International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 623
Kill Cancer Tumour Cells Using Radio-frequency Ablation
Hemant Sahu1, Davender Singh2
1PG Student, Department Of Electronics and Communication Engineering
2Assistant Professor, Department Of Electronics and Communication Engineering
1,2 Manav Institute of Technology, Hisar, Haryana 125001, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - Radiofrequency ablation is the most commonly
used percutaneous ablationtechniqueand well-documented
in the literature on focal therapies. It has become the image-
guided ablation method of choice because of its efficacy,
safety, and ease of use. Radiofrequency ablation has shown
promise in treating selected solid tumors, particularly those
involving the liver, kidneys, lungs, and the musculoskeletal
system. It is a minimally invasive technique often used in
inoperable patients with other comorbidities.
Radiofrequency ablation requires a minimal hospital stayor
can be performed on an outpatient basis. The trocar design
in this paper has smaller size of electrodes and does not
affect the health tissue nearby the electrode.Thisisachieved
because of the electrode shapes which cure volume of 12
mm.
Key Words: RFAblation,FEM,Liver,Trocar,BloodVessel,
2D, 3D.
1. INTRODUCTION
In last decade, there has been a rapid advancement in the
utilization of percutaneous, image-guided tumor ablation
methods. Radiofrequency (RF) ablation has become the
method of choice because of its safety and efficacy. Image-
guided RF ablation is minimally invasive and usually
appropriate for inoperable patients with other
comorbidities. It requires a minimal hospital stay or can be
performed on an outpatient basis. This paper present a
heating device to get a significant temperaturebyinsertinga
four armed electric rod and electric current is passed
through it. Equations for the electric field for this technique
shows in the Electric Potential section and which is coupled
to the bio-heat equation which are used to analyze the
temperature variation in the tissue. The heat source
generating from the electric field is also called as resistive
heating or Joule heating. The COMSOL Multi-physics model
provides the RF heating energy with DC currents.
Temperature above 45°C to 50°C is the least significant
temperature required to start the killing of the tumor tissue
[3]. The treatment needs a local heat source, which
physicians create by inserting a small electric rod [4]. Liver
tissue boiling and charring act as electrical insulators and
limit the effect of RFA through increased resistance. The
important liver tissue properties for RFA are electrical and
thermal conductivity [4]. Radio-frequency ablation is also
reasonable by the heat-sink effect, a process that occurs
when thermal energy is scatters from the target wound due
to blood flow in the blood vessels adjacent to it [5].
Consequently, the shape and sizeoftheablationzonemaybe
unpredictable and the efficiency of RFA may be restricted as
multiple sessions are necessary for complete tumour
eradication [6]. In order to attain larger necrosis volumes,
numerous innovative electrode modifications are applied
such as expandable electrodes or internally cooled
electrodes as well as multiple electrodes. The result is
ablation zones of lesions up to 2-5 mm. A margin of 0.5-1.0
mm of healthy liver tissue is mandatory to be ablated in
order to secure treatment of the peripheral tumour,
including any microscopic extension beyond the radio
graphically visible margins [7]. The proposed rod is made of
a trocar (the main rod) attached to the four electrode arms
as shown in figure 1[8]. The trocar is made up of electrically
insulated steel except near the electrode arms as named
called rod tip. An electric field in the tissue is created by the
electric current provided in the rod. Around the rod electric
field generated by joule's heating have maximum value and
decrease when calculated far from the electric rod.
Figure 1: Cylindrical Liver Design [8].
2. MODEL DISCRIPTION
The Bioheat physics, the Electric Currents physics,
multiphysics feature and Electromagnetic Heat Source to
apply a transient analysis is used in the model. Kelvin (K) is
the predefined temperature unit in COMSOL Multiphysics.
The model designed uses the Celsius temperature unit,
which is convenient for the bioheat equation. The model
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 624
approximates the liver tissue with a large cylinder and
having its temperature constant at 37 °C for the entire
procedure. The tumor is to be found near the center of the
liver and has the same thermal properties as the nearby
tissue. The proposed model locates the rod along the
cylinder’s center line such that its electrodes distance the
region where the tumor is located. The geometry also
includes a large blood vane.
Figure 2: Basic Geometry of trocar tip.
The rod is made of a trocar attached with four electrode
arms. The main rod has a radius of 1 mm and the four
electrode arms has a radius of 0.25 mm. Blood vain has a
radius of 5mm can see in figure 2.
Table 1: Material Properties.
