A mathematical analysis of a two-compartment model of urea kinetics

A model of urea distribution comprising well-mixed intracellular and extracellular compartments, with diffusive transfer of urea between compartments, is used to study blood urea variation during haemodialysis. Assuming that a typical adult patient (weight 70 kg and urea generation rate 5 mg min-1) is dialysed using a high-efficiency dialyser (urea clearance 0.2-0.251 min-1) at an ultrafiltration rate of 10 ml min-1, it is shown that a perturbation analysis can account for the effects of ultrafiltration and urea generation. This permits an analytical solution of the equations which describe the variation in solute concentration in each of the compartments, which may be compared with the solution obtained when urea generation and ultrafiltration are neglected. For a typical adult patient with urea distribution volume in the range 25-40 l undergoing high-efficiency haemodialysis, the analysis suggests that the contribution of ultrafiltration to the variation in urea concentration during dialysis is similar in magnitude to the experimental errors in measuring the blood concentration of urea and that a constant volume model will be sufficiently accurate to describe urea clearance in many patients.