https://orcid.org/0000-0003-2071-4089
Abstract
Magnetic drug delivery to cancerous tissue as a noninvasive method is a promising cancer therapy. Several complex phenomena and parameters are involved in guiding nanoparticles to the targeted tissue and guaranteeing a predetermined distribution. A comprehensive Euler–Lagrangian method is utilized to simulate a realistic process of nanoparticle delivery and deposition in a cancerous tissue. Non-Newtonian and conductive blood flow in a typical vessel through a cancerous tissue in the presence of an external magnetic field is numerically modeled (both Lorentz and magnetization forces are considered). The cancerous tissue is assumed to be a multizone region with necrotic and live cell blocks. The effect of blood delivery to tissue cells via capillary vessels and blood drainage by the lymphatic system is taken into account. Particle paths and deposition are obtained using the contribution of all forces involved. The effects of Reynolds number (Re), magnetic number, addition of second magnetic source, and distribution of particles are also investigated. For all investigated conditions, the optimum magnetic number to maximize deposition is obtained.
Issue Section:
Technical Papers
References
1.
de Escalona
M. M.
, Sáez-Fernándeza
E.
, Pradosb
J. C.
, Melguizo
C.
, and Arias
J. L.
, “Magnetic Solid Lipid Nanoparticles in Hyperthermia against Colon Cancer
,” International Journal of Pharmaceutics
504
, nos. 1–2
(May 2016
): 11
–19
, https://doi.org/10.1016/j.ijpharm.2016.03.0052.
Coïsson
M.
, Barrera
G.
, Celegato
F.
, Martino
L.
, Vinai
F.
, Martino
P.
, Ferraro
G.
, and Tiberto
P.
, “Specific Absorption Rate Determination of Magnetic Nanoparticles through Hyperthermia Measurements in Non-Adiabatic Conditions
,” Journal of Magnetism and Magnetic Materials
415
, (October 2016
): 2
–7
, https://doi.org/10.1016/j.jmmm.2015.11.0443.
Shevtsov
M. A.
, Nikolaev
B. P.
, Ryzhov
V. A.
, Yakoleva
L. Y.
, Dobrodumov
A. V.
, Marchenko
Y. Y.
, Margulis
B. A.
, et al., “Detection of Experimental Myocardium Infarction in Rats by MRI Using Heat Shock Protein 70 Conjugated Superparamagnetic Iron Oxide Nanoparticle
,” Nanomedicine: Nanotechnology, Biology and Medicine
12
, no. 3
(April 2016
): 611
–621
, https://doi.org/10.1016/j.nano.2015.10.0174.
Yazdani
F.
, Fattahi
B.
, and Azizi
N.
, “Synthesis of Functionalized Magnetite Nanoparticles to Use as Liver Targeting MRI Contrast Agent
,” Journal of Magnetism and Magnetic Materials
406
(May 2016
): 207
–211
, https://doi.org/10.1016/j.jmmm.2016.01.0265.
Ansardamavandi
A.
, Tafazzoli-Shadpour
M.
, Omidvar
R.
, and Jahanzad
I.
, “Quantification of Effects of Cancer on Elastic Properties of Breast Tissue by Atomic Force Microscopy
,” Journal of the Mechanical Behavior of Biomedical Materials
60
(July 2016
): 234
–242
, https://doi.org/10.1016/j.jmbbm.2015.12.0286.
Barnes
S. C.
, Lawless
B. M.
, Shepherd
D. E. T.
, Espino
D. M.
, Bicknell
G. R.
, and Bryan
R. T.
, “Viscoelastic Properties of Human Bladder Tumours
,” Journal of the Mechanical Behavior of Biomedical Materials
61
(August 2016
): 250
–257
, https://doi.org/10.1016/j.jmbbm.2016.03.0127.
Zhao
Y.
, Chen
C.
, Pan
W.
, Gao
M.
, He
W.
, Mao
R.
, Lin
T.
, and Huang
J.
