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Research Paper

Magnetic Drug Targeting in the Permeable Blood Vessel—The Effect of Blood Rheology

[+] Author and Article Information
S. Shaw

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721 302, India

P. V. S. N. Murthy1

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721 302, Indiapvsnm@maths.iitkgp.ernet.in

1

Corresponding author.

J. Nanotechnol. Eng. Med 1(2), 021001 (Apr 16, 2010) (11 pages) doi:10.1115/1.4001477 History: Received March 07, 2010; Revised March 17, 2010; Published April 16, 2010; Online April 16, 2010

The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel, which is subjected to the external magnetic field. We consider the physical model that was given in the work of Furlani and Furlani (2007, “A Model for Predicting Magnetic Targeting of Multifunctional Particles in the Microvasculature,” J. Magn. Magn. Mater., 312, pp. 187–193), but deviating by taking the non-Newtonian fluid model for the blood in the permeable microvessel. Both the Herschel–Bulkley fluid and Casson models are considered to analyze the present problem. The expression for the fluid velocity in the permeable microvessel is obtained using the analogy given by Decuzzi (2006, “The Effective Dispersion of Nanovectors Within the Tumor Microvasculature,” Ann. Biomed. Eng., 34, pp. 633–641) first. Then the expression for the fluidic force for the carrier particle traversing in the non-Newtonian fluid is obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the permeability of the inner wall, size of the carrier particle, the volume fraction of embedded nanoparticles, and the diameter of the microvessel are considered in the present problem. The trajectories of the carrier particles are found in both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases in both the Casson and Herschel–Bulkley fluid models. The present results for the permeable microvessel are compared with the impermeable inner wall trajectories given by Shaw (2010, “Effect of Non-Newtonian Characteristics of Blood on Magnetic Targeting in the Impermeable Micro Vessel,” J. Magn. Magn. Mater., 322, pp. 1037–1043). Also, a prediction of the capture of therapeutic magnetic nanoparticle in the human permeable microvasculature is made for different radii and volume fractions in both the invasive and noninvasive cases.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 11

Comparison of the trajectories of the carrier particle between the general and special cases in the Herschel–Bulkley fluid of the permeable microvessel with different values of Rcp with n=1, ξc=0.4, βvf=56%, and d=55 mm

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Figure 1

Geometrical representation of the permeable microvessel with external magnetic field

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Figure 2

(a) Velocity of the Casson fluid in the permeable microvessel for different values of the permeability parameter Π with ξc=0.4; (b) velocity of the Herschel–Bulkley fluid in the permeable microvessel for different values of the permeability parameter Π with ξc=0.4, and (i) n=0.5, (ii) n=1, and (iii) n=1.5; (c) velocity of the Casson fluid in the permeable microvessel for different ξc with Π=2; (d) velocity of the Herschel–Bulkley fluid in the permeable microvessel for different ξc with Π=2; (e) velocity profile for the Casson and Herschel–Bulkley (n=0.85,1,1.15) fluids for the permeable microvessel with ξc=0.4 and Π=2

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Figure 3

(a) Comparison of the trajectories of the carrier particle for the Casson and Herschel–Bulkley fluids with x/Rv=1, ξc=0.4, Rcp=300 nm, βvf=20%, Π=2, and d=55 mm (special case); (b) comparison of the trajectories of the carrier particle for the Casson and Herschel–Bulkley fluids with different values of x/Rv with ξc=0.4, Rcp=300 nm, βvf=20%, Π=2, and d=55 mm: (i) n=0.85 (ii) n=1, and (iii) n=1.15 (special case); (c) comparison of the trajectories of the carrier particle for the Casson and Herschel–Bulkley fluids for different Rcp with x/Rv=1, ξc=0.4, βvf=20%, n=1, Π=2, and d=55 mm (special case); (d) comparison of the trajectories of the carrier particle for the Casson and Herschel–Bulkley fluids for different d with x/Rv=1, ξc=0.4, n=1, Π=2, and βvf=20% (special case)

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Figure 4

(a) Comparison of the volume fraction required for 100% capture versus Rcp in the Casson fluid for the permeable and impermeable microvessels with ξc=0.4, Π=2 and d=55 mm (special case); (b) comparison of the volume fraction required for 100% capture versus Rcp in the Herschel–Bulkley fluid for the permeable and impermeable microvessels with n=1, ξc=0.4, Π=2, and d=55 mm (special case)

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Figure 5

Trajectories of the carrier particle (Rcp=300 nm) in the Casson fluid for the permeable and impermeable microvessels with ξc=0.4, βvf=20%, Π=2, and d=55 mm (special case)

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Figure 6

Velocity profiles for the Casson and Herschel–Bulkley (n=0.85,1,1.15) fluids for the impermeable microvessel with ξc=0.4

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Figure 7

Volume fraction required for 100% capture versus Rcp in the Herschel–Bulkley fluid for different ξc in the permeable wall d=55 mm with (a) n=0.5, (b) 1, and (c) 1.5 (special case)

Grahic Jump Location
Figure 8

Trajectories of the carrier particle (Rcp=300 nm) in the Herschel–Bulkley fluid for different volume fractions in the permeable microvessel with ξc=0.4, d=55 mm, and (a) n=0.85, (b) 1, and (c) 1.15 (special case)

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Figure 9

Analysis of βvf,100 as a function of the radius of the carrier particle and d in the Herschel–Bulkley fluid for different values of n (ξc=0.4, special case)

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Figure 10

Comparison of the trajectories of the carrier particle (Rcp=500 nm) between the general and special cases in the Herschel–Bulkley fluid of the permeable microvessel with n=1, ξc=0.4, βvf=56%, and d=55 mm

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