A comprehensive model of the dynamic exchange processes during hemodialysis

The present model for the mathematical description of exchange processes during hemodialysis includes submodels for potassium, sodium, chloride, acetate, acid-base status (with CO2, bicarbonate and H(+)-ions), water distribution, oxygen, ventilation, and the uremic catabolites urea, creatinine, and vitamin B12. For potassium, sodium and urea a 2-compartment model is used consisting of the extra- and the intracellular space. For chloride, creatinine and vitamin B12 a 3-compartment model is necessary. For the description of acetate kinetics a 1-compartment model consisting of the extracellular space is sufficient. For description of the acid-base balance the model includes three submodels for CO2, bicarbonate, and hydrogen ions. All submodels are made of eight compartments, namely the intracellular and the interstitial space as well as six spaces for the blood. The three submodels are coupled to each other by the chemical reaction of CO2 to HCO3- and a H(+)-ion. Besides this reaction the diffusive exchange between the compartments, the convective transport with the blood and the elimination through the dialyzer and the lung for the molecules and ions are considered. Because of the strong buffer capacity of plasma and intracellular proteins, the functional compartments for hydrogen ions are larger than the anatomical spaces. Also the influence of extracellular pH on the electrolyte distribution at the cell membrane has been considered. With this model, which will be adapted to the patient by more than 45 individual parameters, the mass transfer and the course of concentrations during hemodialysis therapy can be reproduced adequately. Further on the values of some unknown parameters, such as the metabolic rate for acetate in the organism, can be estimated by varying the parameters systematically for several runs of the computer simulation until the simulation results are optimally fitted to measured data.