Previous mathematical models of hemofilter solute transport have usually employed lumped compartmental representations and uniform membrane processes, and have required a number of assumptions for analytical efficiency. These models often do not address regional variations in membrane transport, convection-diffusion interaction, and region-dependent processes such as hack-filtration. These influences are of particular importance in therapies such as high-volume hemofiltration.
In order to overcome these limitations, we developed a finite element model of hollow fiber membrane transport that incorporates both momentum and mass transport. The geometry is based on the specifications of the AN69S hollow fiber hemofilter (Gambro), and modeled as a 2-D axisymmetric region with distributed blood, membrane and dialysis phases. Navier-Stokes equations were used for momentum transport in blood and dialysis phases, Brinkman equations for porous flow for membrane momentum transport, and the convection-diffusion equation for mass transport in all phases. Anisotropic solute diffusivity and Brinkman permeability coefficients were used to simulate membrane channel transport. Boundary conditions were established for pressure, velocity and concentration at membrane boundaries. The model was solved with FEMLAB (Comsol, Inc.).
The current model supports transport of small solutes in aqueous medium. Model parameters can be adjusted to simulate various hemofilter operating conditions. Model performance parallels that of experimental data for comparable hemofilters.