A multi-domain shear-stress dependent diffusive model of cell transport-aided dialysis: analysis and simulation

Kidney dialysis is the most widespread treatment method for end-stage renal disease, a debilitating health condition common in industrialized societies. While ubiquitous, kidney dialysis suffers from an inability to remove larger toxins, resulting in a gradual buildup of these toxins in dialysis patients, ultimately leading to further health complications. To improve dialysis, hollow fibers incorporating a cell-monolayer with cultured kidney cells have been proposed; however, the design of such a fiber is nontrivial. In particular, the effects of fluid wall-shear stress have an important influence on the ability of the cell layer to transport toxins. In the present work, we introduce a model for cell-transport aided dialysis, incorporating the effects of the shear stress. We analyze the model mathematically and establish its well-posedness. We then present a series of numerical results, which suggest that a hollow-fiber design with a wavy profile may increase the efficiency of the dialysis treatment. We investigate numerically the shape of the wavy channel to maximize the toxin clearance. These results demonstrate the potential for the use of computational models in the study and advancement of renal therapies.