QUANTA: Modelling Dialysis

Abstract

We present a theoretical analysis of the physical mechanisms underlying blood filtration through artificial kidneys, also known as dialysis, enhanced by the introduction of pulsation. We formulate a mathematical modelling framework describing chemical transport and fluid flow on the scale of a single fibre, separating the flow of blood from a counter flow of dialysate, a physiologically similar, toxin-free liquid. The wall, or membrane, of each fibre is porous, allowing transport of toxins, but not red blood cells and other physiologically important molecules, across the membrane from the blood to the dialysate. We model the membrane as a thin porous layer, separating the blood from the dialysate, and formulate mathematical models for the transport of toxins across the membrane and the fluid flow within the blood and dialysate. We use our mathematical modelling framework to examine physical mechanisms underlying enhanced toxin transport under pulsation and to inform future modelling efforts.