Electrode Properties (Titanium Alloy)
Electrical Conductivity 6.7e8 (S/m)
Thermal Conductivity 18 (W/m.K)
Trocar Tip Properties (Conducting Steel)
Electrical Conductivity 4e6 (S/m)
Thermal Conductivity 71 (W/m.K)
Trocar Properties (Insulating Steel)
Electrical Conductivity 1e-5 (S/m)
Thermal Conductivity 0.026 (W/m.K)
Material properties are described in the table 1. Four
electrodes are made up of titanium alloy which is good
electrical conductor, trocartipismadeupofconductingsteel
which is good thermal conductor and trocar main rod made
up of insulating trocar.
The electrodes arms are reveled in figure 3to increase the
effect of heating or we can say to produce thermal heating in
larger radius. The torous tip is of 10 mm height and
complete rod is of 70 mm long.
Figure 3: Revolvery Rods.
Figure 4: Complete Geometry.
The complete Geometry is shown in figure 4 with blood vain
designed model.
3. RESULTS
There are mainly three parameters which are studied inthis
paper are electric potential, temperature and cancercell die.
ELECTRIC POTENTIAL
The governing equation for the Electric Currents interfaceis
(1)
Where V is the potential (V), σ the electrical conductivity
(S/m), Je an externally generated current density (A/m2),
Qjthe current source (A/m3). In this model both JeandQjare
zero. The governing equation therefore simplifies into:
(2)
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 625
Figure 5: Electric Potential in 2D.
The cross like shape at the center of the figure 5shows the
four electrode of trocar red color has the maximum voltage,
blue color has zero potential. Figure 6 shows the applied
electric potential the electrodes has the maximum potential
of 25V. As we go away from the electrode, the electrode
potential decreases.
Figure 6: Electric Potential 3D.
 TEMPERATURE
The heat transfer in electrode and trocar tip is given by
equation below.
(3)
Here it is a time-scaling coefficient; ρ is the tissue density
(kg/m3); C is the tissue’s specific heat (J/(kg·K)); and k is its
thermal conductivity (W/(m·K)). On the right side of the
equality, ρb gives the blood’s density (kg/m3); Cb is the
blood’s specific heat (J/(kg·K));ωbis itsperfusion rate(1/s);
Tb is the arterial blood temperature (Κ); while Qmet and
Qext are the heat sources from metabolism and spatial
heating, respectively (W/m3).The bioheat equation also
models heat transfer in various parts of the probe with the
appropriate values for the specific heat, C (J/(kg·K)), and
thermal conductivity, k (W/(m·K)). For theseparts,all terms
on the right-hand side are zero. The figure 7 shows how the
temperature increases with time in the tissue around the
electrode. The slice plot illustrates the temperature field 60
seconds after starting the procedure. The maximum
temperate achieved in 60 sec is 101 0C,whichisshownatthe
edges of electrode tip and the trocar tip shown by yellow
color.
Figure 7: Temperature Effect.
The temperature at the tip of one of the electrode arms is
shown in figure 8. The temperature rises quickly until it
reaches a steady-state temperatureofabout105 °C,Thatcan
be achieved in less than in one half a minute and it becomes
constant 1100C in 3 minutes.
Figure 8: Temperature Vs Time.
 CANCER CELLS DIE
It is also interesting to visualize the region where cancer
cells die, that is, where the temperature has reached at least
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 626
50 °C. You can visualize this area with an area for that
temperature in figure 9 shows one after 10 minutes.
Figure 9: Died Cancer Cell.
Figure 10 visualize the fraction of necrotic tissue after the
process is completed.
Figure 10: Necrotic Tissue.
Finally, figure 11 shows the fraction of necrotic tissue at five
different points above the electrode arm i.e. 4mm in blue, 8
mm in green,12 mm in red, 16 mm in sky blue and 20mm in
pink. Trocar is inserted into the centre of the tumor. We
observe that necrosis happens faster next to the electrode
and the trocar tip. Cancer cell die in 3 minutes till distance 4
mm from the trocar and at 8 mm distance it will be cured in
9 minutes.
Figure 11: Necrotic Tissue at Five Different Points.
Figure 12: Temperature Vs Distance from Trocar.
Temperature required to cure tumor is to be more than 46
0C, so this temperature is achieved till 12 mm distance from
the tumor after that the temperature is less than the
significant temperature. It can be said that tumor of 24 mm
diameter can be cured by this device within 9 minutes.