, “Comparative Efficacy of Vitamin D Status in Reducing the Risk of Bladder Cancer: A Systematic Review and Network Meta-Analysis
,” Nutrition
32
, no. 5
(May 2016
): 515
–523
, https://doi.org/10.1016/j.nut.2015.10.0238.
Holligan
D. L.
, Gillies
G. T.
, and Dailey
J. P.
, “Magnetic Guidance of Ferrofluidic Nanoparticles in an In Vitro Model of Intraocular Retinal Repair
,” Nanotechnology
14
, no. 6
(April 2003
): 661
–666
, https://doi.org/10.1088/0957-4484/14/6/3189.
Roohi
R.
, Emdad
H.
, and Jafarpur
K.
, “Performing Effective Drug Delivery and Hyperthermia Based on Biological and Treatment Parameters: A Comprehensive Eulerian-Lagrangian Approach
,” Journal of Computational and Theoretical Nanoscience
13
, no. 10
(October 2016
): 6628
–6641
, https://doi.org/10.1166/jctn.2016.560810.
Jurgons
R.
, Seliger
C.
, Hilpert
A.
, Trahms
L.
, Odenbach
S.
, and Alexiou
C.
, “Drug Loaded Magnetic Nanoparticles for Cancer Therapy
,” Journal of Physics: Condensed Matter
18
, no. 38
(September 2006
) 2893
–2902
, https://doi.org/10.1088/0953-8984/18/38/S2411.
Lübbe
A. S.
, Alexiou
C.
, and Bergemann
C.
, “Clinical Applications of Magnetic Drug Targeting
,” Journal of Surgical Research
95
, no. 2
(February 2001
): 200
–206
, https://doi.org/10.1006/jsre.2000.603012.
Orekhova
N. M.
, Akchurin
R. S.
, Belyaev
A. A.
, Smirnov
M. D.
, Ragimov
S. E.
, and Orekhov
A. N.
, “Local Prevention of Thrombosis in Animal Arteries by Means of Magnetic Targeting of Aspirin-Loaded Red Cells
,” Thrombosis Research
57
, no. 4
(February 1990
): 611
–616
, https://doi.org/10.1016/0049-3848(90)90078-Q13.
Roohi
R.
, Emdad
H.
, Jafarpur
K.
, and Mahmoudi
M.
, “Determination of Magnetic Nanoparticles Injection Characteristics for Optimal Hyperthermia Treatment of an Arbitrary Cancerous Cells Distribution
,” Journal of Testing and Evaluation
48
, no. 2
(March 2018
): 1
–17
, https://doi.org/10.1520/JTE2017067714.
Shinkai
M.
, “Functional Magnetic Particles for Medical Application
,” Journal of Bioscience and Bioengineering
94
, no. 6
(December 2002
): 606
–613
https://doi.org/10.1016/S1389-1723(02)80202-X15.
Torchilin
V. P.
, “Drug Targeting
,” European Journal of Pharmaceutical Sciences
11
(October 2000
): 81
–91
, https://doi.org/10.1016/S0928-0987(00)00166-416.
Alexiou
C.
, Arnold
W.
, Klein
R. J.
, Parak
F. G.
, Hulin
P.
, Bergemann
C.
, Erhardt
W.
, Wagenpfeil
S.
, and Lübbe
A. S.
, “Locoregional Cancer Treatment with Magnetic Drug Targeting
,” American Association for Cancer Research
60
, no. 23
(December 2000
): 6641
–6648
.17.
Alexiou
C.
, Jurgons
R.
, Schmid
R.
, Hilpert
A.
, Bergemann
C.
, Parak
F.
, and Iro
H.
, “In Vitro and In Vivo Investigations of Targeted Chemotherapy with Magnetic Nanoparticles
,” Journal of Magnetism and Magnetic Materials
293
, no. 1
(May 2005
): 389
–393
, https://doi.org/10.1016/j.jmmm.2005.02.03618.
Barry
J. W.
, Bookstein
J. J.
, and Alksne
J. F.
, “Ferromagnetic Embolization. Experimental Evaluation
,” Radiology
138
, no. 2
(February 1981
): 341
–349
, https://doi.org/10.1148/radiology.138.2.745511319.
