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Nephrol Dial Transplant (2004) 19: 1326-1327
Nephrol Dial Transplant Vol. 19 No. 5 © ERA-EDTA 2004; all rights reserved

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Sir,

In his accompanying letter to NDT, Lodha raises the issue that the term 0.11(Nae + Ke)/TBW should be included as a component of the y-intercept in the Edelman equation. The relationship between the [Na+]pw and Nae, Ke and TBW was originally demonstrated empirically by Edelman et al. [1]:

(1)

We recently demonstrated quantitatively that there are several physiological parameters in the y-intercept (–25.6) of the Edelman equation, which independently alter the [Na+]pw [2]:

(2)
where the y-intercept in Edelman's equation is represented by four parameters:

Lodha suggests that the term 0.11(Nae + Ke)/TBW should be included as a component of the y-intercept as well. This notion cannot be true. First, equation 2 is mathematically derived based on the assumption that the body fluid compartments are in osmotic equilibrium. Based on this analysis, there is no physiological justification for the inclusion of the additional term 0.11(Nae + Ke)/TBW in the y-intercept. Secondly, according to equation 2, the slope in the Edelman equation is 1. Based on the regression equation which best fit their empirical data, Edelman et al. reported a slope of 1.11 [1]. The suggestion by Lodha to include the additional term 0.11(Nae + Ke)/TBW in the y-intercept is based on the assumption that there is a 0.11 difference in our mathematically derived slope and Edelman's empirically determined slope. Given that the slope of 1.11 was empirically determined, additional theoretical and/or empirical justification is required prior to assuming that there exists a 0.11 difference in the two slopes. Indeed, we have recently shown that the slope in equation 2 should be 1.11 rather than 1 [6]. However, the 0.11 difference is not attributed to the term 0.11 (Nae+Ke)/TBW as suggested by Lodha. Instead, our recent analysis indicates that the slope of 1.11 in the Edelman equation is quantitatively determined by the combined effect of Gibbs–Donnan equilibrium and the osmotic coefficient of Na+ salts under physiological conditions [6]. Finally, it is well known that the Nae and Ke include osmotically active as well as osmotically inactive Na+ and K+ [1,3–5]. The osmotically inactive Nae and Ke are ‘ineffective osmoles’ and they do not contribute to the distribution of water between the extracellular and intracellular spaces. Importantly, only the osmotically active Nae and Ke contribute to the determination of the [Na+]pw, which is accounted for by the first two terms in equation 2:

Therefore, the inclusion of the 0.11(Nae + Ke) / TBW term in the y-intercept cannot be justified from a physiological standpoint.

Lodha also points out that our calculations of the predicted [Na+]p in the two clinical examples are inaccurate, because we failed to consider insensible water losses in calculating TBW. In our calculations of the TBW in these patients, we intentionally did not include insensible water losses. If one were to consider insensible water losses, then one must also take into consideration the water content of food and water of oxidation. In calculating the mass balance of water, one may ignore these sources of insensible water input and output rather than estimating them, since insensible water losses have been shown to be approximately equal to metabolic water production and the water content of food [7]. Indeed, this approach appears to be valid, because if insensible water input and output as well as daily average faecal water losses are excluded from the calculations of TBW, there is an error of only ~1–3% in the target [Na+]p [8].

Conflict of interest statement. None declared.

Minhtri K. Nguyen and Ira Kurtz

Division of Nephrology David Geffen School of Medicine at UCLA Los Angeles USA Email: mtnguyen{at}mednet.ucla.edu

References

  1. Edelman IS, Leibman J, O’Meara MP, Birkenfeld LW. Interrelations between serum sodium concentration, serum osmolality and total exchangeable sodium, total exchangeable potassium and total body water. J Clin Invest 1958; 37: 1236–1256[Web of Science][Medline]
  2. Nguyen MK, Kurtz I. Are the total exchangeable sodium, total exchangeable potassium and total body water the only determinants of the plasma water sodium concentration? Nephrol Dial Transplant 2003; 18: 1266–1271[Free Full Text]
  3. Edelman IS, James AH, Brooks L, Moore FD. Body sodium and potassium – the normal total exchangeable sodium; its measurement and magnitude. Metabolism 1954; 3: 530–538[Medline]
  4. Edelman IS, James AH, Baden H, Moore FD. Electrolyte composition of bone and the penetration of radiosodium and deuterium oxide into dog and human bone. J Clin Invest 1954; 33: 122–131[Web of Science][Medline]
  5. Cameron IL, Hardman WE, Hunter KE, Haskin C, Smith NKR, Fullerton GD. Evidence that a major portion of cellular potassium is ‘bound’. Scan Micros 1990; 4: 89–102
  6. Nguyen MK, Kurtz I. Determinants of the plasma water sodium concentration as reflected in the Edelman equation: role of osmotic and Gibbs–Donnan equilibrium. Am J Physiol Renal Physiol 2004; 286: F828–F837[Abstract/Free Full Text]
  7. Mallie JP, Bichet DG, Halperin ML. Effective water clearance and tonicity balance: the excretion of water revisited. Clin Invest Med 1997; 20: 16–24[Web of Science][Medline]
  8. Nguyen MK, Kurtz I. A new quantitative approach to the treatment of the dysnatremias. Clin Exp Nephrol 2003; 7: 125–137[CrossRef][Medline]

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