Modeling Hemodialysis with Albumin Retention

We develop a new mathematical model for cross filtration in a dialyzer, taking into account the membrane fouling caused by progressive protein deposition. We focus on a single fiber and, starting from the basic laws of fluid dynamics and exploiting the smallness of the fiber aspect ratio, we obtain significant simplifications of the flow equations. We end up with a hyperbolic system that describes the temporal evolution (specifically the decrease) of the filtering efficiency caused by the albumin deposit. Such an effect is then described quantitatively by means of numerical simulations.