Biomedical Engineering Reference
In-Depth Information
TABLE 1.1
Thermophysical Properties
Frozen
Tumor
Tumor
Lung
Subscript
i
c
l
k
[W
/
mK]
2.20
0.52
0.281
ρ
kg
/
m
3
1,000
1,000
550
c
[J
/
kgK]
2,000
4,000
3,710
α
m
2
/
s
10
−
6
10
−
7
10
−
7
1.10
×
1.30
×
1.38
×
10
5
h
sf
=3
.
34
×
[J
/
kg]
1.7.5 Limiting Radius for Freezing a Tumor during
Cryoablation
Some tissue freezes over a fairly large range of temperatures. However, for
the case of lung cancer, the blood comes out from the vessels during the
freezing-thawing sequence. The subsequent freezing takes place around the
probe surrounded by the blood as a conducting medium. To a first approx-
imation, we may use a single temperature for the phase change. Numerical
calculations based on the enthalpy method were carried out for the case, in
which the cryosurgical and biological parameters are given by
0
◦
C
T
f
=
T
0
(body temperature) = 37
◦
C
,S
m
=1
,
200 W/m
3
135
◦
C
,T
i
=
R
p
=1 mm
,T
p
=
−
−
The effective perfusion rate
ω
eff
within the tumor can be quite high since
some blood vessels are connected to the tumor. Here, we assume the effective
perfusion rate in the range of
ω
eff
= 0.004 to 0.04/sec. Moreover, the ther-
mophysical properties for frozen and unfrozen tissues in the lung are listed in
Table 1.1, according to Yokoyama (1993).
For the case in which
T
p
=
135
◦
C,
T
i
=0
◦
C,
T
0
=37
◦
C,
S
m
= 1,200
−
W/m
3
,
ω
eff
= 0.004/s,
R
p
= 1 mm, we have
Ste
i
= 0.808,
Sr
= 0.443,
10
−
5
,
Cr
= 15.4, and
ω
∗
= 0.031. A typical evolution of the
isotherms obtained for a longitudinal tumor of 20 mm
Met
= 6.24
×
27 mm is presented
in Figures 1.14(a)-(c). The outermost isotherm in each figure corresponds to
the freezing front (i.e.,
T
=
T
i
=0
◦
). Figure 1.14(c) clearly indicates that ill
placement of the probe may result in a substantial damage to the surrounding
healthy tissue.
Let us consider the freezing process when the probe is placed in a
large tumor. The temporal evolutions of the freezing front for the cases of
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