Biomedical Engineering Reference
In-Depth Information
q
av
a
(
)
v
ρ
cu
T
T
f
f
0
0
L
0.8
E
=
5.0
0.7
0.6
E = 0.5
0.5
E
=
0.25
0.4
E
=
0
0.3
0
2
4
6
8
10
n
FIGURE 1.9
Effect of the exponent n on the total heat transfer from artery to vein.
the difference in the inversion temperature, the probe temperature during this
process goes up to about 20 C to thaw the frozen tissue. This freezing-thawing
sequence is repeated several times to kill abnormal cells or tissues such as are
found in malignant tumors. Cryoinjury is believed to be due to two primary
mechanisms: one is the direct injury to the cells from the freeze-thaw cycle,
and the other is the indirect injury that results from the biological response
to the damage caused by freezing, primarily the vasculature of the tumor.
As with any medical treatment, there are risks involved, primarily that of
damage to nearby healthy tissue (Butz et al. 2000). We must know the exact
time required to freeze the entire cancer without damaging its surrounding
healthy tissue. However, some standards for setting clinical parameters such
as freezing rate and time are quite empirical today. Therefore, improvements
in cryosurgery depend upon developing reliable mathematical models and pre-
operational simulation tools based on them.
Perhaps, Bischof et al. (1997) is the first to predict ice ball formation
around a single cryosurgical probe. They used a cylindrical model to pre-
dict the interface location and temperature profile. Rewcastle et al. (1998)
proposed a finite difference model for single probe freezing and generated
isotherms within the ice ball during its growth. Keanini and Rubinsky
(1992) and Baissalov et al. (2001) dealt with the problem of optimization in
cryosurgery by regarding the placement of cryoprobes and freezing protocol
design. Wan et al. (2003) appealed to finite element methodology to simu-
late ice ball formation in a multiprobe cryosurgery. Rabin and Shitzer (1998)
and Rossi et al. (2007) introduced fairly sophisticated numerical techniques
for freezing an angioma, while Rossi and Rabin (2007) developed an elegant
 
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