Kuznetsov
A. A.
, Filippov
V. I.
, Alyautdin
R. N.
, Torshina
N. L.
, and Kuznetsov
O. A.
, “Application of Magnetic Liposomes for Magnetically Guided Transport of Muscle Relaxants and Anti-Cancer Photodynamic Drugs
,” Journal of Magnetism and Magnetic Materials
225
, nos. 1
–2
(2001
): 95
–100
, https://doi.org/10.1016/S0304-8853(00)01235-X20.
Decuzzi
P.
, Pasqualini
R.
, Arap
W.
, and Ferrari
M.
, “Intravascular Delivery of Particulate Systems: Does Geometry Really Matter?
,” Pharmaceutical Research
26
, (January 2009
): 235
–243
, https://doi.org/10.1007/s11095-008-9697-x21.
Fournier
R. L.
, Basic Transport Phenomena in Biomedical Engineering
(New York
: Taylor & Francis
, 2007
).22.
Hobbs
S. K.
, Monsky
W. L.
, Yuan
F.
, Roberts
W. G.
, Griffith
L.
, Torchilin
V. P.
, and Jain
R. K.
, “Regulation of Transport Pathways in Tumor Vessels: Role of Tumor Type and Microenvironment
,” PNAS
95
, no. 8
(April 1998
): 4607
–4612
, https://doi.org/10.1073/pnas.95.8.460723.
Saltzman
W. M.
, Drug Delivery: Engineering Principles for Drug Therapy
(New York
: Oxford University Press
, 2001
).24.
Lübbe
A. S.
, Bergemann
C.
, Brock
J.
, and McClure
D. G.
, “Physiological Aspects in Magnetic Drug-Targeting
,” Journal of Magnetism and Magnetic Materials
194
, nos. 1–3
(April 1999
): 149
–155
, https://doi.org/10.1016/S0304-8853(98)00574-525.
Widder
K. J.
, Morris
R. M.
, Poore
G.
, Howard
D. P.
, and Senyei
A. E.
, “Tumor Remission in Yoshida Sarcoma-Bearing Rats by Selective Targeting of Magnetic Albumin Microspheres Containing Doxorubicin
,” Proceedings of the National Academy of Sciences of the United States of America
78
, no. 1
(January 1981
): 579
–581
, https://doi.org/10.1073/pnas.78.1.57926.
Nobuto
H.
, Sugita
T.
, Kubo
T.
, Shimose
S.
, Yasunaga
Y.
, Murakami
T.
, and Ochi
M.
, “Evaluation of Systemic Chemotherapy with Magnetic Liposomal Doxorubicin and a Dipole External Electromagnet
,” International Journal of Cancer
109
, no. 4
(January 2004
): 627
–635
, https://doi.org/10.1002/ijc.2003527.
Xu
H.
, Song
T.
, Bao
X.
, and Hu
L.
, “Site-Directed Research of Magnetic Nanoparticles in Magnetic Drug Targeting
,” Journal of Magnetism and Magnetic Materials
293
, no. 1
(May 2005
): 514
–519
, https://doi.org/10.1016/j.jmmm.2005.01.06728.
Larimi
M. M.
, Ramiar
A.
, and Ranjbar
A. A.
, “Numerical Simulation of Magnetic Nanoparticles Targeting in a Bifurcation Vessel
,” Journal of Magnetism and Magnetic Materials
362
(August 2014
): 58
–71
, https://doi.org/10.1016/j.jmmm.2014.03.00229.
Troendle
E. P.
, Khan
A.
, Searson
P. C.
, and Ulmschneider
M. B.
, “Predicting drug delivery efficiency into tumor tissues through molecular simulation of transport in complex vascular networks
,” Journal of Controlled Release
292
, (December 2018
): 221
–234
, https://doi.org/10.1016/j.jconrel.2018.11.01030.
