The comparison of lesion outline and temperature field determined by different ways in atrial radiofrequency ablation

Background The aim of this study is to research the lesion outline and temperature field in different ways in atrial radiofrequency ablation by using finite element method. Methods This study used the method which considered the thermal dosage to determine the boundary between viable and dead tissue, and compared to the 50 °C isotherm results in analyzing lesion outline. Besides, we used Hyperbolic equation which considered the relaxation time to calculate the temperature field and contrasted it with Pennes’ bioheat transfer equation. Results As the result of the comparison of the lesion outline, when the ablation time was 120 s, the isotherm of the thermal dosage was larger than the 50 °C isotherm and with the increasing of the voltage the gap increased. When the ablation voltage was 30 V, the 50 °C isotherm was larger than the thermal dosage isotherm when the ablation time was less than 160 s. The isotherms overlapped when the time was 160 s. And when the ablation time was more than 160 s, the 50 °C isotherm was less than the thermal dosage isotherm. As to the temperature field, when the ablation voltage was 30 V with the ablation time 120 s the highest temperature decided by Hyperbolic was 0.761 °C higher. The highest temperature changed with relaxation time. In most cases, the highest temperature of the Hyperbolic was higher otherwise the relaxation time was 30–40 s. Conclusions It is better to use CEM43 °C to estimate the lesion outline when the ablative time within 160 s. For temperature distribution, the Hyperbolic reflects the influence of heat transmission speed, so the result is more close to the actual situation.

complexity of the surgical operation limit the popularization of this method [2]. While radiofrequency ablation (RFA) which used electric current to cut the accessory pathways of abnormal tissue and targeted at certain points which produce cardiac arrhythmia. In recent years, due to its advantages of safety, minimally invasive and so on, it was widely used in treatment atrial fibrillation [3].
In the process of RFA the electromagnetic energy is converted to heat. Tissue temperature above 50 °C are reserved for direct treatment, and the therapy is termed ablation [4,5]. Dewhirst found that the cell survival/CEM43 relationship closely aligns with isothermal exposure of tissue to temperatures of 50 °C [6]. During RFA 50 °C isotherm which only consider temperature is regarded as the boundary of necrotic cells and survival cells [7][8][9][10][11]. However, many studies show tissue damage is concerned with both temperature and time. On the basis of the conception, thermal dosage which consider both temperature and time was put forward. 43 °C is used as the benchmark temperature how long the tissue to absorb heat in order to keep 43 °C is expressed as cumulative equivalent minutes at 43 °C (CEM43 °C) [11]. So this study created finite element method (FEM) models of cardiac and determined the temperature field in the tissue solving by the Pennes' bioheat transfer equation [12,13]. And comparison of the lesion range which determined by the 50 °C isotherm with the lesion range which determined by thermal dosage.
In most of the simulations, Pennes' bioheat transfer equation which is based on Fourier's heat theory determined the temperature field. But Fourier's heat conduction theory is the law of macro-continuity. This theory does not have time item, which implies the speed of heat is infinite. So it also applies in the immediate energy diffusion at the infinite propagation speed in the medium. In most situations, Pennes' bioheat transfer equation can meet the conditions, but when involved in very low or high temperature, very high heat flux or very short heating duration Fourier's heat conduction theory breaks down. The reason is the wave nature of heating processes becomes pronounced [14][15][16][17][18][19]. Hyperbolic equation is based on No-Fourier's heat theory which thinks about heat wave propaganda speed (relaxation time). In order to consider the condition of the short heat duration time, this studies took Hyperbolic equation into account and contrasted the temperature field which determined by the two equations.
This paper uses the finite element method of cardiac radiofrequency ablation to determine the damage area size. The simulation research, comprehensive analysis of the differences of the temperature field determined by both thermal dose method and 50 °C isotherm. The thermodynamics equation Pennes' bioheat transfer equation and Hyperbolic equation was also considered. The model was referenced in the paper [20].