4 CONCLUSION
In RFA, an electrical current in the radio-frequency range is
delivered through a needle electrode under imaging or
surgical guidance, producing heat-based thermal heating. A
complete electrical-thermal design is created and simulated
through comsol. Temperatures range between 50 °C to 110
°C and results are obtained accurate and better to the
previous results that goes maximum till 85 0C. These
temperatures are observed near the electrode resulting in a
small area of necrosis, with the larger portion of the final
ablation zone being attributed to thermal conduction into
more peripheral areas around the electrode. The time taken
by the proposed geometry to reach 500 C in just 1 sec and
can cure tumor of 8mm diameter in 2 minutes. Design does
not affect the tissues nearby and also has smaller size of
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 627
electrode. This is achieved because of the electrode shapes
which cure volume of 12 mm.
REFERENCES
1. Sunil Kumar and Vinod Kumar, " Design and
Simulationofa Radio-FrequencyTumuorAblation",
International Journal for Scientific Research &
Development Vol. 4, Issue 07, 2016.
2. Sundeep Singh and Ramjee Repaka, “Pre-clinical
Modelling and Simulation of Hepatic
Radiofrequency Ablation” Excerpt from the
Proceedings of the COMSOL Conference, e-ISSN:
2320-0847 p-ISSN: 2320-0936, Volume-4, Issue-9,
pp-76-80, 2015.
3. K.F. Chu and D.E. Dupuy, "Thermal ablation of
tumours: biological mechanisms and advances in
therapy, Nature Reviews Cancer", Volume 3,
Issue14, pp. 199-208 (2014).
4. Globocon 2012, "Cancer Incidence and Mortality"
Worldwide: International Agency for Research on
Cancer.
5. Altekruse SF, McGlynn KA, Reichman ME.
"Hepatocellular carcinoma incidence,mortality,and
survival trends in the United States from 1975 to
2005". J ClinOncol. 2009;volume27:pp1485–1491.
6. Yang JD, Roberts LR. "Epidemiology and
management of hepatocellular carcinoma". Infect
Dis Clin North Am. 2006; Volume 8, Issue
24:pp899–919.
7. Y. Tsushima, S. Funabasama,J.Aoki,S.Sanada andK.
Endo, "Quantitative perfusion map of malignant
liver tumors, created from dynamic computed
tomography data 1", Academic radiology, issue
11(2), pp215-223 (2004).
8. S. Tungjitkusolmun, E. J. Woo, H. Cao, J. Tsai, V. R.
Vorperian, and J. G. Webster, “Thermal-electrical
finite-element modeling for radio- frequency
cardiac ablation: effects of changesin myocardial
properties,” Med. Biol. Eng. Comput., vol. 38, pp.
562–568, 2000.

Kill Cancer Tumour Cells using Radio-Frequency Ablation

  • 1.
    International Research Journalof Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 623 Kill Cancer Tumour Cells Using Radio-frequency Ablation Hemant Sahu1, Davender Singh2 1PG Student, Department Of Electronics and Communication Engineering 2Assistant Professor, Department Of Electronics and Communication Engineering 1,2 Manav Institute of Technology, Hisar, Haryana 125001, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - Radiofrequency ablation is the most commonly used percutaneous ablationtechniqueand well-documented in the literature on focal therapies. It has become the image- guided ablation method of choice because of its efficacy, safety, and ease of use. Radiofrequency ablation has shown promise in treating selected solid tumors, particularly those involving the liver, kidneys, lungs, and the musculoskeletal system. It is a minimally invasive technique often used in inoperable patients with other comorbidities. Radiofrequency ablation requires a minimal hospital stayor can be performed on an outpatient basis. The trocar design in this paper has smaller size of electrodes and does not affect the health tissue nearby the electrode.Thisisachieved because of the electrode shapes which cure volume of 12 mm. Key Words: RFAblation,FEM,Liver,Trocar,BloodVessel, 2D, 3D. 1. INTRODUCTION In last decade, there has been a rapid advancement in the utilization of percutaneous, image-guided tumor ablation methods. Radiofrequency (RF) ablation has become the method of choice because of its safety and efficacy. Image- guided RF ablation is minimally invasive and usually appropriate for inoperable patients with other comorbidities. It requires a minimal hospital stay or can be performed on an outpatient basis. This paper present a heating device to get a significant temperaturebyinsertinga four armed electric rod and electric current is passed through it. Equations for the electric field for this technique shows in the Electric Potential section and which is coupled to the bio-heat equation which are used to analyze the temperature variation in the tissue. The heat source generating from the electric field is also called as resistive heating or Joule heating. The COMSOL Multi-physics model provides the RF heating energy with DC currents. Temperature above 45°C to 50°C is the least significant temperature required to start the killing of the tumor tissue [3]. The treatment needs a local heat source, which physicians create by inserting a small electric rod [4]. Liver tissue boiling and charring act as electrical insulators and limit the effect of RFA through increased resistance. The important liver tissue properties for RFA are electrical and thermal conductivity [4]. Radio-frequency ablation is also reasonable by the heat-sink effect, a process that occurs when thermal energy is scatters from the target wound due to blood flow in the blood vessels adjacent to it [5]. Consequently, the shape and sizeoftheablationzonemaybe unpredictable and the efficiency of RFA may be restricted