0
Journal of Fluids Engineering | Volume 141 | Issue 8 | research-article
Research Papers: Multiphase Flows

Two-Phase Fluid Modeling of Magnetic Drug Targeting in a Permeable Microvessel Implanted With a Toroidal Permanent Magnetic Stent

[+] Author and Article Information
Chibin Zhang

Professor
School of Mechanical Engineering,
Southeast University,
2 Southeast Road, Jiangning District,
Nanjing 211189, China
e-mail: chibinchang@aliyun.com

Kangli Xia

School of Mechanical Engineering,
Southeast University,
2 Southeast Road, Jiangning District,
Nanjing 211189, China
e-mail: 476961035@qq.com

Keya Xu

School of Energy and Electrical Engineering,
Hohai University,
1 Xikang Road,
Nanjing 210098, China
e-mail: 2114936135@qq.com

Xiaohui Lin

School of Mechanical Engineering,
Southeast University,
2 Southeast Road, Jiangning District,
Nanjing 211189, China
e-mail: lxh60@seu.edu.cn

Shuyun Jiang

Professor
School of Mechanical Engineering,
Southeast University,
2 Southeast Road, Jiangning District,
Nanjing 211189, China
e-mail: jiangshy@seu.edu.cn

Changbao Wang

School of Mechanical Engineering,
Southeast University,
2 Southeast Road, Jiangning District,
Nanjing 211189, China
e-mail: 1140109858@qq.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 15, 2018; final manuscript received November 12, 2018; published online February 13, 2019. Assoc. Editor: Nazmul Islam.

J. Fluids Eng 141(8), 081301 (Feb 13, 2019) (9 pages) Paper No: FE-18-1270; doi: 10.1115/1.4042557 History: Received April 15, 2018; Revised November 12, 2018
Article
References
Figures
Tables

The key to effective magnetic drug targeting (MDT) is to improve the aggregation of magnetic drug carrier particles (MDCPs) at the target site. Compared to related theoretical models, the novelty of this investigation is mainly reflected in that the microvascular blood is considered as a two-phase fluid composed of a continuous phase (plasma) and a discrete phase (red blood cells (RBCs)). And plasma flow state is quantitatively described based on the Navier–Stokes equation of two-phase flow theory, the effect of momentum exchange between the two-phase interface is considered in the Navier–Stokes equation. Besides, the coupling effect between plasma pressure and tissue fluid pressure is considered. The random motion effects and the collision effects of MDCPs transported in the blood are quantitatively described using the Boltzmann equation. The results show that the capture efficiency (CE) presents a nonlinear increase with the increase of magnetic induction intensity and a nonlinear decrease with the increase of plasma velocity, but an approximately linear increase with the increase of the particle radius. Furthermore, greater permeability of the microvessel wall promotes the aggregation of MDCPs. The CE predicted by the model agrees well with the experimental results.
FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

