An energy-rate based blood viscosity model incorporating aggregate network dynamics

Existing time-dependent blood viscosity models that involve aggregation dynamics are mainly based on structural variables and/or viscoelastic models in order to describe the bulk mechanical properties of the fluid, but the implications of important characteristics of blood microstructure, such as the time- and flow-dependent characteristics of the red blood cell network developed due to aggregation at low shear rates, have not been thoroughly investigated. In this paper a time-dependent blood viscosity model is developed based on an energy-rate model previously proposed (Skalak et al., Biophys. J. 35 (1977), 771-781), which describes the total work needed to overcome the various forces developed between aggregated cells, including the adhesive, elastic and dissipative forces. Novel formulations of the forces acting on the fluid are developed and implemented in a volume-averaged version of the energy-rate model. The calculation of the viscosity is based on the relationship between the rate of energy changes and shear stress per unit volume of the fluid. The results show that network characteristics may significantly influence the viscosity blood at low shear rates and exhibit good agreement with experimental observations.