# Sensitivity Analysis of an Implanted Antenna within Surrounding Biological Environment
## 2 Implanted Antenna Scenario and Transmission Link  
In fact, many factors could affect the power transmission efficiency, especially with the presence of an extremely lossy material like human tissue. But these factors are not often studied by researchers nowadays. In this paper, a parametric uncertainty study on a biomedical wireless power transmission link is performed. As presented in Figure 1, a four-layer human arm model (bone, muscle, fat, skin) is designed and used in this electromagnetic simulation. Comparing the previous works [13; 14; 15], the four-layer model that is used in this paper is more realistic without taking much more time to calculate.  
In this model, a miniaturized circular antenna is embedded into the muscle layer and the implantation depth is calculated from the muscle-fat interface to the antenna center. The implanted antenna is embedded along the direction of the muscle fiber in order not to hamper the arm's movement. Table 1 shows the electrical properties of different human tissue at 915 MHz. The length of this human arm model is set to the minimum sufficient value with which the results are not affected in order to save the calculation time.  
The embedded antenna with all relative parameters are presented in Figure 2. The antenna has a circular substrate (thickness = 0.64 mm) and a superstrate of the same size and thickness, which are all made of material Rogers RO3210 (\(\varepsilon_{r}=10.2\), tan\(\delta=0.003\)). A radiating patch situates between the two layers. Two arctic slots are cut from the metallic patch for the appearance of the two resonant frequencies (400 MHz at MedRadio band and 915 MHz at ISM band respectively). A ground plane positions below the substrate and is connected with the radiating patch by a via (radius = 0.15 mm) at point W for miniaturization. A coaxial cable standardized to 50 \(\Omega\) is used for feeding the antenna at  
A metallic wave reflector is placed behind the human tissue model in order to enhance the implanted antenna's power reception. The half-cylindrical reflector (open angle = 180\({}^{\circ}\), thickness = 1.2 mm) is placed behind skin surface (see Figure 1) at the opposite to the patch antenna side. Reflector is made of copper and has a thickness larger than the penetration depth. It is cylindrical and the radius is chosen according to the following formula:  
\[f=\frac{d}{4}\cot\left(\frac{\theta_{0}}{2}\right) \tag{1}\]  
where \(f\) is the reflector's focal distance, \(d\) is the reflector's width and \(\theta_{0}\) is half value of the reflector's open angle.  
In this paper, several different variables are analyzed. The thickness of the muscle and fat and the radius of the bone are all variable in order to simulate different cases of the wearing patient. Also, the implantation depth and the reflector to skin distance are also variable in order to simulate some other uncertainties such as patient's movement or wearing clothes. All these variables and calculation are chosen according to multiple concerns for utilization in real life. Finally, the gain of the antenna inside the human arm model at 915 MHz is the output parameter.  
In order to eliminate the mismatch loss impact from the output results, the reflection coefficients are calculated. As shown in Figure 3, the antenna always has a resonant frequency at 915 MHz and the corresponding S11 is around \(-\)16 dB which indicates that it is matched with the input impedance.  
For all the samples that are used in Section 4, the reflection coefficient S11 is always ensured to be less than \(-\)10 dB in order to avoid the mismatch loss.