A transport model of magnetic drug carrier particles (MDCPs) in permeable microvessel based on statistical mechanics has been developed to investigate capture efficiency (CE) of MDCPs at the tumor position. Casson-Newton two-fluid model is used to describe the flow of blood in permeable microvessel and the Darcy model is used to characterize the permeable nature of the microvessel. Coupling effect between the interstitial fluid flow and blood flow is considered by using the Starling assumptions in the model. The Boltzmann equation is used to depict the transport of MDCPs in microvessel. The elastic collision effect between MDCPs and red blood cell is incorporated. The distribution of blood flow velocity, blood pressure, interstitial fluid pressure, and MDCPs has been obtained through the coupling solutions of the model. Based on these, the CE of the MDCPs is obtained. Present results show that the CE of the MDCPs will increase with the enhancement of the size of the MDCPs and the external magnetic field intensity. In addition, when the permeability of the inner wall is better and the inlet blood flow velocity is slow, the CE of the MDCPs will increase as well. Close agreements between the predictions and experimental results demonstrate the capability of the model in modeling transport of MDCPs in permeable microvessel.

References

References
1.
Alexiou
,
C.
,
Arnold
,
W.
,
Klein
,
R. J.
,
Parak
,
F. G.
,
Hulin
,
P.
,
Bergemann
,
C.
,
Erhardt
,
W.
,
Wagenpfeil
,
S.
, and
Luebbe
,
A. S.
,
2000
, “
Locoregional Cancer Treatment With Magnetic Drug Targeting
,”
Cancer Res.
,
60
(
23
), pp.
6641
6648
.
2.
Torchilin
,
V. P.
,
1995
, “
Targeting of Drugs and Drug Carriers Within the Cardiovascular System
,”
Adv. Drug Delivery Rev.
,
17
(
1
), pp.
75
101
.10.1016/0169-409X(95)00042-6
3.
Crommelin
,
D. J. A.
,
Scherphof
,
G.
, and
Storm
,
G.
,
1995
, “
Active Targeting With Particulate Carrier Systems in the Blood Compartment
,”
Adv. Drug Delivery Rev.
,
17
(
1
), pp.
49
60
.10.1016/0169-409X(95)00040-E
4.
Lübbe
,
A. S.
,
Alexiou
,
C.
, and
Bergemann
,
C.
,
2001
, “
Clinical Applications of Magnetic Drug Targeting
,”
J. Surg. Res.
,
95
(
2
), pp.
200
206
.10.1006/jsre.2000.6030
5.
El-Shahed
,
M.
,
2004
, “
Blood Flow in a Capillary With Permeable Wall
,”
Phys. A
,
338
(
3
), pp.
544
558
.10.1016/j.physa.2004.02.064
6.
Pozrikidis
,
C.
,
2010
, “
Numerical Simulation of Blood and Interstitial Flow Through a Solid Tumor
,”
J. Math. Biol.
,
60
(
1
), pp.
75
94
.10.1007/s00285-009-0259-6
7.
Cokelet
,
G. R.
,
1972
, “
The Rheology of Human Blood
,”
Biomech: Its Foundations and Objectives
, Vol.
72
,
Prentice Hall
,
Englewood Cliffs, NJ
, pp.
63
103
.
8.
Kim
,
S.
,
Namgung
,
B.
,
Ong
,
P. K.
,
Cho
,
Y. I.
,
Chun
,
K. J.
, and
Lim
,
D.
,
2009
, “
Determination of Rheological Properties of Whole Blood With a Scanning Capillary-Tube Rheometer Using Constitutive Models
,”
J. Mech. Sci. Technol.
,
23
(
6
), pp.
1718
1726
.10.1007/s12206-009-0420-6
9.
Tu
,
C.
, and
Deville
,
M.
,
1996
, “
Pulsatile Flow of Non-Newtonian Fluids Through Arterial Stenoses
,”
J. Biomech.
,
29
(
7
), pp.
899
908
.10.1016/0021-9290(95)00151-4
10.
Sankar
,
D. S.
, and
Lee
,
U.
,
2008
, “
Two-Fluid Herschel–Bulkley Model for Blood Flow in Catheterized Arteries
,”
J. Mech. Sci. Technol.
,
22
(
5
), pp.
1008
1018
.10.1007/s12206-008-0123-4
11.
Sankar
,
D. S.
, and
Lee
,
U.
,
2008
, “
Two-Fluid Non-Linear Model for Flow in Catheterized Blood Vessels
,”
Int. J. Non-Linear Mech.
