Numerical Modeling of a Stenosed Artery Using Mathematical Model of Variable Shape

The intention of the present work is to carry out a systematic analysis of flow behavior in a twodimensional tube (modeled as artery) with a locally variable shaped constrictions. The simulated artery, containing a viscous incompressible fluid representing the flowing blood, is treated to be complaint as well as rigid tube. The shape of the stenosis in the arterial lumen is chosen to be symmetric as well as asymmetric about the middle cross section perpendicular to the axis of the tube in order to improve resemblance to the in-vivo situation. The constricted tube is transformed into a straight tube and the resulting governing equations are solved by a numerical method with Reynolds number and ‘n’, a number giving the shape of the constriction as parameters. The influences of these parameters on the haemodynamic factors like wall shear stress, pressure and velocity have been analyzed. The present findings demonstrate that the flow resistance decreases as the shape of a smooth stenosis changes and maximum resistance is attained in case of a symmetric stenosis. But the length of separation increases in case of asymmetric constrictions and the oscillation in the shear layer appears earlier in case of asymmetric constriction than that in the case of symmetric constriction. Maximum resistance is attained in case of rigid stenosed tube rather than the flexible one.