to the editor: Overgaard-Steensen et al. (6) have developed a porcine model of acutely decreasing plasma sodium concentration. They used this model to test Edelman's empirically derived equation (1), which describes plasma sodium concentration, [Na^{+}] (mmol/l), as a function of the sum of total exchangeable sodium and potassium (Na^{+} + K^{+}) (mmol) and total body water, TBW (liters):
^{+}]. They denoted 1.03 in equation 1 as “α,” and mindful that 23.8 is the sum of four variable terms and hence not necessarily constant, they denoted this parameter as “β.” The Overgaard-Steensen et al. equation is written as
*i* and *f* indicate initial and final values. They induced a combined water-retaining and natriuretic hyponatremia, in which the average [Na^{+}] decreased by 2 mmol/h. For this acute hyponatremia, they found that the Edelman equation predicted [Na^{+}]_{f} well; α and β averaged 1.33 ± 0.08 and 13.04 ± 7.68, respectively, and remained constant in individual pigs. They suggested additional studies, including studies of chronic hyponatremia.

The present communication notes that Nguyen and Kurtz (3) derived an analogous equation for Edelman's original human population, whose hyponatremia was likely predominantly chronic. Their equation retains the original Edelman values of α (1.03) and β (23.8) and rearranges to the Overgaard-Steensen equation (*Eq. 2*). If the porcine model, specifically chosen for the similarity of its renal physiology to that of humans, correctly predicts change in plasma [Na^{+}] for humans, then comparing the two equations, which differ only in the values of α and β, may elucidate differences in the response to acute and chronic hyponatremia.

If [Na^{+}] changes solely as a function of Δ(Na^{+}+ K^{+}), then ΔTBW = 0 and (*Eq. 2*) simplifies to
*A* shows that [Na^{+}] is considerably more sensitive to Δ(Na^{+}+ K^{+}) in the Overgaard-Steensen equation than in the Nguyen and Kurtz equation, reflecting the difference in α (1.33 and 1.03, respectively).

If [Na^{+}] changes solely as a function of ΔTBW, then Δ(Na^{+}+ K^{+}) = 0, and (*Eq. 2*) simplifies to

Fig. 1*B* shows that [Na^{+}] is slightly more sensitive to ΔTBW in the Nguyen and Kurtz equation because although its β is considerably larger, the term βΔTBW is small compared with the term [Na^{+}]_{i}TBW_{i}. Nevertheless, in both equations, ΔTBW has a comparatively greater effect on [Na^{+}] than does Δ(Na^{+}+ K^{+}) (6, 12). Water gain in the porcine cohort, for example, accounts for about four times as much of the decrease in plasma [Na^{+}] than does (Na^{+}+ K^{+}) loss (calculated from data in Table 1 (6), p. R124, using the Overgaard-Steensen equation A5, P. R128, as simplified to *Eq. 4* above).

Two mechanisms defend against the effects of decreasing extracellular osmolality: regulatory volume decrease (RVD, achieved by extrusion of osmotic material from cells) and activation of nonosmotic sodium. RVD has been described for selected brain cells (11), but it has not been conclusively demonstrated in skeletal muscle (6). It begins rapidly when extracellular fluid osmolality decreases (7), achieves steady state within 2 days (11), and is maintained during chronic hyponatremia (11). Nonosmotic Na^{+} stores (2, 5, 8, 9, 10) are activated from skin (8) and bone (10), a process that has been inferred to act within the timeframe that athletes develop acute hyponatremia (5). Activation of sodium stores from both skin (8) and bone (9, 10) has been demonstrated over longer time periods. While Overgaard-Steensen et al. (6) did not observe evidence for either mechanism in their porcine cohort, it is possible that the effects of both processes are expressed in the values of α and β.

The comparatively large effect of ΔTBW on [Na^{+}] could obscure the effects of RVD and osmotic activation, whereas the comparatively small effect of Δ(Na^{+} + K^{+}) would amplify these effects. That Δ(Na^{+}+ K^{+}) has a smaller impact on [Na^{+}] chronically than acutely implies that endogenous sodium mobilized from stores mitigates the decrease of [Na^{+}]. The nonelectrolyte fraction of extruded material in RVD reduces [Na^{+}] by increasing extracellular fluid (ECF) water without changing the quantity of ECF sodium. Thus, RVD has its most pronounced effects in acute hyponatremia [Overgaard-Steensen et al., *Eq.* A5, p. R128, (6)], whereas activation of sodium stores is the dominant response in chronic hyponatremia [Nguyen and Kurtz, *Eq. 3*, P. 139 (3)].

## DISCLOSURES

No conflicts of interest, financial, or otherwise, are declared by the author.

- Copyright © 2012 the American Physiological Society