Dynamic response of wall shear stress on the stenosed artery

Abstract

The present study deals with an appropriate mathematical model of an artery in the presence of constriction in which the generated wall shear stress due to blood flow is analysed. The geometry of the stenosed arterial segment in the diseased state, causing malfunction of the cardiovascular system, is formed mathematically. The flowing blood contained in the stenosed artery is treated as non-Newtonian and the flow is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow-field can be obtained primarily following the radial coordinate transformation, using the appropriate boundary conditions and finally adopting a suitable finite difference scheme numerically. The influences of flow unsteadiness, the arterial wall distensibility and the presence of stenosis on the flow-field and the wall shear stresses are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby to validate the applicability of the present theoretical model.

Keywords:

• non-Newtonian fluid
• wall shear stress
• Navier–Stokes equations
• atherosclerosis
• hemodynamics
• distensibility

Acknowledgements

The authors express grateful thanks to the reviewers for their constructive comments and suggestions. The present work is part of the Special Assistance Programme [Grant No. F.510/8/DRS/ 2004(SAP-I)] sponsored by the University Grants Commission (UGC), New Delhi, India.