Analytic solution of the Variable-Volume Double-Pool urea kinetics model applied to parameter estimation in hemodialysis

An analytic solution of the Variable-Volume Double-Pool urea kinetics model and its application to the estimation of clinically relevant parameters of the patient-machine system, are presented. These include the urea distribution volume and generation rate and the mean dialyzer clearance. The estimation of these parameters is based on the assumption of constant values for the diffusion coefficient between the two pools and the intra-extracellular volume ratio. Results obtained by computer simulations show that the effect of a ± 50% variation of these parameters influences the estimates less than standard measurement errors. Starting from these results, four methods to in vivo estimate the urea distribution volume and generation rate from blood samples are compared. Two methods are based on the analytic solution of the double-pool model using seven samples (reference method) or three samples (new clinical method). The remaining methods are based on urea mass-balance and are largely used in the clinical practice. These last techniques differ from each other for the blood sample taken at the end of the treatment or 30 min later. The results obtained from hemofiltration sessions show that the urea generation rate is accurately estimated by all methods. The total distribution volume is still accurately estimated by the new clinical method while it is systematically underestimated by the urea mass-balance when the blood sample at the end of dialysis is used. Instead, a high overcompensation results using the blood sample taken 30 min after the end of dialysis. Finally, the new clinical method also provides reliable estimates for the dialyzer clearance starting from only three blood samples all taken during dialysis.