Models of phosphate kinetics in dialysis patients

During the dialytic treatment, plasma phosphate (Pi) has a very specific time course. It reaches a nadir value approximately 90 minutes after the beginning of the treatment and then, despite the ongoing removal, it exhibits either a constant steady state or a slow rebound. In order to quantitatively describe the kinetics, the authors have proposed a set of different compartmental control models, which have been compared by using criteria based on mathematical indices and physiological considerations. The resulting best model has two compartments, which represent plasma and intra-cellular fluids (IF) respectively, In order to explain the Pi time course, it postulates two fluxes of Pi into plasma: one from IF, proportional to the decrease of plasma Pi from its pre-dialysis value, and one from an endogenous source (probably the bone surface), again proportional to the decrease of plasma Pi but also inversely proportional to Pi concentration in IF. This model was able to achieve a very good fit of all the experimental data (7 subjects) and good precision of parameter estimates. Moreover, it proved capable of correctly predicting also the qualitative time course of Pi in the post dialysis period.