IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 20071177
Finite-Element Analysis of Ex Vivo and In Vivo
Cheolkyun Kim, Ann P. O’Rourke, David M. Mahvi, and John G. Webster*, Life Fellow, IEEE
Abstract—Cryoablation is a widely used method for the treat-
ment of nonresectable primary and metastatic liver tumors. A
model that can accurately predict the size of a cryolesion may
allow more effective treatment of tumor, while sparing normal
liver tissue. We generated a computer model of tissue cryoablation
using the finite-element method (FEM). In our model, we consid-
ered the heat transfer mechanism inside the cryoprobe and also
cryoprobe surfaces so our model could incorporate the effect of
heat transfer along the cryoprobe from the environment at room
temperature. The modeling of the phase shift from liquid to solid
was a key factor in the accurate development of this model. The
model was verified initially in an ex vivo liver model. Temperature
history at three locations around one cryoprobe and between two
cryoprobes was measured. The comparison between the ex vivo
result and the FEM modeling result at each location showed a
good match, where the maximum difference was within the error
range acquired in the experiment (
prediction of the lesion size was within 0.7 mm of experimental
results. We then validated our FEM in an in vivo experimental
porcine model. We considered blood perfusion in conjunction with
blood viscosity depending on temperature. The in vivo iceball size
was smaller than the ex vivo iceball size due to blood perfusion as
predicted in our model. The FEM results predicted this size within
0.1-mm error. The FEM model we report can accurately predict
the extent of cryoablation in the liver.
? ?). The FEM model
Index Terms—Ablation, blood perfusion, cryoablation, cryo-
surgery, ex vivo, finite-element modeling, in vivo, liver ablation.
rapid freezing rates and cellular dehydration at slow freezing
rates. The microvascular shutdown effect is also important
especially in the in vivo case. Multiple factors, such as freezing
rate, thawing rate, number of freeze-thaw cycles, and absolute
temperature contribute to the process. Despite the multifactoral
nature of cell death due to cyroablation, it is believed that tem-
perature below some critical value can kill cells . Smith and
Fraser examined the tissue damage of rat liver in a cryolesion
and found cell death if the temperature was below
. Kane  and Bischof et al.  found that cells will die at
without consideration of the cooling rate in liver and
RYOABLATION kills tissue with cold. Cell death is
mainly caused by both intracellular iceball formation at
Manuscript received July 28, 2005; revised October 18, 2006. This work
was supported in part by the National Institute of Health (NIH) under Grant
DK58839. Asterisk indicates corresponding author.
consin, Madison, WI 53706 USA.
A. P. O’Rourke and D. M. Mahvi are with the Department of Surgery, Uni-
versity of Wisconsin, Madison, WI 53792 USA.
*J. G. Webster is with the Department of Biomedical Engineering, Univer-
sity of Wisconsin, 1550 Engineering Drive, Madison, WI 53706 USA. (e-mail:
Digital Object Identifier 10.1109/TBME.2006.889775
prostate, respectively. Lee et al.  recommended a double
freeze-thaw cycle with a
Weber et al.  demonstrated tissue inside an ice ball to be
necrotic in a in vivo porcine model, implying that any tempera-
ture below 0
will result in cell death either due to the effects
of freezing, or to the effects of ischemia. Even if the required
lethal temperature is not clear, the knowledge of temperature
distribution inside the ice ball will provide a powerful tool for
improving cryoablation systems and modeling the treatment of
Clinically, cryoablation is monitored in real time with ultra-
sound, as the anterior surface of the iceball is highly echogenic
and, therefore, easily seen. Unfortunately, acoustic shadowing
limits the accuracy of the prediction of lesion size, particularly
posterior to the tumor –. CT or MRI imaging is more ac-
curate, and has been studied experimentally as an alternative
imaging method –. MR-guided and CT-guided percu-
taneous cryoablation are available now –. MRI has an
ability to measure the temperature inside the iceball, but it has
a technical problem in relating MR signal to temperature below
 or. EIT (electrical impedance tomog-
raphy)-guided cryoablation technique also shows promising re-
sults for monitoring cryoablation. –.
Commercially, two kinds of cryoablation systems are avail-
able: liquid nitrogen and argon gas. Comparative laboratory
studies revealed that the argon gas system is initially faster, but
not able to achieve as large an ice ball in a warm environment as
the liquid nitrogen system , . Both systems can permit
the use of multiple probes. However, the argon system has the
advantage of faster response time. We have focused our efforts
on an argon-based system, though the models are applicable to
all cold-based ablation systems.
isotherm for prostate ablation.
A. Finite-Element Method Modeling
The process of cryoablation is governed by the bioheat equa-
tion , 
the temperature of blood,
is the specific heat of the blood (
the blood perfusion (1/s).
coefficient accounting for the blood perfusion (
is the energy generated by metabolic processes.
is the density (
is the thermal conductivity (
), is the specific heat (
is the blood density (
is the convective heat transfer
0018-9294/$25.00 © 2007 IEEE
1178 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007
In this study, we neglected blood perfusion for the ex vivo sim-
ulation, but included it for the in vivo simulation. Also, we ne-
glected metabolic heat production as it is small compared to the
other terms , . Additionally, we added a latent heat term
due to the phase change from water to ice.