Woodcock
J. P.
, “Physical Properties of Blood and Their Influence on Blood-Flow Measurement
,” Reports on Progress in Physics
39
, no. 1
(1976
): 65
–127
, https://doi.org/10.1088/0034-4885/39/1/00231.
Czuwala
P. J.
, “McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles
,” Echocardiography
8
, no. 3
(May 1991
): 405
–406
, https://doi.org/10.1111/j.1540-8175.1991.tb01207.x32.
Okuhata
Y.
, “Delivery of Diagnostic Agents for Magnetic Resonance Imaging
,” Advanced Drug Delivery Reviews
37
, nos. 1–3
(April 1999
): 121
–137
, https://doi.org/10.1016/S0169-409X(98)00103-333.
Shi
H.
and Yu
X.
, “An Effective Euler–Lagrange Model for Suspended Sediment Transport by Open Channel Flows
,” International Journal of Sediment Research
30
, no. 4
(December 2015
): 361
–370
, https://doi.org/10.1016/j.ijsrc.2015.03.01234.
Wang
S.
, Zhou
Y.
, Tan
J.
, Xu
J.
, Yang
J.
, and Liu
Y.
, “Computational Modeling of Magnetic Nanoparticle Targeting to Stent Surface under High Gradient Field
,” Computational Mechanics
53
, no. 3
(March 2014
): 403
–412
, https://doi.org/10.1007/s00466-013-0968-y35.
Lampropoulos
N. K.
, Karvelas
E. G.
, and Sarris
I. E.
, “Computational Modeling of an MRI Guided Drug Delivery System Based on Magnetic Nanoparticle Aggregations for the Navigation of Paramagnetic Nanocapsules
,” arXiv:1504.03490, 2015
. http://web.archive.org/web/20181126165306/https://arxiv.org/abs/1504.03490 (26 November 2018).36.
Sokolichin
A.
, Eigenberger
G.
, Lapin
A.
, and Lübert
A.
, “Dynamic Numerical Simulation of Gas-Liquid Two-Phase Flows Euler/Euler versus Euler/Lagrange
,” Chemical Engineering Science
52
, no. 4
(February 1997
): 611
–626
, https://doi.org/10.1016/S0009-2509(96)00425-337.
Fleisch
D. A.
, Student’s
A
Guide to Maxwell’s Equations
(Cambridge
: Cambridge University Press
, 2008
).38.
Lide
D. R.
, Handbook of Chemistry and Physics
, 99th ed. (Boca Raton, FL
: CRC Press
, 2001
).39.
Rosensweig
R. E.
, Ferrohydrodynamics (Mineola, NY
: Dover Publications, Inc.
, 1985
).40.
Tzirtzilakis
E. E.
, Sakalis
V. D.
, Kafoussias
N. G.
, and Hatzikonstantinou
P. M.
, “Biomagnetic Fluid Flow in a 3D Rectangular Duct
,” International Journal for Numerical Methods in Fluids
44
, no. 12
(March 2004
): 1279
–1298
, https://doi.org/10.1002/fld.61841.
Motta
M.
, Haik
Y.
, Gandhari
A.
, and Chen
C.-J.
, “High Magnetic Field Effects on Human Deoxygenated Hemoglobin Light Absorption
,” Bioelectrochemistry and Bioenergetics
47
, no. 2
(December 1998
): 297
–300
, https://doi.org/10.1016/S0302-4598(98)00165-242.
Hanjalić
K.
and Kenjereš
S.
, “‘T-RANs’ Simulation of Deterministic Eddy Structure in Flows Driven by Thermal Buoyancy and Lorentz Force
,” Flow Turbul Combust
66
, no. 4
(July 2001
) 427
–451
, https://doi.org/10.1023/A:101357070581343.
Molla
M. M.
and Paul
M. C.
, “LES of Non-Newtonian Physiological Blood Flow in a Model of Arterial Stenosis
,” Medical Engineering & Physics
34
, no. 8
(October 2012
): 1079
–1087
, https://doi.org/10.1016/j.medengphy.2011.11.01344.
