# Analysis of Human Body Shadowing Effect on Wireless Sensor Networks Operating in the 2.4 GHz Band
## 2 Materials and Methods  
### Analysis of Shadowing Effect with Finite-Difference Time-Domain Based Program  
The human body shadowing effect was analyzed using a computer program based on the FDTD numerical method. This method is commonly used for computer simulations in high frequency electromagnetics. Thanks to the direct implementation of Maxwell equations formulated in the time domain, it is particularly useful for the analysis of objects with very complex structures, made from various materials (dielectrics and conductors) [26; 27]. The simulations of the body shadowing effect presented in this paper were performed using Remcom XFdtdt(tm) software ver. 7.6.0.2 [28], which employs the FDTD method. This software can be used for the simulation of diverse objects segmented into cubic volumetric elements (voxels), following the procedure suggested by [PERSON] [29]. The finite-difference time-domain method is recommended for studying the influence of electromagnetic waves on the human body [30]. Data on the electromagnetic properties of human body tissues are now available for a wide range of frequencies [31]. Many numerical models of the human body have been developed for the purposes of computer simulations employing the FDTD method. These differ mainly in the number of tissues modeled and in the anatomical accuracy of the body structure. The research presented here was performed using the NMR Hershey model, which is available in XFdtdt(tm) software ver. 7.6.0.2 [28]. This anthropomorphic heterogeneous model of the human body can be deployed with different resolutions, from 1 mm to 10 mm. Software that uses the FDTD method performs a segmentation of objects into voxels. The voxel size corresponds to the length of the electromagnetic wave that penetrates the object under analysis. The dimensions of the voxels into which the object is divided influences the accuracy of the calculations. A commonly applied rule is to assume the length of the side of the cell to be equal to one tenth of the length of the shortest electromagnetic wave in the simulated object \(\lambda_{\text{min}}\) (1):  
\[\lambda_{\text{min}}=\frac{c_{0}}{f_{\text{c}}\cdot\sqrt{\mu_{r}\epsilon_{r}}} \tag{1}\]  
where: \(\lambda_{\text{min}}\)--the length of the shortest wave in the model; \(c_{0}\)--the velocity of light in a vacuum; \(f_{\text{c}}\)--the wave frequency; \(\mu_{r}\)--the maximum relative magnetic permeability of the model object; and \(\epsilon_{r}\)--the maximum relative electric permittivity of the modeled object. The need to model the entire simulation domain using voxels with sides a faction of a wavelength limits the use of this method to problems where the physical size is comparable to tens or maximally hundreds of the wavelength. There must be sufficient computer memory to store the data describing material properties and electromagnetic field parameters for all the voxels that fill the simulation domain. In simulations that include human body models, due to the shortening of the wave that occurs as it passes through dielectric material, the voxel size is smaller than the wavelength in free space. In this study, for a human body with average properties, the relative electric permittivity of the model material was \(\varepsilon=38.5\), while its specific conductance was \(\sigma=2.4\) S/m. These values are typical for models used in tests of cellular system terminals [32] and can be used to approximate the average wavelength of a human body. For the 2.45 GHz frequency, the average wavelength in the human body according to formula 1 is \(\lambda_{\text{min}}=19.7\) mm. The average voxel size should then be 1.97 mm. In Remcom XFdtd(tm), the closest approximation of this size is a human body model with 2 mm voxels. This was used for further simulations. To simulate the body shadowing effect in Remcom XFdtd(tm) software, coupling between two antennas was simulated.