Effect of body acceleration on unsteady flow of blood past a time-dependent arterial stenosis

The present investigation deals with the effect of a single cycle of body accelerations on unsteady flow behaviour of blood past a time-dependent arterial stenosis. The artery is modelled mathematically as an anisotropic viscoelastic cylindrical tube containing a viscoelastic fluid representing the flowing blood. The time-variant geometry of the stenosis has been accounted for in order to improve resemblance to the in vivo situation. The unsteady flow mechanism in the stenosed artery subject to a pulsatile pressure gradient arising from the normal functioning of the heart and the body acceleration is presented mathematically. The effects of the surrounding connective tissues on the motion of the arterial wall have been incorporated. The equations governing the motion of the system are sought in the Laplace transform space and their relevant solutions associated with suitable boundary conditions are obtained numerically in the transformed domain using an appropriate finite difference technique. Laplace inversion is also carried out by employing numerical procedures. By incorporating the short-time-range approximations, an extensive 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 pulsatile pressure gradient and time-variant stenosis on the flow characteristics of blood that can be used to validate the applicability of the mathematical model.