On Low Frequency Oscillatory Elastic Arterial Blood Flow with Stenosis

Abstract

We consider the problem of oscillatory blood flow in an elastic artery with an overlapping stenosis, where the pulse frequency is considered too low that can be the case for patients whose hearts beat too slowly. The blood flow in the elastic artery is assumed to be a suspension of red cells in plasma, and we make use of the variable fluid viscosity modelling by taking into account the amount of red cells in the blood flow system. Equations for the blood flow variables and the elastic wall displacements are solved subjected to reasonable modeling and approximation. We determine, in particular, blood pressure force, blood speed, wall shear stress, flow resistance and both axial and radial displacements of the elastic wall versus spatial and time variables and for different values of the parameters such as those representing hematocrit, stenosis extent, wall stiffness, Young modulus, Poisson ratio, and viscous and elastic constraints of the elastic wall for different tethering cases. The mutual effects of the blood pressure and flow quantities on the elastic wall displacements and vice versa are determined.