# A Comprehensive Review of In-Body Biomedical Antennas: Design, Challenges and Applications
## 4 Challenges That Influence the Design of In-Body Antennas
### Effect of Tissue Diversification  
The propagation of a radio wave through the biological tissue is more complex compared to wave propagation in a free space due to the lossy property of the biological tissue causing absorption. Absorption in a radio wave is primarily characterized by considering the permeability, permittivity and conductivity parameters of the medium. An EM wave propagating in the positive \(Z\)-direction is defined as [79]  
\[E\left(z\right)=Ee^{-\gamma z} \tag{4}\]  
where \(E\) and \(\gamma\) are the complex amplitude of the wave in the \(z\)-direction and the complex propagation constant, respectively. \(\gamma\) is defined as [79; 80]  
\[\gamma=j\omega\sqrt{\mu\varepsilon} \tag{5}\]  
The constant increase in \(\gamma\) leads to attenuation of the electromagnetic wave inside the inhomogeneous region, where \(\mu=\mu_{r}\mu_{0}=\mu_{0}\) defines the permeability of the medium, as for biological materials \(\mu_{r}=1\). However, the relative permittivity \(\varepsilon_{r}\) (where \(\varepsilon=\varepsilon_{0}\varepsilon_{r}\)) of human body tissue is a complex frequency-dependent parameter, as the conductivity \(\sigma\) is not zero. The dielectric properties of the human tissue can be obtained from its relative complex permittivity as [81]  
\[\varepsilon_{r}^{*}(\omega)=\varepsilon_{r}^{\prime}(\omega)-\varepsilon_{r}^ {\prime\prime}(\omega) \tag{6}\]  
where \(\varepsilon_{r}^{\prime}\) and \(\varepsilon_{r}^{\prime\prime}\) are the real and imaginary parts of relative complex permittivity. The imaginary part of relative complex permittivity can be determined from the angular frequency \(\omega\) and conductivity \(\sigma\) by  
\[\varepsilon_{r}^{\prime\prime}(\omega)=\frac{\sigma}{\omega\varepsilon_{0}} \tag{7}\]  
Furthermore, the loss tangent, \(\tan\delta\), which is a measure of how lossy the human body can be, is calculated as follows:  
\[\tan\delta=\frac{\varepsilon_{r}^{\prime\prime}}{\varepsilon_{r}^{\prime}} \tag{8}\]  
Therefore, as per Equation (7), greater conductivity demonstrates a higher relative complex permittivity value. Furthermore, the increase in the frequency leads to a lower  
Figure 8: Anesthetized mixed landrace pig with (**a**) exposed left ventricular (LV) apex, (**b**) implanted wireless pressure sensor, (**c**) catheter-tip transducer and (**d**) chest spreader [23]. Reproduced with permission from an open-access article from _Biomedical Microdevices_ (CC-BY). value of imaginary relative complex permittivity in a lossy medium. As a result, the increase in the loss tangent makes the medium significantly lossy. In brief, the complex propagation constant depends on three parameters: permittivity, permeability and conductivity. The increase in conductivity can cause lossy medium, where the radio waves can be significantly attenuated. Therefore, the EM wave attenuates with the increase in the complex propagation constant, as specified in Equation (4). Another major issue with tissue diversification is that the radio wave propagation speed decreases because of the complex inhomogeneous characteristics of biological tissue. Therefore, the radio wave propagation speed primarily depends on the permittivity and conductivity of the medium. Additionally, the propagation speed in any medium is characterized based on phase (\(V_{p}\)) and group (\(V_{g}\)) velocity as [79; 82]  
\[V_{p}=\frac{\omega}{\beta} \tag{9}\]  
\[V_{g}=\frac{\partial\omega}{\partial\beta} \tag{10}\]  
where \(\beta\) is the phase constant, defined from the complex propagation constant as [83]  
\[\beta=\omega\sqrt{\frac{t_{0}e_{0}e_{r}^{\prime}}{2}\left(\sqrt{\left(\frac{ \sigma}{\omega e_{0}e_{r}^{\prime}}\right)^{2}}+1\right)} \tag{11}\]  
In Equations (9) and (10), the propagation speed is characterized based on the phase constant, and it decreases with the increase in the conductivity of the medium. In contrast, the rise in the frequency influences the increase in propagation speed.