We analyze the behavior of blood waves interacting with a prosthesis following the Yomosa nonlinear wave theory extended to include the spatial variation of the arterial radius and wall rigidity. When the prosthesis is short or when its characteristics are close to those of the host artery, the amplitude of the blood solitary wave increases just proximal to the prosthesis and then decreases to a magnitude smaller than the normal value in a healthy vessel. In the presence of an extended prosthesis, we derive the reflection and transmission coefficients at the interfaces, and we thereby obtain the optimal characteristics for an ideal prosthesis. Our results agree qualitatively with known experimental and numerical studies.

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In order to elucidate the dynamical behaviour of nonlinear waves in taperedthin and elastic tubes with localized deformations, we have developed a mathematical model based on equations of inviscid fluid flow in a slowly tapered cone tube. Numerical simulation of the resulting perturbed Kortevegde Vries equation shows that the amplitude of the velocity wave decreases along the tube as the results of the decrease of the radius and the increase of the rigidity; we also find that the velocity of the pulse velocity wave increases. In the localized deformation area, after some fluctuations, the wave suffers important variations consisting firstly (in the case of constriction) by a decrease and then by an increase. The severity and the length of the variation depend respectively on the amplitude and the gradient scale of the localized deformation. Some biological implications are given.

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