inducing thermal lesion on a cholangiocarcinoma considering a saline-enhanced radiofrequency...

8/2/2019 Inducing Thermal Lesion on a Cholangiocarcinoma Considering a Saline-Enhanced Radiofrequency Ablation

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Abstract-Cholangiocarcinoma is an adenocarcinoma of thebile ducts which drain bile from the liver into the small intestine.Unfortunately, most patients are diagnosed on an advanced stageof the disease with almost no chances for surgery, the onlypotentially curative treatment. As nitinol stents can be used toreduce stricture problems of the bile duct, these can be alsoconsidered as potential electrodes for hyperthermia treatments.Previous works show that in fact these metallic stents might beused as part of a feasible solution for delivering radiofrequency(RF) energy into a tumor located in a hollow organ to destroy thetumor tissue. However the tissue lesion induced is not completelyuniform due to convective heat transfer associated to the blood

flow in the nearby vessels. In this paper it is studied the use of saline solution for modifying the electrical conductivity of thetissue in order to obtain a more uniform lesion. A numericalanalysis using finite element method on a simplified model of theporta hepatis is performed. Results show that it is possible toobtain a more regular volume, by this way the tumor tissue ispreferentially heated, although there are still some risks on

exceeding the dimension of the bile duct.

I. I NTRODUCTION

Liver cancer has a very poor prognosis, being the number

of deaths almost the same as the number of new cases. It is

therefore the third most common cause of death from cancer

[1, 2]. Cholangiocarcinoma is a malignant cancer arising from

the neoplastic transformation of the epithelial cells lining theintra-hepatic and extra-hepatic bile ducts, and it is the second

most common primary hepatic malignancy [3]. Because there

are no early symptoms, the majority of patients are diagnosed

at advanced stage, when surgical therapies are excluded [4].

As nitinol stents can be used to reduce stricture problems

of the bile duct, these can be also considered as potentialelectrodes for hyperthermia treatments. Previous works [5-7]show that nitinol stents can be considered as a feasible

solution for delivering radiofrequency (RF) energy in a tumor

located in a hollow organ. However, the tissue lesion induced

using this kind of electrode is not completely uniform due tothe convective heat transfer associated to the blood perfusion

on the portal vein and hepatic artery. Also it was verified thetissue next to the electrode ends are preferentially heated

which also contributes to obtain a non-uniform lesion[8].

In order to overcome this situation, it was considered the

possibility of modifying the properties of the biological tissue, particularly the electrical conductivity in the middle section of

the tumor. It has been demonstrated that it is possible to

increase RF tissue heating during a RF ablation procedure by

injecting a saline solution thus modifying the electrical

conductivity, energy deposition and heating of the tissue [9-

11].In this work is intended to perform a numerical analysis of

a radiofrequency ablation using a stent-based electrode

considering an infused saline solution in the tumor tissue used

to modify its electrical properties so a more regular lesion can

be achieved.

II. MATERIAL AND METHODS

A. The Bioheat Equation

The radiofrequency ablation procedure consists of heating

up the tissue in order to destroy it by converting electric

energy into thermal energy. The current flows from the active

electrode through the tissue to a return electrode pad usually placed on the back or the upper leg of the patient.

The numerical simulation of the models consists of theanalysis of a thermoelectrical coupled field problem. The

temperature at each point of the tissue can be expressed by the

bioheat equation (1):

( )∂

= ∇ ⋅ ∇ + ⋅ − − −∂

b b m

T c k T h T T Q

t ρ J E (1)

where ρ is the density [kg/m3], c is the specific heat [J/kg·K],T is the temperature [K], T b is the blood temperature [K], k is

the thermal conductivity [W/m·K], J is the current density

[A/m], E

is the electric field intensity [V/m], Qm is the energydue to metabolic process [W/ m3] and hb is the blood perfusion

convective heat transfer coefficient. The energy generated by

the metabolic process can be neglected since it is very small.