Geometric model
The idealized 2D axisymmetric simplified model of cardiac radiofrequency ablation was shown in Fig. 1 (Cardiac model) which included myocardium, myocardial coverage (usually identified as blood) and electrode. We used the finite element method (FEM) software Comsol Multiphysics to solve partial differential equations of single field and multi-field in order to achieve the numerical results. As shown in Table 1 [21,22], the thermal and electrical parameters of myocardium, blood and radiofrequency electrode were added to the related materials. These values are derived from physical experiments, and have been cited by others [23][24][25].
The voltage was set at the top of the electrode. The convection coefficient in surface of the electrode was 6090 W/(m 2 K), the convection coefficient of the inner surface of the heart was 10,650 W/(m 2 K) [20]. The initial temperature was 37 °C. The boundary of this model showed in Fig. 2 (boundary condition for analysis).Mesh refined near the radiofrequency electrode automatically. Mesh independence analysis was accomplished to affirm the accuracy and it's reliable to the simulation results for ablation processes.

Electromagnetic and Pennes' bioheat transfer equation
COMSOL provides the electromagnetic field module and heat transfer module. The formulas of both physical fields are as follows.
where σ is the electrical conductivity, ε 0 and ε r are the permittivity of tissue respectively, E is the electric field intensity, and J is the electric current density.  In the first situation the temperature distribution in the cardiac model was obtained by solving the Pennes' bioheat transfer equation [12,[26][27][28].
where ρ is tissue density (kg/m 3 ), c is specific heat of tissue (J/kg °C), k is the thermal conductivity (W/m °C), T is the temperature, Qr is the heat source(W/m 3 ), and Q m is the perfusion heat loss. In this simulation we didn't take the Q m into account for its slight effect compared with the large blood vessel.
In the other situation, the temperature distribution in the cardiac model was obtained by solving the Hyperbolic equation which considered relaxation time [17].

Definition of the boundary between the viable and dead tissue
According to the temperature distribution, there are two main transformation algorithms to estimate the ablation region, and to calculate the transverse width, longitudinal length, and the area of the lesion. In this model, we used 50 °C isotherm and CEM43 °C to estimate the thermal damage region.
For tissue temperature above 50 °C are reserved for direct treatment, and the therapy is termed ablation [4,5]. Dewhirst found that the cell survival/CEM43 relationship closely aligns with isothermal exposure of tissue to temperatures of 50 °C [6]. In RFA, 50 °C is regarded as the boundary of necrotic cells and survival cells, and it is easy and convenient for 50 °C isotherm threshold. So in this model, we use it to analyze.
Cumulative equivalent minutes of thermal treatment at 43 °C (CEM43 °C) method [29] take the temperature history into account, and it commonly used in the hyperthermia. The calculation formula is as follows: where t is time (s),T Δt is the average temperature during time Δt (°C), Δt is time interval (s). R is a parameter when temperature above 43 °C is 0.5 while the temperature below 43 °C is 0.25 [30].
As there is no critical CEM43 °C for cardiac tissue, we estimate CEM43 °C for myocardium to be 128 min (7680 s) to analyze [8].

Results
The comparison of the lesion outline decided by the CEM43 °C and decided by 50 °C isotherm were selected for result illustration. In addition, the distribution of temperature field calculated by the Hyperbolic equation and the Pennes' bioheat transfer equation were both researched. We can see from Fig. 3 that the lesion outline determined by the CEM43 °C was a little smaller than which decided by the 50 °C isotherm. And with the increasing of the voltage, the lesion range and the highest temperature of the two methods increasing. Under the same ablation time, the highest temperature rose about 11 °C with each additional 5 V.  The lesion outline of both methods and the highest temperature increased with the increasing of the time. At the same voltage, the highest temperature rose about 1 °C with every additional 80 s. Tables 2 and 3 shows the lesion diameters at the ablative time of 60 s and 120 s while the voltage 30, 35, 40, 50 and 60 V. It can be seen from the data that the temperature distribution determined by the 50 °C isotherm predicted large. At the time of 60 s, the overestimate rate was from 12.37 to 24.9%. In Table 3, the overestimate rate was from 3.06 to 10.26%. Figure 5 (The temperature field of the atrial tissue determined by Pennes' bioheat and Hyperbolic) shows the temperature field of the heart tissue at 30 V when the ablation time was 120 s. Figure 5a shows the temperature field determined by Pennes' bioheat transfer equation while Fig. 5b shows the temperature field determined by Hyperbolic equation. The shapes of the temperature field of the both figures were similar while the highest temperature which determined by the Hyperbolic equation was a little higher (about 0.7 °C). Figure 6 (The temperature contrast curve of some points) shows the temperature contrast of Pennes equation and Hyperbolic equation. In the start of all the three points, the   Fig. 7 (The change of the maximum temperature in different relaxation time), the highest temperature changing over the relaxation time. The highest

