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INVITED EDITORIAL

Worth one's salt: the master dysnatremia equation

Division of Nephrology and Hypertension
Los Angeles Biomedical Research Institute
Torrance, California
e-mail: kkalantar{at}labiomed.org

Fish, birds, amphibians, reptiles, and mammal share the interesting physiological fact that their plasma salt concentration ([Na⁺]_pw) is virtually identical, amounting to 9 g/l. This is the equivalent of a 0.9% salt solution. In humans, the [Na⁺]_pw is maintained within a very narrow range, where its value varies by only 1% (11). Diseases that perturb the [Na⁺]_pw are collectively known by clinicians as the "dysnatremias." Understanding the physiological basis for changes in the [Na⁺]_pw has remained a major challenge for physiologists and clinicians alike; for unlike the concentration of the majority of substances in plasma, it has been known since the 1950s that the mass balance of Na⁺ per se cannot account quantitatively for changes in the [Na⁺]_pw. In addition to the mass balance of Na⁺, the mass balance of K⁺ and H₂O play an important role in determining the [Na⁺]_pw. In a landmark paper, Edelman et al. (1) reported for the first time an equation relating the [Na⁺]_pw to the exchangeable Na⁺, exchangeable K⁺, total body water (TBW) where [Na⁺]_pw = 1.11(Na⁺ + K⁺)/TBW – 25.6.

Changes in the mass balance of Na⁺, K⁺, and H₂O affected the terms in this equation and therefore the [Na⁺]_pw. In most texts, the equation was simplified to [Na⁺]_pw = (Na⁺ + K⁺)/TBW and the slope and y-intercept were ignored.

Until the landmark studies of Nguyen and Kurtz (3, 5–8, 10), the validity of the simplified equation had remained unquestioned despite the fact that it could not account for several clinical and physiological factors that affect [Na⁺]_pw. These factors included: hyperglymia-induced hyponatremia, the effect of Gibbs-Donnan equilibrium in altering the distribution of Na⁺ ions between the plasma and interstitial fluid (ISF), the fact that not all Na⁺-containing salts are completely dissociated in an aqueous solution, the fact that not all exchangeable Na⁺ and K⁺ is osmotically active, and the effect of osmotically active non-Na⁺ and non K⁺ osmoles in inducing intercompartmental water shifts (2, 4, 12).

One of the important key insights of the recent elegant studies by Nguyen and Kurtz (3, 5–8, 10) was their recognition that all these factors can be explained quantitatively by the original Edelman equation (1). Specifically, the slope and y-intercept represent the effect of various physiological parameters whose total numeric value is 1.11 and 25.6, respectively. Moreover, these authors have shown that the slope and y-intercept are not invariant mathematical constants. Rather, the value of the slope and y-intercept will change depending on the value of the individual physiological parameters of which they are composed. For example, changing the plasma glucose alters several components in the y-intercept, resulting in a change quantitatively in the [Na⁺]_pw.

In this issue of the Journal of Applied Physiology, Nguyen and Kurtz (9) have taken their analysis one step further. The authors have solved the difficult problem of characterizing the quantitative interrelationship between the Gibbs-Donnan equilibrium, the osmolality of body fluid compartments, and the [Na⁺]_pw. Their analysis demonstrates quantitatively how the altered distribution of osmotically active non-Na⁺ ions due to the Gibbs-Donnan equilibrium will have a modulating effect on the [Na⁺]_pw by affecting the distribution of H₂O between the plasma and ISF. Moreover, they validate their model using empirical data from the literature. The results of their analysis are relevant not only for clinicians but also for physiologists who wish to use their new published "master equation" when teaching students. This equation greatly simplifies the task of conveying to students the quantitative relationship between all known factors that modulate the [Na⁺]_pw.

