This article presents a retrospective of work performed at the Technion, Israel Institute of Technology, over the last 3-odd decades. Results of analytical and numerical studies are presented briefly as well as in vitro and in vivo experimental data and their comparison to the derived results. Studies include the analysis of both the direct (Stefan) and the inverse-Stefan phase-change heat transfer problems in a tissue-simulating medium (gel) by the application of both surface and insertion cryoprobes. The effects of blood perfusion and metabolic heat generation rates on the advancement of the freezing front are discussed. The simultaneous operation of needle cryoprobes in a number of different configurations and the effects of a thermally significant blood vessel in the vicinity of the cryoprobe are also presented. Typical results demonstrate that metabolic rate in the yet nonfrozen tissue, will have only minor effects on the advancement of the frozen front. Capillary blood perfusion, on the other hand, does affect the course of change of the temperature distribution, hindering, as it is increased, the advancement of the frozen front. The volumes enclosed by the “lethal” isotherm (assumed as 40°C), achieve most of their final size in the first few minutes of operation, thus obviating the need for prolonged applications. Volumes occupied by this lethal isotherm were shown to be rather small. Thus, after 10 min of operation, these volumes will occupy only about 6% (single probe), 6–11% (two probes, varying distances apart), and 6–15% (three probes, different placement configurations), relative to the total frozen volume. For cryosurgery to become the treatment-of-choice, much more work will be required to cover the following issues: (1) A clear cut understanding and definition of the tissue-specific thermal conditions that are required to ensure the complete destruction of a tissue undergoing a controlled cryosurgical process. (2) Comprehensive analyses of the complete freeze/thaw cycle(s) and it effects on the final outcome. (3) Improved technical means to control the temperature variations of the cryoprobe to achieve the desired thermal conditions required for tissue destruction. (4) Improvement in the pretreatment design process to include optimal placement schemes of multiprobes and their separate and specific operation. (5) Understanding the effects of thermally significant blood vessels, and other related thermal perturbations, which are situated adjacent to, or even within, the tissue volume to be treated.

1.
Onik
,
G.
, 1996, “
Cryosurgery
,”
Crit. Rev. Oncol. Hematol.
1040-8428,
23
, pp.
1
24
.
2.
Rubinsky
,
B.
, and
Onik
,
G.
, 1991, “
Cryosurgery: Advances in the Application of Low Temperatures to Medicine
,”
Int. J. Refrig.
0140-7007,
14
, pp.
190
199
.
3.
Shepherd
,
J.
, and
Dawber
,
R. P. R.
, 1982, “
The Historical and Scientific Basis of Cryosurgery
,”
Clin. Exp. Dermatol.
0307-6938,
7
, pp.
321
328
.
4.
Gage
,
A. A.
, and
Huben
,
R. P.
, 2000, “
Cryosurgical Ablation of the Prostate
,”
Semin. Urol. Oncol.
,
5
, pp.
11
19
.
5.
Zouboulis
,
C. C.
, 1998, “
Cryosurgery in Dermatology
,”
Eur. J. Dermatol.
1167-1122,
8
, pp.
466
474
.
7.
Mazur
,
P.
, 1968, “
Physical-Chemical Factors Underlying Cell Injury in Cryosurgical Freezing
,”
Cryosurgery
,
R.
Rand
,
A.
Rinfret
, and
H.
von Leden
, eds.,
Thomas
,
Springfield, IL
, pp.
32
51
.
8.
Saliken
,
J. C.
,
Donnelly
,
B. J.
, and
Rewcastle
,
J. C.
, 2002, “
The Evolution and State of Modern Technology for Prostate Cryosurgery
,”
Urology
0090-4295,
60
, pp.
26
33
.
9.
Zisman
,
A.
,
Pantuck
,
A. J.
,
Cohen
,
J. K.
, and
Belldegrun
,
A. S.
, 2001, “
Prostate Cryoablation Using Direct Transperineal Placement of Ultrathin Probes Through a 17-Gauge Brachytherapy Template—Technique and Preliminary Results
,”
Urology
0090-4295,
58
, pp.
988
993
.
10.
Orpwood
,
R. D.
, 1981, “
Biophysical and Engineering Aspects of Cryosurgery
,”
Phys. Med. Biol.
