Optimization of dialyzer design to maximize solute removal with a two-dimensional transport model

Abstract A systematic analysis of the effect of all the dialyzer-related factors on solute clearance has not been reported in the literature, making it difficult to optimize dialyzer design to maximize solute removal from patient's blood. In this paper, a two-dimensional axisymmetric mathematical model of momentum and mass transport in dialyzers is proposed to investigate the effect of the most relevant geometrical and operational dimensionless groups on solute clearance. Navier-Stokes and Darcy-Brinkman equations are used to describe steady-state momentum transport in blood and dialysate compartments, and across the membrane, respectively. Transport of low and middle molecular weight solutes from the blood through the membrane into the dialysate compartment is described with convection-diffusion equations. The effect of non-Newtonian blood behavior and concentration polarization is also taken into account. The complete set of dimensionless groups determining dialyzer efficiency is obtained from dimensional analysis of model equations. Their effect on solute clearances is investigated by solving model equations for values of geometrical and operational dimensionless groups typical in clinical practice. The most relevant dimensionless groups determining dialyzer efficiency were identified and a novel design approach to optimize dialyzers in order to maximize solute clearances in a cost-effective way is proposed based on their values.