Computational flow modeling in hollow-fiber dialyzers

A three-dimensional finite volume model of the blood-dialysate interface over the complete length of the dialyzer was developed. Different equations govern dialyzer flow and pressure distribution (Navier-Stokes) and radial transport (Darcy). Blood was modeled as a non-Newtonian fluid with a viscosity varying in radial and axial direction determined by the local hematocrit, the diameter of the capillaries, and the local shear rate. The dialysate flow was assumed to be an incompressible, isothermal laminar Newtonian flow with a constant viscosity. The permeability characteristics of the membrane were calculated from laboratory tests for forward and backfiltration. The oncotic pressure induced by the plasma proteins was implemented as well as the reduction of the overall permeability caused by the adhesion of proteins to the membrane. From the calculated pressure distribution, the impact of flow, hematocrit, and capillary dimensions on the presence and localization of backfiltration can be investigated.