Two-layered blood flow analysis through progressive bell-shaped arterial stenosis

Abstract

Stenosis is the unwanted deposition in the artery that reduces blood flow, and it is the major cause of cardiovascular disease. As time progresses, a bell-shaped stenosis becomes more severe, resulting in increased arterial narrowing and enhanced flow obstruction. In this work, a progressive, time-dependent bell-shaped stenosis is modeled to investigate its hemodynamic effects using a two-layer blood flow framework. The bell-shaped stenosis exhibits a sharp head, which causes a significant obstruction to blood flow even in its early stage. The geometry of the bell-shaped stenosis, which gradually narrows the artery, is used in the Navier–Stokes equations and solved separately in each layer by taking suitable boundary conditions because of their distinct rheological properties. The core layer is modeled as a non-Newtonian fluid, while the peripheral layer is treated as Newtonian, allowing for a comparison of flow behavior between the two regions. Analytical solutions of key flow characteristics, including velocity profile, volumetric flow rate, pressure drop and its ratio, and shear stress and its ratio, are calculated in terms of time, viscosity, and consistency index. The findings indicate that an increase in time, viscosity, and consistency index decreases velocity, volumetric flow rate, and shear stress ratios, whereas pressure drop and its ratio increase markedly. Among the governing parameters, viscosity exerts a more dominant influence than temporal variations on velocity profile, volumetric flow rate, and pressure drop, while time primarily modulates the evolution of these effects. Furthermore, due to its non-Newtonian nature, the core layer exhibits stronger sensitivity to rheological parameters than the Newtonian peripheral layer. Incorporating the temporal term in bell-shaped arterial geometry to get more accurate results and understand vascular conditions in such morphological structures using two-layered blood rheology is our novel work. This model may help with the interpretation of the imaging results, treatment planning and surgical intervention, and the early diagnosis of cardiovascular disease.