Finite Element Analysis of

Radiofrequency Ablation

Abirvab Deb- BME MEng lsquo14Brice Lekavich- BME MEng lsquo14Cristian Vilorio- BME MEng lsquo14

Background

Radiofrequency AblationWhat is it- Arrhythmias- Tumors- Varicose Veins

Radiofrequency Ablation (RFA) Johns Hopkins Medicine Johns Hopkins Medicine nd Web 21 Apr 2014 lthttpwwwhopkinsmedicineorgliver_tumor_centertreatmentsablative_techniques radio_frequency_ablationhtmlgt

FEA Motivationbull Lesion has to be deep enough into targeted tissue yet limit

the amount of irreversible damage occurring to normal cardiac tissue

bull The ablated tissue area has to be large enough to compensate for the uncertainties in the electrical mapping that is used to localize the target tissue

bull RF energy is effective in ablating some arrhythmias bull Multiple attempts often have to be made prior to successfully

destroying the targeted tissue bull Lesions produced are not deep enough to eliminate the target

electrical pathway bull Lesion depth is a problem in the left ventricle where the heart wall

is thick

ObjectiveOne of the most important reasons to model heat transfer in living

tissues is to allow for the prediction of the level and area of potential damage caused by temperature change

bull We therefore aim to develop a model that allows for determination of the transient temperature distribution in living tissue under biological conditions and use this distribution to evaluate the potential lesion depth due to radiofrequency ablation

Control Volume of Tissue Element Body (Human) Heat Transfer THERMOPEDIA 10 Feb 2011 Web 20 Apr 2014 lthttpwwwthermopediacomcontent587gt

FEA Methodology

Preprocessing- Geometry generation

- Material Properties- Initial Conditions

- Boundary Conditions

- Mesh Generation

Solution- Duration of RF

energy- Time Steps

Postprocessing- Temperature Distribution

- Lesion Dimensions

- Convergence Test

Bioheat Transfer amp Pennesrsquo Equation

There are two main approaches to bioheat transfer models 1 Continuum approach- thermal impact of all blood vessels is accounted

for by perfusion through the effective conductivity of the tissue2 Vascular approach- models the impact of each vessel individually

attempting to reproduce the real vascularity of the tissue

The most widely used continuum model is that given by Harry Pennes (1948) Since then multiple variations have been developed to improve or account for different factors

Pennesrsquo Bioheat Equation

Assumptions of Pennesrsquo Equation 1) Pre-arteriolepost-venule heat transfer between

the tissue and blood is neglected2) Blood flow in small capillaries is assumed to be

isotropic (ignores blood flow directionality)3) Does not consider local vascular geometry (role

of larger blood vessels near capillary beds is neglected)

4) Blood is assumed to reach arterioles supplying the capillary beds at the body core temperature (assumed instantaneous exchange of energy and equilibrium with local tissue temperature)

Sakaguchi et al In Vitro Engineering of Vascularized Tissue Surrogates Scientific Reports 3 1316 1-7 (2013)

Cardiac cells

vascularization

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Background

Radiofrequency AblationWhat is it- Arrhythmias- Tumors- Varicose Veins

Radiofrequency Ablation (RFA) Johns Hopkins Medicine Johns Hopkins Medicine nd Web 21 Apr 2014 lthttpwwwhopkinsmedicineorgliver_tumor_centertreatmentsablative_techniques radio_frequency_ablationhtmlgt

FEA Motivationbull Lesion has to be deep enough into targeted tissue yet limit

the amount of irreversible damage occurring to normal cardiac tissue

bull The ablated tissue area has to be large enough to compensate for the uncertainties in the electrical mapping that is used to localize the target tissue

bull RF energy is effective in ablating some arrhythmias bull Multiple attempts often have to be made prior to successfully

destroying the targeted tissue bull Lesions produced are not deep enough to eliminate the target

electrical pathway bull Lesion depth is a problem in the left ventricle where the heart wall

is thick

ObjectiveOne of the most important reasons to model heat transfer in living

tissues is to allow for the prediction of the level and area of potential damage caused by temperature change

bull We therefore aim to develop a model that allows for determination of the transient temperature distribution in living tissue under biological conditions and use this distribution to evaluate the potential lesion depth due to radiofrequency ablation

