The Effect of Thermal and Electrical Conductivities on the Ablation Volume during Radiofrequency Ablation Process

—Radiofrequency ablation (RFA) is the treatment of choice for certain types of cancers, especially liver cancer. However, the main issue with RFA is that the larger the tumor volume, the longer the ablation period. That causes more pain for the patient, so the surgeons perform a larger number of ablation sessions or surgeries. The current commonly used electrode material, nickel-titanium alloy, used in RFA is characterized by low thermal and electrical conductivities. Using an electrode material with higher electrical conductivity and thermal conductivity provides more thermal energy to tumors. In this paper, we design two models: a cool-tip RF electrode and a multi-hook RF electrode, which aim to study the effect of the thermal and electrical conductivities of the electrode material on ablation volume. Gold, silver, and platinum have higher thermal and electrical conductivity than nickel and titanium alloy, and therefore we studied the effect of these materials on the ablation volume using two different designs, which are the RF cooling tip electrode and the multi-hook electrode. The proposed model reduces the ablation time and damages healthy tissue while increasing the ablation volume with values ranging from 2.6 cm 3 to 15.4 cm 3 . The results show ablation volume increasing with materials characterized by higher thermal and electrical conductivities and thus reducing patient pain.


INTRODUCTION
Cancer is one of the leading causes of death in both men and women, with 11.3 million deaths in 2020 [1]. The second most common cause of death in Egypt [2]. Liver cancer is the fourth most common type of cancer worldwide [3] and the second most common cancer in Egypt [2]. The most common way to treat liver tumors is resection (RES), microwave ablation (MWA), and radiofrequency ablation (RFA) [4]. RFA is based on passing high-frequency (400-500 kHz) electric currents through the tissue between two excitation electrodes, causing the tissues to heat up, which results in tissue ablation [5,6]. The main limitation with RFA is that as tumor volume increases the whole-tumor ablation duration increases, which the patient's pain. Therefore, RFA is effective for small tumors (i.e., tumors with a diameter of 3 cm), but still not very effective for large tumors [7,8]. Radiofrequency (RF) electrode materials should be biocompatible with the human body and have low relative permittivity to be compatible with any device [9,10]. Fang et al., suggested several factors contribute to increased ablation volume with reduced ablation time, such as electrode design and the material of the electrode [11]. Electrodes made of materials with high thermal conductivity and high electrical conductivity can contribute to increased ablation volume and reduced time of ablation [12,13]. Current electrode materials used in RFA are characterized by low thermal and electrical conductivity, such as nickeltitanium alloy [14]. The finite element model (FEM) is a numerical technique used to perform finite element analysis (FEA) of any given physical phenomenon [15]. Alemayehu, et al., have simulated a medical problem about bones and joints using FEM to solve the problems of cartilage erosion [16]. In [17], the authors have used FEM in various fields of dentistry for calculating the strength and behavior of structures and have succeeded in calculating deflection, stress, vibration, and buckling behavior. While on the other side, the authors simulated FEM to ablate breast cancer by using RFA and succeeded in abating 80% of the tumor [18]. In [19], the authors designed FEM to ablate liver tumors by using cool-tip RF electrodes.
Many studies are conducted in ex-vivo studies [20,21] and clinical studies [22,23] on the effect of electrode materials on volume ablation due to their electrical and thermal properties. Thermal conductivity gets high attention for researchers in theory because, as the thermal conductivity of the material increases, so the thermal emission capacity of the material does [24,25]. Several theoretical studies compared materials that have high thermal conductivity with those of low thermal conductivity [26,27], while other several studies compared materials that have high electrical conductivity with those that have low electrical conductivity [28][29][30]. These studies found that the use of materials of high thermal and electrical conductivities helps to increase the ablation volume while reducing the ablation time.
The aim of this paper is to study the effect of different materials having high thermal conductivity and high electrical conductivity for RF electrodes on the ablation volume using a FEM. Although our results are specific to the case of RFA of the liver, they may also be important for other ablation applications, such as kidney cancer. In this paper, we design two models based on the cool tip RF electrode and the multihook RF electrode. www.ijacsa.thesai.org The two models are based on a numerical finite element analysis to compute the distribution of heat and electric potential inside the damaged and surrounding tissue during an RF ablation. These two models simulate the ablation of large tumors while trying to reduce the damage to healthy cells in less time. This paper is organized as follows: First, an explanation of the methodology of the proposed model, including its equations. Second, the results and discussions of the proposed model show the differences in results between our model and others, and finally, the conclusions.

II. METHODS
We used COMSOL 5.4 software [31] to implement FEM to develop two models (cool-tip and multi-hook RF electrode models). Each model is included within a cylindrical domain that contains both the liver domain and an electrode domain. The radius of the base of the cylinder is 5 cm, and the height is 12 cm.

