A nonlinear two-dimensional model of blood flow in an overlapping arterial stenosis subjected to body acceleration

This paper presents a theoretical study on the nonlinear behaviour of blood flow over a single cardiac cycle through an arterial segment having an overlapping stenosis when it is subjected to whole body acceleration. An improved shape of the time-variant stenosis in the realm of the formation of the arterial narrowing caused by atheroma is constructed mathematically in order to update resemblance to the in-vivo situation. The artery has been treated as an elastic (moving wall) cylindrical tube containing a Newtonian fluid representing the flowing blood. The nonlinear terms appearing in the Navier-Stokes equations governing blood flow are accounted for. The unsteady flow mechanism in the stenosed artery subject to pulsatile pressure gradient arising from the normal functioning of the heart and the body acceleration is presented mathematically. The present analytical treatment bears the potential to calculate the axial and the radial velocity profiles with low computational complexity by exploiting the appropriate boundary conditions. A thorough quantitative analysis is performed through numerical computations of the desired quantities. Results are presented graphically at the end of the paper. They yield an estimate of the effects of the body acceleration, the pressure gradient, the vessel wall deformability and the severity of the stenosis on the unsteady flow characteristics of blood. Some important conclusions are drawn that sufficiently substantiate the applicability of the present model.