# Channel Modeling for In-Body Optical Wireless Communications +
## 3 Results
### Pathloss  
Based on the extracted accurate expressions for the reduced scattering and absorption coefficients of various complex tissues that take into account the particularities of the channel, we can estimate the pathloss. Therefore, Figure 3a depicts the pathloss as a function of the wavelength due to absorption and scattering in skin tissues with different values of thickness. In order to ensure a fair comparison between the plotted tissues, it is necessary to use the same tissue thickness, with the determining tissue being the skin, whose average thickness varies between 0.5 and 4 mm [22]. Thus, we selected a slightly wider range of thickness for the analysis, i.e., 1-5 mm. Additionally, it is highlighted that, in order to increase the readability of Figure 3, the area below each line is depicted in a specific color that corresponds to a specific skin thickness value. From this figure, it is evident that the complete pathloss (continuous line) decreased with the wavelength and increased with the skin thickness, while the pathloss due to absorption (dashed line) had more fluctuations throughout the visible spectrum. In more detail, we observed that the optimal wavelength was 1000 nm. Furthermore, in the following, we assumed a transmission window to be the spectrum region where the pathloss did not exceed 6 dB (red dotted line), i.e., the residual optical signal was at least a quarter of the transmitted signal. Thus, for \(\delta=1\) mm, a transmission window existed for wavelength values higher than 450 nm, which shrank as the transmission distance increased. For instance, for \(\delta=3\) mm it reduced to wavelengths higher than 650 nm, while for \(\delta>3\) mm, it became even smaller. On the other hand, when taking into consideration the scattering coefficient, the complete pathloss exhibited a more linear behavior. Specifically, the impact of scattering in the propagation of light through biological tissues was approximately two orders of magnitude higher than that of the absorption, which constitutes the dominant phenomenon concerning the optical transmission. For example, if we assume \(\delta=5\) mm and \(\lambda=600\) nm, the scattering coefficient exceeds \(\mu_{a}\) 100 times, while for \(\lambda=600\) nm, \(\mu_{s}\) is 125 times higher. As a result, it is obvious that the absorption coefficient decreases with an increased rate compared to \(\mu_{s}\). Figure 3b illustrates the pathloss due to the existence of brain tissue as a function of the wavelength for different values of \(\delta\). As expected, for higher values of \(\delta\), the pathloss was also higher, while the behavior of pathloss for wavelength variations was not linear. For example, as \(\lambda\) increased from 500 to 550 nm the pathloss increased, and while for the same increased from 550 to 600 nm, pathloss decreased. Additionally, the optimal transmission wavelength was 700 nm. In addition, two transmission windows existed for \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Tissue** & \(B\) & \(S\) & \(W\) & \(F\) & \(M\) & \(f_{\text{Ray}}\) & \(\beta\) & \(\mu_{s}^{\prime}(\delta_{0})\) & \(g\) & **Source** \\ \hline Skin & 0.41 & 99.2 & 26.1 & 22.5 & 1.15 & 0.409 & 0.702 & 48 & 0.92 & [16, 17, 18] \\ \hline Breast & 0.5 & 52 & 50 & 13 & 0 & 0.288 & 0.685 & 18.7 & 0.96 & [16, 15, 14] \\ \hline Bone & 0.15 & 30 & 30 & 7 & 0 & 0.174 & 0.447 & 19.3 & 0.93 & [11, 12, 13] \\ \hline Brain & 1.71 & 58.7 & 50 & 20 & 0 & 0.32 & 1.09 & 12.72 & 0.9 & [8, 9, 10] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Tissue parameters related to optical absorption and scattering for skin, bone, brain, and breast tissue. \(\delta=4\) mm. The first was between 450 and 550 nm, while the second was after 600 nm. However, as the transmission distance increased, only the second window was valid.