The current numerical investigation tackles the fluid-structure interaction in a blood vessel subjected to a prescribed heating scheme on tumor tissues under thermal therapy. A pulsating incompressible laminar blood flow was employed to examine its impact on the flow and temperature distribution within the blood vessel. In addition, the arterial wall was modeled using the volume-averaged porous media theory. The motion of a continuous and deformable arterial wall can be described by a continuous displacement field resulting from blood pressure acting on the tissue. Moreover, discretization of the transport equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. The numerical results were validated by comparing them against documented studies in the literature. Three various heating schemes were considered: constant temperature, constant wall flux, and a step-wise heat flux. The first two uniform schemes were found to exhibit large temperature variation within the tumor, which might affect the surrounding healthy tissues. Meanwhile, larger vessels and flexible arterial wall models render higher variation of the temperature within the treated tumor, owing to the enhanced mixing in the vicinity of the bottom wall.

References

1.
Xuan
,
Y. M.
, and
Roetzel
,
W.
,
1997
, “
Bioheat Equation of the Human Thermal System
,”
Chem. Eng. Technol.
,
20
, pp.
268
276
.10.1002/ceat.270200407
2.
Xuan
,
Y. M.
, and
Roetzel
,
W.
,
1998
, “
Transfer Response of the Human Limb to an External Stimulus
,”
Int. J. Heat Mass Transfer
,
41
, pp.
229
239
.10.1016/S0017-9310(96)00160-3
3.
Khaled
,
A.-R. A.
, and
Vafai
,
K.
,
2003
, “
The Role of Porous Media in Modeling Flow and Heat Transfer in Biological Tissues
,”
Int. J. Heat Mass Transfer
,
46
, pp.
4989
5003
.10.1016/S0017-9310(03)00301-6
4.
Khanafer
,
K.
, and
Vafai
,
K.
,
2006
, “
The Role of Porous Media in Biomedical Engineering as Related to Magnetic Resonance Imaging and Drug Delivery
,”
Heat Mass Transfer
,
42
, pp.
939
953
.10.1007/s00231-006-0142-6
5.
Khanafer
,
K.
,
Bull
,
J. L.
,
Pop
,
I.
, and
Berguer
,
R.
,
2007
, “
Influence of Pulsative Blood Flow and Heating Scheme on the Temperature Distribution During Hyperthermia Treatment
,”
Int. J. Heat Mass Transfer
,
50
, pp.
4883
4890
.10.1016/j.ijheatmasstransfer.2007.01.062
6.
Nakayama
,
A.
, and
Kuwahara
,
F.
,
2008
, “
A General Bioheat Transfer Model Based on the Theory of Porous Media
,”
Int. J. Heat Mass Transfer
,
51
, pp.
3190
3199
.10.1016/j.ijheatmasstransfer.2007.05.030
7.
Mahjoob
,
S.
, and
Vafai
,
K.
,
2009
, “
Analytical Characterization of Heat Transfer Through Biological Media Incorporating Hyperthermia Treatment
,”
Int. J. Heat Mass Transfer
,
52
, pp.
1608
1618
.10.1016/j.ijheatmasstransfer.2008.07.038
8.
Khanafer
,
K.
, and
Vafai
,
K.
,
2009
, “
Synthesis of Mathematical Models Representing Bioheat Transport
,”
Advances in Numerical Heat Transfer
, Vol.
3
,
CRC Press
,
Boca Raton, FL
, pp.
1
28
.
9.
Shih
,
T. C.
,
Horng
,
T. L.
,
Huang
,
H. W.
,
Ju
,
K. C.
,
Huang
,
T. C.
, and
Chen
,
P.
,
2012
, “
Numerical Analysis of Coupled Effects of Pulsatile Blood Flow and Thermal Relaxation Time During Thermal Therapy
,”
Int. J. Heat Mass Transfer
,
55
, pp.
3763
3773
.10.1016/j.ijheatmasstransfer.2012.02.069
10.
