Oscillatory Blood Flow in Elastic Artery with Stenosis

We investigate oscillatory blood flow in an elastic artery and in the presence of stenosis, whose form is given analytically. The stenosis is a condition where an artery wall thickens as a result of fatty materials such as cholesterol. We consider the case of very low pulse frequency that can be the case for patients whose hearts beat too slowly, but with arbitrary value of the ratio γ of the artery radius to the axial extent of the stenosis. The arbitrary value of such ratio makes the present problem more applicable to more general applications for arterial blood flow systems. The blood flow is assumed to be a suspension of red cells in plasma, and we make use of the variable fluid viscosity modeling by counting the red cells in the plasma. The coupled differential equations for the blood flow velocity and blood pressure are simplified first subjected to reasonable modeling and approximations and then solved mostly theoretically. In this paper, blood speed, blood pressure force and the wall shear stress are computed for different values of γ, axial variable, time variable and the hematocrit due to percentage level of the red cells in the plasma. We find, in particular, that the magnitudes of the oscillations of the blood pressure force and the wall shear stress increases with the hematocrit effect, while such magnitude for the blood speed decreases with increasing the hematocrit effect. Key-Words: arterial flow, blood flow, stenosis, oscillatory flow, low frequency, blood cells, blood plasma