Also, the term hb(T − T b) which refers to blood perfusion isneglected due to the presence of the porta vein and the hepatic

artery. The blood temperature in these large blood vessels is

considered unaffected by the thermal field in the surroundingtissue [12] and the blood flow is considered as a moving heat

sink which adds the following contribution to the right hand of

(1):

− ⋅ ∇b b bC T ρ u (2)

where ρb is the blood density [kg/m

3

], C b is the blood specificheat [J/kg·K] and ub is the velocity of the blood [m/s].

Most commercial generators of radiofrequency ablation

work between 375 to 480 kHz. At this frequency range most

part of the energy dissipated by the electric probe is through

electrical conduction and so quasi-static approximation is

valid [13]. The electrode energy deposition in (1) due to Joule

loss can be calculated considering a RF voltage is applied between the stent and the return pad. The resulting voltage

through the domain obeys Laplace’s equation:

0σ ∇ ⋅ ∇ =V (3)

Inducing Thermal Lesion on a Cholangiocarcinoma Considering a Saline-

Enhanced Radiofrequency Ablation

Carlos L. Antunes(1, 2), Tony R. Almeida(1) and Nélia Raposeiro(2) (1)

Department of Electrical Engineering and Computer Science

University of Coimbra, Portugal(2)

RIANDA Research – Centro de Investigação em Energia, Saúde e Ambiente

Coimbra, [email protected]



where σ corresponds to the electrical conductivity [S/m] and V

to the electric potential [V].

At each iteration, equation (3) is evaluated in order to

calculate the distributed heat source J·E to be used in (1) plus

the contribution (2). Then temperature distribution is

calculated and the tissue’s electrical conductivity, which is

temperature-dependent, is recalculated. The steps during the

solution of the finite element model started at 0.01s and they

were subsequently and automatically controlled by the solver software.

B. Model Geometry

In this work it was considered a simplified 3D model of

the porta hepatis. The porta hepatis is a transverse fissure of

the liver where the portal vein and the hepatic artery enter the

liver and the bile duct leaves. Cholangiocarcinoma can occur

anywhere along the intrahepatic or extrahepatic biliary tree,

and approximately 60% to 80% of cholangiocarcinomasencountered are located in the perihilar region [14].

The 3D models were created considering an external

cylinder (liver) with 200 mm diameter and 100 mm height.

The bile duct and the portal vein are cylinders of radius 5 mmand the hepatic artery is a cylinder of radius 2 mm [15].

The portal vein and the bile duct are positioned on a

circumference of 6 mm radius separated by an angle of 120º.

The hepatic artery is located so the distance between the three

ducts is the same. Fig. 1 shows the position of the blood

vessels and the bile duct considering a circumference of

r = 6 mm.

Fig. 1 Location of the blood vessels and the bile duct.

Fig. 2. Model considered for numerical simulation

The tumor is represented by a tube of 40 mm length, 5 mm

radius and 3 mm thickness, placed in the middle of the bile

duct. The tumor volume was cross-section divided into three parts for simulation volume regions with different electrical

conductivities. The center section of the tumor is 15 mm long

and the tumor ends are 12.5 mm long.

TABLE IMATERIAL PROPERTIES USED IN SIMULATION [7, 16, 17]

Element Material ρ [kg/m3] c[J/kg·K] k [W/m·K] σ [S/m]

Electrode Nitinol 6450 840 18 1·108

Hole Air 1.202 1 0.025 0

Tissue Liver 1060 3600 0.512 σ l (T)

Tumor tissue

Tumor 1060 3600 0.512 σ t (T)

Bloodvessels

Blood 1000 4180 0.543 0.667

TABLE IIBLOOD VESSELS PROPERTIES USED IN SIMULATION [15]

Blood Vessel Diameter [mm] Blood Perfusion [ml/min]

Vena Cava 10 327.55

Hepatic Artery 4 20.5

The electrode is made up of 24 nitinol wires with 0.25 mm

diameter. Each wire is a helix of radius 2 mm with a pitch of

25 mm. The whole electrode is 40 mm long placed inside the

tumor. The whole model using across all simulations is

presented in Fig. 2.

