Analysis of physiological pulsating flow of Carreau fluid in a curved cerebral artery

The study of blood flow in curved arteries aims to understand how hemodynamic behavior is affected by geometric factors, which is crucial for revealing the formation and progression of vascular diseases. Currently, most studies on blood flow in curved vessels have utilized computational fluid dynamics software. Numerical calculations have typically concentrated on the steady flow of Newtonian fluid in curved vessels with circular cross sections, while non-Newtonian fluid flow has predominantly been calculated in curved pipes with rectangular cross sections. In this paper, the governing equation of Carreau fluid flow in a curved cerebral artery with constant curvature is established using a curvilinear coordinate system, with the flow driven by a physiological pulsatile pressure gradient. Deriving support from finite difference method, numerical solutions are acquired, whose convergence and validity are verified. It is concluded that time-averaged wall shear stress peaks at the inner side of the artery, resulting in the risk of atherosclerosis, while relative residence time peaks at the outer side, causing the likelihood of cerebral infarction there. While an increase in δ amplifies the amplitude of both, it has barely any effect on their values at θ = π/2 and θ = 3π/2. Time-averaged Dean number is first defined to evaluate the development of secondary flow in curved arteries over a cardiac cycle. Near the wall, it peaks at the inner side of the vessel and escalates markedly with larger δ. This study can provide an effective reference for the early prevention and diagnosis of cerebral artery infarction.