Control Volume of Tissue Element Body (Human) Heat Transfer THERMOPEDIA 10 Feb 2011 Web 20 Apr 2014 lthttpwwwthermopediacomcontent587gt

FEA Methodology

Preprocessing- Geometry generation

- Material Properties- Initial Conditions

- Boundary Conditions

- Mesh Generation

Solution- Duration of RF

energy- Time Steps

Postprocessing- Temperature Distribution

- Lesion Dimensions

- Convergence Test

Bioheat Transfer amp Pennesrsquo Equation

There are two main approaches to bioheat transfer models 1 Continuum approach- thermal impact of all blood vessels is accounted

for by perfusion through the effective conductivity of the tissue2 Vascular approach- models the impact of each vessel individually

attempting to reproduce the real vascularity of the tissue

The most widely used continuum model is that given by Harry Pennes (1948) Since then multiple variations have been developed to improve or account for different factors

Pennesrsquo Bioheat Equation

Assumptions of Pennesrsquo Equation 1) Pre-arteriolepost-venule heat transfer between

the tissue and blood is neglected2) Blood flow in small capillaries is assumed to be

isotropic (ignores blood flow directionality)3) Does not consider local vascular geometry (role

of larger blood vessels near capillary beds is neglected)

4) Blood is assumed to reach arterioles supplying the capillary beds at the body core temperature (assumed instantaneous exchange of energy and equilibrium with local tissue temperature)

Sakaguchi et al In Vitro Engineering of Vascularized Tissue Surrogates Scientific Reports 3 1316 1-7 (2013)

Cardiac cells

vascularization

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

FEA Motivationbull Lesion has to be deep enough into targeted tissue yet limit

the amount of irreversible damage occurring to normal cardiac tissue

bull The ablated tissue area has to be large enough to compensate for the uncertainties in the electrical mapping that is used to localize the target tissue

bull RF energy is effective in ablating some arrhythmias bull Multiple attempts often have to be made prior to successfully

destroying the targeted tissue bull Lesions produced are not deep enough to eliminate the target

electrical pathway bull Lesion depth is a problem in the left ventricle where the heart wall

is thick

ObjectiveOne of the most important reasons to model heat transfer in living

tissues is to allow for the prediction of the level and area of potential damage caused by temperature change

bull We therefore aim to develop a model that allows for determination of the transient temperature distribution in living tissue under biological conditions and use this distribution to evaluate the potential lesion depth due to radiofrequency ablation

Control Volume of Tissue Element Body (Human) Heat Transfer THERMOPEDIA 10 Feb 2011 Web 20 Apr 2014 lthttpwwwthermopediacomcontent587gt

FEA Methodology

Preprocessing- Geometry generation

- Material Properties- Initial Conditions

- Boundary Conditions

- Mesh Generation

Solution- Duration of RF

energy- Time Steps

Postprocessing- Temperature Distribution

- Lesion Dimensions

- Convergence Test

Bioheat Transfer amp Pennesrsquo Equation

There are two main approaches to bioheat transfer models 1 Continuum approach- thermal impact of all blood vessels is accounted

for by perfusion through the effective conductivity of the tissue2 Vascular approach- models the impact of each vessel individually

attempting to reproduce the real vascularity of the tissue

The most widely used continuum model is that given by Harry Pennes (1948) Since then multiple variations have been developed to improve or account for different factors

Pennesrsquo Bioheat Equation

Assumptions of Pennesrsquo Equation 1) Pre-arteriolepost-venule heat transfer between

the tissue and blood is neglected2) Blood flow in small capillaries is assumed to be

isotropic (ignores blood flow directionality)3) Does not consider local vascular geometry (role

of larger blood vessels near capillary beds is neglected)

4) Blood is assumed to reach arterioles supplying the capillary beds at the body core temperature (assumed instantaneous exchange of energy and equilibrium with local tissue temperature)

Sakaguchi et al In Vitro Engineering of Vascularized Tissue Surrogates Scientific Reports 3 1316 1-7 (2013)

Cardiac cells

vascularization

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

ObjectiveOne of the most important reasons to model heat transfer in living

tissues is to allow for the prediction of the level and area of potential damage caused by temperature change

bull We therefore aim to develop a model that allows for determination of the transient temperature distribution in living tissue under biological conditions and use this distribution to evaluate the potential lesion depth due to radiofrequency ablation

