Research Papers

Statistical Mechanics Transport Model of Magnetic Drug Targeting in Permeable Microvessel

[+] Author and Article Information
Xiaohui Lin

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

Chibin Zhang

School of Mechanical Engineering,
Southeast University,
Nanjing 211189, China
e-mail: chibinchang@aliyun.com

Kai Li

School of Mechanical Engineering,
Southeast University,
Nanjing 211189, China
e-mail: likai_seu@163.com

1Corresponding author.

Manuscript received December 23, 2014; final manuscript received May 30, 2015; published online June 30, 2015. Assoc. Editor: Feng Xu.

J. Nanotechnol. Eng. Med 6(1), 011001 (Feb 01, 2015) (9 pages) Paper No: NANO-14-1081; doi: 10.1115/1.4030787 History: Received December 23, 2014; Revised May 30, 2015; Online June 30, 2015

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.

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Fig. 1

Schematic of theoretical model

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Fig. 6

The density distribution of the MDCPs along the permeable microvessel with the value of the permeability parameter Π = 3

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Fig. 5

Dimensionless equilibrium distribution of MDCPs (a) along the radial of the permeable microvessel and (b) in velocity spatial, with the value of the permeability parameter Π = 3

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Fig. 7

The CE of the MDCPs as a function of the magnetic force with the parameter values rcp = 150 nm, u = 21 mm/s, Π = 3

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Fig. 10

The CE of the MDCPs as a function of the inlet blood velocity with the parameter values d = 3 cm, rcp = 150 nm, Π = 3

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Fig. 11

The CE of the MDCPs as a function of the permeability parameter with the parameter values d = 3 cm, rcp = 150 nm, u = 21 mm/s

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Fig. 8

The CE of the MDCPs as a function of the distance between microvessel and magnet with the parameter values rcp = 150 nm, u = 21 mm/s, Π = 3

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Fig. 9

The CE of the MDCPs as a function of the radius of the MDCPs with the parameter values d = 3 cm, u = 21 mm/s, Π = 3

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Fig. 4

The radial distributions of blood flow velocity along the vessel with the value of nondimensional penetration parameter Π = 1 and Π = 5

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Fig. 3

Dimensionless interstitial fluid pressure distribution along the radial of extravascular space for different cross section of the microvessel with Π = 6

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Fig. 2

Dimensionless distribution of (a) blood pressure and (b) interstitial fluid axial pressure, in the axial direction of the permeable microvessel for different values of the permeability parameter Π with p0 = 100 kPa, p1 = 25 kPa (permeability parameters Π is defined as Π=4l/RηNKp/R)



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