A. FEM Modeling 1) Liver domain:
The liver tissue is the main tissue capable of generating glucose from lactate, glycerol, and amino acids (mainly alanine from muscle). It is located in the right upper quadrant of the abdominal cavity, rests just below the diaphragm, to the right of the stomach, and overlies the gallbladder. The liver domain includes everything surrounding the electrode: blood, blood vessels, and liver tissues.
2) Electrode domains a) A cool-tip RF electrode domain: It is distinguished by its excellent resistance to rust and corrosion as well as by its high flexibility, which avoids breakage or distortion, both of which pose risks to the patient's safety. The proposed model disregards the inner tube for brine injection responsible for cooling.
The cool tip RF electrode domain, consists of an electrode domain and a trocar domain as shown in Fig. 1 [32].
The RF electrode consists of:  An insulated stainless-steel trocar with a diameter of 0.73 mm and a height of 12 cm.
 A nickel-titanium alloy (nitinol) electrode with a height of 3 cm and a diameter of 0.73 mm with a tip in a cone.   In our study, we set the power equal to 15 watts and assumed that the tumor was spherical, as 56% of liver cancer patients had spherical tumors [33]. We also assumed that the tumor size was 16 cm 3 , which is the largest volume that has been recorded for a liver tumor in Egypt in the last ten years [34]. Fig. 3 shows the design of multi-hook electrodes.  A stainless-steel electrode measures 1 cm in height and 2 mm in diameter, with a nickel-titanium alloy with a 1.5 cm major diameter and 0.5 mm minor diameter tip in a hook.

a) A multi-hook RF electrode domain
In our model, the initial conditions and boundary conditions of the simulation model are defined. We set the multi-hook RF electrode as the voltage source and set power equal to 15 watts, while we defined the liver boundary as the ground. 3) Thermal and electrical properties: Table I lists the different properties at 500 kHz used in our model to describe the gold (Au), the silver (Ag), the platinum (Pt), the nickeltitanium alloy (Nitinol), artery wall, and blood. The table  shows the relative permittivity, density, and melting point  values of the materials in the table are close. On the other  hand, the table shows a clear variance in thermal and electrical conductivity values. So, we chose these two characteristics to study their effect on the ablation volume. During the ablation process, the tissue temperature increases. Changes in temperature lead to changes in the electrical conductivity of biological tissues [35]. The changes that occurred in the electrical conductivity of the tissues within the model are described as follows: (1) where: is the initial electrical conductivity at the reference temperature (30 ), is the temperature coefficient, is the temperature difference from the initial reference temperature.
The linear electrical conductivity of the model is determined by. (2) Expect the artery wall, and the equation is. (3) Both equations are bounded at 30-80 .

4) Mathematical equations a) Electric field:
The electro-magnetic problem has been solved using a simplified version of Maxwell's equation that uses the quasistatic approximation because the displacement current is so minimal relative to the resistive current at the frequency range employed in the RFA technique (450-550 kHz). As a result, the generalized Laplace equation has been used to calculate the electric field. (4) Where: is (S/m) the electrical conductivity and V is the electric potential (V). The current study takes into account the tissue's electrical conductivity, which is temperature-dependent and increases linearly (10% per °C).
In the model tissues, the losses due to heat contact with the tissues are not significant, so we neglected the losses in our model [39]. The electric field E (V/m) is calculated from the equation. (5) where is the operating factor. Then, current density J (A/m 2 ) is calculated from where is the electrical resistivity of the material (Ω m) b) Bioheat equation: Calculations of the temperature distributions were made using FEM. By resolving the heat transfer equation (Equation 7), where we ignored the metabolic heat production and blood perfusion heat loss due to their comparatively small magnitudes, we were able to determine the temperature distribution throughout the tissue: Bioheat transfer due to RF current can be mathematically explained by the following Pennes equation [40].
where is the density of tissue (kg/m 3 ), is the specific heat capacity of the tissue (J/kg/K), is the tissue thermal conductivity (W/m/K), is the blood perfusion rate (1/s), is the volumetric heat produced by the metabolism (W/m 3 ), is joule heating that represents heat generated from RF, where is the density of current, is the intensity of the electric field, is the conductivity with a unit of , is the voltage impressed on the electrode, is the volumetric heat produced by radiofrequency heating (Wm -3 ) calculated using Equation (2), is the core blood temperature (supposed to be 37°C), because the blood vessels effect was discarded in this study then we can assume and T are equal then was set to zero Wm  The complete FEM model's initial voltage and temperature have been taken into account to be 0 V and 37°C, respectively. The cylinder domain's bottom surface has been adjusted to 0 V to mimic a dispersive ground pad. In the FEM model, an RF generator-controlled variable voltage source has been added to the electrode borders. All of the FEM model's remaining outside boundaries has been subjected to an electrical insulation boundary condition. For ten minutes, all of the numerical simulations of temperaturecontrolled RFA in various tissues were run. Furthermore, multiple temperature values were ranging from 50°C to 60°C.  The ablated temperature, equal to 50 °C, is the temperature required to destroy tumor-infected, damaged cells.
 Enthalpy change is the amount of heat evolved or absorbed in liver tissues (0 J/kg).

