Theoretical Model of Blood Flow through Hollow Fibres considering Hematocrit-Dependent, Non-Newtonian Blood Properties

Accounting for the non-Newtonian blood viscosity by the Quemada descriptive viscosity equation, we deduced velocity profiles and volumetric capillary flows from the Navier-Stokes-equation. An arbitrary axial and/or radial hematocrit profile can be chosen. The hematocrit dependence of the intrinsic viscosities k0 (H) (characterizing, at least in part, the RBC aggregation) and k infinity (H) (describing orientation/deformation of RBC) was taken into account. Velocity profiles for pressure gradients of 4-4000 Pa/cm show a distinct flattening, if a pronounced axial migration of RBC is assumed. The higher the axial concentration, the higher the flow at the same pressure gradient. Small deviations (less than or equal to 10%) of the capillary number per dialyzer or of the radius of capillaries lead to a strong change of the pressure gradient with the same dialyzer flow. Whereas small hydraulic conductivities do not significantly change this gradient, high conductivities decrease the pressure gradient by about 10%. Impaired blood flow properties (hemoconcentration) result in a slight deviation from the linear axial pressure drop.