NDT Advance Access originally published online on August 5, 2008
Nephrology Dialysis Transplantation 2008 23(10):3367-3368; doi:10.1093/ndt/gfn418
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Reply
Nephrol Dial Transplant 2008; doi:10.1093/ndt/gfn414E-mail: mtnguyen{at}mednet.ucla.edu
Sir,
In their letter, Ring et al. criticize our new quantitative approach for correcting hypervolaemic hypernatraemia by achieving negative Na+ and K+ balance in excess of negative H2O balance [1]. Ring et al. stated that our new formula is not simple to use because it requires an estimate of the initial total body water (TBW1) and frequent measurements of urinary [Na+ + K+]. First, the utility of an equation should not be based on its simplicity of usage, but rather on the extent to which it accurately models human physiology. In this regard, our new formula is derived based on the known empirical relationship between the plasma water sodium concentration ([Na+]pw) and total exchangeable sodium (Nae), total exchangeable potassium (Ke) and total body water (TBW) originally reported by Edelman et al. [2]. Since TBW is a determinant of the plasma sodium concentration ([Na+]p), any formula used in predicting alterations in the [Na+]p requires an estimate of TBW1. For instance, the sodium deficit, free water deficit and Adrogue–Madias formulas all require an estimate of TBW1. Second, since Nae and Ke are the major determinants of the [Na+]p, alterations in the mass balance of Na+ and K+ will result in changes in the [Na+]p. Therefore, measurements of urinary [Na+ + K+] are required to account for changes in the mass balance of Na+ and K+ that will result in changes in the [Na+]p. Furthermore, our mathematical model can be legitimately criticized only if it were to assume that the body is a closed system. Therefore, consideration of urinary losses of Na+ and K+ by our formula should rather be regarded as a strength, since our formula accounts for the physiologic fact that the body is an open system. It is not clear to us why Ring et al. would prefer a formula that assumes that the body is a closed system.
Ring et al. also claimed to have derived a ‘new ancillary formula...with the intent of avoiding accidents secondary to using the formula given by Nguyen and Kurtz’. Since the body is an open system, our Equation (4) accounts for infusate (IVF) and non-infusate (Einput and Vinput) inputs and renal (urine) and non-renal (Eoutput and Voutput) outputs [1]:
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In our clinical example, there is no significant non-infusate input and non-renal output. In such clinical settings, Equation (4) can be simplified and rearranged to the following equation:
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Ring et al. also argue that our patient's history is ‘extraordinary’ in that the ‘patient is not stated to be demented, to have diabetes insipidus or osmotic diuresis, or to have been denied access to water...yet this elderly lady with congestive heart failure develops hypernatraemia said to be secondary to furosemide treatment’. In the clinical example, our elderly patient remained hypervolaemic with physical and laboratory findings consistent with congestive heart failure at the time she developed hypernatraemia. Our analysis revealed that the development of hypernatraemia was due to the furosemide treatment. In contrast to what is stated by Ring et al., furosemide treatment can predispose to the development of hypernatraemia due to the hypotonic urinary losses [3]. It is ironic that Ring et al. argue that osmotic diuresis can result in hypernatraemia and yet furosemide therapy cannot cause hypernatraemia. It is well known that both osmotic diuresis and furosemide lead to urinary excretion of H2O in excess of Na+ and K+, thereby predisposing to the development of hypernatraemia [3]. Second, we disagree with Ring et al. that our patient does not have a component of diabetes insipidus. It is well appreciated that furosemide can cause a decrease in urinary concentrating ability due to interference with the countercurrent mechanism by inhibiting sodium chloride reabsorption in the thick ascending limb of the loop of Henle [4]. This is the reason why diuretic-induced hyponatraemia is caused almost exclusively by thiazide diuretics [4]. Although furosemide can predispose to the generation of hypernatraemia, hypernatraemia cannot occur unless there is a defect in the thirst mechanism or inadequate access to H2O [3]. Therefore, our elderly patient likely has a defect in her thirst mechanism. However, it is important to appreciate that a patient with a defect in the thirst mechanism can develop hypernatraemia even if the patient is not demented or has adequate access to H2O.
