A simple mathematical model of intradialytic sodium kinetics: 'In vivo' validation during hemodialysis with constant or variable sodium

A simple mathematical model of the intradialytic relationship between natraemia and dialysate sodium concentration is presented. The model includes a bicompartmental description of sodium, urea and fluid kinetics and an algebraic characterization of diffusive/convective mass-transfer across the dialysis membrane. Its ability to provide realistic responses has been validated comparing model predictions by a priori parameter tuning against quantities measured during in vivo sessions with both constant and variable dialysate sodium concentration. A quantitative analysis of model predictions indicates that the mean deviation between data calculated by the model and those measured in vivo is 1.32 mEq/l for sodium and 0.76 mmol/l for urea, values which do not greatly exceed the measurement errors. of current instruments. The model's predictive capacity thus proves reliable. The ability of the model to calculate the amount of sodium removed and the time course of intra-extracellular volumes during the dialysis session makes if possible to forecast the patient's clinical tolerance to a given sodium dialysate concentration.