Dynamics of solitary blood waves in arteries with prostheses

Abstract

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.

Disturbance and repair of solitary waves in blood vessels with aneurysm

“…Therefore conditions (7a) and (7b) mean that we are under weak nonlinearity and weak dispersion. Numerous contributions in this area use the basic set of equations as proposed by Yomosa [17] and can be classified into two main categories: Firstly the one that applies some strong assumptions to obtain a simplified equation such as KdV equation [5,6,8]. However, those resulting equations are not able to cover some main aspects such as reflection.…”

“…The study of solitary waves propagation in elastic cylindrical tube filled with fluid has been a great exploration during this last decade because of its direct applications to the dynamics of blood waves in arteries [1][2][3][4][5][6][7][8]. In fact, the increase in the number of death owing to vascular diseases has brought many researchers to pay attention in this field.…”

The design of a reflectionless arterial prosthesis

“…Many authors [4,7,8] showed that the stationary radius and the variation of elasticity along the wall will obey the relations…”

“…σ ti is the approximated exponential function for the stress-strain relationship given in [15,16]. This approximated relation is widely known as [3,4,6,7] …”

“…The nonlinear studies that came after brought out the importance of the fluid convective term and particularly took into account the dynamical properties of the tube wall where the nonlinear stress-strain relationship is considered [3][4][5][6]. Most of the works that followed contributed to improve the modeling, in a more realistic way, of elastic tubes [7][8][9] and took into account viscosity, tapering aspect of the tubes [5,10], pathological cases of vessels and prostheses [11].…”