Our new quantitative approach is derived based on the known empirical relationship between the plasma sodium concentration ([Na+]p) and total exchangeable sodium (Nae), total exchangeable potassium (Ke) and total body water (TBW): [Na+]p = 1.03(Nae + Ke)/TBW – 23.8 [2,5]. Ring et al. argue that the ‘modelled intercept term 23.8 from Edelman is very uncertain with 99% CI including 0’. In a previous letter, Ring also argues that the slope of the Edelman equation should be 1 [6]. However, Ring's assertion not only is not supported by physiological and clinical data but also is incorrect based on theoretical principles that govern certain factors that modulate the distribution of Na+ [7–9]. We have previously demonstrated that there are theoretical and physiologic considerations independent of the empirical data in Edelman's study, which support Edelman et al. that the slope is greater than unity and the y-intercept must have a non-zero value [7–9]. If the slope and y-intercept of the Edelman equa- tion were to be 1 and 0, respectively (as assumed by Ring et al.), then only alterations in the mass balance of Na+, K+ and H2O will result in a change in the [Na+]p. We therefore welcome Ring et al. to provide a scientifically valid explanation as to how one can account quantitatively for all the causes of the dysnatremias resulting from factors that do not alter the value of the (Nae + Ke)/TBW term in the Edelman equation such as (1) changes in the [Na+]p due to inter-compartmental water shifts due to non-Na+ and non-K+ osmoles such as hyperglycaemia, mannitol, sucrose, maltose and contrast agents; (2) transcellular shifts of Na+ and K+ in hypokalaemia-induced hyponatraemia and (3) a component of the Nae and Ke is osmotically inactive and incapable of modulating the [Na+]p [7–9]. Moreover, based on the measured Nae, Ke, TBW and [Na+]pw in Edelman's study [2], the ratio of (Nae + Ke)/TBW is significantly greater than the [Na+]pw. Given that the ratio of (Nae + Ke)/TBW is significantly greater than the [Na+]pw, we welcome Ring et al. to provide a mathematical explanation as to how one can equate the ratio of (Nae + Ke)/TBW to the [Na+]pw if the slope and y-intercept of the Edelman equation were to be 1 and 0, respectively (as argued by Ring et al.).
Ring et al. also argue that our new formula ‘would not be much helped’ since it requires frequent monitoring of urinary Na+, K+ and H2O losses to guide further adjustments in the fluid prescription. We disagree with this simplistic view. We feel that taking a quantitative approach to adjusting the rate of fluid administration based on ongoing urinary losses is a more logical approach than simply guessing blindly at the rate of fluid administration. Moreover, consideration of ongoing urinary hypotonic loss is particularly relevant in the treatment of hypernatraemia, since ongoing urinary loss of H2O in excess of Na+ and K+ induced by furosemide would tend to result in a worsening of the hypernatraemia if not accounted for.
Lastly, Ring et al. also questioned why our patient did not exhibit the expected increased Na+ excretion. Although the urinary [Na+] was not exceedingly high ([Na+]urine = 63 mmol/L), our patient did exhibit a significant natriuresis (479 mmol of Na+ excreted) since the total urinary output was 
7.6 L. Indeed, reliance on urinary [Na+] as an estimate of urinary Na+ excretion can be misleading since urinary [Na+] is not only a function of the quantity of Na+ excreted but also a function of the urinary volume excreted.
Conflict of interest statement. None declared.
Department of Medicine, UCLA Los Angeles, CA, USA
References
- Nguyen MK, Kurtz I. Correction of hypervolaemic hypernatraemia by inducing negative Na+ and K+ balance in excess of negative water balance. Nephrol Dial Transplant (2008) 23:2223–2227.
[Abstract/Free Full Text] - Edelman IS, Leibman J, O’Meara MP, et al. 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]
- Adrogue HJ, Madias NE. Hypernatremia. N Engl J Med (2000) 342:1493–1499.
[Free Full Text] - Liamis G, Milionis H, Elisaf M. A review of drug-induced hyponatremia. Am J Kidney Dis (2008) 41:292–309.[CrossRef]
- 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] - Ring T. Quantitative analysis of the dysnatremias. Kidney Int (2006) 69:416.[CrossRef][Web of Science][Medline]
- Nguyen MK, Landaw EM, Kurtz I. Quantitative analysis of the dysnatremias (Authors’ reply). Kidney Int (2006) 70:1379–1381.[CrossRef][Web of Science][Medline]
- 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] - Nguyen MK, Kurtz I. Quantitative interrelationship between Gibbs–Donnan equilibrium, osmolality of body fluid compartments, and plasma water sodium concentration. J Appl Physiol (2006) 100:1293–1300.
[Abstract/Free Full Text]
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