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Abstract
In this study, the derivation of mathematical model for the wave modulation through an incompressible viscous fluid contained in a prestressed thin stenosed elastic tube is presented. The artery is assumed to be incompressible, prestressed thin walled elastic tube with a symmetrical stenosis, whereas the blood is considered to be incompressible and Newtonian fluid. By utilizing the nonlinear equations of tube and fluid, the weakly nonlinear wave modulation in such a medium is examined. Employing the reductive perturbation method and considering the long-wave approximation, we showed that the third-order term in the perturbation expansion is governed by the dissipative nonlinear Schrodinger equation with variable coefficient. Our results shown that this type of equation admits a downward bell-shape wave propagates to the right as time increases with decreasing wave amplitude.
Highlights
Cholesterol is a sterol which serves principally as a constituent of blood plasma
Employing the reductive perturbation method and considering the long-wave approximation, we showed that the third-order term in the perturbation expansion is governed by the dissipative nonlinear Schrodinger equation with variable coefficient
Our results shown that this type of equation admits a downward bell-shape wave propagates to the right as time increases with decreasing wave amplitude
Summary
Cholesterol is a sterol which serves principally as a constituent of blood plasma. High concentration of cholesterol in the blood will build up plaque on the inner walls of arteries. The decomposition of plaque causes the arteries become less flexible and this leads to the phenomenon of narrowing of the arteries which commonly referred as stenosis. The stenosis will further cause the artherosclerosis which is hardening of the arteries. The artherosclerosis leads the arteries lose their elastic properties and the volume of blood carried through the arteries is reduced. Motivated with the stenosis in the artery, the study of wave propagation in a stenosed artery has been investigated by Kim (2006). Tay et al (2007) and Gaik and Demiray (2008) Motivated with the stenosis in the artery, the study of wave propagation in a stenosed artery has been investigated by Kim (2006). Tay et al (2007) and Gaik and Demiray (2008)
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