,
43
(
7
), pp.
622
631
.10.1016/j.ijnonlinmec.2008.02.007
12.
Furlani
,
E. P.
, and
Ng
,
K. C.
,
2006
, “
Analytic Model of Magnetic Nanoparticle Transport and Capture in the Microvasculature
,”
Phys. Rev. E.
,
73
(
6
), p.
061919
.10.1103/PhysRevE.73.061919
13.
Shaw
,
S.
,
Murthy
,
P. V. S. N.
, and
Pradhan
,
S. C.
,
2010
, “
Effect of Non-Newtonian Characteristics of Blood on Magnetic Targeting in the Impermeable Micro-Vessel
,”
J. Magn. Magn. Mater.
,
322
(
8
), pp.
1037
1043
.10.1016/j.jmmm.2009.12.010
14.
Decuzzi
,
P.
,
Causa
,
F.
,
Ferrari
,
M.
, and
Netti
,
P. A.
,
2006
, “
The Effective Dispersion of Nanovectors Within the Tumor Microvasculature
,”
Ann. Biomed. Eng.
,
34
(
4
), pp.
633
641
.10.1007/s10439-005-9072-6
15.
Shaw
,
S.
, and
Murthy
,
P. V. S. N.
,
2010
, “
Magnetic Drug Targeting in the Permeable Blood Vessel—The Effect of Blood Rheology
,”
ASME J. Nanotechnol. Eng. Med.
,
1
(
2
), p.
021001
.10.1115/1.4001477
16.
Shaw
,
S.
,
Murthy
,
P. V. S. N.
, and
Sibanda
,
P.
,
2013
, “
Magnetic Drug Targeting in a Permeable Microvessel
,”
Microvasc. Res.
,
85
, pp.
77
85
.10.1016/j.mvr.2012.10.011
17.
Canelas
,
D. A.
,
Herlihy
,
K. P.
, and
DeSimone
,
J. M.
,
2009
, “
Top-Down Particle Fabrication: Control of Size and Shape for Diagnostic Imaging and Drug Delivery
,”
Wiley Interdiscip. Rev.: Nanomed. Nanobiotechnol.
,
1
(
4
), pp.
391
404
.10.1002/wnan.40
18.
Doshi
,
N.
, and
Mitragotri
,
S.
,
2009
, “
Designer Biomaterials for Nanomedicine
,”
Adv. Funct. Mater.
,
19
(
24
), pp.
3843
3854
.10.1002/adfm.200901538
19.
Enayati
,
M.
,
Ahmad
,
Z.
,
Stride
,
E.
, and
Edirisinghe
,
M.
,
2009
, “
Preparation of Polymeric Carriers for Drug Delivery With Different Shape and Size Using an Electric Jet
,”
Curr. Pharm. Biotechnol.
,
10
(
6
), pp.
600
608
.10.2174/138920109789069323
20.
Gerber
,
R.
,
Takayasu
,
M.
, and
Friedlander
,
F. J.
,
1983
, “
Generalization of Hgms Theory the Capture of Ultra-Fine Particles
,”
IEEE Trans. Magn.
,
19
(
5
), pp.
2115
2117
.10.1109/TMAG.1983.1062795
21.
Taylor
,
M.
,
1955
, “
The Flow of Blood in Narrow Tubes. II. The Axial Stream and Its Formation, as Determined by Changes in Optical Density
,”
Aust. J. Exp. Biol. Med. Sci.
,
33
(
1
), pp.
1
16
.10.1038/icb.1955.1
22.
Phillips
,
R. J.
,
Armstrong
,
R. C.
,
Brown
,
R. A.
,
Graham
,
A. L.
, and
Abbott
,
J. R.
,
1992
, “
A Constitutive Equation for Concentrated Suspensions That Accounts For Shear-Induced Particle Migration
,”
Phys. Fluids A
,
4
(
1
), pp.
30
40
.10.1063/1.858498
23.
Baxter
,
L. T.
, and
Jain
,
R. K.
,
1989
, “
Transport of Fluid and Macromolecules in Tumors. I. Role of Interstitial Pressure and Convection
,”
Microvasc. Res.
,
37
(
1
), pp.
77
104
.10.1016/0026-2862(89)90074-5
24.
Baxter
,
L. T.
, and
Jain
,
R. K.
,
1990
, “
Transport of Fluid and Macromolecules in Tumors. II. Role of Heterogeneous Perfusion and Lymphatics
,”
Microvasc. Res.