As a result, the governing equation for simulation is
pulse around the transition temperature range, which has to sat-
was determined to release the latent heat uniformly
over the transition temperature range from 0
lower limit of phase transition temperature.
),whichaccountsfor heat extractionfrom thetissue and
the cryoprobe cooling due to argon expansion.
In summary, we applied an appropriate form based on this
equation to each subdomain in computer modeling as follows:
is the latent heat () and is a normalized
is the heat sink
Equation (3) was applied to the tissue region, where the heat
transfer term due to blood perfusion was disregarded in the case
of ex vivo verification. Equation (4) was applied to the small
region where argon starts to expand inside the cryoprobe. Equa-
tion (5) was applied to the cryoprobe surface and the regions in-
side the cryoprobe full of argon, where the region was divided
into five subdomains and had different thermal conductivities
accounting for the argon flow pattern to generate the tempera-
ture profile measured on the cryoprobe surface. In (4) and (5),
the thermal properties of argon were applied to the regions in-
side the cryoprobe and those of stainless steel to the cryoprobes
We used FEMLAB 3.1i (COMSOL) in this FEM modeling.
It can generate the geometric model, assign material proper-
ties and boundary conditions, and control the mesh. We used an
Intel-based PC, which has the Windows XP operating system,
1 GB RAM and 100 GB of hard disk space.
B. Calculation of Heat Sink Value,
First, we measured how much heat is extracted by a cry-
oprobe during the ablation procedure. We recorded the temper-
atures from the built-in thermocouple of the cryoprobe and sev-
eral locations inside the affected tissue region every second. To
minimize the interference between thermocouples, we used at
most 4 thermocouples at a time around the cryoprobe in a cir-
cular pattern. Also, we inserted our thermocouples parallel to
the cryoprobe to get as accurate temperature readings as pos-
ducts heat from the surface, thereby underestimating the tem-
perature drop. For each experiment, the initial temperature was
Fig. 1. The iceball formation after 10 min cryoablation in ex vivo bovine liver.
A cryoprobe is located at the center of the iceball. Each line marker on the ther-
mocouple along with the cryoprobe was 5 mm apart. The width was 33.6 mm
in diameter and the depth from the cryoprobe tip was 10 mm.
Fig. 2. (a) Each circle means a measurement location except the one at the tip.
The origin of the coordinate is the tip of the cryoprobe. The first number (as
in 15?20) describes longitudinal distance in millimeters from the tip of the
cryoprobe and the second number describes radial distance in millimeters from
the center axis of the cryoprobe. (b) We calculated the extracted heat from each
shell formed at each measurement location.
a cross section of an iceball acquired after 10-min cryoablation.
The iceball was completely axisymmetric and had a maximum
width at 15 mm above the cryoprobe tip. With this basic knowl-
edge, we determined 32 locations and measured the tempera-
ture history of each location at least three times during a 10-min
cryoablation [Fig. 2(a)]. With those acquired temperature data,
we made a grid across the volume and calculated the entire heat
extracted from each shell at each time interval considering tem-
perature change, volume, density, specific heat capacity, latent
upper half part of the affected region for
culated total heat sink value was 9.279 kJ. Then, the negative
was assigned to the small subdomain inside the
cryoprobe [Fig. 3(b)]. This negativeheat source was assumed to
calculation. The cal-
KIM et al.: FINITE-ELEMENT ANALYSIS OF EX VIVO AND IN VIVO HEPATIC CRYOABLATION 1179
Fig. 3. (a) Cryoprobe. (United States patent number 5,800,487) The argon
inlet tube winds up around the center axis. It has a 30-mm active region and
a thermal barrier at the tip end. Thermal exchange occurs only in the active
region. (b) Modeling of cryoprobe. Argon expands only in the active region.
The negative heat source is located 2 mm above from the tip end.
Fig. 4. Geometry in the FEM for one probe formation. Active region of the
cryoprobe is 30 mm long from the cryoprobe tip and insertion depth was 50 mm
into the tissue. Dimensions are in meters.
increase linearly up to 10 s and then settle to the constant final
value is equal to the sum of heat loss from
the tissue and cryoprobe cooling. So it can be considered as the
freezing capacity of a 3.4-mm cryoprobe of an argon expansion
cooling system. We applied this
in all simulations.
Fig. 5. Geometry in the FEM for the two probe formation. The distance be-
tween two probes is 0.03 m and the temperature was measured at 0.005, 0.015,
and 0.03 m from the probe tip along the center line (? marks). Dimensions are
C. FEM Geometry
The Endocare CRYOcareTM surgical system (Irvine, CA)
supplies many kinds of probes. We modeled one type of cry-
oprobe with an active region 30 mm long and 3.4 mm in di-
ameter with a round tip [Fig. 3(a)]. Thermal exchange occurs
only in the active region and reaches the low temperatures nec-
essary for ablation. The probe has a stainless steel surface and a
1-mm-long thermal barrier at the tip. The cylindrical computer
tissue model had a 40-mm radius and 70-mm height, and had
thermal properties of liver. We selected this size because there
cryoprobe. The boundary conditions of the thermal insulation
were applied to the boundaries on the sides and bottom, while
free thermal convection was considered on the top boundary.
