Model of fluid and solute shifts during hemodialysis with active transport of sodium and potassium

BACKGROUND: Mathematical models are useful tools to predict fluid shifts between body compartments in patients undergoing hemodialysis (HD). The ability of a model to accurately describe the transport of water between cells and interstitium (J(v,ISIC)), and the consequent changes in intracellular volume (ICV), is important for a complete assessment of fluid distribution and plasma refilling. In this study, we propose a model describing transport of fluid in the three main body compartments (intracellular, interstitial and vascular), complemented by transport mechanisms for proteins and small solutes. METHODS: The model was applied to data from 23 patients who underwent standard HD. The substances described in the baseline model were: water, proteins, Na, K, and urea. Small solutes were described with two-compartment kinetics between intracellular and extracellular compartments. Solute transport across the cell membrane took place via passive diffusion and, for Na and K, through the ATPase pump, characterized by the maximum transport rate, Jp(MAX). From the data we estimated Jp(MAX) and two other parameters linked to transcapillary transport of fluid and protein: the capillary filtration coefficient Lp and its large pores fraction α(LP). In an Expanded model one more generic solute was included to evaluate the impact of the number of substances appearing in the equation describing J(v,ISIC). RESULTS: In the baseline model, median values (interquartile range) of estimated parameters were: Lp: 11.63 (7.9, 14.2) mL/min/mmHg, α(LP): 0.056 (0.050, 0.058), and Jp(MAX): 5.52 (3.75, 7.54) mmol/min. These values were significantly different from those obtained by the Expanded model: Lp: 8.14 (6.29, 10.01) mL/min/mmHg, α(LP): 0.046 (0.038, 0.052), and Jp(MAX): 16.7 (11.9, 25.2) mmol/min. The relative RMSE (root mean squared error)averaged between all simulated quantities compared to data was 3.9 (3.1, 5.6) %. CONCLUSIONS: The model was able to accurately reproduce most of the changes observed in HD by tuning only three parameters. While the drop in ICV was overestimated by the model, the difference between simulations and data was less than the measurement error. The biggest change in the estimated parameters in the Expanded model was a marked increase of Jp(MAX) indicating that this parameter is highly sensitive to the number of species modeled, and that the value of Jp(MAX) should be interpreted only in relation to this factor.