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The Deformation Behavior of Multiple Red Blood Cells in a Capillary Vessel

[+] Author and Article Information
Xiaobo Gong1

Organ and Body Scale Team, Computational Science Research Program, RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japangong@riken.jp

Kazuyasu Sugiyama

Department of Mechanical Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japansugiyama@fel.t.u-tokyo.ac.jp

Shu Takagi

Organ and Body Scale Team, Computational Science Research Program, RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan; Department of Mechanical Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japantakagish@riken.jp

Yoichiro Matsumoto

Department of Mechanical Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japanymats@mech.t.u-tokyo.ac.jp

1

Corresponding author.

J Biomech Eng 131(7), 074504 (Jun 04, 2009) (5 pages) doi:10.1115/1.3127255 History: Received August 31, 2008; Revised January 26, 2009; Published June 04, 2009

The deformation of multiple red blood cells in a capillary flow was studied numerically. The immersed boundary method was used for the fluid red blood cells interaction. The membrane of the red blood cell was modeled as a hyperelastic thin shell. The numerical results show that the apparent viscosity in the capillary flow is more sensitive to the change of shear coefficient of the membrane than the bending coefficient and surface dilation coefficient, and the increase in the shear coefficient results in an increase in the pressure drop in the blood flow in capillary vessels in order to sustain the same flux rate of red blood cells.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 5

The distribution of the time-averaged axial velocity on the cross section of the capillary flow (the dash-dot-dot line stands for the analytical solution of Poiseuille flow without red blood cells, the solid and dash lines stand for the simulation results in the capillary flow with ten red blood cells; for the case shown with solid line, the shear coefficient of the membrane B=1.7×10−6 N/m, which referred to the experiment of Chien (17), and for the dash line B=4.2×10−6 N/m referred to Ref. 18)

Grahic Jump Location
Figure 4

The deformed profile of the red blood cells with different membrane properties (the solid line shows the deformation when shear coefficient B=1.7×10−6 N/m, surface dilation coefficient C=1.0×10−4 N/m; the dashed line shows when B increases about 2.5 times to B=4.2×10−6 N/m; the dashed-dotted line shows when C increases 10 times to C=1.0×10−3 N/m)

Grahic Jump Location
Figure 3

The time evolution of the cross section of a pair of red blood cells in the capillary flow with 10 red blood cells: (a) the red blood cells were distributed symmetrically at initial stage; (b) the red blood cells were distributed asymmetrically at initial stage; dsym,0 and dasym,0 are the projected diameters that the red blood cell pair initially took in the capillary; dsym and dasym are the projected diameters of the pair at a developed stage when t=16.0)

Grahic Jump Location
Figure 2

The deformation profile of ten red blood cells in a capillary flow at the initial and developed stages ((a) and (b) are the initial stages of ten red blood cells distributed symmetrically and asymmetrically, respectively; (c) and (d) are the developed stages of the blood cells corresponding to the initial stages shown in (a) and (b), respectively)

Grahic Jump Location
Figure 1

The time evolution of the cross section of a red blood cell in a simple shear flow (the dimensionless numbers for this calculation are Cb=μoutγa/B=0.15, CC=μoutγa/C=0.01, and Cb=μoutγa3/kb=10.0, where a is the equivalent radius of the cell, B is the shear coefficient, C is the surface dilation coefficient, kb is the bending rigidity, γ is the shear rate in the flow, which is set as 875 (1/s) for the this calculation, and 1/γ is used as the time scale; the viscosity ratio between inside and outside the red blood cell μin/μout=5.0; the size of the computational domain is set to 8a×8a×8a and the number of grid points is 80×80×80. More details were shown in our previous study for the deformation behavior of vesicles in a linear shear flow (13)).

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