Computation of Na and water deficit of iso-osmolar dehydration

The presence of altered plasma Na concentration (PNa) allows calculations of changes in water and electrolyte contents, which are not feasible during normonatremic derangements. We have developed a computational algorithm whereby the changes in solute (ΔNa and ΔCl) and solvent (ΔV) contents can be computed exactly when Na is lost entirely as NaCl (or NaHCO(3)) and nearly exactly in all other circumstances, except when the losses of Na and Cl occur in the same proportions as those of the normal plasma concentration of these ions.

In computer experiments, we simulated different fluid depletions containing 140 mEq/l of Na (which is to say, ΔNa/ΔV ≈ 140), coupled with variable ratios in Na to Cl losses (variable ΔNa/ΔCl). The data were back-calculated with our algorithms from the ensuing plasma ion concentrations (PNa(1), PCl(1) and POAN(1), where subscript (0) and (1) indicate normal and deranged plasma concentration values, respectively, and OAN indicates anions other than Cl), as if they had been measured on patients, and from known normal values (TBW(0), ECV(0), Na(0)). These were compared to the true values used to build the simulations. This procedure was reproduced in 17 patients suffering from iso-osmolar dehydration, where true data were obtained by balance studies.

True and calculated data were compared with linear regression analysis. We obtained significant correlations both in computer-simulated and real patients (R(2) = 0.83, p < 0.005 and R(2) = 0.63, p < 0.05, respectively).

This new math model and its related computational method are useful in the correct evaluation and treatment of iso-osmolar dehydration.