III. RESULTS AND DISCUSSION
Cool-tip RF electrodes and multi-hook electrode ablation in our study depended on three materials: gold, silver, and platinum. This study analyzed these materials to provide guidance in clinical practice. Table II shows the ablation volumes due to the used electrode materials at different ablation durations. The ablation volume of tumor results output from gold, silver, platinum, nickel-titanium alloys, and electrodes respectively is shown in Fig. 4, 5, 6, and 7, respectively. Fig. 4. View of the fraction of damage and the ablation volume resulting from using a cool-tip RF electrode made of Gold after ten minutes. Fig. 5. View of the fraction of damage and the ablation volume resulting from using a cool-tip RF electrode made of Silver after ten minutes. Fig. 6. View of the fraction of damage and the ablation volume resulting from using a cool-tip RF electrode made of Platinum after ten minutes. Fig. 7. View of the fraction of damage and the ablation volume resulting from using a cool-tip RF electrode made of Nickel-Titanium alloy after ten minutes. The simulation results and the percentage of ablation achieved from gold, silver, platinum, and nickel-titanium alloy are shown graphically in Fig. 8. Table III shows the results for the simulations with the new design of multi-hook RF electrode shown in Table III. At the same time and with the same power, there was an appreciable difference in the ablation volume between the different electrode materials. 490 | P a g e www.ijacsa.thesai.org

B. Multi-hook RF Electrode
The ablation volume of tumor results output from gold, silver, platinum, and nickel-titanium alloy RF electrodes, respectively, is shown in Fig. 9, 10, 11, and 12, respectively. Fig. 9. View of temperature distribution and the ablation volume resulting from using a multi-hook RF electrode made of Gold after ten minutes. Fig. 10. View of temperature distribution and the ablation volume resulting from using a multi-hook RF electrode made of Silver after ten minutes. Fig. 11. View of temperature distribution and the ablation volume resulting from using a multi-hook RF electrode made of Platinum after ten minutes. Fig. 12. View of temperature distribution and the ablation volume resulting from using a multi-hook electrode made of Nickel-Titanium alloy after ten minutes.
The simulation results and the percentage of ablation achieved from gold, silver, platinum, and nickel-titanium alloy are shown graphically in Fig. 13. 491 | P a g e www.ijacsa.thesai.org In this paper, we designed a computer model to investigate whether gold, silver, and platinum RF electrodes create larger volume ablation than nickel-titanium alloy electrodes using the same conditions. As shown from the results, for RF and multi-hook electrodes, there is a difference in the percentage of ablation using RF electrodes made of gold, silver, and platinum materials compared to using an electrode made of a nickel-titanium alloy by an amount ranging from five percent to ten percent after a minute, while the difference in the percentage of ablation ranged from 14% to 30%. On the other hand, the ablation rate with the multi-hook electrode is 2% greater than the ablation rate with the cool-tip RF electrode in all kinds of materials used as the multi-hook electrode covers a larger area due to the design difference between the two electrodes.
Previous theoretical research looked into the impacts of using Pt, Ag, and Au as the electrode material for RF ablation rather than nitinol since these metals have higher thermal and electrical conductivities. According to the results, a different amount of ablation was produced, with each of the four electrode materials. Using varied powers at various intervals, we investigated in this study whether Pt, Ag, and Au electrodes produced thermal ablation more successfully than nitinol electrodes. In all simulations, we proved that as the temperature rose, more power was given via the Pt, Ag, and Au electrodes, leading to greater maximum tissue temperatures and a larger ablation volume, as depicted in Fig. 14, 15, and 16. We discovered that the four electrodes' ablation volumes varied.

IV. CONCLUSION
The results show that using gamma titanium instead of nickel-titanium achieved an increase in the ablation volume because it has higher electrical and thermal conductivity than nickel-titanium alloy. Also, the results show the effect of tuning parameters (ablation power, ablation time and design of the electrode) on increasing the ablation volume and decreasing the ablation time. The results show that the electrode design is the most important tuning parameter because with the change of design from the reference model to our developed model, the effect and success of the rest of the tunning parameters appeared. That helps to reduce the patient's pain and increase the accuracy. Future work can study the effect of the RF multi-hooks electrodes on large tumors by using the same tuning parameters and compare it with a RF cool-tip electrode. Tumor ablation percentage using cool-tip RF electrode Tumor ablation percentage by multi-hooks RF electrode