Hemodiafiltration with on-line regeneration of ultrafiltrate (HFR) is a technique indicated for the treatment of dialysis patients affected by inflammatory syndrome and malnutrition. In the present work, a mathematical model, which describes intradialytic fluid and solute kinetics during standard diffusive dialysis, has been adapted to analyze solutes and fluid dynamics during HFR. The model is an improved version of our previous ones, and represents a good compromise between simplicity and reliability. It considers the intradialytic kinetics of sodium, potassium and urea, and two body fluid compartments: intracellular and extracellular. Moreover, the model includes simple equations to predict the intradialytic time pattern of osmolarity. The model has been experimentally validated by using 9 HFR sessions on 9 patients (one per each patient), comparing the time course of plasma solutes and osmolarity measured every 30 minutes during HFR, with those predicted by the model. Predictions are performed a priori, i.e., without any parameter adjustment, but just starting from knowledge of a few quantities (plasma sodium, potassium, urea, osmolarity and body weight) at the beginning of the session. The average deviations between model and real data (sodium: 1.9 mEq/L; potassium: 0.32 mEq/L; urea: 1.04 mmol/L; osmolarity: 5.02 mosm/L) are of the same order as measurement errors and similar to those obtained using our previous models in standard and profiled hemodialysis. Moreover, the prediction on sodium concentration only scarcely worsens (from 1.9 to 2.02 mEq/L) if default values are used for the initial value of other solutes in blood (i.e., if the algorithm uses only initial body weight and initial sodium concentration in plasma). The results confirm the good predictive capacity of the model in HFR, and suggest its possible innovative use to optimize sodium balance in HFR, from knowledge of only the sodium concentration in the ultrafiltrate.