# Computer Simulations of Dual-Antenna Microwave Ablation and Comparison to Experimental Measurements
## 2 Materials and Methods
### Model Validation Based on Ex Vivo Experiments  
The ex vivo experiments were carried out at a room temperature of 25 \({}^{\circ}\)C. During the MWA procedure, a thermometer was placed at a position midway horizontally between the two antennas to monitor the temperature changes during porcine liver heating. Fifteen sets of valid data were obtained for each antenna setting. The average temperature at the measurement point was taken as the experimental data. After each group of experiments, the porcine liver was dissected along the longitudinal axis, and the coagulation zone sizes  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Tissue** & \(\rho\) **(kg/m\({}^{3}\))** & \(C_{\text{p}}\) **(J/(kg\(\cdot\)K))** & **\(k\) (W/(m\(\cdot\)K))** & \(\sigma\) **(S/m)** & \(\varepsilon\) \\ \hline Porcine liver & 1050 & 3628 & 0.565 & 1.8 & 44.3 \\ \hline \end{tabular}
\end{table}
Table 2: The values of characteristic parameters of ex vivo porcine liver at 25 \({}^{\circ}\)C.  
were measured. Some characteristic lengths of the MWA coagulation zone are shown in Figure 3, where \(R_{\text{max}}\) indicates the maximum transverse length of the fused coagulation zone, \(R_{\text{L}}\) indicates the maximum longitudinal length, and \(R_{\text{f}}\) indicates the longitudinal length at the interface of the two coagulation zones.  
The coagulation zone is the most direct measure of effectiveness of liver tumor MWA and its accurate characterization is, therefore, critical. The isothermal model [30] and the Arrhenius model [31] were compared to obtain the accurate evaluation model of the MWA coagulation zone. The Arrhenius model considers the cumulative effect of energy based on time and temperature. It can characterize the thermal coagulation degree of the tissue in a period of time. The Arrhenius model is given by [32]:  
\[\Omega(\tau)=\ln\frac{c(0)}{c(\tau)}=\int_{0}^{\tau}Ae^{\frac{-E_{\text{R}}}{kT (t)}}\text{dt} \tag{9}\]  
where \(\Omega(\tau)\) denotes the degree of tissue necrosis; \(c(0)\) denotes the proportion of undamaged cells within biological tissue cells when unexposed; \(c(\tau)\) denotes the proportion of undamaged cells within the tissue at the \(\tau\) moment of exposure(s); \(A\) denotes the frequency factor (s\({}^{-1}\)); \(E\) denotes the biological reaction energy (J/mol); \(R\) denotes the flux gas constant \(R=8.314\) J/(mol\(\cdot\)K); \(T(t)\) denotes the absolute temperature (K).  
The thermal damage parameters and frequency factors [33] for the tumor were \(A=3.247\times 10^{43}\) s\({}^{-1}\) and \(E\)a = 2.814 \(\times\) 10\({}^{5}\) J/mol [34], respectively. The \(\Omega(\tau)\) range is [0, 1], with 0 indicating that the tissue is not necrotic and 1 indicating that the tissue is completely necrotic.  
The isothermal model is one in which a specific temperature is used as a threshold. The portion of tissue that reaches this threshold is considered to have undergone necrosis [35]. Studies have shown that cells die instantaneously at temperatures above 60 \({}^{\circ}\)C and that heating at 50-60 \({}^{\circ}\)C for a period of time can destroy the tumor irreversibly. For liver tumors, an isothermal threshold of 54 \({}^{\circ}\)C is the most frequently used [36].  
In order to obtain a more accurate and convenient method of characterizing the coagulation zone for dual-antenna MWA, the isothermal model and the Arrhenius model were compared with the ex vivo experiments, respectively.