0031-9155,
26
, pp.
555
575
.
11.
Crister
,
J. K.
, and
Morbaaten
,
L. E.
, 2000, “
Cryopreservation of Murine Spermatozoa
,” Institute for Laboratory Animal Research,
J. Cryobiology of Embryos, Germ Cells & Ovaries
,
41
(
1
), pp.
197
206
.
12.
Gage
,
A.
, and
Baust
,
J.
, 1998, “
Mechanisms of Tissue Injury in Cryosurgery
,”
Cryobiology
0011-2240,
37
, pp.
171
186
.
13.
Hoffmann
,
N. E.
, and
Bischof
,
J. C.
, 2002, “
The Cryobiology of Cryosurgical Injury
,”
Urology
0090-4295,
60
, pp.
40
49
.
14.
Stefan
,
J.
, 1891, “
Uber die Theorie des Eisbildung, insbesondere uber die Eisbildung im Polarmeere
,”
Ann. Phys. Chem.
0003-3804,
42
(
2
), pp.
269
286
.
15.
Neumann
,
F.
, 1912, “
Lectures Given in the 1860’s
,”
Die Partielen Differentialglechungen der Mathematischen Physik
,
5th ed.
,
B
Riemann
and
H.
Weber
, eds.,
Vieweg und Sohn
,
Braunschweig
, Vol.
2
, pp.
117
121
.
16.
Ozisik
,
M. N.
, and
Uzzell
,
J. C.
, 1979, “
Exact Solution for Freezing in Cylindrical Symmetry With Extended Freezing Temperature Range
,”
ASME J. Heat Transfer
0022-1481,
101
, pp.
331
334
.
17.
Rubinsky
,
B.
, and
Shitzer
,
A.
, 1976, “
Analysis of a Stefan-Like Problem in a Biological Tissue Around a Cryosurgical Probe
,”
ASME J. Heat Transfer
0022-1481,
38
, pp.
514
519
.
18.
Trezek
,
G. J.
, 1985, “
Thermal Analysis for Cryosurgery
,”
Heat Transfer in Medicine and Biology: Analysis and Applications
,
A.
Shitzer
and
R. C.
Eberhart
, eds.,
Plenum
,
New York
, pp.
239
259
.
19.
Rabin
,
Y.
, and
Shitzer
,
A.
, 1995, “
Exact Solution for the Inverse Stefan Problem in Non-Ideal Biological Tissues
,”
ASME J. Heat Transfer
0022-1481,
117
, pp.
425
431
.
20.
Shamsundar
,
N.
, and
Sparrow
,
E. M.
, 1975, “
Analysis of Multidimensional Conduction Phase Change Problem via the Enthalpy Method
,”
ASME J. Heat Transfer
0022-1481,
97
, pp.
333
340
.
21.
Weill
,
A.
,
Shitzer
,
A.
, and
Bar-Yoseph
,
P.
, 1993, “
Finite Elements Analysis of the Temperature Field Around Two Adjacent Cryo-Probes
,”
ASME J. Biomech. Eng.
0148-0731,
115
, pp.
374
379
.
22.
Dalhuijsen
,
A. J.
, and
Segal
,
A.
, 1986, “
Comparison of Finite Element Techniques for Solidification Problems
,”
Int. J. Numer. Methods Eng.
0029-5981,
23
, pp.
1807
1829
.
23.
Keanini
,
R. G.
, and
Rubinsky
,
B.
, 1992, “
Optimization of Multiprobe Cryosurgery
,”
ASME J. Heat Transfer
0022-1481,
114
, pp.
796
801
.
24.
Rabin
,
Y.
, and
Stahovich
,
T. F.
, 2003, “
Cryoheater as a Means of Cryosurgery Control
,”
Phys. Med. Biol.
0031-9155,
48
, pp.
619
632
.
25.
Rabin
,
Y.
,
Lung
,
D. C.
, and
Stahovich
,
T. F.
, 2004, “
Computerized Planning of Cryosurgery Using Cryoprobes and Cryocatheters
,”
Technol. Cancer Res. Treat.
1533-0346,
3
(
3
), pp.
229
243
.
26.
