Blood flow through an artery with mild stenosis: A two-layered model, different shapes of stenoses and slip velocity at the wall

A mathematical model for blood flow through stenosed arteries with axially variable peripheral layer thickness and variable slip at the wall has been considered. The model consists of a core surrounded by a peripheral layer. It is assumed that the fluids of both the regions (core and peripheral) are Newtonian having different viscosities. For such models, in literature, the peripheral layer thickness and slip are assumed a priori based on experimental observations. In the present analysis, analytic expressions for the thickness of the peripheral layer, slip and core viscosity have been obtained in terms of measurable quantities (flow rate (Q), centerline velocity (U), pressure gradient (-dp/dz) and plasma viscosity (μp)). Using the experimental values of Q, U, (-dp/dz) and μp the values of the peripheral layer thickness, red cell concentration in the core, core viscosity and slip velocity at the wall have been determined. The theoretically obtained peripheral layer thickness has been compared with its experimental value. It is found that the agreement between the two is very good (error <1.0%). It is important to mention that in the present analysis, core viscosity has been obtained by two methods. First by calculating from the formula obtained in the present analysis and the second by calculating the red cell concentration in the core and then using concentration versus relative viscosity curve. A comparison of these two values of the core viscosity shows a reasonably good agreement between them (difference up to 14%). The analysis developed here could be used to determine the more accurate values of the apparent viscosity of blood, agreeability, rigidity and deformability of red cells. This information of blood could be useful in the development of new diagnosis tools for many diseases. © 2007 Asian Network for Scientific Information.