Mathematical modelling of hollow-fiber haemodialysis modules

Abstract

This chapter provides an overview of the principles and modelling of membrane-based modules for haemodialysis, the most common renal replacement therapy. Following an introduction on the structure, function and diseases of the kidney, the technological evolution of membranes for blood purification is outlined and the main transport mechanisms involved are described, making a distinction between pure haemodialysis, haemodiafiltration and haemofiltration. The main performance figures of a hollow-fiber module are introduced and their dependence on the parameters that characterize the device is illustrated. A multi-scale modelling approach is then presented, in which preliminary single-fiber CFD simulations are used to derive the hydraulic permeability of a fiber bundle and the relevant mass transfer coefficients as functions of the local velocities. The predicted correlations are then fed to a module-scale model, in which blood and dialysate compartments are simulated as interpenetrated porous media while appropriate source terms account for the exchange of solutes andwater between the two fluids. The model predictions are three-dimensional flow and concentration distributions, from which, in particular, performance figures such as clearance and ultrafiltration flow rate can be extracted as functions of the module geometrical and physical characteristics. Validation tests are also presented and the results of a parametrical sensitivity assessment are discussed.