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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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References

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Figures

Grahic Jump Location
(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
Grahic Jump Location
(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.
Grahic Jump Location
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
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
(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.
Grahic Jump Location
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
Grahic Jump Location
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.
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
(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′ ))
Grahic Jump Location
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)).
Grahic Jump Location
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)).
Grahic Jump Location
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).
Grahic Jump Location
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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