissues are characterized with the Cole-Cole extrapolation technique [27]. Their dielectric parameters for each frequency of interest were taken from the literature [28]. This heterogeneous model consists of 24 different tissue materials divided on 1 mm voxels. In Figure 2, the cross-section of the head model is presented and the tissue materials are indicated with different colors. The width of the model (\(x\) direction dimension) is 277 mm, depth (\(y\) direction dimension) is 181 mm, and model height (\(z\) direction dimension) is 299 mm. The total number of voxels is 7,139,900 and the mass is 7.969 kg. The number of voxels and mass of each tissue are given in Table 1 in  
The numerical experiments were performed assuming the plane electromagnetic wave as the source of energy. The simulations were made for the frequency equal to 750 MHz and 3600 MHz. The angles of wave incidence \(\varphi\) and \(\theta\) are defined in Figure 1. The simulations were made for \(0^{\circ}\leq\varphi\leq\)180\({}^{\circ}\) and \(0^{\circ}\leq\theta\leq 90^{\circ}\) in 30\({}^{\circ}\) steps. The wave was linearly polarized in vertical direction (parallel to \(z\) axis). The maximum level of exposure of an electromagnetic field is regulated by Polish law [29] that is harmonized with European Union regulations. According to this, the general population exposure limit for electric field strength at 750 MHz is 37.6 V/m and 61 V/m for 3600 MHz.