## 2 Materials and Methods
### Material Properties and Boundary Conditions  
The thermal and electrical properties of materials used in the ablation model are listed in Table 1 [22; 24; 25; 26; 27]. The values of the electrical and thermal conductivities of the myocardium  
Figure 1: Geometry of (**a**) the ablation model, (**b**) the circumferential multipolar catheter (CMC) model from top view, and (**c**) detailed dimensions of electrode and catheter body (not to scale). The thicknesses of blood, myocardium, connective tissue, and lung and muscle were fixed to 9, 5, 2, and 18 mm, respectively, and the dimensions of X, Y, and Z (X = Y) were obtained by employing a convergence test. The catheter was inserted into the myocardium to a depth of 0.1 mm. The active electrode had a diameter of 1.1 mm and a length of 1 mm. The tip of the first electrode was round. The electrodes were placed 3 mm apart. For convenience, the electrodes were numbered 1 to 10.  
shown in Table 1 were assessed at an ambient temperature of 37 \({}^{\circ}\)C. These two parameters are temperature-dependent and follow unique piecewise relations [19; 20]. The electrical conductivity increased exponentially at a rate of 1.5% \({}^{\circ}\)C\({}^{-1}\) below 100 \({}^{\circ}\)C and then dropped by four orders of magnitude between 100 \({}^{\circ}\)C and 105 \({}^{\circ}\)C. The thermal conductivity increased linearly at a rate of 0.12% \({}^{\circ}\)C\({}^{-1}\) up to 100 \({}^{\circ}\)C and remained constant thereafter.  
Figure 2 displays the electrical and thermal boundary conditions of the MEU and MEB modes. For the MEU mode, each electrode was applied with a constant power of 20 W. The bottom surface of the model had a rating of 0 V, acting as the ground pad or dispersive electrode. The RF current in this configuration was driven between the active and dispersive electrodes. For the MEB mode, the power and the voltages on every two non-overlapping electrodes in sequence (i.e., Electrode 1 and Electrode 2, Electrodes 3 and 4, etc.) were set to 10 W and 0 V, respectively. The RF current was forced to flow between the adjacent electrodes with different applied powers. A control algorithm was introduced for the applied power source in case of overheating. It was implemented by a step function with a starting level referring to the power required for each ablation mode and a final level of 0 in amplitude. The maximum resulting temperature in the myocardium was inspected and could be held around a temperature threshold of 95 \({}^{\circ}\)C, which was set as the position of the step.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\rho\) (kg m\({}^{-3}\)) & \(c\)(J kg\({}^{-1}\) K\({}^{-1}\)) & \(K\)(W m\({}^{-1}\) K\({}^{-1}\)) & \(\sigma\) (S m\({}^{-1}\)) & **References** \\ \hline Electrode & 21,500 & 132 & 71 & \(4.6\times 10^{6}\) & [24; 25] \\ Catheter body & 70 & 1045 & 0.026 & \(1\times 10^{-5}\) & [24; 25] \\ Blood & 1000 & 4180 & 0.541 & 0.667 & [27] \\ Myocardium & 1060 & 3212 & 0.531 & 0.541 & [24; 25] \\ Connective tissue & 1000 & 3200 & 0.400 & 0.090 & [22] \\ Lung & 600 & 1280 & 0.350 & 0.250 & [22] \\ Muscle & 1090 & 3421 & 0.490 & 0.446 & [26] \\ \hline \end{tabular} Thermal conductivity and electrical conductivity were measured at 37 \({}^{\circ}\)C.  
\end{table}
Table 1: Thermal and electrical properties of human and porcine tissue.  
Figure 2: (a) Electrical condition of electrodes and a schematic of the electrical and thermal boundary conditions of (b) multielectrode unipolar (MEU) and (c) multielectrode bipolar (MEB) modes.  
A constant temperature of 37 \({}^{\circ}\)C was applied to all boundaries of the model. The effect of blood flowing inside the atrium was modeled by two thermal convection coefficients at the electrode-blood interface, hE = 3636 W m\({}^{-1}\) K\({}^{-1}\), and the tissue-blood interface, hT = 708 W m\({}^{-1}\) K\({}^{-1}\), which were calculated under a medium flow condition of 10.3 cm s\({}^{-1}\)[21].