Mathematical modelling of blood flow through an overlapping arterial stenosis

Of concern in the paper is a theoretical study of blood flow in an arterial segment in the presence of a time-dependent overlapping stenosis using an appropriate mathematical model. A remarkably new shape of the stenosis in the realm of the formation of the arterial narrowing caused by atheroma is constructed mathematically. The artery is simulated as an elastic (moving wall) cylindrical tube containing a viscoelastic fluid representing blood. The unsteady flow mechanism of the present investigation is subjected to a pulsatile pressure gradient arising from the normal functioning of the heart. The equations governing the motion of the system are sought in the Laplace transform space and their relevant solutions supplemented by the suitable boundary conditions are obtained numerically in the transformed domain through the use of an appropriate finite difference technique. Laplace inversion is also carried out by employing numerical techniques. A thorough quantitative analysis is performed at the end of the paper for the flow velocity, the flux, the resistive impedances, and the wall shear stresses together with their variations with the time, the pressure gradient, and the severity of the stenosis in order to illustrate the applicability of the present mathematical model under consideration.