C. Material Properties

The material properties required for solving the modelsconsidered in this work were obtained from the literature [7,

15-17] and are summarized in Table I and II.

For the electrical conductivity of the outer sections of thetumor it was considered a value of 0.269S/m [17]. The middle

section corresponds to the tumor volume with a saline

solution, so its electrical conductivity is increased and it is

considered a multiple of the electrical conductivity of the outer sections, i. e.,

σ tc = ks·σ te (4)

where σ tc is the electrical conductivity of the middle section of

the tumor, σ te is the electrical conductivity of the tumor ends

and ks is a proportional factor. In the present work it wasconsidered ks varying from 1 (no saline solution) to 5. Finally,

the electrical conductivity of liver tissue is 0.13 S/m [7]. Theelectrical conductivities of the healthy and tumor tissues were

considered temperature-dependent, increasing 2% per degree

Celcius, dropping to 0.01S/m above 100ºC, allowing this way

to simulate the electrical insulation verified when gas forms at

this temperature value [18].

D. Model Conditions

Numerical simulations were performed in all models

considering constant source voltages of 20, 22, 24, 26, 28 and

30 volts. The external boundary of the model was considered

at ground potential (zero volts).

The temperature at the external surfaces of the model wasset to 37ºC. The initial temperature of the tissue was set also to

37ºC. Also the blood temperature was set to 37ºC.

E. Software

The stent structure was created in AutoCAD and exported

in 3D ACIS format to COMSOL Multiphysics 4.1 (COMSOL,

Inc. Burlington, MA, USA). The remain model was created

within Comsol, which was also used for 3D finite element

analysis.

All models were solved with PARDISO solver considering



Fig. 3. Volume of lesion obtained for an applied voltage of 20V considering

isothermal surfaces of 50ºC.

Fig. 4. Volume of lesion obtained for an applied voltage of 20V consideringisothermal surfaces of 60ºC.

Fig. 5. Volume of lesion obtained for an applied voltage of 30V consideringisothermal surfaces of 60ºC.

a RF ablation procedure of 180 seconds. Each model took anaverage time of 12.5 hours to solve using a computer with a

Intel Core 2 Quad CPU @ 2.34Ghz, with 8Gb of RAM, on a

64 bits platform (Windows Vista).

III. R ESULTS AND DISCUSSION

Considering that cellular cytotoxicity is induced in 4 to 6

minutes for temperatures from 46ºC up to 50-52ºC, and that

there is near instantaneous irreversible cellular damage above

60ºC [19, 20], isothermal surfaces of 50ºC and 60ºC were

considered for analysis of the volume of lesion induced by the

Fig. 6. Volume of lesion obtained for several voltage values considering

isothermal surfaces of 60ºC (ks=1).

Fig. 7. Volume of lesion obtained for several voltage values consideringisothermal surfaces of 60ºC (ks=3).

Fig. 8. Volume of lesion obtained for several voltage values consideringisothermal surfaces of 60ºC (ks=5).

radiofrequency thermoablation procedure. Taking into accountthe time interval simulated – 180s – it is expected that the

volume included in the 60ºC isothermal surface represents a

higher probability of inducing a volume of damaged tissue.

After each simulation, 50ºC and 60ºC isothermal surfaces

were obtained and the volume contained in each of these

surfaces was calculated using Comsol.In Fig. 3 and Fig. 4 are presented the volumes obtained for

an applied voltage of 20V, considering both volumes defined

by 50ºC and 60ºC isothermal volumes, respectively. In both

graphs it is shown that the volume obtained is larger as theelectrical conductivity of the middle section of the tumor – σ tc



15s 30s 60s 120s 180s

Fig. 9. Temperature distribution for an applied voltage of 20V (ks = 3).