The heat sink region was established at a position 2 mm above
the cryoprobe tip in the active region of the cryoprobe. The ex-
of the cryoprobe. Thermal conductivity of the active region was
found by trial and error simulation to generate the same temper-
ature distribution on the cryoprobe surface. The surface tem-
perature of this cryoprobe model was compared to temperature
measurement from the experimentat several locations along the
For one probe formation ex vivo (Fig. 4), the cryoprobe was
located at the center of the tissue and the depth into the liver
was 50 mm, and for a two-probe formation ex vivo (Fig. 5),
two cryoprobes were located 30 mm apart. We set the tissue
size for a two-probe formation to 40-mm radius to reduce com-
putation load. The entire active region of each cryoprobe was
inside the liver for both formations. In both cases, we used La-
grange-quadratic elements. The model had 85881 degrees of
freedom and 63345 elements for the one probe formation and
131415 and 97391 for the two-probe formation, respectively.
We set the model initial temperature of the ex vivo liver tissue to
1180IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007
temperatures were kept constant in ex vivo and in vivo experi-
ments. We simulated 10 min freezing in the ex vivo simulation
and 5 min freezing in the in vivo simulation.
and temperatureof thein vivo livertissueto 34. These
D. Thermal Properties in Modeling
not fixed values, but change significantly with temperature. Pre-
vious researchers have used several different assumptions about
the varying history of these thermal properties from the thawed
state to the freezing state , –. In this study, we as-
sumed thermal properties of tissue were constant when the tem-
perature was above 0
. Thermal conductivity values, specific
heat values, and heat convection rate due to blood perfusion
values were acquired from the literature , . However,
when tissue is frozen, thermal properties are believed to change
with temperature. The thermal properties of ice are clearly de-
pendent on temperature; notably, the thermal conductivity of
ice increases as the temperature decreases. Lentz showed that
frozen muscle typically has a thermal conductivity value three
times larger than that of unfrozen muscle . In essence, the
thermal properties of ice and muscle change in a similar pat-
tern at subzero temperatures. Although we could not find exact
data about the thermal properties of liver tissue at subzero tem-
peratures, we assumed thermal properties at subzero tempera-
tures would change in the same pattern as muscle, because of
the similar water contents of liver and muscle. Hence, we ap-
plied varying thermal properties according to temperature when
liver was in the frozen state.
We determined the phase transition temperature range based
on temperature histories at a point 15 mm higher than the cry-
oprobe tip and 10 mm longitudinally away from the axis of cry-
oprobe in ex vivo experiments, where the iceball surface was
parallel to the cryoprobe. In this location, most heat transfer oc-
axial directions in cylindricalcoordinates. Under this condition,
we could reduce (3) at that point to the following for the ex vivo
From temperature measurement in this point at
it starts to become ice, the temperature change rate was deter-
mined by curve fit (Fig. 6). The calculated
as. Fig. 7 shows temperature-depen-
dent thermal properties of liver in this computer model.
In the in vivo simulation, we considered the fact that blood
decreased the blood perfusion rate as tissue cooled down and
assumed it stopped if the temperature was below 0
and II summarize all quantities.
was about 0.1,
. Tables I
E. Finite-Element Method Validation
To begin with, we compared the ex vivo experimental
results to simulated temperature measurements recorded at
five locations along the cryoprobe surface. Also, we compared
history at a location 15 mm high from the cryoprobe tip and 10 mm away from
the cryoprobe center (a) Temperature history at this point. ?
(b) Temperature distribution in radial direction at the height of 15 mm from the
cryoprobe tip at ? ? ??? ?. ?
??? ? ??????.
??? ? ??????
Fig. 7. Thermal conductivity and specific heat vary because of phase change.
KIM et al.: FINITE-ELEMENT ANALYSIS OF EX VIVO AND IN VIVO HEPATIC CRYOABLATION 1181
MATERIAL PROPERTIES OF LIVER USED IN FEM. ? IS TEMPERATURE IN DEGREES CELCIUS
MATERIAL PROPERTIES OF STAINLESS STEEL PROBE SURFACE USED IN FEM.
? IS TEMPERATURE IN DEGREES CELCIUS
temperature history recorded by the built-in thermocouple in-
side the cryoprobe tip to that acquired at the same location of
cryoprobe in our computer model.
For ex vivo experiments we utilized fresh bovine liver ob-
tained from a local animal processing facility. The temperature
was measured during the 10-min freezing process five times. In
15, and 20 mm radially from the center of the cryoprobe and 10
mm longitudinally along the cryoprobe from its tip end. In the
two-probe formation, the measurement location was the center
of the probes and 10 mm from the bottom line connecting both
tip ends (Fig. 5).
For the in vivo experiment we utilized a porcine model.
