A Two-Zone Shear-Induced Red Blood Cell Migration Model for Blood Flow in Microvessels

Rachid Chebbi

doi:10.3389/fphy.2019.00206

Abstract

The Fahraeus and Fahraeus-Lindqvist effects are both associated with the concentration of red blood cells (RBCs) in the core region of microvessels. The annular region is a cell-free layer. Blood flow dynamics and both effects are related to the hematocrit level profile. The aim is to propose a model for blood flow in microvessels that is not compute intensive like many other models such as those using finite element methods. Modeling blood flow requires solving for both the hematocrit level and velocity profiles as blood viscosity depends on the hematocrit level. The two-zone shear-induced model for blood flow is adopted while including an annular cell-free layer, as in the marginal zone theory and in consistency with experimental observations. In the core region, the hematocrit level is not considered to be uniform, and the concentration and viscous fluxes are equal in magnitude and opposite in directions in the fully developed velocity and concentration profiles case. The momentum and hematocrit balance equations are solved. Both analytical and numerical solutions for the velocity and hematocrit level profiles are determined. The numerical results are found to exactly match the analytical solutions, and to be in very good agreement with published experimental data for the cell-free layer thickness, the velocity profile, and the hematocrit ratio.

Highlights

Resistance to blood flow mainly occurs in the microvascular system [1]
The Fåhraeus [2] and FåhraeusLindqvist effects [3, 4] are both associated with the concentration of red blood cells (RBCs) in the core region of microvessels, leading to lower tube hematocrit compared to the discharge hematocrit level, and to lower viscosity for vessel radius in the approximate range of 15–500 μm [5]
The marginal zone model introduced by Haynes [10], in which the annular zone is a cell-free layer, is extended in Fournier [5], Sharan and Popel [11], Sriram et al [12], and Chebbi [13] with blood flow in vessel bifurcations addressed in Chebbi [13]

Summary

Introduction

Resistance to blood flow mainly occurs in the microvascular system [1]. For tubes of small diameter, RBCs concentrate in the core region, leaving a cell-free layer near the capillary wall. The marginal zone model introduced by Haynes [10], in which the annular zone is a cell-free layer (with all the RBCs concentrated in the core region), is extended in Fournier [5], Sharan and Popel [11], Sriram et al [12], and Chebbi [13] with blood flow in vessel bifurcations addressed in Chebbi [13].

Results

Conclusion