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TECHNICAL PAPERS: Cell

The Fluid Shear Stress Distribution on the Membrane of Leukocytes in the Microcirculation

[+] Author and Article Information
Masako Sugihara-Seki

Faculty of Engineering, Kansai University, Suita, Osaka, Japan

Geert W. Schmid-Schönbein

Department of Bioengineering, The Whitaker Institute for Bioengineering, University of California, San Diego, La Jolla, California

J Biomech Eng 125(5), 628-638 (Oct 09, 2003) (11 pages) doi:10.1115/1.1611515 History: Received January 07, 2003; Revised April 29, 2003; Online October 09, 2003
Copyright © 2003 by ASME
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Figures

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(a) Normalized translational velocity (closed circles) and angular velocity (open circles) of a freely suspended leukocyte with a/R=0.8. (b) The additional loss of pressure head due to the presence of a leukocyte with a/R=0.8. Large open square marks in (a) and (b) show the values by Wang & Skalak 24.
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The distribution of the shear stress acting on the surface of a freely suspended leukocyte with a/R=0.8 at c/R=0.15
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Temporal variations of the normalized shear stress acting on a point located at the circumference in the xy-plane, for a freely suspended leukocyte with a/R=0.8; (a): c/R=0.05, (b): c/R=0.10, and (c): c/R=0.15. Here, we assumed that the point initially lies at φ=0, and τ0 denotes the undisturbed shear stress at the vessel wall: τ0=4μV/R.
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The distribution of the shear stress acting on the surface of an adherent leukocyte with a/R=0.8. The scale of each arrow is 0.4 of that in Fig. 3.
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(A) The distribution of the shear stress exerted on the surface of a leukocyte along a circumference in the xy-plane at a/R=0.8. The results for freely suspended leukocytes are represented by thin curves; (a): c/R=0, (b): c/R=0.05, (c): c/R=0.10, and (d): c/R=0.15. The results for attached or rolling leukocytes are represented by thick curves; (e): Ur/V=0 (stationary adherent leukocyte), (f): Ur/V=0.1 and (g): Ur/V=0.2. (B) The distributions of the pressure along the circumference, where p0 represents the mean pressure over the surface of the leukocyte.
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The distribution of the shear stress exerted on the vessel wall when a leukocyte is freely suspended at c/R=0.15, for a/R=0.8
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The distribution of the shear stress exerted on the vessel wall when a leukocyte is stationary adherent to the wall, for a/R=0.8. The scale of each arrow is a half of that in Fig. 7.
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The shear stress exerted on the vessel wall along the line at Ψ=0 (A) and its temporal gradient (B), when a leukocyte with a/R=0.8 is freely suspended at (a) c/R=0, (b) 0.05, (c) 0.1, and (d) 0.15
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The shear stress exerted on the vessel wall along the line at Ψ=π (A) and its temporal gradient (B), when a leukocyte with a/R=0.8 is freely suspended at (a) c/R=0, (b) 0.05, (c) 0.1, and (d) 0.15
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(A) The shear stress and (B) the pressure on the vessel wall along the lines at Ψ=0 ((a),(b),(c)) and Ψ=π ((a′ ),(b′ ),(c′ )), when a leukocyte is rolling along the vessel wall with velocity Ur/V=0 ((a),(a′ )), 0.1 ((b),(b′ )) and 0.2 ((c),(c′ ))
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The shear stress normalized by τ0*, exerted on the surface of a leukocyte with a/R=0.8 along a circumference in the xy-plane, freely suspended at c/R=0 (a1–a3), 0.15 (b1–b3), and stationary adherent (c1–c3). The vessel length is L=1000 μm ((a1),(b1),(c1)), 500 μm ((a2),(b2),(c2)), and 100 μm ((a3),(b3),(c3)).
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The shear stress normalized by τ0*, exerted on the vessel wall along the lines at Ψ=0 ((a1–a3),(b1–b3), (c1–c3)) and at Ψ=π ((a′ 1–a′ 3),(b′ 1–b′ 3),(c′ 1–c′ 3)), when a leukocyte is freely suspended at c/R=0 ((a1–a3), (a′ 1–a′ 3)), 0.15 ((b1–b3),(b′ 1–b′ 3)), and stationary adherent ((c1–c3),(c′ 1–c′ 3)), with a/R=0.8. The vessel length is L=1000 μm ((a1),(b1),(c1),(a′ 1),(b′ 1),(c′ 1)), 500 μm ((a2),(b2),(c2),(a′ 2),(b′ 2),(c′ 2)), and 100 μm ((a3),(b3),(c3), (a′ 3),(b′ 3),(c′ 3)).
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The distribution of the shear stress acting on the surface of a freely suspended leukocyte in an unbounded simple shear flow with shear rate γ; a view along the z-axis (left), and a view along the y-axis (right).
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Normalized shear stress distribution on a leukocyte surface along a circumference in the xy-plane shown as a function of the azimuth angle φ. (a) A leukocyte translating in the direction of the x-axis with velocity U in an unbounded quiescent fluid. (b) A leukocyte freely suspended in an unbounded simple shear flow with shear rate γ along the x-axis. (c) A stationary leukocyte located on the vessel centerline in a Poiseuille flow with mean velocity V. (d) A leukocyte translating along the vessel centerline with velocity U in an otherwise quiescent fluid, and (e) a leukocyte freely suspended in a Poiseuille flow located at the vessel centerline (case (i) in the present study). The shear stresses are normalized for these cases by τ0=μU/a, μγ, μV/a,μU/a, and μV/a, respectively. In cases (c), (d) and (e), the radius ratio of the leukocyte to the vessel is a/R=0.8. The graphs in cases (c) and (d) were rescaled for the purpose of this comparison and need be multiplied by a factor 10.
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(a) Geometry for a freely suspended leukocyte in a circular cylindrical vessel and (b) for a leukocyte adherent to or rolling along the vessel wall

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