Pennes
,
H. H.
,
1948
, “
Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm
,”
J. Appl. Physiol.
,
1
, pp.
93
122
.
11.
Arkin
,
H.
,
Xu
,
L. X.
, and
Holmes
,
K. R.
,
1994
, “
Recent Developments in Modeling Heat Transfer in Blood Perfused Tissues
,”
IEEE Trans. Biomed. Eng.
,
41
, pp.
97
107
.10.1109/10.284920
12.
Charny
,
C. K.
, and
Levin
,
R. L.
,
1989
, “
Bioheat Transfer in a Branching Countercurrent Network During Hyperthermia
,”
ASME J. Biomech. Eng.
,
111
(4), pp.
263
270
.10.1115/1.3168377
13.
McGrail
,
T. W.
, and
Seagrave
,
R. C.
,
1980
, “
Application of the Bioheat Transfer Equation in Fetal-Placental Studies
,”
Ann. N.Y. Acad. Sci.
,
335
, pp.
161
172
.10.1111/j.1749-6632.1980.tb50745.x
14.
Wood
,
C.
, and
Beard
,
R. W.
,
1964
, “
Temperature of the Human Fetus
,”
J. Obstet. Gynec. Brit. Commun.
,
71
, pp.
768
769
.10.1111/j.1471-0528.1964.tb04355.x
15.
Walker
,
D.
,
Walker
,
A.
, and
Wood
,
C.
,
1969
, “
Temperature of the Human Fetus
,”
J. Obstet. Gynec. Brit. Commun.
,
76
, pp.
503
511
.10.1111/j.1471-0528.1969.tb05870.x
16.
Wulff
,
W.
,
1974
, “
The Energy Conservation Equation for Living Tissues
,”
IEEE Trans. Biomed. Eng.
,
21
, pp.
494
495
.10.1109/TBME.1974.324342
17.
Klinger
,
H. G.
,
1974
, “
Heat Transfer in Perfused Tissue—I: General Theory
,”
Bull. Math. Biol.
,
36
, pp.
403
415
.10.1007/BF02464617
18.
Chen
,
M. M.
, and
Holmes
,
K. R.
,
1980
, “
Microvascular Contributions in Tissue Heat Transfer
,”
Ann. N.Y. Acad. Sci.
,
335
, pp.
137
150
.10.1111/j.1749-6632.1980.tb50742.x
19.
Weinbaum
,
S.
, and
Jiji
,
L. M.
,
1979
, “
A Two Phase Theory for the Influence of Circulation on the Heat Transfer in Surface Tissue
,”
Advances in Bioengineering
,
M. K.
Wells
, ed.,
ASME
,
New York
, pp.
179
182
.
20.
Weinbaum
,
S.
,
Jiji
,
L. M.
, and
Lemons
,
D. E.
,
1984
, “
Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part I: Anatomical Foundation and Model Conceptualization
,”
ASME J. Biomech. Eng.
,
106
(4), pp.
321
330
.10.1115/1.3138501
21.
Weinbaum
,
S.
,
Jiji
,
L. M.
, and
Lemons
,
D. E.
,
1984
, “
Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part II: Model Formulation and Solution
,”
ASME J. Biomech. Eng.
,
106
(4), pp.
331
341
.10.1115/1.3138502
22.
Craciunescu
,
O. I.
, and
Clegg
,
S. T.
,
2001
, “
Pulsatile Blood Flow Effects on Temperature Distribution and Heat Transfer in Rigid Vessels
,”
ASME J. Biomech. Eng.
,
123
(5), pp.
500
505
.10.1115/1.1392318
23.
Ai
,
L.
, and
Vafai
,
K.
,
2006
, “
A Coupling Model for Macromolecule Transport in a Stenosed Arterial Wall
,”
Int. J. Heat Mass Transfer
,
49
, pp.
1568
1591
.10.1016/j.ijheatmasstransfer.2005.10.041
24.
Yang
,
N.
