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 H 2 O, 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 (Na e ), total exchangeable potassium (K e ), 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(Na e + K e )/TBW − 25.6. The interrelationship between [Na + ] pw and Na e , K e , 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(Na e + K e )/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 Na e , K e , and TBW by the following linear regression equation: [Na + ] pw = 0.487(Na e + K e )/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 Na e , K e , and TBW despite dynamic changes in the osmotically inactive Na + and K + storage pool.