Johnston
D. W.
, Johnston
M.
, Pollard
B.
, Kinmonth
A.-L.
, and Mant
D.
, “Motivation is Not Enough: Prediction of Risk Behavior Following Diagnosis of Coronary Heart Disease from the Theory of Planned Behavior
,” Health Psychology
23
, no. 5
(September 2004
): 533
–583
, https://doi.org/10.1037/0278-6133.23.5.53345.
González
H. A.
and Moraga
N. O.
, “On Predicting Unsteady Non-Newtonian Blood Flow
,” Applied Mathematics and Computation
170
, no. 2
(November 2005
): 909
–923
, https://doi.org/10.1016/j.amc.2004.12.02946.
Banerjee
M. K.
, Datta
A.
, and Ganguly
R.
, “Magnetic Drug Targeting in Partly Occluded Blood Vessels Using Magnetic Microspheres
,” Journal of Nanotechnology in Engineering and Medicine
1
, no. 4
(October 2010
): 1
–9
, https://doi.org/10.1115/1.400241847.
Morsi
A. J.
and Alexander
S. A.
, “An Investigation of Particle Trajectories in Two-Phase Flow Systems
,” Journal of Fluid Mechanics
02
(1972
): 193
–208
, https://doi.org/10.1017/S002211207200180648.
Soltani
M.
and Chen
P.
, “Effect of Tumor Shape and Size on Drug Delivery to Solid Tumors
,” Journal of Biological Engineering
6
, no. 4
(December 2012
): 1
–15
, https://doi.org/10.1186/1754-1611-6-449.
Sommerfeld
M.
, “Analysis of collision effects for turbulent gas–particle flow in a horizontal channel: Part I. Particle transport
,” International Journal of Multiphase Flow
29
, no. 4
(April 2003
): 675
–699
, https://doi.org/10.1016/S0301-9322(03)00031-450.
Wen
D.
, Zhang
L.
, and He
Y.
, “Flow and Migration of Nanoparticle in a Single Channel
,” Heat and Mass Transfer
45
, no. 8
(June 2009
): 1061
–1067
, https://doi.org/10.1007/s00231-009-0479-851.
Riegler
J.
, Wells
J. A.
, Kyrtatos
P. G.
, Price
A. N.
, Pankhurst
Q. A.
, and Lythgoe
M. F.
, “Targeted Magnetic Delivery and Tracking of Cells Using a Magnetic Resonance Imaging System
,” Biomaterials
31
, no. 20
(July 2010
): 5366
–5371
, https://doi.org/10.1016/j.biomaterials.2010.03.03252.
Saffman
P. G.
, “The Lift on a Small Sphere in a Slow Shear Flow
,” Journal of Fluid Mechanics
22
, no. 2
(June 1965
): 385
–400
, https://doi.org/10.1017/S002211206500082453.
Stuart
D. C. C.
, Kleijn
C. R.
, and Kenjereš
S.
, “An Efficient and Robust Method for Lagrangian Magnetic Particle Tracking in Fluid Flow Simulations on Unstructured Grids
,” Computers & Fluids
40
, no. 1
(January 2011
): 188
–194
, https://doi.org/10.1016/j.compfluid.2010.09.00154.
Shaw
S.
, Murthy
P. V. S. N.
, and Pradhan
S. C.
, “Effect of Non-Newtonian Characteristics of Blood on Magnetic Targeting in the Impermeable Micro-Vessel
,” Journal of Magnetism and Magnetic Materials
322
, no. 8
(April 2010
): 1037
–1043
, https://doi.org/10.1016/j.jmmm.2009.12.01055.
Shaw
S.
, Sutradhar
A.
, and Murthy
P.
, “Permeability and Stress-jump effects on Magnetic Drug Targeting in a Permeable Microvessel using Darcy model
,” Journal of Magnetism and Magnetic Materials
429
(May 2017
): 227
–235
, https://doi.org/10.1016/j.jmmm.2017.01.023
This content is only available via PDF.
All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ASTM International.
You do not currently have access to this content.
