Dynamics of solitary blood waves in arteries with prostheses

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.