Transport and reaction phenomena in multilayer membranes functioning as bioartificial kidney devices

In this work, a 3D mathematical model of the BAK is developed. The transport and reaction mechanisms associated with the removal of PBUT indoxyl sulfate are considered and various conditions are simulated. The model describes a single hollow fiber membrane and considers different domains for the blood flow, the membrane, the cell monolayer, and the dialysate region. A mathematical description of the relevant transport and/or reaction mechanisms is provided in each domain, and the corresponding differential equations are solved numerically. Since not all the modeling constants are experimentally available, a parametric study is performed for their quantification, including the active transport kinetics of the toxins through the cell monolayer, in comparison to the passive transport rates by diffusion. The parametric study also provides a background for the extraction of usually unknown quantities, including notably the Organic Anion Transporter (OAT) concentrations, with the support of experimental data. Satisfactory reproduction of experimental findings is achieved, and the role of systemic variables that affect significantly the uremic toxin removal is identified.