as multiple sessions are necessary for complete tumour eradication [6]. In order to attain larger necrosis volumes, numerous innovative electrode modifications are applied such as expandable electrodes or internally cooled electrodes as well as multiple electrodes. The result is ablation zones of lesions up to 2-5 mm. A margin of 0.5-1.0 mm of healthy liver tissue is mandatory to be ablated in order to secure treatment of the peripheral tumour, including any microscopic extension beyond the radio graphically visible margins [7]. The proposed rod is made of a trocar (the main rod) attached to the four electrode arms as shown in figure 1[8]. The trocar is made up of electrically insulated steel except near the electrode arms as named called rod tip. An electric field in the tissue is created by the electric current provided in the rod. Around the rod electric field generated by joule's heating have maximum value and decrease when calculated far from the electric rod. Figure 1: Cylindrical Liver Design [8]. 2. MODEL DISCRIPTION The Bioheat physics, the Electric Currents physics, multiphysics feature and Electromagnetic Heat Source to apply a transient analysis is used in the model. Kelvin (K) is the predefined temperature unit in COMSOL Multiphysics. The model designed uses the Celsius temperature unit, which is convenient for the bioheat equation. The model
  • 2.
    International Research Journalof Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 624 approximates the liver tissue with a large cylinder and having its temperature constant at 37 °C for the entire procedure. The tumor is to be found near the center of the liver and has the same thermal properties as the nearby tissue. The proposed model locates the rod along the cylinder’s center line such that its electrodes distance the region where the tumor is located. The geometry also includes a large blood vane. Figure 2: Basic Geometry of trocar tip. The rod is made of a trocar attached with four electrode arms. The main rod has a radius of 1 mm and the four electrode arms has a radius of 0.25 mm. Blood vain has a radius of 5mm can see in figure 2. Table 1: Material Properties. Electrode Properties (Titanium Alloy) Electrical Conductivity 6.7e8 (S/m) Thermal Conductivity 18 (W/m.K) Trocar Tip Properties (Conducting Steel) Electrical Conductivity 4e6 (S/m) Thermal Conductivity 71 (W/m.K) Trocar Properties (Insulating Steel) Electrical Conductivity 1e-5 (S/m) Thermal Conductivity 0.026 (W/m.K) Material properties are described in the table 1. Four electrodes are made up of titanium alloy which is good electrical conductor, trocartipismadeupofconductingsteel which is good thermal conductor and trocar main rod made up of insulating trocar. The electrodes arms are reveled in figure 3to increase the effect of heating or we can say to produce thermal heating in larger radius. The torous tip is of 10 mm height and complete rod is of 70 mm long. Figure 3: Revolvery Rods. Figure 4: Complete Geometry. The complete Geometry is shown in figure 4 with blood vain designed model. 3. RESULTS There are mainly three parameters which are studied inthis paper are electric potential, temperature and cancercell die. ELECTRIC POTENTIAL The governing equation for the Electric Currents interfaceis (1) Where V is the potential (V), σ the electrical conductivity (S/m), Je an externally generated current density (A/m2), Qjthe current source (A/m3). In this model both JeandQjare zero. The governing equation therefore simplifies into: (2)
  • 3.
    International Research Journalof Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 625 Figure 5: Electric Potential in 2D. The cross like shape at the center of the figure 5shows the four electrode of trocar red color has the maximum voltage, blue color has zero potential. Figure 6 shows the applied electric potential the electrodes has the maximum potential of 25V. As we go away from the electrode, the electrode potential decreases. Figure 6: Electric Potential 3D.  TEMPERATURE The heat transfer in electrode and trocar tip is given by equation below. (3) Here it is a time-scaling coefficient; ρ is the tissue density (kg/m3); C is the tissue’s specific heat (J/(kg·K)); and k is its thermal conductivity (W/(m·K)). On the right side of the equality, ρb gives the blood’s density (kg/m3); Cb is the blood’s specific heat (J/(kg·K));ωbis itsperfusion rate(1/s); Tb is the arterial blood temperature (Κ); while Qmet and Qext are the heat sources from metabolism and spatial heating, respectively (W/m3).The bioheat equation also models heat transfer in various parts of the probe with the appropriate values for the specific heat, C (J/(kg·K)), and thermal conductivity, k (W/(m·K)). For theseparts,all terms on the right-hand side are zero. The figure 7 shows how the temperature increases with time in the tissue around the electrode. The slice plot illustrates the temperature field 60 seconds after starting the procedure. The maximum temperate achieved in 60 sec is 101 0C,whichisshownatthe edges of electrode tip and the trocar tip shown by yellow color. Figure 7: Temperature Effect. The temperature at the tip of one of the electrode arms is shown in figure 8. The temperature rises quickly until it reaches a steady-state temperatureofabout105 °C,Thatcan be achieved in less than in one half a minute and it becomes constant 1100C in 3 minutes. Figure 8: Temperature Vs Time.  CANCER CELLS DIE It is also interesting to visualize the region where cancer cells die, that is, where the temperature has reached at least
  • 4.
