On Some Mathematical Models in Hemorheology

Abstract

ABSTRACTBlood viscosity is one of the most important factors determining the blood flow. Blood under flow exhibits non-Newtonian characteristics such as shear-thinning, viscoelastic and thixotropic behaviour. Modelling and analysis of hemorheological data of the dependences of shear stress and blood viscosity measured as a function of the shear rate with constitutive equations, are presented in this study. An overview of some mathematical models describing the rheological behaviour of blood is done. Different constitutive equations and models are used for the description of experimental data obtained by us with the viscometer Low Shear 30 (LS 30) and with Low Shear 40 (LS 40) Contraves, reported in the literature, in a wide range of shear rates. On the basis of a mathematical analysis of the experimental results the rheological properties of blood samples from patients with cerebrovascular, hematological diseases and drug abusers is done. A quantitative description of rheological properties of blood in terms of the model parameters and hence comparison the results between the studied groups of patients is presented. The models are discussed in terms of their accuracy to fit the experimental data, as well as the physical and physiological sense of their parameters for analysis of hemorheological experiments and data. Our study discusses some hypotheses, models and parameters describing red blood cell deformability and aggregation.