Propagation of pulse solitary waves in fluid filled elastic tube with cosine shaped stenosis

Abstract

Blood flow in stenosed arteries will be transitional or turbulent. The stenosis in the artery may induce turbulence and consequently create significant flow resistance, large pressure drop and disturbed wall shear stress and wall motion patterns. Further, to date research on anatomical risk factors in endovascular treatment has focused only on the degree of stenosis and plaque irregularity but did not investigate the significance of length of stenosis. Keeping that in mind, in the present work, we assume the artery as an incompressible, prestressed, thin-walled elastic tube, with a cosine shaped symmetrical stenosis and the blood as a Newtonian fluid. We analyse the nature of propagation of nonlinear waves in such a medium by invoking a standard reductive perturbation method in a long wave approximation. The fluid dynamical equations are recasted into Korteweg-de Vries equation with variable co-efficient. We numerically simulate the fluid pressure pulse waves in a fluid filled artery with axisymmetric cosine shaped stenosis with varying diameter reductions of 30%, 40%and 50% respectively. Also, we investigate the effect of length of stenosis varying along the axial direction on the evolution of radial displacement, fluid pressure pulse solitary wave profile and the wave speed in the artery. Since, the length of stenosis has been identified as a strong and independent risk factor for peri-procedural stroke or death in endovascular treatment, this study may be helpful in diagnosing the diseased arteries.