Abstract

The freezing front in a tumor during percutaneous cryoablation therapy was traced both analytically and numerically exploiting a bioheat equation. It has been shown that there exists a limiting size of the tumor, which one single cryoprobe can freeze at the maximum. The freezing front moves radially outward from the cryoprobe and reaches the end, where the heat from the surrounding tissue to the frozen tissue balances with the heat being absorbed by the cryoprobe. An excellent agreement between the analytical and numerical results has been achieved for the time required to freeze the tumor using the cryoprobe of a single needle. An analytical expression for estimating the limiting radius has been derived to give useful information for cryotherapy treatment plans.

1.
Nakatsuka
,
S.
,
Kawamura
,
M.
,
Sugiura
,
H.
,
Nakano
,
K.
,
Izumi
,
Y.
,
Kobayashi
,
K.
,
Jinzaki
,
M.
,
Hashimoto
,
S.
,
Kuribayashi
,
S.
,
Wakabayashi
,
G.
, and
Kitajima
,
M.
, 2004, “
Preliminary Experience With Percutaneous Cryoablation for Malignant Lung Tumors Under CT Fluoroscopic Guidance
,”
Low Temp. Med.
,
30
(
1
), pp.
9
15
.
2.
Butz
,
T.
,
Warfield
,
S. K.
,
Tuncali
,
K.
,
Silverman
,
S. G.
,
van Sonnenberg
,
E.
,
Jolesz
,
F. A.
, and
Kikinis
,
R.
, 2000, “
Pre- and Intra-Operative Planning and Simulation of Percutaneous Tumor Ablation
,”
Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI)
,
Pittsburgh, PA
, Oct. 11–14, pp.
317
326
.
3.
Bischof
,
J. C.
,
Smith
,
D.
,
Pazhayannur
,
P. V.
,
Manivel
,
C.
,
Hulbert
,
J.
, and
Roberts
,
K. P.
, 1997, “
Cryosurgery of Dunning AT-1 Rat Prostate Tumor: Thermal, Biophysical, and Viability Response at the Cellular and Tissue Level
,”
Cryobiology
0011-2240,
34
, pp.
42
69
.
4.
Rewcastle
,
J.
,
Sandison
,
G.
,
Hahn
,
L.
,
Saliken
,
J.
,
McKinnon
,
J.
, and
Donnelly
,
B.
, 1998, “
A Model for the Time-Dependent Thermal Distribution Within an Ice Ball Surrounding a Cryoprobe
,”
Phys. Med. Biol.
0031-9155,
43
, pp.
3519
3534
.
5.
Keanini
,
R. G.
, and
Rubinsky
,
B.
, 1992, “
Optimization of Multi-Probe Cryosurgery
,”
ASME Trans. J. Heat Transfer
0022-1481,
114
, pp.
796
802
.
6.
Baissalov
,
R.
,
Sandison
,
G. A.
,
Reynolds
,
D.
, and
Muldrew
,
K.
, 2001, “
Simultaneous Optimization of Cryoprobe Placement and Thermal Protocol for Cryosurgery
,”
Phys. Med. Biol.
0031-9155,
46
, pp.
1799
1814
.
7.
Wan
,
R.
,
Liu
,
Z.
,
Muldrew
,
K.
, and
Rewcastle
,
J.
, 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
.
8.
Rabin
,
Y.
, and
Shitzer
,
A.
, 1998, “
Numerical Solution of the Multidimensional Freezing Problem During Cryosurgery
,”
ASME Trans. J. Heat Transfer
0022-1481,
120
, pp.
32
37
.
9.
Rossi
,
M. R.
,
Tanaka
,
D.
,
Shimada
,
K.
, and
Rabin
,
Y.
, 2007, “
An Efficient Numerical Technique for Bioheat Simulations and its Application to Computerized Cryosurgery Planning
,”
Comput. Methods Programs Biomed.
0169-2607,
85
, pp.
41
50
.
10.
Rossi
,
M. R.
, and
Rabin
,
Y.
, 2007, “
Experimental Verification of Numerical Simulations of Cryosurgery With Application to Computerized Planning
,”
Phys. Med. Biol.
0031-9155,
52
, pp.
4553
4567
.
11.
Nakayama
,
A.
, and
Kuwahara
,
F.
, 2008, “
A General Bioheat Transfer Model Based on the Theory of Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
51
, pp.
3190
3199
.
12.
Pennes
,
H. H.
, 1948, “
Analysis of Tissue and Arterial Blood Temperature Blood Temperature in the Resting Human Forearm
,”
J. Appl. Physiol.
0021-8987,
1
, pp.
93
122
.
13.
Wulff
,
W.
, 1974, “
The Energy Conservation Equation for Living Tissue
,”
IEEE Trans. Biomed. Eng.
0018-9294,
BME 21
, pp.
494
495
.
14.
Klinger
,
H. G.
, 1978, “
Heat Transfer in Perfused Biological Tissue. II. The ‘Macroscopic’ Temperature Distribution in Tissue
,”
Bull. Math. Biol.
0092-8240,
40
, pp.
183
199
.
15.
Chen
,
M. M.
, and
Holmes
,
K. R.
, 1980, “
Microvascular Contributions in Tissue Heat Transfer
,”
Ann. N.Y. Acad. Sci.
0077-8923,
335
, pp.
137
150
.
16.
Xuan
,
Y.
, and
Roetzel
,
W.
, 1997, “
Bioheat Equation of the Human Thermal System
,”
Chem. Eng. Technol.
0930-7516,
20
, pp.
268
276
.
17.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere
,
Washington, D.C.
18.
Nakayama
,
A.
, 1995,
PC-Aided Numerical Heat Transfer and Convective Flow
,
CRC
,
Boca Raton, FL
.
19.
Yokoyama
,
S.
, 1993,
Bioheat Transfer Phenomena (in Japanese)
,
Hokkaido University Press
,
Hokkaido, Japan
.
You do not currently have access to this content.