A simple mathematical model applied to selection of the sodium profile during profiled haemodialysis

Among dialysis patients in the last 10 years the incidence of intradialytic dysequilibrium syndrome and symptomatic hypotension has increased significantly. Profiled haemodialysis (PHD), a new dialysis technique based on intradialytic modulation of the dialysate sodium concentration according to pre-elaborated individual profiles, has been set up to reduce intradialytic imbalances and the incidence of dysequilibrium syndrome and symptomatic hypotension. The present paper illustrates a new mathematical model for solute kinetics, single-compartment for sodium and two-compartment for urea, aimed at improving the use of PHD. The model allows the sodium profile to be elaborated a priori, before each dialysis session, according to the patient's clinical needs and respecting the individual sodium mass removal and weight gain.

The mathematical model was first derived and then applied to determining a rational dialysate sodium profile. A procedure which allows the method to be tuned to individual clinical needs on the basis of routine measurements performed before each session is also presented. The proposed method was validated in vivo during seven dialysis sessions, each performed on a different patient.

The comparison between data predicted by the model and those obtained in vivo shows a good correspondence in particular concerning the time pattern of blood urea and sodium. The comparison between the model prediction and in vivo determined sodium and urea plasma curves showed standard deviations (2.25 mEq/l for sodium and 0.87 mmol/l for urea) only slightly higher than those attributable to laboratory measurement errors. Moreover, in vivo implementation of PHD by our model enables one to remove an amount of sodium mass comparable with the a priori quantity predicted by the model.