– increases. At some instant, it is possible to observe that the

lesion volume does not increase significantly with time: thelower the value of ks the sooner the volume stops increasing

considerably. This can be explained with the sudden decrease

of the electrical temperature of the tissue as soon as the

temperature reaches 100ºC. From this point, the electrical

current decreases and so the tissue is no longer significantly

heated, which leads to a steady volume lesion. As the value of

ks decreases, the tissue surrounding the electrode heats upmore quickly. This leads to an earlier electrical isolation of the

electrode and so a smaller volume of damaged tissue is

obtained. This was verified for both volumes delimited either by a 50ºC isothermal surface or by a 60ºC isothermal surface

at every value of voltage considered. This can be observed inFig. 5 which depicts the volumes obtained for an applied

voltage of 30V considering a 60ºC isothermal surface.

From Fig. 3 to Fig. 5 it can be also observed that, at a first

stage, the volumes obtained are very similar regardless of the

value of ks. Later, these values diverge with time, obtaining

larger volumes as the value of ks increases. This can beverified for volumes obtained from isothermal surfaces of

50ºC and 60ºC. Also, the higher the value of the voltage

applied the sooner the values of damaged tissue volume

diverge. For example, for an applied voltage of 20V,

considering a induced lesion volume delimited by a 60ºCisothermal (Fig. 4), it can be observed that up to 80 seconds

from the beginning of the simulation the induced lesion

volume obtained is almost identical for every value of ks.

After that, the volumes obtained diverge. Increasing thevoltage to 30V (Fig. 5) these values of volume begin to

diverge after 20 seconds.In Fig. 6 to Fig. 8 it is depicted the different values of

volume delimited by a 60ºC isothermal surface obtained for a

constant value of ks considering different applied voltages.

These graphs clearly show that the amount of damaged tissue

is smaller for larger values of voltage. On the other hand, as ks increases, the volume of damaged tissue also increases, as itwas stated before. It is therefore necessary to set a

compromise between the applied voltage and the enhanced

electrical conductivity of the tissue.

At this point not only the size of the volume obtained is

important but also its shape is clearly an important factor totake into account. It is important to achieve a regular volume

so the tumor tissue is preferably damaged.

As it was mentioned before, the values of volume obtained

are very close at an initial time interval. Although these are

15s 30s 60s 120s 180s

Fig. 10. Volume of lesion considering an isothermal surface of 60ºC at 20V(ks = 1).

15s 30s 60s 120s 180s


15s 30s 60s 120s 180s




15s 30s 60s 120s 180s


15s 30s 60s 120s 180s


initially very alike, the shape of the volumes obtained

differs. In Fig. 10 to Fig. 12 are depicted the volume obtained

considering a 60ºC isothermal surface at 20V, for several

values of ks

. In these images it is possible to observe that attime instant of 15 and 30 seconds, the volumes obtained arealmost identical, which agrees with the information attained

from the graph in Fig. 4. However, at time instant of 60

seconds the shape of the volumes obtained are different. The

main difference is in the middle portion of the volume. As ks increases, the volume grows thicker on the opposite side to the

blood vessels. Yet, it does not develop in the same manner on

the side next to the blood vessels. The tumor tissue on this side

takes much longer to heat due to convective heat transfer in

the vicinity of the blood vessels. As time elapses, the volume

keeps growing on the opposite side of the blood vessels, becoming bigger for larger values of ks. Same results can be

observed for larger values of voltage. For example, Fig. 13

and Fig. 14 show the volume shapes obtained for an appliedvoltage of 30V. In this case, at time instant of 30 seconds, the

shape of the volumes obtained for ks = 2 and ks = 5 are almostidentical but they differ at time instant of 60 seconds.

From Fig. 9 to Fig. 14 two things become evident: 1) the

tumor tissue ends are preferably heated at first; and 2) later,the middle part of the volume is heated more intensely,

obtaining in this region a thicker volume lesion as the applied

voltage increases.As soon as the voltage is applied, a large current density is

attained, especially at both ends of the electrode which

1s 15s 30s 45sFig. 15. Current density (norm) obtained for an applied voltage of 30V with

ks = 3.

causes the high heating of the ends of the tumor tissue (Fig.

