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 New-tonian, while rheology of the RBC-rich core is modeled using the Quemada constitutive law. Results: Our model provides a realistic description of experimen-tally 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 incorporat-ing 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. KEY WORDS: blood rheology, hematocrit, shear thinning, plasma layer, apparent viscosity, shear stress Abbreviations used: CFL, cell-free layer; MRI, magnetic reso-nance imaging; NO, nitric oxide; PIV, particle image velocimetry; RBC, red blood cell; RMSE, root mean square error; WSS, wall shear stress