Protocol approval was obtained from our institutional animal
research committee and the policy on humane care and use
of laboratory animals was met for all experimentation. An-
imals were anesthetized with tiletamine and zolazepam, 7
mg/kg (Telazol; Fort Dodge Animal Health, Fort Dodge, IA)
and xylazine 0.45 mg/kg intramuscularly (Rompun; Phoenix
Pharmaceutical, St. Joseph, MO). Animals were intubated
and anesthesia was maintained with inhaled isoflurane gas.
The liver was exposed through a bilateral subcostal incision.
Using ultrasound guidance, we placed a 3.4-mm argon-cooled
cryoprobe. Because the porcine liver was much smaller than a
human liver, the entire iceball would not fit inside the tissue.
We, therefore, limited ablation time to 5 min rather than the
typical 10-min clinical ablation protocol. We measured the
temperature at 9 and 15 mm radially from the center of the
cryoprobe. Temperature was monitored by Luxtron fiberoptic
Fig. 8. Temperature comparison between ex vivo temperature measurements
and simulation results on the cryoprobe surface and at built-in thermocouple
location inside the cryoprobe.
temperature probes. Lesion size was followed and measured in
two dimensions using ultrasound. Following each procedure,
the animal was euthanized (Euthasol 0.2 ml/kg, Delmarva
Laboratories, Midlothian VA). The liver was removed and
each cryoablated lesion was resected and measured in two
Fig. 8 shows temperature comparison between the ex vivo
experimental results and simulated temperature measurements
recorded at five locations along the cryoprobe surface and the
thermocouple in the cryoprobe tip. The modeled and experi-
mental results showed a match within 3
model a cryoprobe in the tissue as heat transfer occurred during
We simulated cryoablation with a single probe in both a per-
tion with 2 probes in an ex vivo model. These models were then
compared to ex vivo and in vivo cryoablation. The parameters
we evaluated were temperature and lesion size at the comple-
tion of treatment.
error. So we could
1182IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007
Fig. 9. Ex vivo temperature comparison at 10, 15, and 20 mm in the radial
direction from the cryoprobe center at the height of 10 mm from the bottom of
the cryoprobe. Solid lines and dotted lines show results from experiment and
Fig. 10. Ex vivo temperature comparison at the center of two cryoprobes. The
height was 5, 15, and 30 mm from the baseline connecting two cryoprobe tips at
the center of two probes. Solid lines and dotted lines show results from exper-
iment and simulation, respectively. In the process of cryoablation, the freezing
tories at three locations from the cryoprobe (Fig. 9). The ex-
perimental curve was acquired by averaging five experiments at
each location every 5 s. The maximum difference in tempera-
ture between experiment and simulation over the entire ablation
time was 3
. The error margin of temperature measurement
and was calculated by considering the precision of
the thermocouple (
) and the worst case deviation from
For the two-probe ex vivo case, we performed four experi-
ments and measured temperature histories at the center between
the two probes. Fig. 10 compares the averaged experimental
the cryoprobe center at the height of 15 mm from the bottom of the cryoprobe.
Solid lines and dotted lines show results from experiment and simulation, re-
be 40 mm to guarantee no temperature change at the edge. But,
periences much more cooling and freezes faster. Therefore, the
larger compared to that from the cryoprobe to the edge. Using
that result, we set the tissue size in the computer model with a
40-mm radius just as in the one probe case. When we increased
the tissue size to a 55-mm radius, the temperature difference
was about 1
at the tissue edge and the temperature inside
the iceball didn’t change much compared to that for a 40-mm
radius. The maximum deviation from the experimental average
during cryoablation. Because the two iceballs grow
at the same rate, the iceball fronts from each probe meet at the
center between the cryoprobes for the case when the height is
15 mm. Just before the two iceball fronts meet, latent heat is
released from both sides. Thus, the temperature changes slowly
aroundthe 5-min mark. Atthe height of 30mm at thecenter, we
note that the iceball front propagated most slowly among these
three locations. The temperature region of slowest propagation
occurs later than the other two locations. This slowing was ex-
actly predicted by the simulation.
The maximum simulated radius of the iceball was 16.3 mm
from the center of the cryoprobe and the maximum depth was
10.4 mm from the tip of cryoprobe. At the completion of the ex-
periment, we measured the iceball size by dissecting the iceball
from the surrounding liver. The mean radius of the iceball size
viation between simulation and experiment was 0.7 mm.
The FEM model was then validated in an in vivo perfused
liver. Using ultrasound monitoring, we performed four single
cryoablations, one in each lobe of the liver. In two of four cases,
the iceball growth became larger than the liver thickness. We
eliminated these two cases from our size calculations but in-
cluded them in our temperature calculations. Average values
from the experimental results were compared to our models at
KIM et al.: FINITE-ELEMENT ANALYSIS OF EX VIVO AND IN VIVO HEPATIC CRYOABLATION1183
ERROR IN TEMPERATURE MEASUREMENTS DUE TO THERMOCOUPLE PLACEMENT ERROR AND TEMPERATURE GRADIENT. TEMPERATURE GRADIENT WAS
CORRELATED TO FREEZING RATE
two locations (Fig. 11). The error margin from the average tem-
perature in experiments was
ference between experimental result and simulation was 3.1
during the 5-min ablation. The mean radius of the iceball in the
5-min in vivo experiment was 10.8 mm (
lation result predicted a 10.7-mm iceball radius.
