Biological tissues undergo complex phase change heat transfer processes during cryosurgery, and a theoretical model is preferable to forecast this heat experience. A mathematical model for phase change heat transfer in cryosurgery was established. In this model, a fractal treelike branched network was used to describe the complicated geometrical frame of blood vessels. The temperature distribution and ice crystal growth process in biological tissue including normal tissue and tumor embedded with two cryoprobes were numerically simulated. The effects of cooling rate, initial temperature, and distance of two cryoprobes on freezing process of tissue were also studied. The results show that the ice crystal grows more rapidly in the initial freezing stage (<600 s) and then slows down in the following process, and the precooling of cryoprobes has no obvious effect on freezing rate of tissue. It also can be seen that the distance of 10 mm between two cryoprobes produces an optimal freezing effect for the tumor size (20 mm × 10 mm) in the present study compared with the distances of 6 mm and 14 mm. The numerical results are significant in providing technical reference for application of cryosurgery in clinical medicine.

References

References
1.
Gage
,
A.A.
, and
Baust
,
J.
, 1998,
“REVIEW—Mechanisms of Tissue injury in Cryosurgery”
Cryobiology
,
37
(
3
), pp.
171
186
.
2.
Bharat
,
G.
,
Bronia
,
T.
,
Suan
,
A.
,
Naeem
,
S.
, and
Damian
,
R. G.
, 2007,
“Cryosurgery for Prostate Cancer-Experience With Third-Generation Cryosurgery and Novel Developments in the Field,”
Eur. Urol. Suppl.
,
6
(
8
), pp.
516
520
.
3.
Hoffmann
,
N. E.
, and
Bischof
,
J. C.
, 2001,
“Cryosurgery of Normal and Tumor Tissue in the Dorsal Skin Flap Chamber: Part 1—Thermal Response,”
J. Biomech. Eng.
,
23
(
4
), pp.
301
309
.
4.
Xu
,
L. X.
,
Zhu
,
L.
, and
Holmes
,
K. R.
, 1998,
“Thermoregulation in the Canine Prostate During Transurethral Microwave Hyperthermia. Part II: Blood Flow Response,”
Int. J. Hyperthermia
,
14
(
1
), pp.
65
73
.
5.
Rabin
,
Y.
, and
Shitzer
,
A.
, 1998,
“Numerical Solution of the Multidimensional Freezing Problem During Cryosurgery,”
J. Biomech. Eng.
,
120
(
1
), pp.
32
37
.
6.
Xu
,
L. X.
, 1999,
“New Developments in Bioheat and Mass Transfer Modeling,”
Annual Review of Heat Transfer
,
C. L.
,
Tien
, ed.,
Begell House
,
New York
, Vol.
10
, pp.
1
23
.
7.
Rubinsky
,
B.
, and
Pegg
,
D. E.
, 1988,
“A Mathematical Model for the Freezing Process in Biological Tissue,”
Cryobiology
,
25
(
6
), pp.
546
561
.
8.
Rewcastle
,
J. C.
, and
Sandison
,
G. A.
, 2001,
“A Model for the Time Dependent Three-Dimensional Thermal Distribution Within Iceballs Surrounding Multiple Cryoprobes,”
Med. Phys.
,
28
(
6
), pp.
1125
1137
.
9.
Zhang
,
A.
,
Xu
,
L. X.
,
Sandison
,
G. A.
, and
Zhang
,
J.
, 2003,
“A Microscale Model for Prediction of Breast Cancer Cell Damage During Cryosurgery,”
Cryobiology
,
47
(
2
), pp.
143
154
.
10.
Zhang
,
J. Y.
,
Sandison
,
G. A.
,
Murthy
,
J. Y.
, and
Xu
,
L. X.
, 2005,
“Numerical Simulation for Heat Transfer in Prostate Cancer Cryosurgery,”
J. Biomech. Eng.
,
127
(
2
), pp.
279
294
.
11.
Deng
,
Z. S.
, and
Liu
,
J.
, 2005,
“Numerical Simulation of Selective Freezing of Target Biological Tissues Following Injection of Solutions With Specific Thermal Properties,”
Cryobiology
,
50
(
2
), pp.
183
192
.
12.
Magalov
,
Z.
,
Shitzer
,
A.
, and
Degan
,
D.
, 2007,
“Isothermal Volume Contours Generated in a Freezing Gel by Embedded Cryo-Needles with Applications to Cryo-Surgery,”
Cryobiology
,
55
(
2
), pp.
127
137
.
13.
Baish
,
J. W.
, 1994,
“Formulation of a Statistical Model of Heat Transfer in Perfused Tissue,”
J. Biomech. Eng.
,
116
(
4
), pp.