1
Breen, S. , Kofoed, S. , Ritchie, D. , Dryden, T. , Maguire, R. , Kearney, N. , and Aranda, S. , 2016, “Remote Real-Time Monitoring for Chemotherapy Side-Effects in Patients With Blood Cancers,” Collegian, 24(6), pp. 541–549. [CrossRef]
2
Lindley, C. , Mccune, J. S. , Thomason, T. E. , Lauder, D. , Sauls, A. , Adkins, S. , and Sawyer, W. T. , 1999, “Perception of Chemotherapy Side Effects Cancer Versus Noncancer Patients,” Cancer Pract., 7(2), pp. 59–65. [CrossRef] [PubMed]
3
Senyei, A. , Widder, K. , and Czerlinski, G. , 1978, “Magnetic Guidance of Drug-Carrying Microspheres,” J. Appl. Phys., 49(6), pp. 3578–3583. [CrossRef]
4
Widder, K. J. , Senyei, A. E. , and Scarpeui, D. G. , 1978, “Magnetic Microsphere: A Model System for Site Specific Drug Delivery In Vivo,” Proc. Soc. Exp. Biol. Med., 158(2), pp. 141–146. [CrossRef] [PubMed]
5
Lübbe, A. S. , Bergemann, C. , Riess, H. , Schriever, F. , Reichardt, P. , Possinger, K. , Matthias, M. , Dörken, B. , Herrmann, F. , Gürtler, R. , Hohenberger, P. , Haas, N. , Sohr, R. , Sander, B. , Lemke, A. J. , Ohlendorf, D. , Huhnt, W. , and Huhn, D. , 1996, “Clinical Experiences With Magnetic Drug Targeting: A Phase I Study With 4'-Epidoxorubicin in 14 Patients With Advanced Solid Tumors,” Cancer Res., 56(20), pp. 4686–4693. https://www.ncbi.nlm.nih.gov/pubmed/8840985 [PubMed]
6
Rotariu, O. , and Strachan, N. J. C. , 2005, “Modelling Magnetic Carrier Particle Targeting in the Tumor Microvasculature for Cancer Treatment,” J. Magn. Magn. Mater., 293(1), pp. 639–646. [CrossRef]
7
Xu, H. , Song, T. , Bao, X. , and Hu, L. , 2005, “Site-Directed Research of Magnetic Nanoparticles in Magnetic Drug Targeting,” J. Magn. Magn. Mater., 293(1), pp. 514–519. [CrossRef]
8
Avilés, M. O. , Ebner, A. D. , and Ritter, J. A. , 2007, “Ferromagnetic Seeding for the Magnetic Targeting of Drugs and Radiation in Capillary Beds,” J. Magn. Magn. Mater., 310(1), pp. 131–144. [CrossRef]
9
Avilés, M. O. , Chen, H. , Ebner, A. D. , Rosengart, A. J. , Kaminski, M. D. , and Ritter, J. A. , 2007, “In Vitro Study of Ferromagnetic Stents for Implant Assisted-Magnetic Drug Targeting,” J. Magn. Magn. Mater., 311(1), pp. 306–311. [CrossRef]
10
Avilés, M. O. , Ebner, A. D. , and Ritter, J. A. , 2008, “In Vitro Study of Magnetic Particle Seeding for Implant Assisted-Magnetic Drug Targeting,” J. Magn. Magn. Mater., 320(21), pp. 2640–2646. [CrossRef]
11
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 Carrier Particle Capture,” J. Magn. Magn. Mater., 321(10), pp. 1586–1590. [CrossRef]
12
Furlani, E. P. , and Ng, K. C. , 2006, “Analytical Model of Magnetic Nanoparticle Transport and Capture in the Microvasculature,” Phys. Rev. E, 73(6), p. 061919. [CrossRef]
13
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. [CrossRef]
14
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. [CrossRef]
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. [CrossRef]
16
Shaw, S. , and Murthy, P. V. S. N. , 2010, “Magnetic Targeting in the Impermeable Microvessel With Two-Phase Fluid Model—Non-Newtonian Characteristics of Blood,” Microvascular Res., 80(2), pp. 209–220. [CrossRef]
17
Shaw, S. , Murthy, P. V. S. N. , and Sibanda, P. , 2013, “Magnetic Drug Targeting in a Permeable Microvessel,” Microvascular Res., 85, pp. 77–85. [CrossRef]
18