, and
Vafai
,
K.
,
2006
, “
Modeling of Low-Density Lipoprotein (LDL) Transport in the Artery—Effects of Hypertension
,”
Int. J. Heat Mass Transfer
,
49
, pp.
850
867
.10.1016/j.ijheatmasstransfer.2005.09.019
25.
Yang
,
N.
, and
Vafai
,
K.
,
2008
, “
Low Density Lipoprotein (LDL) Transport in an Artery—A Simplified Analytical Solution
,”
Int. J. Heat Mass Transfer
,
51
, pp.
497
505
.10.1016/j.ijheatmasstransfer.2007.05.023
26.
Khakpour
,
M.
, and
Vafai
,
K.
,
2008
, “
A Critical Assessment of Arterial Transport Models
,”
Int. J. Heat Mass Transfer
,
51
, pp.
807
822
.10.1016/j.ijheatmasstransfer.2007.04.021
27.
Khanafer
,
K.
,
Bull
,
J. L.
, and
Berguer
,
R.
,
2009
, “
Fluid–Structure Interaction of Turbulent Pulsatile Flow Within a Flexible Wall Axisymmetric Aortic Aneurysm Model
,”
Eur. J. Mech. B/Fluids
,
28
, pp.
88
102
.10.1016/j.euromechflu.2007.12.003
28.
Khanafer
,
K.
, and
Berguer
,
R.
,
2009
, “
Fluid–Structure Interaction Analysis of Turbulent Pulsatile Flow Within a Layered Aortic Wall as Related to Aortic Dissection
,”
J. Biomech.
,
42
, pp.
2642
2648
.10.1016/j.jbiomech.2009.08.010
29.
Xu
,
X. Y.
,
Collins
,
M. W.
, and
Jones
,
C. J. H.
,
1992
, “
Flow Studies in Canine Artery Bifurcations Using a Numerical Simulation Method
,”
ASME J. Biomech. Eng.
,
114
(4), pp.
504
511
.10.1115/1.2894102
30.
Prosi
,
M.
,
Zunino
,
P.
,
Perktold
,
K.
, and
Quarteroni
,
A.
,
2005
, “
Mathematical and Numerical Models for Transfer of Low-Density Lipoprotein Through the Arterial Walls: A New Methodology for the Model Setup With Applications to the Study of Disturbed Laminar Flow
,”
J. Biomech.
,
38
, pp.
903
917
.10.1016/j.jbiomech.2004.04.024
31.
Chung
,
S.
, and
Vafai
,
K.
,
2012
, “
Effect of the Fluid-Structure Interactions on Low-Density Lipoprotein Within a Multi-Layered Arterial Wall
,”
J. Biomech.
,
45
, pp.
371
381
.10.1016/j.jbiomech.2011.10.002
32.
Amiri
,
A.
, and
Vafai
,
K.
,
1994
, “
Analysis of Dispersion Effects and Non-Thermal Equilibrium, Non-Darcian, Variable Porosity Incompressible Flow Through Porous Media
,”
Int. J. Heat Mass Transfer
,
37
, pp.
939
954
.10.1016/0017-9310(94)90219-4
33.
Harris
,
C. M.
,
1988
,
Shock and Vibration Handbook
, 3rd ed.,
McGraw-Hill Book Company
,
New York
, Chap. 29.
34.
Atabek
,
H. B.
,
Chang
,
C. C.
, and
Fingerson
,
L. M.
,
1964
, “
Measurement of Laminar Oscillatory Flow in the Inlet Length of a Circular Tube
,”
Phys. Medicine Biol.
,
9
, pp.
219
227
.10.1088/0031-9155/9/2/309
35.
Levental
,
I.
,
Georges
,
P. C.
, and
Janmey
,
P. A.
,
2007
, “
Soft Biological Materials and Their Impact on Cell Function
,”
Soft Matter
,
3
, pp.
299
306
.10.1039/b610522j
You do not currently have access to this content.