A one-dimensional model of viscous blood flow in an elastic vessel

Abstract

In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessel's wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment of a blood vessel demonstrate that the model can produce realistic flow fields that may appear under normal conditions in healthy blood vessels; as well as flow that could appear during abnormal conditions. In particular we show that weakening of the elastic properties of the wall may provoke a reverse blood flow in the vessel.

Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls

“…If the elements Q 21 and Q 31 vanish then the function u is a polynomial of second degree in z: u(s, z) = (0, α, β) T z 2 + u (1) (s)z + u (2) (s), where α and β are constants.…”

“…Now system (97) takes the form 1 1 = 0, where b 1 and b 2 are constants. Therefore Next let us look for solution to (95) in the form…”

“…A general two-dimensional model describing the elastic behaviour of the wall of a flexible vessel has been presented in the case of a straight vessel in [9,11], in the case of a curved vessel in [7] and for numerical results see [1,2]. The wall has a laminate structure consisting of several anisotropic elastic layers of varying thickness and is assumed to be much thinner than the radius of the channel which itself is allowed to vary.…”

Modeling of fluid flow in a flexible vessel with elastic walls

“…A general two-dimensional model describing the elastic behaviour of the wall of a flexible vessel has been presented in the case of a straight vessel in [6], [8], in the case of a curved vessel in [1] and for numerical results see [3], [4]. The wall has a laminate structure consisting of several anisotropic elastic layers of varying thickness and is assumed to be much thinner than the radius of the channel which itself is allowed to vary.…”

A Hypothetical Vascular Stent with Locally Enlarged Segment and the Hemodynamic Evaluation

“…Given consideration to that the energy difference caused by the changes of elevation in blood flow is minor and can be neglected [17,18], it is obvious to draw the conclusion that the decrease in velocity of blood contributes to the rise of blood supply pressure and may compensate for the inadequate blood supply near branch lesions. e decrease of blood velocity may result from the enlargement of cross-segment area of vessel when the flow rate remains the same or appears in the flow stagnant zone [19] of disturbed laminar flow where Reynold's number exceeds 200 [20]. Our research is based on the theory that aims at lifting the blood supply pressure by designing enlarged segment in the vascular stent at side branches.…”