Hemodynamics in stenotic vessels of small diameter under steady state conditions: Effect of viscoelasticity and migration of red blood cells

Abstract

Background: In microcirculation, the non-Newtonian behavior of blood and the complexity of the microvessel network are responsible for the high flow resistance and the large reduction of the blood pressure. Red blood cell aggregation along with inward radial migration are two significant mechanisms determining the former. Yet, their impact on hemodynamics in non-straight vessels is not well understood.

Objective: In this study, the steady state blood flow in stenotic rigid vessels is examined, employing a sophisticated non-homogeneous constitutive law. The effect of red blood cells migration on the hydrodynamics is quantified and the constitutive model's accuracy is evaluated.

Methods: A numerical algorithm based on the two-dimensional mixed finite element method and the EVSS/SUPG technique for a stable discretization of the mass and momentum conservation equations in addition to the constitutive model is employed.

Results: The numerical simulations show that a cell-depleted layer develops along the vessel wall with an almost constant thickness for slow flow conditions. This causes the reduction of the drag force and the increase of the pressure gradient as the constriction ratio decreases.

Conclusions: Viscoelastic effects in blood flow were found to be responsible for steeper decreases of tube and discharge hematocrits as decreasing function of constriction ratio.

Keywords: Fahraeus–Lindqvist effect; RBC migration; blood viscoelasticity; cell-depleted layer; shear-induced migration; stenotic microvessels.