Determinants of plasma water sodium concentration as reflected in the Edelman equation: role of osmotic and Gibbs-Donnan equilibrium.

Edelman et al. have empirically shown that plasma water sodium concentration ([Na(+)](pw)) is equal to 1.11(Na(e) + K(e))/TBW - 25.6 (Edelman IS, Leibman J, O'Meara MP, Birkenfeld LW. J Clin Invest 37: 1236-1256, 1958). However, the physiological significance of the slope and y-intercept in this equation has not been previously considered. Our analysis demonstrates that there are several clinically relevant parameters determining the magnitude of the y-intercept that independently alter [Na(+)](pw):1) osmotically inactive exchangeable Na(+) and K(+); 2) plasma water K(+) concentration; and 3) osmotically active non-Na(+) and non-K(+) osmoles. In addition, we demonstrate quantitatively the physiological significance of the slope in the Edelman equation and its role in modulating [Na(+)](pw). The slope of 1.11 in this equation which Edelman et al. determined empirically can be theoretically predicted by considering the combined effect of the osmotic coefficient of Na(+) salts at physiological concentrations and Gibbs-Donnan equilibrium. In addition, our results demonstrate that the slope has an independent quantitative impact on the magnitude of the y-intercept in the Edelman equation. From a physiological standpoint, the components of both the slope and the y-intercept need to be addressed when considering the factors that modulate [Na(+)](pw).