Abstract
Flow-induced damage to red blood cells has been an issue of considerable importance since the introduction of the first cardiovascular devices. Early blood damage prediction models were based on measurements of damage by shear stress only. Subsequently, these models were extrapolated to include other components of the fluid stress tensor. However, the expanded models were not validated by measurements of damage in response to the added types of stress. Recent investigations have proposed that extensional stress might be more damaging to red cells than shear stress. In this study, experiments were conducted to compare human red cell deformation under laminar extensional stress versus laminar shear stress. It was found that the deformation caused by shear stress is matched by that produced by an extensional stress that is approximately 34 times smaller. Assuming that blood damage scales directly with cell deformation, this result indicates that mechanistic blood damage prediction models should weigh extensional stress more than shear stress.
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Notes
The stress used here is the axial extensional stress \(\sigma_{zz} ,\) whereas Lee et al. (2009) applied the Trouton extensional viscosity (Trouton 1906), which is defined as the ratio of the principal stress difference \(\sigma_{1} - \sigma_{3}\) to the extension rate for uniaxial extension, where the subscripts correspond to the principal axes. By continuity for an incompressible fluid, the extension rates along the second and third axes are -1/2 times the extension rate along the first axis. Therefore, for a Newtonian fluid, the Trouton extensional viscosity is 3 times the shear viscosity. For planar extension, such as in the hyperbolic contractions used in this work and that of Lee et al. (2009), there are two extensional viscosities. One, the planar extensional viscosity, is the ratio of \(\sigma_{1} - \sigma_{3}\) to the extension rate, which is 4 times the shear viscosity. The second extensional viscosity, or cross-viscosity, is the ratio of \(\sigma_{2} - \sigma_{3}\) to the extension rate, where axis 2 is that along which there is zero deformation. The cross-viscosity is 2 times the shear viscosity.
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Faghih, M.M., Sharp, M.K. Deformation of human red blood cells in extensional flow through a hyperbolic contraction. Biomech Model Mechanobiol 19, 251–261 (2020). https://doi.org/10.1007/s10237-019-01208-3
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DOI: https://doi.org/10.1007/s10237-019-01208-3