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. [CrossRef]
19
Cregg, P. J. , Murphy, K. , Mardinoglu, A. , and Prina-Mello, A. , 2010, “Many Particle Magnetic Dipole-Dipole and Hydrodynamic Interactions in Magnetizable Stent Assisted Magnetic Drug Targeting,” J. Magn. Magn. Mater., 322(15), pp. 2087–2094. [CrossRef]
20
Cregg, P. J. , Murphy, K. , and Mardinoglu, A. , 2012, “Inclusion of Interactions in Mathematical Modelling of Implant Assisted Magnetic Drug Targeting,” Appl. Math. Modell., 36(1), pp. 1–34. [CrossRef]
21
Rukshin, I. , Mohrenweiser, J. , Yue, P. , and Afkhami, S. , 2017, “Modeling Superparamagnetic Particles in Blood Flow for Applications in Magnetic Drug Targeting,” Fluids, 2(2), pp. 29–31. [CrossRef]
22
EI-shahed, M. , 2004, “Blood Flow in a Capillary With Permeable Wall,” Phys. A, 338, pp. 544–558. [CrossRef]
23
Shaw, S. , Sutradhar, A. , and Murthy, P. , 2017, “Permeability and Stress-Jump Effects on Magnetic Drug Targeting in a Permeable Microvessel Using Darcy Model,” J. Magn. Magn. Mater., 429, pp. 227–235. [CrossRef]
24
Sutradhar, A. , Mondal, J. K. , Murthy, P. , and Gorla, R. S. R. , 2016, “Influence of Starling's Hypothesis and Joule Heating on Peristaltic Flow of an Electrically Conducting Casson Fluid in a Permeable Microvessel,” ASME. J. Fluids Eng., 138(11), p. 111106. [CrossRef]
25
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. [CrossRef]
26
Takayasu, M. , Gerber, R. , and Friedlander, F. J. , 1983, “Magnetic Separation of Sub-Micron Particles,” IEEE Trans. Magn., 19(5), pp. 2112–2114. [CrossRef]
27
Fletcher, D. , 1991, “Fine Particle High Gradient Magnetic Entrapment,” IEEE Trans. Magn., 27(4), pp. 3655–3677. [CrossRef]
28
Fernández-Pacheco, R. , Marquina, C. , Gabriel Valdivia, J. , Gutiérrez, M. , Soledad Romero, M. , Cornudella, R. , Laborda, A. , Viloria, A. , Higuera, T. , García, A. , De Jalón, J. A. G. , and Ricardo Ibarra, M. , 2007, “Magnetic Nanoparticles for Local Drug Delivery Using Magnetic Implants,” J. Magn. Magn. Mater., 311(1), pp. 318–322. [CrossRef]
29
Wang, H. , and Skalak, R. , 1969, “Viscous Flow in a Cylindrical Tube Containing a Line of Spherical Particles,” J. Fluid Mech., 38(1), pp. 75–96. [CrossRef]
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. [CrossRef]
31
Taylor, M. , 1955, “The Flow of Blood in Narrow Tubes II: The Axial Stream and Its Formation, as Determined by Changes in Optical Density,” Austral. J. Exp. Biol., 33(1), pp. 1–16. [CrossRef]
32
Sankar, D. S. , and Lee, U. , 2010, “Two-Fluid Casson Model for Pulsatile Blood Flow Through Stenosed Arteries: A Theoretical Model,” Commun. Nonlinear Sci. Numer. Simul., 15(8), pp. 2086–2097. [CrossRef]
33
Sankar, D. S. , and Lee, U. , 2011, “Nonlinear Mathematical Analysis for Blood Flow in a Constricted Artery Under Periodic Body Acceleration,” Commun. Nonlinear Sci. Numer. Simul., 16(11), pp. 4390–4402. [CrossRef]
34
Sankar, D. S. , and Ismail, A. I. , 2009, “Two-Fluid Mathematical Models for Blood Flow in Stenosed Arteries: A Comparative Study,” Boundary Value Probl., 2009(1), pp. 1–15.
35
Sankar, D. S. , 2011, “Two-Phase Non-Linear Model for Blood Flow in Asymmetric and Axisymmetric Stenosed Arteries,” Int. J. Non-Linear Mech., 46(1), pp. 296–305. [CrossRef]
36
