A mathematical model of solute kinetics for the improvement of hemodialysis treatment is presented. It includes a two-compartment description of the main solutes and a three-compartment model of body fluids (plasma, interstitial and intracellular). The main model parameters can be individually assigned a priori, on the basis of body weight and plasma concentration values measured before beginning the session. Model predictions are compared with clinical data obtained in vivo during 11 different hemodialysis sessions performed on 6 patients with a profiled sodium concentration in the dialysate and a profiled ultrafiltration rate. In all cases, the agreement between the time pattern of model solute concentrations in plasma and the in vivo data proves fairly good as to urea, sodium, chloride, potassium and bicarbonate kinetics. Only in two sessions was blood volume directly measured in the patient, and in both cases the agreement with model predictions was good. In conclusion, the model allows a priori computation of the amount of sodium removed during hemodialysis, and makes it possible to predict the plasma volume changes and plasma osmolarity changes induced by a given sodium concentration profile in the dialysate and by a given ultrafiltration profile. Hence, it can be used to improve clinical tolerance to the dialysis session taking the characteristics of individual patients into account, in order to minimize intradialytic hypotension.