Non‐Newtonian Flow of Blood in Arterioles: Consequences for Wall Shear Stress Measurements

OBJECTIVE: Our primary goal is to investigate the effects of non-Newtonian blood properties on wall shear stress in microvessels. The secondary goal is to derive a correction factor for the Poiseuille-law-based indirect measurements of wall shear stress. METHODS: The flow is assumed to exhibit two distinct, immiscible and homogeneous fluid layers: an inner region densely packed with RBCs, and an outer cell-free layer whose thickness depends on discharge hematocrit. The cell-free layer is assumed to be Newtonian, while rheology of the RBC-rich core is modeled using the Quemada constitutive law. RESULTS: Our model provides a realistic description of experimentally observed blood velocity profiles, tube hematocrit, core hematocrit, and apparent viscosity over a wide range of vessel radii and discharge hematocrits. CONCLUSIONS: Our analysis reveals the importance of incorporating this complex blood rheology into estimates of WSS in microvessels. The latter is accomplished by specifying a correction factor, which accounts for the deviation of blood flow from the Poiseuille law.