# Design and Analysis of an Inductive Coupling System for the Early Detection of Heart Failure
## 3 Transceiver and Receiver Coil Geometries and Performance Analysis
### Performance Analysis in the Heterogeneous Phantom  
In order to validate the performance of the inductive coupling method in a real-time environment, we defined a heterogeneous phantom composed of layers of muscle, (dry) skin, fat, and heart. Taking into consideration the actual size of the heart [22; 23; 24; 25], the heart layer's thickness was estimated to be 50 mm. The heterogeneous phantom consisted of a thickness of 10 mm for each muscle, skin, and fat layer; however, the heart layer's thickness was estimated to be 50 mm. The geometries of \(Rx_{1}\), \(Rx_{2}\), and \(Tx\) in the heterogeneous phantom were employed in the simulation analysis, where \(Tx\) resided in the air and \(Rx_{1}\) and \(Rx_{2}\) were located within the heart layer, as depicted in the Figure 4c. As indicated in Table 2, these layers were examined subjected to the loss tangent (\(tan\delta\)), conductivity (\(\sigma\)), and relative permittivity (\(\epsilon_{r}\)) at 13.56 MHz of the bodily tissue. With \(C_{1}\) = 680 pF, \(C_{2}\) = 680 pF, and \(C_{3}\) = 1000 pF, the resonant frequency in the coils was attained. The values \(R_{S}\) and \(R_{L}\) were set to 100 \(\Omega\) across \(Tx\), \(Rx_{1}\), and \(Rx_{2}\).  
The variations in blood dielectric properties affected the conductivity, so the \(S_{33}\) was simulated with different conductivity ranging from 0.6 (S/m) to 1 (S/m). Based on the reported results in Figure 5, at the resonant frequency, a considerable shift in the reflection coefficient was noticed due to the change in conductivity.  
Generally, a human's body is permeable to frequencies under 20 MHz, hence, the allowed exposure limit for frequencies is less than 20 MHz [26; 27]. To evaluate the safe operation of the proposed method's SAR, the FCC-mandated basic fundamental exposure limit for whole-body exposure was determined over a tissue mass of 1 g. Conductivity (\(\sigma\)) and density (\(\rho\)) of the tissue are directly and inversely proportional to SAR, respectively, and that was estimated with the formula \(\sigma|E|^{2}/\rho\), where \(E\) is the electric field [28; 29]. The United State's FCC now enforces a SAR limit of 1.6 W/kg over 1 g of tissue for the general population, and South Korea follows the same standard [30]. Japan and the European Union Council propose a level of 2.0 W/kg, over 10 g of actual tissue, on average. Figure 6 demonstrates that the highest average SAR simulated for a heterogeneous phantom was  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tissue** & **Relative** & **Loss Tangent** & **Conductivity** \\  & **Permitivity (\(\epsilon_{r}\))** & **(\(tan\delta\))** & **(\(\sigma\))** \\ \hline Air & 1.0 & 0.0 & 0.0 \\ Skin & 285 & 1.10 & 0.23 \\ Fat & 11.8 & 3.40 & 0.03 \\ Muscle & 138 & 6.01 & 0.62 \\ Heart & 239 & 2.91 & 0.52 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The biological tissues’ dielectric characteristics at 13.56 MHz [26].  
Figure 5: (a) S33 at different conductivities in the tissue medium under simulation; (b) S33 at varied distances in the tissue medium under simulation.  
0.85 W/kg. Therefore, the SAR clearly demonstrated that the value was far less than the permissible W/kg.  
The SAR value varied with \(D_{12}\) and it was observed that the SAR for different \(D_{12}\), 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm, was also far less than the permissible W/kg.