Control Volume of Tissue Element Body (Human) Heat Transfer THERMOPEDIA 10 Feb 2011 Web 20 Apr 2014 lthttpwwwthermopediacomcontent587gt

FEA Methodology

Preprocessing- Geometry generation

- Material Properties- Initial Conditions

- Boundary Conditions

- Mesh Generation

Solution- Duration of RF

energy- Time Steps

Postprocessing- Temperature Distribution

- Lesion Dimensions

- Convergence Test

Bioheat Transfer amp Pennesrsquo Equation

There are two main approaches to bioheat transfer models 1 Continuum approach- thermal impact of all blood vessels is accounted

for by perfusion through the effective conductivity of the tissue2 Vascular approach- models the impact of each vessel individually

attempting to reproduce the real vascularity of the tissue

The most widely used continuum model is that given by Harry Pennes (1948) Since then multiple variations have been developed to improve or account for different factors

Pennesrsquo Bioheat Equation

Assumptions of Pennesrsquo Equation 1) Pre-arteriolepost-venule heat transfer between

the tissue and blood is neglected2) Blood flow in small capillaries is assumed to be

isotropic (ignores blood flow directionality)3) Does not consider local vascular geometry (role

of larger blood vessels near capillary beds is neglected)

4) Blood is assumed to reach arterioles supplying the capillary beds at the body core temperature (assumed instantaneous exchange of energy and equilibrium with local tissue temperature)

Sakaguchi et al In Vitro Engineering of Vascularized Tissue Surrogates Scientific Reports 3 1316 1-7 (2013)

Cardiac cells

vascularization

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

FEA Methodology

Preprocessing- Geometry generation

- Material Properties- Initial Conditions

- Boundary Conditions

- Mesh Generation

Solution- Duration of RF

energy- Time Steps

Postprocessing- Temperature Distribution

- Lesion Dimensions

- Convergence Test

Bioheat Transfer amp Pennesrsquo Equation

There are two main approaches to bioheat transfer models 1 Continuum approach- thermal impact of all blood vessels is accounted

for by perfusion through the effective conductivity of the tissue2 Vascular approach- models the impact of each vessel individually

attempting to reproduce the real vascularity of the tissue

The most widely used continuum model is that given by Harry Pennes (1948) Since then multiple variations have been developed to improve or account for different factors

Pennesrsquo Bioheat Equation

Assumptions of Pennesrsquo Equation 1) Pre-arteriolepost-venule heat transfer between

the tissue and blood is neglected2) Blood flow in small capillaries is assumed to be

isotropic (ignores blood flow directionality)3) Does not consider local vascular geometry (role

of larger blood vessels near capillary beds is neglected)

4) Blood is assumed to reach arterioles supplying the capillary beds at the body core temperature (assumed instantaneous exchange of energy and equilibrium with local tissue temperature)

Sakaguchi et al In Vitro Engineering of Vascularized Tissue Surrogates Scientific Reports 3 1316 1-7 (2013)

Cardiac cells

vascularization

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Bioheat Transfer amp Pennesrsquo Equation

There are two main approaches to bioheat transfer models 1 Continuum approach- thermal impact of all blood vessels is accounted

for by perfusion through the effective conductivity of the tissue2 Vascular approach- models the impact of each vessel individually

attempting to reproduce the real vascularity of the tissue

The most widely used continuum model is that given by Harry Pennes (1948) Since then multiple variations have been developed to improve or account for different factors

Pennesrsquo Bioheat Equation

Assumptions of Pennesrsquo Equation 1) Pre-arteriolepost-venule heat transfer between

the tissue and blood is neglected2) Blood flow in small capillaries is assumed to be

isotropic (ignores blood flow directionality)3) Does not consider local vascular geometry (role

of larger blood vessels near capillary beds is neglected)

4) Blood is assumed to reach arterioles supplying the capillary beds at the body core temperature (assumed instantaneous exchange of energy and equilibrium with local tissue temperature)

Sakaguchi et al In Vitro Engineering of Vascularized Tissue Surrogates Scientific Reports 3 1316 1-7 (2013)

Cardiac cells

vascularization

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Assumptions of Pennesrsquo Equation 1) Pre-arteriolepost-venule heat transfer between

the tissue and blood is neglected2) Blood flow in small capillaries is assumed to be

isotropic (ignores blood flow directionality)3) Does not consider local vascular geometry (role

of larger blood vessels near capillary beds is neglected)