Discussion
Due to the blood flow, the temperature in the blood can hardly raise, the temperature field looks like a semicircle in the myocardium. In above figures, it can be known the temperature increase with both the increase of voltage and the time, and the temperature increase with voltage is more obviously than the increase with time.
In this study, we used 50 °C isotherm and thermal dosage to analyze the lesion outline, and both of them increased with the increase of the voltage and time. From results we can see that the lesion outline of the thermal dosage is smaller than the lesions outline of the 50 °C isotherm in all the time when the voltage increased. The lesion range of CEM43 is smaller than the lesion range of the 50 °C isotherm when the time within 160 s.
In cardiac ablation, the duration time is 60 s to 120 s, and the voltage is 30-60 V in clinical currently. Since we compared the lesion size when the time was 60 and 120 s and the voltage 30-60 V, the size of 50 °C isotherm were larger than the size of the CEM43. Some studies researched in ex vivo liver [31] and found the two methods give similar results, but the critical isotherm was chosen; and others found that the isotherm overestimate 4.8% for the final lesion diameter than the critical CEM43 °C [8] since the RF has been shut down. Therefore the thermal dose gets more precise data.
We contrasted the temperature field determined by Pennes' bioheat transfer equation and Hyperbolic equation. And in this study, we assumed the relaxation time was Fig. 7 The change of the maximum temperature in different relaxation time 16 s to analyze at first. And the results showed the shape of the temperature distribution similarly. We also chose 10 values from the relaxation time from 10 to 50 s to simulate, and we found that only the maximum temperature which determined by the Hyperbolic equation is little higher in addition to the relaxation time between 30 and 40 s. The temperature determined by the Hyperbolic equation was smaller than which determined by the Pennes equation in the start and with the growth of the time it become larger than the temperature of Pennes. The highest temperature determined by the Hyperbolic equation changes up and down in a small range which is smaller than 2 °C.
In pre-ablation, due to the theory of the Hyperbolic considers the limitation of the transfer of the energy heat, at the beginning of the ablation, the heat that produced by the myocardium cannot deliver in the layer and transfer through the surface blood convection. Thus the lesion area was smaller than the Pennes transfer method. As the ablation time was over the relaxation time, the electric field produced more heat, and the heat is trapped inside the myocardium, so the area was bigger than the Pennes in post ablation.

Conclusions
Compared to 50 °C isotherm, CEM43 °C considers the temperature history, it can be more accuracy to describe the change of temperature. And from above we can know that the 50 °C isotherm overestimate the thermal dose when the ablative time within 160 s. Now the cardiac ablation time is 60-120 s, so use thermal dose to analyze can get more accurate data and its necessary for treatment.
Pennes' bioheat transfer equation does not consider the speed of the heat while Hyperbolic equation take it into account, and the Hyperbolic method reflects the influence of heat propagation speed. In this study, we contrasted the maximum temperature in different relaxation time and found that the highest temperature changing over it. The result of the Hyperbolic is more close to the actual situation of cardiac radiofrequency ablation, so the latter can describe temperature more exactly in cardiac ablation.
There are still some limits in this research. As lack of a time-varying blood perfusion data in clinic, we did not consider this condition into the simulation. In future, we'll take this condition into account and to get more accuracy data to compare the results.

Declarations
Authors' contributions ZT was responsible for the design, data collection and overall investigation. ZT, QN and XHN were responsible for computational modeling and data analysis part. TD and RRW were responsible for the statistical analysis part. All authors (1) have made substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; (2) have been involved in drafting the manuscript or revising it critically for important intellectual content; and (3) have given final approval of the version to be published. Each author has participated sufficiently in the work to take public responsibility for appropriate portions of the content. All authors read and approved the final manuscript.