Mathematical Modeling of Solute Kinetics and Body Fluid Changes during Profiled Hemodialysis

Abstract

A mathematical model of solute kinetics oriented to improve hemodialysis treatment is presented. It includes a two-compartment description of the main solutes (K⁺, Na⁺, Cl^–, urea, HCO^–₃, H⁺, CO₂), acid-base equilibrium through two buffer systems (bicarbonate and non-carbonic buffers) 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 during 11 different hemodialysis sessions performed on six patients with profiled sodium concentration in the dialysate and profiled ultrafiltration rate. In all cases, the agreement between the time pattern of model solute concentrations in plasma and clinical data turns out fairly good as to urea, sodium, chloride and potassium kinetics. Finally, the time patterns of plasma bicarbonate concentration and pH can be reproduced fairly well with the model, provided CO₂ concentration remains constant. Only in two sessions, blood volume was 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 may enable the prediction of 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 the dialysis session taking the characteristics of individual patients into account, in order to minimize intradialytic imbalances (such as hypotension or disequilibrium syndrome).