In this study, the cryoprobes and thermocouples were
placed by marking distances on them and by using two plastic
templates. After the experiments, the distances between the
cryoprobe and the thermocouples were checked by looking at
the small track left in the tissue. The average placement error
. The temperature gradient was larger at a location
closer to the cryoprobe, because it was experiencing more se-
vere cooling. We, therefore, correlated cooling rate at a location
with temperature gradient. Table III shows the temperature
error in experiments due to thermocouple placement error and
the temperature gradient considering the cooling rate.
and the maximum dif-
). The simu-
In recent years, minimally invasive thermal ablation tech-
lation, techniques like laser ablation , radiofrequency abla-
ablation  use heat instead of cold. The heat-based thermal
advantage of cryoablation compared to heat-based treatments is
the ability to easily monitor the iceball using ultrasound during
the procedure .
Ultrasound imaging, however, does not effectively evaluate
the tumor ablation interface posterior to the tumor. Surgeons
have typically solved this problem by covering the targeted
volume with a large margin of normal liver tissue. In cases
of multiple tumors, even more normal liver is destroyed. This
study shows the promise that pretreatment computer modeling
may more exactly target tumor volume, possibly allowing for
the preservation of normal liver.
We demonstrated that FEM analysis could predict tempera-
ture distribution over time in liver tissue during cryoablation.
We further demonstrated that the size of an iceball in both per-
fused and nonperfused liver could be predicted. We considered
the effect of blood perfusion on iceball propagation. Without
blood perfusion, the iceball size had about 0.6 mm larger radius
larger volume for 5 min of in vivo cryoablation.
For 10 min of in vivo cryoablation, the radius was 1 mm larger.
This lesion-shrinking effect of blood perfusion is not significant
compared to hyperthermic ablation techniques –. This
can be explained in the way blood perfusion decreases as tem-
thereby lessening the effects of perfusion. Also we considered
the fact that blood viscosity increases as temperature decreases.
As cooling propagates into the tissue, the excessive heat supply
due to blood perfusion in the unfrozen tissue region decreases.
Several researchers showed quite promising computer simula-
tion results in their ex vivo or in vivo experimental setups, but
some of them did not consider blood perfusion in their mod-
eling. Especially when we use multiple cryoprobes, the iceball
size can be overestimated when blood perfusion is not consid-
We included a cryoprobe and its surface in our model. In-
transfer of argon inside the cryoprobe, we treated the argon re-
gion as a black box and simply changed thermal conductivities
surface temperature. Technically, this description is wrong. But
the purpose of this modeling was to determine the tempera-
ture history inside the iceball. So the complex and time-con-
suming simulation of this region was unnecessary. In the region
where argon starts to expand, the flow velocity is very high,
while the flow velocity is low in the region where expanded
argon exits from the active region into the atmosphere. Also, we
considered heat transfer along the cryoprobe surface. Rewcastle
et al. measured a time-dependent normalized longitudinal tem-
perature gradient on the cryoprobe surface in precooled gelatin
(1.4% by mass) phantoms and applied it as a boundary con-
dition, which was a heat source in their modeling . How-
ever, because the cryoprobe surface temperature is dependent
on the ablated tissue, insertion depth and initial temperature of
target material, the relative temperature on the cryoprobe sur-
face cannot be known for an actual liver. For example, when
and its gradient is different because the thermal conductivity of
environment along the cryoprobe shaft changes the cryoprobe
surface temperature. In our model, instead, we assessed how
much heat a system can extract with a cryoprobe. This
resents the freezing capacity of one 3.4-mm cryoprobe using
used to freeze the tissue medium and a cryoprobe. So we could
apply that amount of heat sink source to each situation without
the need to measure cryoprobe surface temperature each time.
an array of cryoprobes in prostate cryoablation. Our approach
only works specifically for the conditions in this paper, where
probes are not in close proximity.
1184 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007
Polenda and Berger incorporated a point heat source disre-
garding a cryoprobe and showed a completely spherical iceball
formation only dependent on heat transfer in radial directions
, but the actual iceball is pear-shaped and the temperature
distribution differs in the azimuthal and radial directions.
Among the unique features of cryoablation that affect our
cult to model. Researchers havesuggested their own schemes to
In this study, we addressed this by assuming the thermal prop-
erties change linearly over some temperature range. We used
the temperature range for phase change. This temperature range
determines temperature distribution in the frozen state. The
As for the latent heat, we considered the water content in liver
and the fraction of bound water remaining when the tissue was
frozen to calculate the latent heat. Furthermore, the simulation
showed the amount of latent heat was the most controlling
factor to predict temperature history. Some researchers have
suggested time-dependence of latent heat release , but we
simply incorporated temperature-dependent latent heat release
to reduce computation load. The modeled data showed quite a
good match to that of experimental data.