Sankar, D. S. , Goh, J. , and Ismail, A. I. M. , 2010, “FDM Analysis for Blood Flow Through Stenosed Tapered Arteries,” Boundary Value Probl., 1, pp. 1–16.
37
Sankar, D. S. , 2010, “Pulsatile Flow of a Two-Fluid Model for Blood Flow Through Arterial Stenosis,” Math. Probl. Eng., 4, pp. 242–256.
38
Sankar, D. S. , and Lee, U. , 2010, “Pulsatile Flow of Two-Fluid Nonlinear Models for Blood Flow Through Catheterized Arteries: A Comparative Study,” Math. Probl. Eng., 2010, p. 21.
39
Bugliarello, G. , and Sevilla, J. , 1970, “Velocity Distribution and Other Characteristics of Steady and Pulsatile Blood Flow in Fine Glass Tubes,” Biorheology, 7(2), pp. 85–107. [CrossRef] [PubMed]
40
Sharan, M. , and Popel, A. S. , 2001, “A Two-Phase Model for Flow of Blood in Narrow Tubes With Increased Effective Viscosity Near the Wall,” Biorheology, 38(5–6), pp. 415–428. [PubMed]
41
Chakravarty, S. , Sarifuddin ., and Mandal, P. K. , 2004, “Unsteady Flow of a Two-Layer Blood Stream Past a Tapered Flexible Artery Under Stenotic Conditions,” Comput. Methods Appl. Math., 4(4), pp. 391–409. [CrossRef]
42
Pozrikidis, C. , 2005, “Axisymmetric Motion of a File of Red Blood Cells Through Intravascular,” Phys. Fluids, 17(3), p. 031503. [CrossRef]
43
Ni, J. , Wang, G. , and Zhang, H. , 1991, The Basic Theory of Solid Liquid Two-Phase Flow and Its Latest Applications, Science Press, Beijing, China, pp. 35–52.
44
Vaidheeswaran, A. , and Bertodano, M. L. D. , 2016, “Interfacial Pressure Coefficient for Ellipsoids and Its Effect on the Two-Fluid Model Eigenvalues,” ASME J. Fluids Eng., 138(8), p. 081302. [CrossRef]
45
Ni, J. , Wang, G. , and Zhang, H. , 1991, The Basic Theory of Solid-Liquid Two Phase Flow and Its Latest Applications, Science Press, Beijing, China, pp. 28–73.
46
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. [CrossRef] [PubMed]
47
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. [CrossRef] [PubMed]
48
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. [CrossRef] [PubMed]
49
Darcy, H. , 1856, Les Fontaines Publiques de la Ville de Dijon: Exposition et Application, Victor Dalmont, Paris, France.
50
Zarandi, M. A. F. , Pillai, K. M. , and Kimmel, A. S. , 2017, “Spontaneous Imbibition of Liquids in Glass‐Fiber Wicks—Part I: Usefulness of a Sharp‐Front Approach,” Aiche J., 64(1), pp. 294–305. [CrossRef]
51
Masoodi, R. , Tan, H. , and Pillai, K. M. , “Darcy's Law–Based Numerical Simulation for Modeling 3D Liquid Absorption Into Porous Wicks,” Aiche J., 57(5), pp. 1132–1143. [CrossRef]
52
Salathe, E. P. , and An, K. N. , 1976, “A Mathematical Analysis of Fluid Movement Across Capillary Walls,” Microvascular Res., 11(1), pp. 1–23. [CrossRef]
53
Selvaggi, J. P. , Salon, S. J. , and Chari, M. V. K. , 2010, “Computing the Magnetic Induction Field Due to a Radially Magnetized Finite Cylindrical Permanent Magnet by Employing Toroidal Harmonics,” PIERS Proceedings, Cambridge, MA, July 5–8, pp. 244–251.
54
Huang, Z. , and Ding, E. , 2006, Transport Theory, Science Press, Beijing, China, pp. 154–248.
55
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), pp. 403–416. [CrossRef] [PubMed]
56
Polak, E. , 1974, “A Globally Converging Secant Method With Application to Boundary Value Problem,” SIAM J. Numer. Anal., 11(3), pp. 529–537. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Model of the blood flow in a permeable microvessel