,
40
(
2
), pp.
246
263
.10.1016/0026-2862(90)90023-K
25.
Baxter
,
L. T.
, and
Jain
,
R. K.
,
1991
, “
Transport of Fluid and Macromolecules in Tumors. III. Role of Binding and Metabolism
,”
Microvasc. Res.
,
41
(
1
), pp.
5
23
.10.1016/0026-2862(91)90003-T
26.
Salathe
,
E. P.
, and
An
,
K. N.
,
1976
, “
A Mathematical Analysis of Fluid Movement Across Capillary Walls
,”
Microvasc. Res.
,
11
(
1
), pp.
1
23
.10.1016/0026-2862(76)90072-8
27.
Furlani
,
E. J.
, and
Furlani
,
E. P.
,
2007
, “
A Model for Predicting Magnetic Targeting of Multifunctional Particles in the Microvasculature
,”
J. Magn. Magn. Mater.
,
312
(
1
), pp.
187
193
.10.1016/j.jmmm.2006.09.026
28.
Tao
,
Z.
,
1984
,
Biological Fluid
,
Mechanics Science Press
,
Beijing
.
29.
Pozrikidis
,
C.
,
2005
, “
Axisymmetric Motion of a File of Red Blood Cells Through Capillaries
,”
Phys. Fluids
,
17
(
3
), p.
031503
.10.1063/1.1830484
30.
Chen
,
T. C.
, and
Skalak
,
R.
,
1970
, “
Stokes Flow in a Cylindrical Tube Containing a Line of Spheroidal Particles
,”
Appl. Sci. Res.
,
22
(
1
), pp.
403
441
.
31.
Sugii
,
Y.
,
Nishio
,
S.
, and
Okamoto
,
K.
,
2002
, “
In Vivo PIV Measurement of Red Blood Cell Velocity Field in Microvessels Considering Mesentery Motion
,”
Physiol. Meas.
,
23
(
2
), p.
403
.10.1088/0967-3334/23/2/315
32.
Huang
,
Z.
, and
Ding
,
E.
,
2008
,
Transport Theory
,
Science Press
,
Beijing
.
33.
Duderstadt
,
J. J.
, and
Martin
,
W. R.
,
1979
,
Transport Theory
,
Wiley
,
New York
.
34.
He
,
Y. B.
,
Laskowski
,
J. S.
, and
Klein
,
B.
,
2001
, “
Particle Movement in Non-Newtonian Slurries: The Effect of Yield Stress on Dense Medium Separation
,”
Chem. Eng. Sci.
,
56
(
9
), pp.
2991
2998
.10.1016/S0009-2509(00)00479-6
35.
Avilés
,
M. O.
,
Ebner
,
A. D.
, and
Ritter
,
J. A.
,
2009
, “
In Vitro Study of Magnetic Particle Seeding for Implant-Assisted-Magnetic Drug Targeting: Seed and Magnetic Drug MDCPs Capture
,”
J. Magn. Magn. Mater.
,
321
(
10
), pp.
1586
1590
.10.1016/j.jmmm.2009.02.091
36.
Rowland
,
M.
, and
Tozer
,
T. N.
,
1995
,
Clinical Pharmacokinetics: Concepts and Applications
,
Williams and Wilkins
,
Baltimore
.
37.
Avilés
,
M. O.
,
Ebner
,
A. D.
, and
Ritter
,
J. A.
,
2008
, “
Implant Assisted-Magnetic Drug Targeting: Comparison of In Vitro Experiments With Theory
,”
J. Magn. Magn. Mater.
,
320
(
21
), pp.
2704
2713
.10.1016/j.jmmm.2008.06.001
38.
Shubik
,
P.
,
1982
, “
Vascularization of Tumors: A Review
,”
J. Cancer Res. Clin. Oncol.
,
103
(
3
), pp.
211
226
.10.1007/BF00409698
39.
Yamaura
,
H.
, and
Sato
,
H.
,
1974
, “
Quantitative Studies on the Developing Vascular System of Rat Hepatoma
,”
J. Natl. Cancer Inst.
,
53
(
5
), pp.
1229
1240
.10.1093/jnci/53.5.1229
40.
Rubin
,
P.
, and
Casarett
,
G.
,
1966
, “
Microcirculation of Tumors Part I: Anatomy, Function, and Necrosis
,”
Clin. Radiol.
,
17
(
3
), pp.
220
229
.10.1016/S0009-9260(66)80027-2
You do not currently have access to this content.