# Comparison of Thermal Response for RF Exposure in Human and Rat Models
## 2 Models and Methods
### Computational Models
#### 2.2.2 Temperature Computation  
The BHTE considers heat exchange mechanisms, including heat conduction, blood perfusion, and resistive heating, and was shown as follows [35]:  
\[ \begin{array}{c}C(\mathbf{r})\rho(\mathbf{r})\frac{\partial T(\mathbf{r},t)}{ \partial t}=\
abla(K(\mathbf{r})\
abla T(\mathbf{r},t))+\rho(\mathbf{r})SAR( \mathbf{r})\\ +M(\mathbf{r})-B(\mathbf{r},t)(T(\mathbf{r},t)-T_{B}),\end{array}  \tag{2}\]  
where \(\mathbf{r}\) and \(t\) denote the position vectors in tissue and the time, respectively, terms \(T\) and \(T_{B}\) denote the temperatures of tissue and blood, respectively, the term \(C\) denotes the specific heat of the tissue, \(K\) denotes the thermal conductivity of the tissue, \(M\) denotes the metabolic heat, and \(B\) denotes the factor related to the blood perfusion. The SAR obtained from Equation (1) was substituted into Equation (2) as a heat load. While the electromagnetic wave instantaneously reaches steady state, the time constant of the heat takes several minutes at superficial tissues [12], and over 30 min at deep tissues [36]; the time variation of SAR is much smaller than the thermal constant and thus can be assumed as a constant during exposure. The boundary condition between tissues and internal/external air is as follows:  
\[-K(\mathbf{r})\frac{\partial T(\mathbf{r},t)}{\partial n}=H(T(\mathbf{r},t)-T _{a}), \tag{3}\]  
where \(T_{a}\), \(H\), and \(n\) denote the ambient temperature, heat transfer coefficient, and vector normal to the body surface, respectively. The initial temperature \(T_{0}\) was found using Equations (2) and (3) for SAR = 0 W/kg, \(T_{B0}\) = 37 \({}^{\circ}\)C, and \(T_{a}\) = 27 \({}^{\circ}\)C.  
The blood temperature in the rat model changed to satisfy the first law of thermodynamics as follows [8; 37]:  
\[T_{B}(t)=\int\frac{Q_{BT}(t)-Q_{BT}(0)}{C_{B}\rho_{B}V_{B}}dt, \tag{4}\]\[Q_{BT}(t)=\int B(t)(T_{B}(t)-T(\textbf{r},t))dV, \tag{5}\]  
where \(Q_{BT}\) denotes the total heat quantity of tissue and blood, and terms \(C_{B}\) (=4000 J/kg/\({}^{\circ}\)C), \(\rho_{B}\) (=1058 kg/m\({}^{3}\)), \(T_{B0}\), and \(V_{B}\) denote the specific heat of blood, mass density of blood, initial blood temperature, and total volume of blood, respectively. The average blood volume per unit of rat body mass was considered to be 64 mL/kg [38]. The blood volume of the rat model was set to 18.9 mL. The blood temperature in the human model was fixed at 37 \({}^{\circ}\)C and sweating was ignored, because it marginally affects the temperature elevation for local RF exposure [29]. Skin blood perfusion was expressed as follows, based on the cutaneous veins of a dog with local warming [39]:  
\[B(\textbf{r},t)=\{B_{0}(\textbf{r})+F_{HS}\Delta T_{H}(t)+F_{SS}\Delta T_{S}(t )\}\cdot 2^{\Delta T(\textbf{r})/6}, \tag{6}\]  
where \(B_{0}\) denotes the basal blood perfusion of each tissue, \(\Delta T_{S}(t)\) denotes the average temperature elevation of the skin, and \(\Delta T_{H}(t)\) denotes the elevation of the core temperature. Additionally, \(F_{HS}\) (=17,500 W/m\({}^{3}\)/\({}^{\circ}\)C) and \(F_{SS}\) (=1100 W/m\({}^{3}\)/\({}^{\circ}\)C) are the coefficients that determine the changes in the blood perfusion characteristics over time [40]. Thus, the blood and hypothalamus temperature elevations were used as the approximate body core temperature in rat and human models, respectively. The blood perfusion in the brain was given as follows, based on our rat measurements for local RF exposure [7]:  
\[B(\textbf{r},t)=B_{0}(\textbf{r})(1+F_{HS}\Delta T_{H}(t))\cdot 2^{\Delta T( \textbf{r})/F_{BB}}, \tag{7}\]  
where \(F_{HB}\) (=0.053 \({}^{\circ}\)C\({}^{-1}\)) and \(F_{BB}\) (=13.9 \({}^{\circ}\)C) denote weighting coefficients in relation to the variations in the core and brain temperature elevations, respectively [25]. Vasodilation in tissues, except for the skin and brain, was given as follows [41; 42]:  
\[