## 4 Design of TLQoS
### Parameter Estimation
#### 4.9.4 Temperature Estimation  
TLQoS exploits the temperature estimation procedure as described in [3,4]. In particular, the temperature rise of the tissue surrounding the WBAN nodes is measured. The major sources that are predominant for thermal increase of the implant devices include radiation from the node antenna and power dissipation of the implanted electronics. Specific absorption rate (SAR) is used to determine the level of radiation being absorbed by body tissue. The space near the antenna is known as near field, the extent of which is \(\frac{\lambda}{2\pi}\), where \(\lambda\) is the radio frequency (RF) wavelength for the wireless communication. According to [10,24], the SAR in the near field (\(\leq\frac{\lambda}{2\pi}\)) and far field (\(>\frac{\lambda}{2\pi}\)) can be estimated as follows:  
\[SAR_{NF}=\frac{\sigma\mu\omega}{\rho\sqrt{\sigma^{2}+\epsilon^{2}\omega^{2}}} \Big{(}\frac{Idlsin\theta e^{-\alpha R}}{4\pi}\Big{(}\frac{1}{R^{2}}+\frac{ \gamma}{R}\Big{)}\Big{)}^{2} \tag{27}\]  
\[SAR_{FF}=\frac{\sigma}{\rho}\Big{(}\frac{\overline{\alpha}^{2}+\overline{ \beta}^{2}}{\sqrt{\sigma^{2}+\omega^{2}\epsilon^{2}}}\frac{Idl}{4\pi}\Big{)}^{ 2}\frac{sin^{2}\theta e^{-2\alpha R}}{R^{2}} \tag{28}\]  
where, \(R\) is the distance from the source to the observation point, \(\gamma\) is the propagation constant, \(dl\) is the length of short conducting wire for a short dipole antenna, \(\sigma\) is the medium conductivity, \(I\) is the amount of current, \(\epsilon\) is the relative permittivity, \(\mu\) is the permeability, \(\rho\) is the mass density and \(sin\theta=1\).  
The power dissipation of the sensor node circuitry, can be quantified as power dissipation density, \(P_{c}\) (the power consumed by the sensor circuitry divided by the volume of the sensor) [3]. Considering both the sources for temperature rise, the temperature of a node at a grid point (x,y) at time \(t\), denoted as \(T^{t}(x,y)\) can be estimated as follows [3]:  
\[T^{t}(x,y)=\left(1-\frac{\Delta_{t}b}{\rho C_{p}}-\frac{4\Delta _{t}K}{\rho C_{p}\Delta^{2}}\right)T^{t-1}(x,y)+\frac{\Delta_{t}}{C_{p}}SAR\\ +\frac{\Delta_{t}b}{\rho C_{p}}T_{b}+\frac{\Delta}{\rho C_{p}}P_{ c}+\frac{\Delta_{t}K}{\rho C_{p}\Delta^{2}}\Big{(}T^{t-1}(x+1,y)\\ +T^{t-1}(x,y+1)+T^{t-1}(x-1,y)+T^{t-1}(x,y-1)\Big{)} \tag{29}\]  
The Equation (29) exploits the Finite-Difference Time-Domain (FDTD) modeling technique [25] that discretizes the differential form of time and space, and the problem space is discretized into small grids. In Equation (29), \(\Delta_{t}\) is the discretized time step, \(\Delta\) is the discretized space step, \(b\) is the blood pressure perfusion constant, \(C_{p}\) is the specific heat of the tissue, \(T_{b}\) is the fixed blood temperature, \(K\) is the thermal conductivity of the tissue. From Equation (29), the temperature of a node at grid point (x, y) at time \(t\) can be determined through a function of the temperature at (x, y) at time \(t-1\), and the function of the temperature of neighboring nodes at grid points ((x + 1, y), (x, y + 1), (x - 1, y) and (x, y - 1)). Since the sensor nodes are surgically implanted, hence the position of the nodes are fixed and can be easily known. Once the properties of the tissue, the properties of blood flow, and the heat absorbed by the tissue will be obtained, the temperature at a given time can be measured. Reference [3] provides the details of this temperature estimation modeling.