Shear stress in the microvasculature: influence of red blood cell morphology and endothelial wall undulation
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The effect of red blood cells and the undulation of the endothelium on the shear stress in the microvasculature is studied numerically using the lattice Boltzmann–immersed boundary method. The results demonstrate a significant effect of both the undulation of the endothelium and red blood cells on wall shear stress. Our results also reveal that morphological alterations of red blood cells, as occur in certain pathologies, can significantly affect the values of wall shear stress. The resulting fluctuations in wall shear stress greatly exceed the nominal values, emphasizing the importance of the particulate nature of blood as well as a more realistic description of vessel wall geometry in the study of hemodynamic forces. We find that within the channel widths investigated, which correspond to those found in the microvasculature, the inverse minimum distance normalized to the channel width between the red blood cell and the wall is predictive of the maximum wall shear stress observed in straight channels with a flowing red blood cell. We find that the maximum wall shear stress varies several factors more over a range of capillary numbers (dimensionless number relating strength of flow to membrane elasticity) and reduced areas (measure of deflation of the red blood cell) than the minimum wall shear stress. We see that waviness reduces variation in minimum and maximum shear stresses among different capillary and reduced areas.
KeywordsHemodynamic forces Shear stress Endothelium Red blood cells
Brenna Hogan is supported by a doctoral fellowship from Ecole Polytechnique. This research is funded in part by a permanent endowment in Cardiovascular Cellular Engineering from the AXA Research Fund, the Centre National d’Etudes Spatiales (CNES), and the French–German university program (Living Fluids, Grant CFDA-Q1-14).
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