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Research Papers

Temporal and Spatial Variations of Wall Shear Stress in the Entrance Region of Microvessels

[+] Author and Article Information
Othmane Oulaid

Bharti School of Engineering,
Laurentian University,
935 Ramsey Lake Road,
Sudbury, ON P3E 2C6, Canada

Junfeng Zhang

Bharti School of Engineering,
Laurentian University,
935 Ramsey Lake Road,
Sudbury, ON P3E 2C6, Canada
e-mail: jzhang@laurentian.ca

1Corresponding author.

Manuscript received November 4, 2014; final manuscript received March 6, 2015; published online April 6, 2015. Assoc. Editor: Tim David.

J Biomech Eng 137(6), 061008 (Jun 01, 2015) (9 pages) Paper No: BIO-14-1548; doi: 10.1115/1.4030055 History: Received November 04, 2014; Revised March 06, 2015; Online April 06, 2015

Using a simplified two-dimensional divider-channel setup, we simulate the development process of red blood cell (RBC) flows in the entrance region of microvessels to study the wall shear stress (WSS) behaviors. Significant temporal and spatial variation in WSS is noticed. The maximum WSS magnitude and the strongest variation are observed at the channel inlet due to the close cell-wall contact. From the channel inlet, both the mean WSS and variation magnitude decrease, with a abrupt drop in the close vicinity near the inlet and then a slow relaxation over a relatively long distance; and a relative stable state with approximately constant mean and variation is established when the flow is well developed. The correlations between the WSS variation features and the cell free layer (CFL) structure are explored, and the effects of several hemodynamic parameters on the WSS variation are examined. In spite of the model limitations, the qualitative information revealed in this study could be useful for better understanding relevant processes and phenomena in the microcirculation.

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Figures

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Fig. 1

Schematic drawings (a) for the RBC separation at a bifurcation and flow development in branch microvessels (arrows for the flow directions, different colors/shades for the concentrate RBC region and the CFL, and an elliptical circle for the flow development region to be simulated in this study), (b) for the divider-channel setup utilized in this study to mimic the flow development process in the entrance region (the channel length is shortened to fit the page width, and the cells are not plotted for clarity), and (c) for the lattice nodes and RBC membrane representation

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Fig. 2

The RBC distribution and configuration (shaded patches in (b)), flow field (arrows in (b)), and instantaneous WSS distributions on the top (a) and bottom (c) walls at t = 55×105Δt. The x location has been shifted to the starting point of the flat part of the channel walls at x0 = 300Δx.

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Fig. 3

The temporal variations of cell-wall gap distance (top panels) and WSS (bottom panels) during the simulation period 89-94 × 105Δt on the bottom wall at x = 300 (a), 320 (b), 400 (c), 500 (d), 1000 (e), and 3000 Δx (f). The nominal CFL thickness δ¯ at each location is provided in number and plotted as a dashed line in the top panels; and the mean and SD values for the temporal WSS variation at each location are also shown in the bottom panel as numbers and dashed lines (top: mean + SD; middle: mean; bottom: mean − SD).

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Fig. 4

The distribution profiles of mean WSS τ¯w (a), WSS SD στ (b), and SD/mean ratio (c) along the channel. Mean and SD values calculated on both the top and bottom walls, as well as the average of them, are displayed in (a) and (b) with different colors and line styles, and the SD/mean ratio in (c) is obtained using the average mean and SD curves in (a) and (b) only. The curves are plotted over the entire channel length (x-x0 = 0-3160 Δx) for completeness; however, the right ends of these curves (x-x0 = 3000-3160 Δx) should be excluded for consideration of the exit effect.

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Fig. 5

The distribution profiles of mean WSS τ¯w (a) and WSS SD στ (b) for the five cases considered in this study. Short horizontal bars with corresponding colors and line styles on the left figure edges are plotted to indicate the maximum values at x = x0 = 300 Δx of these curves (also available in Table 2), which will otherwise be undistinguishable. The curves are plotted over the entire channel length (x-x0 = 0-3160 Δx) for completeness; however, the right ends of these curves (x-x0 = 3000-3160 Δx) should be excluded for consideration of the exit effect.

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