521
527
.
14.
Deng
,
Z. S.
,
Liu
,
J.
, and
Wang
,
H. W.
, 2008,
“Disclosure of the Significant Thermal Effects of Large Blood Vessels During Cryosurgery Through Infrared Temperature Mapping,”
Int. J. Therm. Sci.
,
47
(
5
), pp.
530
545
.
15.
Zhao
,
G.
,
Zhang
,
H. F.
,
Guo
,
X. J.
,
Luo
,
D. W.
, and
Gao
,
D. Y.
, 2007,
“Effect of Blood Flow and Metabolism on Multidimensional Heat Transfer During Cryosurgery,”
Med. Eng. Phys.
,
29
(
2
), pp.
205
215
.
16.
Zhang
,
Y. T.
,
Liu
,
J.
, and
Zhou
,
Y. X.
, 2002,
“Pilot Study on Cryogenic Heat Transfer in Biological Tissues Embedded With Large Bloods Vessels,”
Forsch. Ingenieurwes.
,
67
(
5
), pp.
188
197
.
17.
Parker
,
J. C.
,
Cave
,
C. B.
,
Ardell
,
J. L.
,
Hamm
,
C. R.
, and
Williams
,
S. G.
, 1997,
“Vascular Tree Structure Affects Lung Blood Flow Heterogeneity Simulated in Three Dimensions,”
J. Appl. Physiol.
,
83
(
4
), pp.
1370
1382
18.
Gabryś
,
E.
,
Rybaczuk
,
M.
, and
Kędzia
,
A.
, 2006,
“Blood Flow Simulation Through Fractal Models of Circulatory System,”
Chaos, Solitons Fractals
,
27
(
1
), pp.
1
7
.
19.
Zamir
,
M.
, 1999,
“On Fractal Properties of Arterial Trees,”
J. Theor. Biol.
,
197
(
4
), pp.
517
526
.
20.
Ghodoossi
,
L.
, 2005,
“Thermal and Hydrodynamic Analysis of a Fractal Microchannel Network,”
Energy Convers. Manage.
,
46
(
5
), pp.
771
788
.
21.
Xu
,
P.
,
Yu
,
B. M.
,
Yun
,
M. J.
, and
Zou
,
M. Q.
, 2006,
“Heat Conduction in Fractal Tree-Like Branched Networks,”
Int. J. Heat Mass Transfer
,
49
(
19–20
), pp.
3746
3751
.
22.
Mandelbrot
,
B. B.
, 1982,
The Fractal Geometry of Nature
,
Wh Freeman
,
New York
, p.
37
.
23.
Guo
,
K. L.
,
Kong
X. Q.
, and
Chen
S. N.
, 1988,
Computational Heat Transfer
,
Science and Technology of China Press
,
Hefei
, p.
68
.
24.
Budman
,
H. M.
,
Dayan
,
J.
, and
Shitzer
,
A.
, 1991,
“Controlled Freezing of Nondieal Solutions With Application to Cryosurgical Processes,”
J. Biomech. Eng.
,
113
(
4
), pp.
430
437
.
25.
Li
,
H. J.
,
Zhang
,
X. X.
, and
Yin
,
Y. F.
, 2003,
“Experimental Research of Blood Perfusion Estimation Using Temperature Response to Constant Surface Flux Heating,”
Chin. J. Biomed. Eng.
,
22
(
5
), pp.
393
398
.
26.
Chua
,
K. J.
,
Chou
,
S. K.
, and
Ho
,
J. C.
, 2007,
“An Analytical Study on the Thermal Effects of Cryosurgery on Selective Cell Destruction,”
J. Biomech.
,
40
(
1
), pp.
100
116
.
27.
Shih
,
T. C.
,
Kou
,
H. S.
, and
Lin
,
W. L.
, 2002,
“Effect of Effective Tissue Conductivity of Thermal Dose Distributions of Living Tissue With Directional Blood Flow During Thermal Therapy,”
Heat Mass Transfers
,
29
(
1
), pp.
115
126
.
28.
Liu
,
J.
, and
Wang
,
C. C.
, 1997,
Biologic Heat Transfer
,
Science Publication
,
Beijing
, pp.
418
420
.
29.
Gage
,
A. A.
, 1978,
“Experimental Cryogenic Injury of the Palate: Observations Pertinent to the Cryosurgical Destruction of Tumors,”
Cryobiology
,
15
(
4
), pp.
415
425
.
30.
Gage
,
A. A.
,
Caruana
,
J. A.
, and
Montes
,
M.
, 1982,
“Critical Temperature for Skin Necrosis in Experimental Cryosurgery,”
Cryobiology
,
19
(
3
), pp.
273
282
.
You do not currently have access to this content.