A constitutive hemorheological model addressing both the deformability and aggregation of red blood cells

Abstract

Red blood cells (RBCs) in physiological conditions are capable of deforming and aggregating. However, both deformation and aggregation are seldom considered together when modeling the rheological behavior of blood. This is particularly important since each mechanism is dominant under specific conditions. To address this void, we herein propose a new model that accounts for the deformability of red blood cells, by modeling them as deformed droplets with a constant volume, and of their aggregation, by properly characterizing the network formed by red blood cells under small shear rates. To derive the model, we employ non-equilibrium thermodynamics that allows us to consistently couple the two mechanisms and guarantees model admissibility with the thermodynamic laws. Relative to our previous model, which addresses the rheological behavior of non-aggregating deformable red blood cells, one additional structural variable, λ, to properly characterize the network formed by RBCs, and another additional parameter, ε, that quantifies the relative importance between the regeneration/buildup and flow-induced breakup of the network, are considered here. The new model predicts a yield shear stress, in accord with experimental data, but also predicts non-vanishing yield normal stresses. Although no rheological measurements of yield normal stresses of blood have been reported in the literature, the recent measurement of yield normal stresses of other yield stress fluids indicates their potential existence in blood as well. We show that the new model is in complete accord with the experimental rheological behavior of normal blood in both steady-state and transient (step-change in shear-rate) simple shear.