We can, thus, use the FEM model to predict the temperature
distribution within the cryolesion and surrounding liver to esti-
mate the critical temperature for killing cells. Tumor cell death
is not solely the result of temperature, but also is dependent on
the rate of tissue freezing. Our model can also predict the rate
of freezing and, thus, the efficacy of ablation.
tumor cells around the large blood vessels , . Based on
this successful FEM simulation prediction, we now plan to in-
perature distribution around it. We hope to determine how close
the cryoprobe must be located to eradicate tumors around large
blood vessels in order to kill tumor cells. The FEM we present
here may become a powerful tool both for development of new
devices and prediction of the efficacy of current technology. We
could improve this model when we fine tune the latent heat and
thermal properties to estimate blood flow.
In conclusion, we considered as many factors as possible to
affect cryoablation efficacy in our model. Unlike other cryoab-
lation models reported previously, we applied heat sink
the change of blood perfusion rate dependent on temperatures
even above 0
. The heat transfer along the cryoprobe sur-
face was also considered. In this model, we determined phase
transition range from the experimental results. Also, we applied
the change of thermal properties after the tissue is completely
puter modeling of cryoablation.
 A. A. Gage and J. G. Baust, “Cryosurgery – A review of recent ad-
vances and current issues,” Cryoletters, vol. 23, pp. 69–78, 2002.
 J. J. Smith and J. Fraser, “An estimation of tissue damage and thermal
history in the cryolesion,” Cryobiology, vol. 11, pp. 139–147, Apr.
 R. A. Kane, “Ultrasound guided hepatic cryosurgery for tumor abla-
tion,” Sem. Interv. Radiol., vol. 10, pp. 132–142, 1993.
 J. C. Bischof, N. Merry, and J. Hulbert, “Rectal protection during
prostate cryosurgery: Design and characterization of an insulating
probe,” Cryobiology, vol. 34, pp. 80–92, 1997.
 F. Lee, D. Bahn, T. McHugh, G. Onik, and F. Lee, Jr, “US-guided
percutaneous cryoablation of prostate cancer,” Radiology, vol. 192, pp.
 S. M. Weber, F. Lee, Jr, D. O. Chinn, T. F. Warner, S. G. Chosy, and
D. M. Mahvi, “Perivascular and intralesional tissue necrosis after he-
patic cryoablation: Results in a porcine model,” Surgery, vol. 122, pp.
 J. C. Gilbert, G. M. Onik, W. Haddick, and B. Rubinsky, “The use of
ultrasound imaging for monitoring cryosurgery,” IEEE Trans. Biomed.
Eng., vol. BME-31, p. 563, 1984.
 G. Onik, C. Cooper, H. I. Goldberg, A. A. Moss, B. Rubinsky, and M.
Christianson, “Ultrasonic characteristics of frozen liver,” Cryobiology,
vol. 21, pp. 321–328, 1984.
 E. Laplace, P. Laugier, A. Saied, and G. Berger, “New device for ul-
trasonic monitoring of cryosurgery,” in Proc. IEEE Ultrasonics Symp.,
1994, vol. 3, pp. 1581–1584.
 H. Isoda, “Sequential MRI and CT monitoring in cryosurgery–An ex-
perimental study in rats,” Nippon Igaku Hoshasen Gakkai Zasshi, vol.
49, pp. 1499–1508, Dec. 1989.
 R. Baissalov, G. A. Sandison, B. J. Donnelly, J. C. Saliken, J. G. McK-
innon, K. Muldrew, and J. C. Rewcastle, “Suppression of high-density
plication to cryotherapy,” Phys. Med. Biol., vol. 45, pp. N53–59, May
 E. M. Remer, E. J. Weinberg, A. Oto, C. M. O’Malley, and I. S. Gill,
“MR imaging of the kidneys after laparoscopic cryoablation,” Am. J.
Roentgenol., vol. 174, pp. 635–640, Mar. 2000.
 J. Tacke, G. Adam, P. Haage, B. Sellhaus, S. Großkortenhaus, and
R. W. Günther, “MR-guided percutaneous cryotherapy of the liver:
In vivo evaluation with histologic correlation in an animal model,” J.
Magn. Reson. Imag., vol. 13, pp. 50–56, Jan. 2001.
 Q. Song, Y. Zhan, and L. J. Li, “Clinical application of CT-guided per-
cutaneous targeted argon-helium cryoablation for soft tissue sarcoma,”
Nan Fang Yi Ke Da Xue Xue Bao, vol. 26, pp. 229–230, Feb. 2006.
 C. A. Warlick, G. C. Lima, M. E. Allaf, I. Varkarakis, S.
Permpongkosol, E. M. Schaeffer, L. R. Kavoussi, T. W. Jarrett, and S.
B. Solomon, “Clinical sequelae of radiographic iceball involvement of
collecting system during computed tomography-guided percutaneous
renal tumor cryoablation,” Urology, vol. 67, pp. 918–922, May 2006.
 J.S.Hong,S.Wong,G.Pease,andB.Rubinsky, “MRimagingassisted
12, pp. 1021–1031, 1994.
