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TECHNICAL PAPERS: Fluids/Heat/Transport

Pulsatile Blood Flow and Gas Exchange Across a Cylindrical Fiber Array

[+] Author and Article Information
Kit Yan Chan1

Department of Biomedical Engineering, The University of Michigan, Ann Arbor, Michigan 48109

Hideki Fujioka, James B. Grotberg

Department of Biomedical Engineering, The University of Michigan, Ann Arbor, Michigan 48109

Ronald B. Hirshl, Robert H. Bartlett

Department of Surgery, The University of Michigan, Ann Arbor, Michigan 48109

1

Corresponding author.

J Biomech Eng 129(5), 676-687 (Feb 18, 2007) (12 pages) doi:10.1115/1.2768105 History: Received April 18, 2006; Revised February 18, 2007

The pulsatile blood flow and gas transport of oxygen and carbon dioxide through a cylindrical array of microfibers are numerically simulated. Blood is modeled as a homogeneous Casson fluid, and hemoglobin molecules in blood are assumed to be in local equilibrium with oxygen and carbon dioxide. It is shown that flow pulsatility enhances gas transport and the amount of gas exchange is sensitive to the blood flow field across the fibers. The steady Sherwood number dependence on Reynolds number was shown to have a linear relation consistent with experimental findings. For most cases, an enhancement in gas transport is accompanied with an increase in flow resistance. Maximum local shear stress is provided as a possible indicator of thrombosis, and the computed shear stress is shown to be below the threshold value for thrombosis formation for all cases evaluated.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

The implantable artificial lung. (Adapted from www.mc3crop.com, with permission) The device is surgically attached to the native lung (either in series or in parallel) and it is driven by the patient’s heart. Oxygen-rich gas is externally supplied into the device.

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Figure 2

Array geometries

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Figure 3

Unit cells and flow boundary conditions

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Figure 4

Sinusoidal and cardiac pulsatile flow cycle

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Figure 5

Oxygen and carbon dioxide saturation curves

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Figure 6

Gas concentration computational domain and boundary conditions

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Figure 7

Sample computational grid

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Figure 8

Streamlines and viscosity contours. (a) Re=1 and (b) Re=10 (α=0, ε=0.8036). High viscosity regions are found in areas along the symmetry lines and at the front and back ends of the fibers.

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Figure 9

Local shear stress contours. (a) Re=1 and (b) Re=10 (α=0, ε=0.8036). High shear regions are found on the fiber surfaces.

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Figure 10

Steady Sherwood number as a function of Reynolds number. (a) Squared array: ε=0.49734. (b) Squared array: ε=0.8036. (c) Staggered array: ε=0.49734. (d) Staggered array: ε=0.8036 (squares, oxygen data points; triangles, carbon dioxide data points). The steady Sherwood numbers exhibit linear relations with Reynolds number.

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Figure 11

Partial pressures and streamlines at t=π∕2. (a) PO2* distribution, (b) PCO2* distribution, and (c) instantaneous streamlines.

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Figure 12

Partial pressures and streamlines at t=3π∕2. (a) PO2* distribution, (b) PCO2* distribution, and (c) instantaneous streamlines.

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Figure 13

Partial pressures and streamlines at t=π∕2. (a) PO2* distribution, (b) PCO2* distribution, and (c) instantaneous streamlines.

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Figure 14

Partial pressures and streamlines at t=3π∕2. (a) PO2* distribution, (b) PCO2* distribution, and (c) instantaneous streamlines.

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Figure 15

α influence on the Sherwood number time cycle. (a) Oxygen and (b) carbon dioxide (Re=10, ε=0.8036).

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Figure 16

PO2* distribution at t=π∕10 (α=2, Re=10, and ε=0.8036).

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Figure 17

Re influence on the Sherwood number time cycle. (a) Oxygen and (b) carbon dioxide (α=1, ε=0.8036).

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Figure 18

ε influence on the Sherwood number time cycle. (a) Oxygen and (b) carbon dioxide (α=1, Re=10).

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Figure 19

Sherwood number time cycle. (a) Oxygen and (b) carbon dioxide (α=1, Re=10, and ε=0.8036).

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