Mathematical models for phosphate kinetics in patients on maintenance hemodialysis

In maintenance hemodialysis patients, efficient removal of phosphate during the hemodialysis session is crucial for the control of hyperphosphatemia and other frequent abnormalities of mineral metabolism. A mathematical model that integrates different distribution compartments and forms of phosphate may provide deeper insight and elucidation of observed kinetics of phosphate levels in plasma. Three mathematical models were constructed to describe the kinetics of phosphate during a one-week cycle of three dialysis sessions. The models included the extracellular and intracellular compartments for phosphate ions, plasma and interstitial compartments for phosphate ions bound to protein, and a compartment for fast exchangeable phosphate ions, and differing by the presence or exclusion of the fast or the intracellular compartment. The models included also an intracellular store of phosphate that might be released at an increasing rate during dialysis sessions. The weekly kinetics of total phosphate levels in plasma predicted by the three models were similar and agreed with the clinical data. The inclusion of free phosphate ion and protein bound phosphate separately provided small but significant modifications of the predicted profiles. The time dependent release of phosphate from the intracellular store was critical for the correct description of phosphate kinetics in plasma. The hypothesis that a fast compartment and an intracellular store compartment separately or combined contribute significantly to the kinetics of total phosphate in plasma was shown to be compatible with clinical data.