Mathematical Modeling of the Dynamic Exchange of Solutes in a Prototype Hemodialyzer

Abstract

Hemodialysis (HD) is one type of procedure for eliminating toxic chemicals and infusing bicarbonate in patients with end-stage renal disease (ESRD). Research and development in the hemodialyzer industry have, hitherto, depended mostly on empirical evidence to optimize HD therapy. This is often costly and involves numerous clinical trials. Developing a comprehensive time-dependent mathematical model to examine the dynamic exchange of solutes ( HC<span>O</span>^-<sub style="margin-left:-6px;">3</sub> and pCO 2 ), blood pH and H + ions in a prototype hollow-fiber hemodialyzer is essential in optimizing future design and improvement. A comprehensive mathematical model which is represented by a coupled set of transport equations and delineates the blood and dialyzate compartments of the hemodialyzer, and includes bicarbonate-buffering reaction in the blood channel and bicarbonate replenishment mechanism in the dialysate, is used to describe the time-dependent bulk concentration and exit concentration of solutes, blood pH and H + ions in the hollow-fiber prototype hemodialyzer. A numerical simulation of the model is used to test several time-dependent bulks and exit concentration profiles of solutes in the blood and dialyzate. Results obtained from the numerical solution of the model show the bulk and exit concentrations of solute at various distances along the blood and dialyzate channels at different times. This modeling exercise will also allow us in our next study to examine some physical mechanisms of the hemodialyzer.