Accuracy of hemodialysis modeling

Abstract

Background. One- and two-compartmental models of hemodialysis (HD) are well known. These models make it possible to analyze the course of treatment and to predict the effect of dialysis procedures. Mathematical modeling helps physicians to match dialysis therapy to the individual needs of the patient; however, the efficiency of the models depends on the accuracy of the coefficients. How to select coefficients in the case of one-compartmental models is known for urea and creatinine. Less information is available for two-compartmental models. Results on modeling of uric acid concentrations have not been published. Methods. The identification of the mathematical model coefficients was based on the concentration measurements of three markers of uremic toxicity (urea, creatinine, and uric acid) in both patients' blood and dialysate. Blood samples were taken from the arterial line several times throughout the dialysis period. Simultaneously, dialysate samples were taken from a test port in the dialyzer outflow line. The mathematical model parameters were determined so as to minimize the deviations between the measured points and the calculated curves. In this way, distribution volumes, cellular clearances, and dialyzer mass transfer coefficients were estimated. Results. For a one-compartmental model, the median value of distribution volume V = 0.56 DW was obtained, where DW is the patient's dry weight. For a two-compartmental model, intercompartment volume Vi = 0.36 DW and extracompartment volume Ve = 0.21 DW. The following median values for cellular clearances were established: urea 415 (mL/min), creatinine 207 (mL/min), and uric acid 257 (mL/min). Conclusions. One- and two-compartmental models describe the concentration of the urea, creatinine, and uric acid very effectively, in contrast with phosphorus, in which modeling results are not satisfactory. Although two-compartmental models are more effective, they are much more complicated than one-compartmental models, which justifies using the one-compartmental model for hemodialysis modeling. A two-compartmental model must be used in the case of rebound phenomenon modeling. The total body water values we have obtained are similar to the anthropometrically based values for urea and creatinine and to a lesser degree for uric acid. Distribution volumes for one- and two-compartmental models obtained from patient weight are the simplest coefficients for mathematical models and have sufficient precision as well. The global value of both compartments is slightly greater than the corresponding value for a one-compartmental model. The effectiveness of dialyzers is in practice lower than might be expected on the basis of the data provided by their manufacturers. Urea cellular clearance is two times greater than creatinine and uric acid cellular clearances. The clearance differences are more prominent for the cellular membrane than for artificial semipermeable membranes.