# Monitoring of Surgically Treated Upper Arm Fracture by Implanted Antenna at 402 MHz
## 4 Simulation and Discussion  
The model described in Section 3.1 is simulated by CST. Due to the morphology of the human upper arm, there is limited space for the implanted antenna. We select a half-wave dipole antenna due to its simplicity and suitability to be implanted in the cylindrical model. In the half-wave dipole antenna, two conductors are installed in line with a small gap left between them. The voltage is attached to the center of both conductors, and the length of the dipole ought to be half of the wavelength [32]. The voltage and current levels vary along the length of the radiating section of the antenna. This occurs because the standing waves are set up along the length of the radiating element. The current then reaches the maximum level and the voltage reaches the minimum level at a length equal to an electrical quarter wavelength from the ends. This process takes place in the center as it is a half-wave dipole. As excitation to the antenna is delivered at the center, it can be said that feeding to the dipole is presented at the quarter wavelength point. It is a linear current whose amplitude varies as one-half of a sine wave with a maximum at the center of the antenna. The energy from the driving current provides the energy radiated as radio waves. The antenna is implanted parallel to the bone axis between the bone and the muscle tissue. The upper arm is considered to be concentric with the z-axis, whereas the transverse fracture is modeled by a circular layer at a right angle to it. Two cases of oblique fracture are represented by elliptical layers that make 30\({}^{\circ}\) and 60\({}^{\circ}\) with the y-axis. Figure 5 shows the bone shaft with transverse fracture and oblique fracture layer with angle \(\theta\). Figure 4: Variation in specific absorption rate along the tissues at different frequencies. Figure 5: Bone shaft with transverse and oblique fracture layers. For biocompatibility with human tissue, the radiator part and the substrate of FR-4 (lossy) of \(\varepsilon_{\mathrm{r}}\) =4.3 and a loss tangent of 0.025 were coated by an ultrathin sheet of silicon. Figure 6 shows a cross-sectional elevation, while the plan of the antenna and the dimensions within the human body are illustrated in Table 5.  
When simulating the antenna in air, the wavelength is 745.75 mm, and the first resonance of the dipole is expected to occur at 0.47 wavelength [17]. For a trace width of 1 mm, a minimum return loss of \(-\)33.5 dB is obtained at a length of 350.5 mm. The simulation experiences a total efficiency of 0.9873 and a realized gain of 2.145 dB in air. The power pattern of the antenna in the air shows a symmetric pattern around the radiator as in Figure 7a. According to the electrical properties of the human tissues, the wavelength of the 402 MHz frequency in the muscle is 312.09 mm, and in the bone is 206.02 mm. As the antenna in the proposed technique is implanted in the bone to the muscle interface, it resonates at a length of 111 mm and a trace width of 1 mm. The power pattern of the antenna within human tissue is shown in Figure 7b. The challenges of such an implant are low radiation efficiency, strong coupling to the surrounding lossy tissues, and the dispersive tissue and antenna impedance detuning. The antenna within the human tissue provides a total efficiency of 0.0247 and realized gain of \(-\)13.4 dB, as demonstrated in Figure 7c, while Figure 7d shows the variation in the realized gain and total efficiency with the frequency band. The result of the maximum simulated SAR value of the antenna embedded in the human arm tissue is 1.62 W/kg, as shown in Figure 8, for the average input power of 20 mW. This value satisfies the IEEE C95 standard. Figure 6: Planar half-wave dipole antenna.