 B. L. Daniel, K. Butts, and W. F. Block, “Magnetic resonance imaging
for frozen tissues: Temperature-dependent MR signal characteristics
and relevance for MR monitoring of cryosurgery,” Mag. Reson. Med.,
vol. 41, pp. 627–630, 1999.
 M. M. Radai, S. Abboud, and B. Rubinsky, “Evaluation of the
impedance technique for cryosurgery in a theoretical model of the
head,” Cryobiology, vol. 38, pp. 51–59, Feb. 1999.
 D. M. Otten and B. Rubinsky, “Cryosurgical monitoring using
bioimpedance measurements–A feasibility study for electrical
impedance tomography,” IEEE Trans. Biomed. Eng., vol. 47, no. 10,
pp. 1376–1381, Oct. 2000.
 D. M. Otten, G. Onik, and B. Rubinsky, “Distributed network imaging
and electrical impedance tomography of minimally invasive surgery,”
Technol. Cancer. Res. Treat., vol. 3, pp. 125–134, Apr. 2004.
 D. M. Otten and B. Rubinsky, “Front-tracking image reconstruction
algorithm for EIT-monitored cryosurgery using the boundary element
method,” Physiol. Meas., vol. 26, pp. 503–516, Aug. 2005.
 P. M. Hewitt, J. Zhao, J. Akhter, and D. L. Morris, “A comparative
Cryobiology, vol. 35, pp. 303–308, 1997.
 J. C. Rewcastle, G. A. Sandison, J. C. Saliken, B. J. Donnelly, and J. G.
Mckinnon, “Considerations during clinical operation of two commer-
cially available cryomachines,” J. Surg. Oncol., vol. 71, pp. 106–111,
 J. C. Rewcastle, G. A. Sandison, L. J. Hahn, J. C. Saliken, J. G. McK-
innon, and B. J. Donnelly, “A model for the time-dependent thermal
distribution within an iceball surrounding a cryoprobe,” Phys. Med.
Biol., vol. 43, pp. 3519–3534, Dec. 1998.
 H. H. Pennes, “Analysis of tissue and arterial blood temperature in
resting human forarm,” J. Appl. Phys., vol. 1, pp. 93–122, 1948.
KIM et al.: FINITE-ELEMENT ANALYSIS OF EX VIVO AND IN VIVO HEPATIC CRYOABLATION1185
 Y. Rabin, R. Coleman, D. Mordohovich, R. Ber, and A. Shitzer, “A
new cryosurgical device for controlled freezing,” Cryobiology, vol. 33,
pp. 93–105, Feb. 1996.
 B. Rubinsky and E. G. Cravalho, “A finite element method for the so-
lution of one-dimensional phase change problems,” Int. J. Heat Mass
Trans., vol. 24, pp. 1987–1989, 1981.
 J. C. Bischof, J. Bastacky, and B. Rubinsky, “An analytical study of
 H. Budman, A. Shitzer, and S. Del Giudice, “Investigation of temper-
ature fields around embedded cryoprobes,” J. Biomech. Eng., vol. 108,
pp. 42–48, Feb. 1986.
 L. J. Hayes and K. R. Diller, “Implementation of phase change in nu-
merical models of heat transfer,” J. Energy Res. Tech., vol. 105, pp.
 Y. Rabin and A. Shitzer, “Numerical solution of the multidimensional
freezing problem during cryosurgery,” J. Biomech. Eng., vol. 120, pp.
32–37, Feb. 1998.
 J. S. David, V. D. Ramachandra, and J. C. Bischof, “Prediction of
thermal history and interface propagation during freezing in biological
systems – Latent heat and temperature-dependent property effects,” in
 F. A. Duck, PhysicalProperties of Tissue:A Comprehensive Reference
Book. San Diego, CA: Academic, 1990.
 E. S. Ebbini, S. I. Umemura, M. Ibbini, and C. A. Cain, “A cylin-
drical-section ultrasound phased-array applicator for hyperthermia
cancer therapy,” IEEE Trans. Biomed. Eng., vol. BME-35, pp.
Food Technol., vol. 15, pp. 243–247, 1961.
 Y. Cinar, A. M. Senyol, and K. Duman, “Blood viscosity and blood
pressure: Role of temperature and hyperglycemia,” Am. J. Hypertens.,
vol. 14, pp. 433–438, May 2001.
 T. J. Vogl, M. G. Mack, A. Roggan, R. Straub, K. C. Eichler, P. K.
Muller, V. Knappe, and R. Felix, “Internally cooled power laser for
MR-guided interstitial laser-induced thermotherapy of liver lesions:
Initial clinical results,” Radiology, vol. 209, pp. 381–385, Nov. 1998.
 D. Haemmerich, L. Chachati, A. S. Wright, D. M. Mahvi, F. T. Lee,
Jr, and J. G. Webster, “Hepatic radiofrequency ablation with internally
cooled probes: Effect of coolant temperature on lesion size,” IEEE
Trans. Biomed. Eng., vol. 50, no. 4, pp. 493–500, Apr. 2003.