Rewcastle
,
J. C.
,
Sandison
,
G. A.
,
Hahn
,
L. J.
,
Saliken
,
J. C.
,
McKinnon
,
J. G.
, and
Donnelley
,
B. J.
, 1998, “
A Model for the Time-Dependent Thermal Distribution Within an Iceball Surrounding a Cryoprobe
,”
Phys. Med. Biol.
0031-9155,
43
, pp.
3519
3534
.
27.
Jankun
,
M.
,
Kelly
,
T. J.
,
Zaim
,
A.
,
Young
,
K.
,
Keck
,
R. W.
,
Selman
,
S. H.
, and
Jankun
,
J.
, 1999, “
Computer Model for Cryosurgery of the Prostate
,”
Comput. Aided Surg.
1092-9088,
4
, pp.
193
199
.
28.
Baissalov
,
R.
,
Sandison
,
G. A.
,
Donnelley
,
B. J.
,
Saliken
,
J. C.
,
McKinnon
,
J. G.
,
Muldrew
,
K.
, and
Rewcastle
,
J. C.
, 2000, “
A Semi-Empirical Planning Model for Optimization of Multiprobe Cryosurgery
,”
Phys. Med. Biol.
0031-9155,
45
, pp.
1085
1098
.
29.
Rewcastle
,
J. C.
,
Sandison
,
G. A.
,
Muldrew
,
K.
,
Saliken
,
J. C.
, and
Donnelley
,
B. J.
, 2001, “
A Model for the Time Dependent Three-Dimensional Thermal Distribution Within Iceballs Surrounding Multiple Cryoprobes
,”
Med. Phys.
0094-2405,
28
(
6
), pp.
1125
1137
.
30.
Wan
,
R.
,
Liu
,
Z.
,
Muldrew
,
K.
, and
Rewcastle
,
J. C.
, 2003, “
A Finite Element Model for Ice Ball Evolution in a Multi-Probe Cryosurgery
,”
Comput. Methods Biomech. Biomed. Eng.
1025-5842,
6
(
3
), pp.
197
208
.
31.
Pennes
,
H. H.
, 1948, “
Analysis of Tissue and Arterial Blood Temperature in the Resting Human Forearm
,”
J. Appl. Physiol.
0021-8987,
1
, pp.
93
122
.
32.
Bonacina
,
C.
,
Comini
,
G.
,
Fasano
,
A.
, and
Primicerio
,
M.
, 1974, “
On the Estimation of Thermophysical Properties in Nonlinear Heat Conduction Problems
,”
Int. J. Heat Mass Transfer
0017-9310,
17
, pp.
861
867
.
33.
Rabin
,
Y.
, and
Shitzer
,
A.
, 1997, “
Combined Solution of the Inverse Stefan Problem for Successive Freezing/Thawing in Nonideal Biological Tissues
,”
ASME J. Biomech. Eng.
0148-0731,
119
(
2
), pp.
146
152
.
34.
Budman
,
H.
,
Shitzer
,
A.
, and
Del Giudice
,
S.
, 1986, “
Investigation of Temperature Fields Around Embedded Cryoprobes
,”
ASME J. Biomech. Eng.
0148-0731,
108
(
1
), pp.
42
48
.
35.
Goodman
,
T. R.
, 1958, “
The Heat Balance Integral and Its Application to Problems Involving a Change of Phase
,”
Trans. ASME
0097-6822,
80
, pp.
335
342
.
36.
Rubinsky
,
B.
, and
Shitzer
,
A.
, 1978, “
Analytic Solutions to the Heat Equation Involving a Moving Boundary With Application to the Change of Phase Problem (The Inverse Stefan Problem)
,”
ASME J. Heat Transfer
0022-1481,
100
, pp.
300
303
.
37.
Budman
,
H.
,
Shitzer
,
A.
, and
Dayan
,
Y.
, 1995, “
Analysis of the Inverse-Stefan Problem of Freezing and Thawing of a Binary Solution During Cryosurgical Processes
,”
ASME J. Biomech. Eng.
0148-0731,
117
(
2
), pp.
193
202
.
38.
Budman
,
H.
,
Dayan
,
J.
, and
Shitzer
,
A.
, 1991, “
Control of the Cryosurgical Process in Non-Ideal Materials
,”
IEEE Trans. Biomed. Eng.