15). The ends of the tumor model confront the air volumelocated above and below it. This leads to a larger energydeposition at these points than in the middle portion of the

tumor. As the tissue is heated up over 100ºC, the electric

conductivity decreases as well as the electrical current. The

electrical current becomes very low at the ends of the tumor at

first and it finally drops significantly all over the tissue (time

instants of 15, 30 and 45 seconds in Fig. 15), leading to a slowdamaged tissue growth with time, as stated in Fig. 3 to Fig. 8.

Another important observation is related to the voltage

applied and the shape of the volume obtained. As it was

already mentioned, the volume of damaged tissue decreases as

the applied voltage increases. However, the volumes obtained

for higher voltages are more regular. As the applied voltagerises the tissue is heated more rapidly, this way overcoming

the convective heat transfer due to the blood vessels.

Finally, one last remark about the volumes obtained when

considering a 60ºC isothermal surface. In Fig. 6 to Fig. 8 it is possible to observe that the curves obtained for the values of damaged tissue present an overshoot: the volume grows with

time reaching a peak, then the value slightly decreases duringthe rest of the simulation, except for the case where ks = 1 (no

saline solution). For this case the value of the volume obtained

decreases during a brief time interval. After this the volume

resumes increasing very slowly.When the electric conductivity drops there is a reduction of

energy deposition. The heat transfer due to RF procedure is

less than the convective heat transfer due to the blood flow in

the nearby vessels and so the tissue is cooled. This can be

easily observed in the top view of Fig. 10 to Fig. 14. It is

noticeable at first that the isothermal surface increases andthen it begins to recede because the tissue next to the blood

vessels is being cooled down. Taking into account that there is

near instantaneous irreversible cellular damage above 60ºC,

there is a high probability that the damaged tissue is higher than the value obtained after 180 seconds.

IV. CONCLUSION

The study presented is an overview of the modeling,simulation and analysis of a saline-enhanced radiofrequency

tissue thermoablation of a cholangiocarcinoma considering a

stent-based electrode. It was intended to obtain a more regular

volume of damaged tissue in order to heat and preferentially

destroy the tumor tissue, modifying its electric conductivity

with a saline solution. Several cases with different electric



conductivities for the tumor tissue at different applied voltages

were considered and the results were analyzed taking into

account volumes delimited by isothermal surfaces of 50ºC and60ºC.

As expected, altering the electric conductivity in the

middle section of tumor tissue led to different shapes of

volumes of damaged tissue. Two important facts should be

highlighted:

1.

As the electric conductivity of the middle section of the tumor increases the size of the volume of induced

damage also increases;

2. As the applied voltage increases the volume obtaineddecreases.

Besides the dimension of the volume attained, also the

shape of the volume is essential. According to previous work [8], the ends of the tumor are rather heated than the middle

section of it. Increasing the electrical conductivity excessively

might lead, in a first stage, to an irregular shape of volume. On

the other hand, higher values of voltage produce more regular

shapes.

Because it is more important to heat the tumor, we are notreally concerned with a large volume of damaged tissue.

Instead, it is important to induce a well-located lesion so the bile duct is not damaged as well during the radiofrequency

ablation procedure. Combining a relative high voltage while

increasing slightly the electrical conductivity of the tumor might have this effect.

Finally, the volume obtained is not completely regular as

expected and the simulations performed point out that theinduced lesion can still exceed the tumor itself, which might

damage the bile duct.

It should be noticed that, unlike the simplified modelconsidered for the present numerical simulation, the porta

hepatis is a more complex structure, with different pulsating

blood flows and stroma which was not considered in the

present work. Actual work is being performed in order to takeinto account some of these limitations so a more controlled

volume shape can be obtained, preserving the healthy tissue.

V. ACKNOWLEDGMENT

This work was financially supported by the Foundation for Science and Technology (FCT, Portugal) through the project

number PTDC/EEA-ACR/72276/2006.

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inducing thermal lesion on a cholangiocarcinoma considering a saline-enhanced radiofrequency...

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