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Research Papers

Numerical Analysis for Elucidation of Nonlinear Frictional Characteristics of a Deformed Erythrocyte Moving on a Plate in Medium Subject to Inclined Centrifugal Force

[+] Author and Article Information
Takashi Oshibe

Graduate School of Engineering,
Tohoku University,
6-6-01 Aramaki Aza Aoba, Aoba-ku,
Sendai 980-8579, Japan

Toshiyuki Hayase

Institute of Fluid Science,
Tohoku University,
2-1-1 Katahira, Aoba-ku,
Sendai 980-8577, Japan
e-mail: hayase@ifs.tohoku.ac.jp

Kenichi Funamoto, Atsushi Shirai

Institute of Fluid Science,
Tohoku University,
2-1-1 Katahira, Aoba-ku,
Sendai 980-8577, Japan

1Corresponding author.

Manuscript received June 20, 2014; final manuscript received September 26, 2014; accepted manuscript posted October 2, 2014; published online October 17, 2014. Assoc. Editor: Mohammad Mofrad.

J Biomech Eng 136(12), 121003 (Oct 17, 2014) (9 pages) Paper No: BIO-14-1278; doi: 10.1115/1.4028723 History: Received June 20, 2014; Revised September 26, 2014; Accepted September 28, 2014

Complex interactions between blood cells, plasma proteins, and glycocalyx in the endothelial surface layer are crucial in microcirculation. To obtain measurement data of such interactions, we have previously performed experiments using an inclined centrifuge microscope, which revealed that the nonlinear velocity-friction characteristics of erythrocytes moving on an endothelia-cultured glass plate in medium under inclined centrifugal force are much larger than those on plain or material-coated glass plates. The purpose of this study was to elucidate the nonlinear frictional characteristics of an erythrocyte on plain or material-coated glass plates as the basis to clarify the interaction between the erythrocyte and the endothelial cells. We propose a model in which steady motion of the cell is realized as an equilibrium state of the force and moment due to inclined centrifugal force and hydrodynamic flow force acting on the cell. Other electrochemical effects on the surfaces of the erythrocyte and the plate are ignored for the sake of simplicity. Numerical analysis was performed for a three-dimensional flow of a mixture of plasma and saline around a rigid erythrocyte model of an undeformed biconcave shape and a deformed shape with a concave top surface and a flat bottom surface. A variety of conditions for the concentration of plasma in a medium, the velocity of the cell, and the minimum gap width and the angle of attack of the cell from the plate, were examined to obtain the equilibrium states. A simple flat plate model based on the lubrication theory was also examined to elucidate the physical meaning of the model. The equilibrium angle of attack was obtained only for the deformed cell model and was represented as a power function of the minimum gap width. A simple flat plate model qualitatively explains the power function relation of the frictional characteristics, but it cannot explain the equilibrium relation, confirming the computational result that the deformation of the cell is necessary for the equilibrium. The frictional characteristics obtained from the present computation qualitatively agree with those of former experiments, showing the validity of the proposed model.

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Figures

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Fig. 1

Inclined centrifuge microscope: (a) overview, (b) principle of measurement, and (c) example of moving erythrocytes on a plain glass plate [10]

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Fig. 2

Nondimensional friction force as functions of nondimensional cell velocity

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Fig. 3

Geometry and computational conditions: (a) undeformed and deformed cell model configurations, (b) computational domain, and (c) definition of the cell position relative to the base plate and forces and moment acting on the cell

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Fig. 4

Variations of forces and moments acting on the cell with the angle of attack for U = 50 μm/s, h = 0.1 μm, r = 1: figures on the left correspond to the deformed cell model of case B and the flat plate model and figures on the right to the undeformed one of case A, (a) lift FL, (b) drag FD, and (c) moment M

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Fig. 5

Streamlines around the cell models for U = 50 μm/s, h = 0.1 μm, and r = 1; deformed cell model of case B with (a) α = α0 = 1.8 deg, (b) α = 0 deg, and (c) undeformed cell model of case A with α = 0 deg

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Fig. 6

Distributions of pressure on the bottom surface of the cell models for U = 50 μm/s, h = 0.1 μm, and r = 1; deformed cell model of case B with (a) α = α0 = 1.8 deg, (b) α = 0 deg, and (c) undeformed cell model of case A with α = 0 deg

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Fig. 7

Distributions of pressure on the bottom wall in the x–y symmetrical plane for U = 50 μm/s, h = 0.1 μm, and r = 1; the deformed cell model of case B and the flat plate model with (a) α = α0 = 1.8 deg, (b) α = 0 deg, and (c) the undeformed cell model of case A and the flat plate model with α = 0 deg

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Fig. 8

Equilibrium angle of attack with the minimum gap width

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Fig. 9

Minimum gap widths as functions of nondimensional cell velocity

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