Impact of geometrical fiber dimensions on dialyzer efficiency

Abstract

While dialyzer manufacturers only provide information about their products as a black box, this study aimed at optimizing dialyzer geometry by looking in detail at transport processes and fluid properties inside the dialyzer using numerical modeling. A three‐dimensional computer model of a single hollow fiber with its surrounding membrane and dialysate compartment was developed. Different equations govern blood and dialysate flow (Navier‐Stokes), radial filtration flow (Darcy), and solute transport (convection‐diffusion). Blood was modeled as a non‐ Newtonian fluid with a viscosity varying in radial and axial direction because of the influence of local hematocrit, diameter of the capillaries, and local shear rate. Dialysate flow was assumed as an incompressible, laminar Newtonian flow with a constant viscosity. The permeability characteristics of the asymmetrical polysulphone membrane were calculated from laboratory tests for forward and backfiltration. The influence of the oncotic pressure induced by the plasma proteins was implemented as well as the reduction of the overall permeability caused by the adhesion of a protein layer on the membrane. Urea (MW60) was used as a marker to simulate small molecule removal, while middle molecule transport was modeled using vitamin B12 (MW1355) and inulin (MW5200). The corresponding diffusion coefficients were determined by counting for the fluid and membrane characteristics. Fiber diameter and length were changed in a wide range for evaluation of solute removal efficiency. The presented model allowed us to investigate the impact of flow, hematocrit, and capillary dimensions on the presence and localization of backfiltration. Furthermore, mass transfer was found enhanced for increased fiber lengths and/or smaller diameters, most pronounced for the middle molecules compared to urea.