Modeling indoxyl sulfate transport in a bioartificial kidney: Two-step binding kinetics or lumped parameters model for uremic toxin clearance?

Toxin removal by the kidney is deficient in a patient suffering from end-stage kidney disease (ESKD), and current dialysis therapies are insufficient in subsidizing this loss. A bioartificial kidney (BAK) aspires to offer ESKD patients a more effective alternative to dialysis. Mathematical models are necessary to support further developments and improve designs for the BAK before clinical trials. The BAK differentiates itself from dialysis by incorporating a living proximal tubule cell monolayer to account for the active transport of protein-bound uremic toxins, namely indoxyl sulfate (IS) in this study. Optimizing such a device is far from trivial due to the non-intuitive spatiotemporal dynamics of the IS removal process. This study used mathematical models to compare two types of active transport kinetics. i.e., two-step binding and lumped parameter. The modeling results indicated that the transporter density is the most influential parameter for the IS clearance. Moreover, a uniform distribution of transporters increases the IS clearance, highlighting the need for a high-quality, functional proximal tubule monolayer in the BAK. In summary, this study contributed to an improved understanding of IS transport in the BAK, which can be used along with laboratory experiments to develop promising renal replacement therapies in the future.