In the clinical context, patients with a decreased albumin concentration due to renal or gastrointestinal diseases often have alterations in the [Na⁺]_pw. Changes in the plasma protein concentration alter the distribution of Na⁺ and non-Na⁺ ions in the plasma and ISF as reflected by the changes in the osmolality of these compartments. Mathematically, these changes are accounted for by the terms _pw and _ISF in the Gibbs-Donnan correction factor "g." This new insight demonstrates that just as the y-intercept in the Edelman equation was previously shown to vary in hyperglycemic states, in clinical conditions characterized by hemoconcentration, hemodilution, or hypoalbuminemia, the [Na⁺]_pw must vary as a result of changes in slope of the Edelman equation (variation in the Gibbs-Donnan correction factor "g").

In their current paper (9) and previous quantitative analyses of the factors modulating the [Na⁺]_pw, Nguyen and Kurtz have helped us recognize the subtle beauty of how all known factors that modulate the [Na⁺]_pw are related mathematically. In this way, they have reminded us of the elegant studies performed by Edelman and colleagues over 50 years ago, while providing physiologists and clinicians with indispensable tools for updating our approach to teaching the dysnatremias. Although questions remain that are difficult to study in humans, such as whether the exchangeable osmotically inactive Na⁺ and K⁺ are essentially fixed or variable, it is likely that future advances in our understanding of the regulation of the physiological parameters uncovered by Nguyen and Kurtz that determine the [Na⁺]_pw will result from animal studies where these issues can be addressed more easily.

GRANTS

Dr. Kalantar is supported by a National Institute of Diabetes, Digestive, and Kidney Disease grant (DK-61162).

REFERENCES

1. Edelman IS, Leibman J, O'Meara MP, and Birkenfeld LW. Interrelations between serum sodium concentration, serum osmolarity and total exchangeable sodium, total exchangeable potassium and total body water. J Clin Invest 37: 1236–1256, 1958.[ISI][Medline]
2. Katz MA. Hyperglycemia-induced hyponatremia—calculation of expected serum sodium depression. N Engl J Med 289: 843–844, 1973.[ISI][Medline]
3. Kurtz I and Nguyen MK. A simple quantitative approach to analyzing the generation of the dysnatremias. Clin Exp Nephrol 7: 138–143, 2003.[CrossRef][Medline]
4. Kutchai HC. Cellular membranes and transmembrane transport of solutes and water. In: Physiology, edited by Berne RM, Levy MN, Koeppen BM, and Stanton BA. St. Louis: Mosby, 2004, p. 3–21.
5. Nguyen MK and 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 18: 1266–1271, 2003.[Free Full Text]
6. Nguyen MK and Kurtz I. Derivation of a new formula for calculating urinary electrolyte-free water clearance based on the Edelman equation. Am J Physiol Renal Physiol Renal Physiol 288: F1–F7, 2005.[Abstract/Free Full Text]
7. Nguyen MK and Kurtz I. Determinants of plasma water sodium concentration as reflected in the Edelman equation: role of osmotic and Gibbs-Donnan equilibrium. Am J Physiol Renal Physiol 286: F828–F837, 2004.[Abstract/Free Full Text]
8. Nguyen MK and Kurtz I. A new quantitative approach to the treatment of the dysnatremias. Clin Exp Nephrol 7: 125–137, 2003.[CrossRef][Medline]
9. Nguyen MK and Kurtz I. Quantitative interrelationship between Gibbs-Donnan equilibrium, osmolality of body fluid compartments, and plasma water sodium concentration. J Appl Physiol 100: 1293–1300, 2006.[Abstract/Free Full Text]
10. Nguyen MK and Kurtz I. Role of potassium in hypokalemia-induced hyponatremia: lessons learned from the Edelman equation. Clin Exp Nephrol 8: 98–102, 2004.[Medline]
11. Rose BD. Clinical Physiology of Acid-Base and Electrolyte Disorders. New York: McGraw-Hill Professional, 2000.
12. Sperelakis N. Gibbs-Donnan equilibrium potentials. In: Cell Physiology Sourcebook: A Molecular Approach (3rd ed.), edited by Sperelakis N. San Diego: Academic, 2001, p. 243–247.

This article has been cited by other articles:

				K. L. Dorrington Master dysnatremia equation for Gibbs-Donnan equilibrium and plasma sodium concentration: proof or spoof? J Appl Physiol, February 1, 2008; 104(2): 569 - 569. [Full Text] [PDF]

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