4) Blood is assumed to reach arterioles supplying the capillary beds at the body core temperature (assumed instantaneous exchange of energy and equilibrium with local tissue temperature)

Sakaguchi et al In Vitro Engineering of Vascularized Tissue Surrogates Scientific Reports 3 1316 1-7 (2013)

Cardiac cells

vascularization

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Modifying Pennes Bioheat Equation

Perfusion Term Qp

bull Heat exchanged between the tissue and blood which is proportional to the product of the volumetric perfusion rate and the difference between the arterial blood entering the tissue and the venous blood leaving the tissue

bull Assumption thermal equilibrium exist between the tissue and venous blood and arterial blood temperature is equal to core body temperature

bull Blood is regarded as a local heat regulator by means of heat convectionCase 1 Qp is positive = blood acts like a heat source to the tissueCase 2 Qp is negative = the blood acts as a heat sink to the

tissue

In our case the core body temperature (Tb) is lower than the tissue temperature (T) and therefore Qp is negative and Case 2 is satisfied

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Modifying Pennes Bioheat Equation

Metabolic Term Qm

bull Metabolic heat generation term is considered insignificant compared to the heat generated by the heat source

bull Typical values for Qm are around the order of 1000 Wm3 while the heating done by the power source is on the magnitude of 2 to 3 orders higher

Heat Source qbull There are two different types of ablationmdash ldquotemperature-controlledrdquo and

ldquovoltage-controlledrdquo For simplification temperature-controlled ablation was modelled where the electrode tip was held at a constant temperature during ablation

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Governing EquationsBCs

TemperatureHeat FluxConvection

Weak form

119888 120597119879120597119905 minus120571 ∙ (119896120571 119879 )=119876119894119899 120570

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 + 119869 ∙119864minus120596119887119888119887(119879 minus119879119887)

120588 119888 120597119879120597119905 =120571 ∙119896120571119879 +119902minus119876119901+119876119898

119879=119879 119904 ( 119909 119910 119911 119905 ) 119900119899 120548119879119902 ∙ =minus119902119904 119900119899120548 119902119902 ∙ =h (119879 minus119879infin )119900119899120548 h

119872 +119870 119879 = 119891

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Time IntegrationHave equation of the form

θ-method time integration

Where

Plugging and into the θ-family of

approximation and rearranging terms to be of the equivalent form of

Where

To allow for unconditional stability (Crank-Nicolson Method)

Solve for at each time step

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

ANSYS Simulation Constants

Tissue Density ρ (kgm3)

Specific Heat cp (Jkg˚C)

Thermal Conductivity k (Wm

˚C)Heart 1081 3686 056

Liver 1079 3540 052

Kidney 1066 3763 053Pancreas

1087 3164 051

Lung 394 3886 039

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

ANSYS Simulation ResultsContours

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

ANSYS Simulation ResultsLesion size

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Lesion Size after 60sec of Ablation

bull ~35 mm widebull ~2 mm deep

Overall higher temperature contours hit an equilibrium where heat in is balanced by heat outbull Tissue still continues to

heat up as expected at lower temperatures

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Convergence Test

100 1000 1000015

2

25

3

35

4

45

Lesion Depth

Number of Elements

Dep

th [m

m]

550 Elements

100 1000 100003

32343638

442444648

5

Lesion Width

Number of Elements

Wid

th [m

m]

1600 Elements

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type

Lesion Size by Tissue Type

Heart Kidney Liver Pancreas Lung195

2

205

21

215

22

225

23

235

Lesion Depth

Dep

th [m

m]

Lung Pancreas Heart Liver Kidney3

31

32

33

34

35

36

37

Lesion Width

Wid

th [m

m]

• Finite Element Analysis of Radiofrequency Ablation
• Background
• FEA Motivation
• Objective
• FEA Methodology
• Bioheat Transfer amp Pennesrsquo Equation
• Assumptions of Pennesrsquo Equation
• Modifying Pennes Bioheat Equation
• Modifying Pennes Bioheat Equation (2)
• Governing Equations
• Time Integration
• ANSYS Simulation Constants
• ANSYS Simulation Results
• ANSYS Simulation Results (2)
• Lesion Size after 60sec of Ablation
• Convergence Test
• Lesion Size by Tissue Type