  Mathematical modeling is an important theoretical tool which provides
researchers with quantification of the permeability of dialyzing systems in
renal replacement therapy. In the paper we provide a short review of the most
successful theoretical approaches and refer to the corresponding experimental
methods studying these phenomena in both biological and synthetic filters in
dialysis. Two levels of modeling of fluid and solute transport are considered
in the review: thermodynamic and kinetic modeling of hemodialysis and
peritoneal dialysis. A brief account for hindered diffusion across cake layers
formed due to membrane filters fouling is given, too.
