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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]
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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
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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
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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
Fig. 11. Volume of lesion considering an isothermal surface of 60ºC at 20V(ks = 2).
15s 30s 60s 120s 180s
Fig. 12. Volume of lesion considering an isothermal surface of 60ºC at 20V(ks = 5).
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15s 30s 60s 120s 180s
Fig. 13. Volume of lesion considering an isothermal surface of 60ºC at 30V(ks = 2).
15s 30s 60s 120s 180s
Fig. 14. Volume of lesion considering an isothermal surface of 60ºC at 30V(ks = 5).
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
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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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