An Overview of Some Mathematical Models of Blood Rheology

Abstract

Experimental investigations over many years reveal that blood flow exhib-its non-Newtonian characteristics such as shear-thinning, viscoelasticity and thixotropic behaviour. The complex rheology of blood is influenced by nu-merous factors including plasma viscosity, rate of shear, hematocrit, level of erythrocytes aggregation and deformability. Hemodynamic analysis of blood flow in vascular beds and prosthetic devices requires the rheological beha-viour of blood to be characterized through appropriate constitutive equations relating the stress to deformation and rate of deformation. The objective of this paper is to present a short overview of some macro-scopic constitutive models that can mathematically characterize the rheology of blood and describe its known phenomenological properties. Some numer-ical simulations obtained in geometrically reconstructed real vessels will be also presented to illustrate the hemodynamic behaviour using Newtonian and non-Newtonian inelastic models under a given set of physiological flow con-ditions.