0018-9294,
38
(
11
), pp.
1141
1153
.
39.
Budman
,
H.
,
Dayan
,
J.
, and
Shitzer
,
A.
, 1991, “
Controlled Freezing of Non-Ideal Solutions With Applications to Cryosurgical Processes
,”
ASME J. Biomech. Eng.
0148-0731,
113
(
4
), pp.
430
437
.
40.
Rabin
,
Y.
, and
Shitzer
,
A.
, 1998, “
Numerical Solution of the Multidimensional Freezing Problem During Cryosurgery
,”
ASME J. Biomech. Eng.
0148-0731,
120
, pp.
32
37
.
41.
Chang
,
Z.
,
Finkelstein
,
J. J.
, and
Baust
,
J.
, 1994, “
Development of a High-Performance Multiprobe Cryosurgical Device
,”
Biomed. Instrum. Technol.
0899-8205,
42
, pp.
383
390
.
42.
Magalov
,
Z.
,
Shitzer
,
A.
, and
Degani
,
D.
, 2006, “
Simulation of Cryo-Ablation of the Prostate by 1, 2 and 3 Embedded Cryo-Surgical Probes
,”
Proceedings of the 13th International Heat Transfer Conference
, Vol.
BHT-04
, pp.
1
12
.
43.
Magalov
,
Z.
,
Shitzer
,
A.
, and
Degani
,
D.
, 2007, “
Isothermal Volume Contours Generated in a Freezing Gel by Embedded Cryo-Needles With Applications to Cryo-Surgery
,”
Cryobiology
0011-2240,
55
(
2
), pp.
127
137
.
44.
Magalov
,
Z.
,
Shitzer
,
A.
and
Degani
,
D.
, 2008, “
Experimental and Numerical Study of 1, 2 and 3 Embedded Needle Cryo-Probes Simultaneously Operated by High Pressure Argon Gas
,”
ASME J. Heat Transfer
0022-1481,
130
(
3
), p.
032301
.
45.
Galil-Medical, Ltd., Yokneam, Israel
, 2003, Experimental Data, private communication.
46.
Chayut
,
Y.
, and
Shitzer
,
A.
, 1996, “
Simulating the Effects of a Large Blood Vessel on the Temperature Field around a Surface Cryoprobe
,”
ASME Advances in Heat and Mass Transfer in Biotechnology
,
L. J.
Hayes
and
S.
Clegg
, eds.,
ASME
,
New York
, pp.
21
22
.
47.
Massalha
,
L.
, and
Shitzer
,
A.
, 2004, “
Freezing by a Flat, Circular Surface Cryoprobe of a Tissue Phantom With an Embedded Cylindrical Heat Source Simulating a Blood Vessel
,”
ASME J. Biomech. Eng.
0148-0731,
126
(
6
), pp.
736
744
.
48.
Rybko
,
N.
,
Shitzer
,
A.
, and
Degani
,
D.
, 2009, “
Experimental simulation of a Thermally Significant Blood Vessel in a Tissue Subjected to Cryo-Surgery
,”
Proceedings of the Seventh World Conference on Experimental Heat Transfer, Fluid Flow and Thermodynamics
, Krakow, Poland, pp.
193
200
.
49.
Beckerman
,
G.
,
Shitzer
,
A.
, and
Degani
,
D.
, 2009, “
Numerical Model of the Effects of a Thermally-Significant Blood Vessel on Solidification by a Circular Surface Cryosurgical Probe Compared to Experimental Data
,”
ASME J. Heat Transfer
0022-1481,
131
(
5
), p.
051101
.
50.
Rabin
,
Y.
, and
Shitzer
,
A.
, 1996, “
A New Cryosurgical Device for Controlled Freezing. Part 1: Setup and Validation Tests
,”
Cryobiology
0011-2240,
33
, pp.
82
92
.
51.
Rabin
,
Y.
,
Coleman
,
R.
,
Mordohovich
,
D.
,
Ber
,
R.
, and
Shitzer
,
A.
, 1996, “
A New Cryosurgical Device for Controlled Freezing. Part 2: In Vivo Experiments on Skeletal Muscle of Rabbit Hindlimbs
,”
Cryobiology
0011-2240,
33
, pp.
93
105
.
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