Osmotically inactive sodium and potassium storage: lessons learned from the Edelman and Boling data

Because changes in the plasma water sodium concentration ([Na(+)]pw) are clinically due to changes in the mass balance of Na(+), K(+), and H2O, the analysis and treatment of the dysnatremias are dependent on the validity of the Edelman equation in defining the quantitative interrelationship between the [Na(+)]pw and the total exchangeable sodium (Nae), total exchangeable potassium (Ke), and total body water (TBW) (Edelman IS, Leibman J, O'Meara MP, Birkenfeld LW. J Clin Invest 37: 1236-1256, 1958): [Na(+)]pw = 1.11(Nae + Ke)/TBW - 25.6. The interrelationship between [Na(+)]pw and Nae, Ke, and TBW in the Edelman equation is empirically determined by accounting for measurement errors in all of these variables. In contrast, linear regression analysis of the same data set using [Na(+)]pw as the dependent variable yields the following equation: [Na(+)]pw = 0.93(Nae + Ke)/TBW + 1.37. Moreover, based on the study by Boling et al. (Boling EA, Lipkind JB. 18: 943-949, 1963), the [Na(+)]pw is related to the Nae, Ke, and TBW by the following linear regression equation: [Na(+)]pw = 0.487(Nae + Ke)/TBW + 71.54. The disparities between the slope and y-intercept of these three equations are unknown. In this mathematical analysis, we demonstrate that the disparities between the slope and y-intercept in these three equations can be explained by how the osmotically inactive Na(+) and K(+) storage pool is quantitatively accounted for. Our analysis also indicates that the osmotically inactive Na(+) and K(+) storage pool is dynamically regulated and that changes in the [Na(+)]pw can be predicted based on changes in the Nae, Ke, and TBW despite dynamic changes in the osmotically inactive Na(+) and K(+) storage pool.