 D. Haemmerich, A. W. Wright, D. M. Mahvi, F. T. Lee, Jr, and J. G.
Webster, “Hepatic bipolar radiofrequency ablation creates coagulation
zones close to blood vessels: A finite element study,” Med. Biol. Eng.
Comput., vol. 41, pp. 317–323, May 2003.
 J. E. Kennedy, “High-intensity focused ultrasound in the treatment of
solid tumours,” Nat. Rev. Cancer., vol. 5, pp. 321–327, Apr. 2005.
 A. S. Wright, F. T. Lee, Jr, and D. M. Mahvi, “Hepatic microwave
ablation with multiple antennae results in synergistically larger zones
of coagulation necrosis,” Ann. Surg. Oncol., vol. 10, pp. 275–283, Apr.
 T. Varghese,U.Techavipoo,J. A.Zagzebski,andF.T. Lee,Jr, “Impact
of gas bubbles generated during interstitial ablation on elastographic
depiction of in vitro thermal lesions,” J. Ultrasound Med., vol. 23, pp.
535–44, Apr. 2004.
 L. Chen, G. t. Haar, C. R. Hill, M. Dworkin, P. Carnochan, H. Young,
and J. P. Bensted, “Effect of blood perfusion on the ablation of liver
parenchyma with high-intensity focused ultrasound,” Phys. Med. Biol.,
vol. 38, pp. 1661–1673, Nov. 1993.
coolinglimit coagulation necrosis?,”J. Vasc. Interv. Radiol.,vol. 9, pp.
101–111, Jan.-Feb. 1998.
 M. Takamura, T. Murakami, T. Shibata, T. Ishida, T. Niinobu, S.
Kawata, J. Shimizu, T. Kim, M. Monden, and H. Nakamura, “Mi-
crowave coagulation therapy with interruption of hepatic blood in- or
outflow: An experimental study,” J. Vasc. Interv. Radiol., vol. 12, pp.
619–622, May 2001.
 J. Poledna and W. Berger, “A mathematical model of temperature dis-
tribution in frozen tissue,” Gen. Physiol. Biophys., vol. 15, pp. 3–15,
 W. Jungraithmayr, M. Szarzynski, H. Neeff, J. Haberstroh, G. Kirste,
A. Schmitt-Graeff, E. H. Farthmann, and S. Eggstein, “Significance
of total vascular exclusion for hepatic cryotherapy: An experimental
study,” J. Surg. Res., vol. 116, pp. 32–41, Jan. 2004.
 F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 3rd
ed.New York: Wiley, 1996.
Cheolkyun Kim was born in Kwangju, South
Korea, in 1973. He received the B.S. degree in
electrical engineering from Seoul National Uni-
versity, Seoul, South Korea, in 1996. and the M.S.
degree in biomedical engineering from University
of Madison, WI, in 2002. He is currently working
towards the Ph.D. degree in biomedical engineering
at the University of Madison.
He served as a member of Korean air force and
worked as a Q.C. Manager of Daehan medical
company. His research interests are in the areas of
minimally invasive surgical instruments and computer modeling of ablation
Ann P. O’Rourke received the B.S. degree from
Emory University, Atlanta, GA, in 1993 and the
M.D. degree and the M.S. degree in public health
from the University of Wisconsin, Madison, in 2002
and 2006, respectively.
She is currently a Resident in General Surgery and
SurgicalOncology ResearchFellowat the University
of Wisconsin Hospital.
David M. Mahvi attended the University of Ok-
lahoma, Norman, and subsequently received the
M.D degree in 1981 from the Medical University of
South Carolina, Charleston. He then completed the
following postgraduate medical clinical training pro-
grams at Duke University, Durham, NC: residency in
surgery from 1981–1983; fellowship in immunology
1983–1985; residency in surgery 1985–1989.
In 1989, he joined the Section of Surgical On-
cology, Department of Surgery at the University of
Wisconsin-Madison where he is now Professor of
Surgery and Chief of the Section. He is also a member, University of Wisconsin
Comprehensive Cancer Center.
received the B.E.E. degree from Cornell University,
Ithaca, NY, in 1953, and the M.S.E.E. and Ph.D.
degrees from the University of Rochester, Rochester,
NY, in 1965 and 1967, respectively.
He is Professor Emeritus of Biomedical Engi-
neering at the University of Wisconsin-Madison.
In the field of medical instrumentation he teaches
undergraduateand graduate courses in bioinstrumen-
tation and design. He does research on improving
electrodes for ablating liver to cure cancer. He does
research on safety of electromuscular incapacitating devices. He does research
on a miniature hot flash recorder. He is the editor of the most used text in
biomedical engineering: Medical instrumentation: application and design,
Third Edition (Wiley, 1998) and has developed 22 other books including the
Encyclopedia of medical devices and instrumentation, 2nd edition (Wiley,
2006) and 190 research papers.
Dr. Webster is a fellow of the Instrument Society of America, the American
Institute of Medical and Biological Engineering, and the Institute of Physics.
He has been a member of the IEEE-EMBS Administrative Committee and the
National Institutes of Health (NIH) Surgery and Bioengineering Study Section.
He is the recipient of the 2001 IEEE-EMBS Career Achievement Award.