## 2 Materials and Methods
### Energy Absorption and Heat Generation Measurements  
The process of heat generation in biological tissues, such as fish muscle and scales, during microwave exposure is primarily governed by how well the tissue absorbs and converts electromagnetic energy into heat. This is quantified by a parameter known as the Specific Absorption Rate (SAR), which measures how much energy is absorbed per unit mass of tissue. The SAR is calculated using the following equation:  
\[\text{SAR}=\frac{1}{V}\int_{sample}\frac{\sigma(\mathbf{r})|\mathbf{E}( \mathbf{r})|}{\rho(\mathbf{r})}dr=\frac{\sigma|E|^{2}}{\rho} \tag{3}\]  
where \(\sigma\) is the tissue's electrical conductivity (S/m), \(|E|^{2}\) is the root mean square (RMS) of the electric field strength (V/m), and \(\rho\) is the tissue density (kg/m\({}^{3}\)). This equation shows that tissues with higher conductivity and stronger field exposure absorb more energy and therefore generate more heat. In the case of _Cirrhinus microlepis_, the fish scales exhibited higher conductivity than muscle, contributing to their faster heating during treatment. SAR directly correlates the tissue's ability to absorb energy to its electrical and material properties. According to internationally recognized standards, such as those set by the International Commission on Non-Ionizing Radiation Protection (ICNIRP), the maximum allowable SAR value for localized exposure in humans is 2 W/kg averaged over 10 g of tissue in the context of public exposure to electromagnetic fields [46]. Although these standards are not directly applicable to fish tissue, they provide a general framework for assessing safe exposure levels during dielectric heating.  
Another important parameter is power density (\(P\)), which represents how much energy is dissipated per unit volume of tissue. It is calculated as follows:  
\[P=\sigma\Big{|}E^{2}\Big{|}=2\pi f\varepsilon_{0}\varepsilon^{\prime\prime} \Big{|}E^{2}\Big{|} \tag{4}\]  
Here, \(f\) is the frequency of the applied field, \(\varepsilon_{0}\) is the permittivity of free space, and \(\varepsilon^{\prime\prime}\) is the dielectric loss of the tissue. This expression emphasizes the role of tissue composition, particularly \(\varepsilon^{\prime\prime}\), in determining how efficiently energy is absorbed and converted into heat. Tissues with high water content and ionic conductivity, such as fish muscle, typically have higher \(\varepsilon^{\prime\prime}\) values, making them responsive to microwave energy.  
To estimate how tissue temperature increases during heating, the following simplified bioheat equation is used:  
\[\Delta T=\frac{P\Delta t}{\rho C}=\frac{SAR\times\Delta t}{C} \tag{5}\]  
where \(C\) is the tissue's specific heat capacity (J/kg.\({}^{\circ}\)C), \(\Delta T\) is the change in temperature (\({}^{\circ}\)C), and \(\Delta t\) is the exposure time. This relationship links the absorbed energy to the tissue's thermal properties and mass.  
This relationship connects absorbed energy to the tissue's thermal response over time. For instance, in this study, the scale regions reached 70 \({}^{\circ}\)C within approximately 75 s, while the muscle remained below 50 \({}^{\circ}\)C, demonstrating thermal selectivity.  
In addition, applying salt to the fish scales increased their ionic conductivity, further enhancing energy absorption in these parasite-prone regions. This approach proved effective in improving heating efficiency and minimizing unwanted thermal effects on edible tissue layers.