A study of solitary waves in a tapered aorta by using the theory of solitons

By applying the soliton theory, a method is developed in this paper with an aim to study the flow properties of blood in large blood vessels. The theory takes into account the nonlinear terms of the Navier–Stokes equations as well as the large deformations of the aortic wall. The solutions of the equations of motion are restricted to the propagation of axisymmetric long waves. As for the equations governing the motion of the aorta, the longitudinal motion of the aortic wall is considered negligible. The radial motion is obtained directly from the pressure wave and the material behaviour of the aorta, by considering the motion of an elementary volume of the wall tissues. By using the experimentally measured values of the system parameters, computational work has been carried out to examine the change in radius, rate of change of radius, the dependence of the radius of the aorta on the longitudinal distance and the axial velocity distribution of blood in the aorta within a cardiac cycle. Variation of the stroke volume of the blood pulse is also determined for different taper angles of the aorta.