Dynamic response of arterial blood flow in the presence of multi-stenoses

Abstract

The present paper concerns the rheological study of the effects of multiple stenoses on the flow-behaviour of blood in a stenosed arterial segment through the use of a suitable mathematical model. The artery is modelled as an anisotropic viscoelastic cylindrical tube containing a non-Newtonian viscous incompressible fluid representing blood. The arterial wall is treated to be composed of two different layers, i.e., the media and the adventitia, while the blood flow is assumed to be characterised by the Herschel-Bulkley model. A suitable generalised geometry of multiple stenoses present in the arterial segment under consideration has been accounted for. Particular attention has been paid to the effects of the connective tissues surrounding the arterial wall in order to have the response quite closer to the actual physiological situation. The equations governing the motion of the system are sought in the Laplace transform space as an initial step and then their relevant solutions are obtained in the transformed domain through the use of an appropriate finite difference technique. Finally, Laplace inversion is carried out by employing numerical techniques. A thorough quantitative analysis has been made through numerical computations of the desired variables whose results are exhibited graphically at the end of the paper as a measure to validate the applicability of such a realistic model.