+Model of the blood flow in a permeable microvessel
View Large  |  Save Figure  |  Download Slide (.ppt)
Model of the blood flow in a permeable microvessel
Grahic Jump Location
Fig. 2

A program chart of the numerical solution procedure

+A program chart of the numerical solution procedure
View Large  |  Save Figure  |  Download Slide (.ppt)
A program chart of the numerical solution procedure
Grahic Jump Location
Fig. 3

Plasma pressure distributions along the x-axis for different permeability parameters (x*=(x/L) )

+Plasma pressure distributions along the x-axis for different permeability parameters (x*=(x/L) )
View Large  |  Save Figure  |  Download Slide (.ppt)
Plasma pressure distributions along the x-axis for different permeability parameters (x*=(x/L) )
Grahic Jump Location
Fig. 4

Plasma velocity distributions for different permeability parameters (x*=0)

+Plasma velocity distributions for different permeability parameters (x*=0)
View Large  |  Save Figure  |  Download Slide (.ppt)
Plasma velocity distributions for different permeability parameters (x*=0)
Grahic Jump Location
Fig. 5

The distribution of MDCPs (r*=(r/R)): (a) in the radial direction and (b) in velocity space (V*=(Vη/p∞R))

+The distribution of MDCPs (r*=(r/R)): (a) in the radial direction and (b) in velocity space (V*=(Vη/p∞R))
View Large  |  Save Figure  |  Download Slide (.ppt)
The distribution of MDCPs (r*=(r/R)): (a) in the radial direction and (b) in velocity space (V*=(Vη/p∞R))
Grahic Jump Location
Fig. 6

CE varies with dimensionless magnetic induction intensity B*(B*=(B/B0)=(B/μ0M0), μ0M0=1T, u=4.5 cm/s, rcp=250 nm, and Π=5)

+CE varies with dimensionless magnetic induction intensity B*(B*=(B/B0)=(B/μ0M0), μ0M0=1T, u=4.5 cm/s, rcp=250 nm, and Π=5)
View Large  |  Save Figure  |  Download Slide (.ppt)
CE varies with dimensionless magnetic induction intensity B*(B*=(B/B0)=(B/μ0M0), μ0M0=1T, u=4.5 cm/s, rcp=250 nm, and Π=5)
Grahic Jump Location
Fig. 7

CE varies with dimensionless plasma velocity u* (u*=(ηu/p∞R), B=0.65T, rcp=870nm, and Π=0)

+CE varies with dimensionless plasma velocity u* (u*=(ηu/p∞R), B=0.65T, rcp=870nm, and Π=0)
View Large  |  Save Figure  |  Download Slide (.ppt)
CE varies with dimensionless plasma velocity u* (u*=(ηu/p∞R), B=0.65T, rcp=870nm, and Π=0)
Grahic Jump Location
Fig. 8

CE varies with dimensionless radius rcp* of MDCPs (rcp*=(rcp/R), B=0.1T, u=6.9 mm/s, and Π=0)

+CE varies with dimensionless radius rcp* of MDCPs (rcp*=(rcp/R), B=0.1T, u=6.9 mm/s, and Π=0)
View Large  |  Save Figure  |  Download Slide (.ppt)
CE varies with dimensionless radius rcp* of MDCPs (rcp*=(rcp/R), B=0.1T, u=6.9 mm/s, and Π=0)
Grahic Jump Location
Fig. 9

CE varies with permeability parameter Π (B=0.5T,u=4.5 cm/s, and rcp=250 nm)

+CE varies with permeability parameter Π (B=0.5T,u=4.5 cm/s, and rcp=250 nm)
View Large  |  Save Figure  |  Download Slide (.ppt)
CE varies with permeability parameter Π (B=0.5T,u=4.5 cm/s, and rcp=250 nm)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Completing the Picture
Air Engines> Chapter 11
Introduction
Design of Mechanical Bearings in Cardiac Assist Devices
Example Open-Book Questions
Quick Guide to the API 570 - Certified Pipework Inspector Syllabus> Chapter 14
Introduction
Axial-Flow Compressors> Chapter 1
Two Advanced Methods
Applications of Mathematical Heat Transfer and Fluid Flow Models in Engineering and Medicine
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
This site uses cookies. By continuing to use our website, you are agreeing to our privacy policy. | Accept
Sign In