    International Research Journalof Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 626 50 °C. You can visualize this area with an area for that temperature in figure 9 shows one after 10 minutes. Figure 9: Died Cancer Cell. Figure 10 visualize the fraction of necrotic tissue after the process is completed. Figure 10: Necrotic Tissue. Finally, figure 11 shows the fraction of necrotic tissue at five different points above the electrode arm i.e. 4mm in blue, 8 mm in green,12 mm in red, 16 mm in sky blue and 20mm in pink. Trocar is inserted into the centre of the tumor. We observe that necrosis happens faster next to the electrode and the trocar tip. Cancer cell die in 3 minutes till distance 4 mm from the trocar and at 8 mm distance it will be cured in 9 minutes. Figure 11: Necrotic Tissue at Five Different Points. Figure 12: Temperature Vs Distance from Trocar. Temperature required to cure tumor is to be more than 46 0C, so this temperature is achieved till 12 mm distance from the tumor after that the temperature is less than the significant temperature. It can be said that tumor of 24 mm diameter can be cured by this device within 9 minutes. 4 CONCLUSION In RFA, an electrical current in the radio-frequency range is delivered through a needle electrode under imaging or surgical guidance, producing heat-based thermal heating. A complete electrical-thermal design is created and simulated through comsol. Temperatures range between 50 °C to 110 °C and results are obtained accurate and better to the previous results that goes maximum till 85 0C. These temperatures are observed near the electrode resulting in a small area of necrosis, with the larger portion of the final ablation zone being attributed to thermal conduction into more peripheral areas around the electrode. The time taken by the proposed geometry to reach 500 C in just 1 sec and can cure tumor of 8mm diameter in 2 minutes. Design does not affect the tissues nearby and also has smaller size of
  • 5.
    International Research Journalof Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 627 electrode. This is achieved because of the electrode shapes which cure volume of 12 mm. REFERENCES 1. Sunil Kumar and Vinod Kumar, " Design and Simulationofa Radio-FrequencyTumuorAblation", International Journal for Scientific Research & Development Vol. 4, Issue 07, 2016. 2. Sundeep Singh and Ramjee Repaka, “Pre-clinical Modelling and Simulation of Hepatic Radiofrequency Ablation” Excerpt from the Proceedings of the COMSOL Conference, e-ISSN: 2320-0847 p-ISSN: 2320-0936, Volume-4, Issue-9, pp-76-80, 2015. 3. K.F. Chu and D.E. Dupuy, "Thermal ablation of tumours: biological mechanisms and advances in therapy, Nature Reviews Cancer", Volume 3, Issue14, pp. 199-208 (2014). 4. Globocon 2012, "Cancer Incidence and Mortality" Worldwide: International Agency for Research on Cancer. 5. Altekruse SF, McGlynn KA, Reichman ME. "Hepatocellular carcinoma incidence,mortality,and survival trends in the United States from 1975 to 2005". J ClinOncol. 2009;volume27:pp1485–1491. 6. Yang JD, Roberts LR. "Epidemiology and management of hepatocellular carcinoma". Infect Dis Clin North Am. 2006; Volume 8, Issue 24:pp899–919. 7. Y. Tsushima, S. Funabasama,J.Aoki,S.Sanada andK. Endo, "Quantitative perfusion map of malignant liver tumors, created from dynamic computed tomography data 1", Academic radiology, issue 11(2), pp215-223 (2004). 8. S. Tungjitkusolmun, E. J. Woo, H. Cao, J. Tsai, V. R. Vorperian, and J. G. Webster, “Thermal-electrical finite-element modeling for radio- frequency cardiac ablation: effects of changesin myocardial properties,” Med. Biol. Eng. Comput., vol. 38, pp. 562–568, 2000.