NDT Advance Access published online on August 22, 2008
Nephrology Dialysis Transplantation, doi:10.1093/ndt/gfn476
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Can we really predict the change in serum sodium levels?—an analysis of currently proposed formulae in hypernatraemic patients
1 Intensive Care Unit 13H1, Clinic for Internal Medicine III 2 Department of Nephrology and Dialysis, for Internal Medicine III, Medical University of Vienna, Vienna 3 Department of Nephrology, Krankenhaus der Elisabethinen, Linz, Austria
Correspondence and offprint requests to: Gregor Lindner, Department of Nephrology and Dialysis, Medical University of Vienna, Waehringer Guertel 18-20, 1090 Wien, Austria. Tel: +43-650-412-74-22; Fax: +43-1-40400-4386; E-mail: lindner.gregor{at}gmail.com
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Abstract |
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Background. Hypernatraemia is common in intensive care patients and may present an independent risk factor of mortality. Several formulae have been proposed to guide infusion therapy for correction of serum sodium. Unfortunately, these formulae have never been validated comparatively. We assessed the predictive potential of four different formulae (Adrogué–Madias, Barsoum–Levine, Kurtz–Nguyen and a simple formula based on electrolyte-free water clearance) in correction and maintenance of serum sodium in 66 hyper- and normonatraemic ICU patients.
Methods. With daily measurements of sodium/potassium and fluid/electrolyte balances, a day-to-day prediction of serum sodium levels was calculated using the four formulae. This was compared to the measured changes in serum sodium.
Results. Six hundred and eighty-one patient-days (194 hypernatraemic) in 66 patients were available for calculations. Prediction of serum sodium levels using all four formulae correlated significantly (P < 0.05) with measured changes in serum sodium. Individual variations were extreme, and the mean differences (±SD) for predicted versus measured serum sodium were within the range of 3.4–4.5 (±4.4–4.7) mmol/l similar for the Adrogué–Madias, Barsoum–Levine and Nguyen–Kurtz formulae. In comparison, our proposed formula underestimated the changes of serum sodium (mean ± SD –1.5 ± 5.3). During hypernatraemia, the differences between predicted and measured values were even greater (mean ± SD 5.0–6.7 ± 3.9–4.3) using the published formulae compared to our formula (mean ± SD 0.2 ± 4.0).
Conclusions. Currently available formulae to guide infusion therapy in hyper- and normonatraemic states do not accurately predict changes of serum sodium in the individual ICU patient. In clinical practice, infusion therapy should be based on the reasons for hypernatraemia and serial measurements of serum sodium to avoid evolution of derangements.
Keywords: correction; formula; hypernatraemia; prediction; sodium
Abbreviations: Na1, serum sodium concentration day 1 • Na2, serum sodium concentration day 2 • TBW, total body water: TBW calculated on the day of admission with correction based on the total daily water balance • Nainf and Kinf, sodium and potassium concentration of the infused fluids • Volinf, volume infused in ml • Nainput and Kinput, sodium and potassium concentration of all applicated fluids (oral, intravenous) • Volinput, total volume input in ml (oral, intravenous) • Naurine and Kurine, sodium and potassium concentration of the urine • Volurine, volume urine in ml • 
Vol, difference in volume between measured inputs and outputs • Volout, total volume output: urine + extrarenal fluid loss via tubes (nasogastric suction and wound drains) • (Na+K)out, sodium and potassium concentration of extrarenal losses, calculated as a hypotonic fluid with a fixed value of 110 mmol/l
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Introduction |
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Hypernatraemia is a frequent and clinically relevant electrolyte derangement in the critically ill patients. Its prevalence has been reported to be 5–7% at intensive care units (ICUs) [1,2]. Most cases of hypernatraemia actually develop during a hospital stay, and thus its occurrence has been regarded as an indicator of quality of care [3]. Even small changes in serum sodium are associated with untoward effects, and hypernatraemia has been shown to present an independent risk factor of mortality [1]. The adverse effects of hypernatraemia may be mediated not only by the electrolyte derangement per se but potentially also by an inappropriate correction [4–6].
Because of the detrimental effects of hypernatraemia on the course of disease and the outcome, it is of utmost importance for the physician at the ICU to avoid its development. If hypernatraemia is already present, then its appropriate treatment without inducement of therapy-related side effects is the goal. Several formulae have been proposed to serve as a guide for infusion therapy of dysnatraemic states [7–9]. These mathematical approaches simplify the mechanisms of sodium and water handling and have major limitations [10]. Unfortunately, only one of these formulae was assessed in a larger clinical study regarding the potential in predicting serum sodium concentrations [11]. Some formulae actually were only evaluated in hypothetical cases [8,9].
These formulae were primarily created for the guidance of correction of hyper- and hyponatraemia. With the aim of avoiding the evolution of dysnatraemic states, it is of further interest whether such formulae are also capable to predict the day-per-day change of serum sodium levels in normonatraemic patients in order to preserve the electrolyte balance.
In this retrospective study, we assessed in ICU patients, in whom complete information on electrolyte and water balance was available, the predictive value of three formulae generally proposed for the guidance of infusion therapy. Additionally, a formula incorporating electrolyte-free water loss was assessed. These different formulae were evaluated both in patients with hypernatraemia with the aim of correcting it, and in patients with normonatraemia of maintaining electrolyte equilibrium.
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Subjects and methods |
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A retrospective analysis was performed in 66 intensive care patients with at least one episode of hypernatraemia during the stay on the ICU. All patients with hypernatraemia at the time of admission to the ICU were excluded from the study. A day-per-day prediction of serum sodium levels was obtained based on the currently available formulae (see the Appendix) for the prediction of the change in serum sodium levels in hypernatraemic as well as normonatraemic patients.
We used the Adrogué–Madias, the Barsoum–Levine and the Kurtz–Nguyen formulae and a formula based on the calculation of the electrolyte-free water clearance (EFWC) proposed by ourselves [7–9]. Because not all of the formulae were designed for the prediction of the day-to-day serum sodium concentration, some mathematical derivations had to be made (see the Appendix). At least the calculations were done using the following formulae (for abbreviations see the Appendix).
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| (1) |
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| (2) |
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| (3) |
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| (4) |
According to the adapted formula, the next day serum sodium concentration was calculated by the pre-day serum sodium level and total body water (TBW) together with the inputs and the outputs of fluid volume, sodium and potassium within 24 h. The predicted and measured sodium levels were compared statistically.
The 66 patients stayed for a total of 1034 days at the ICU. In the end, 681 days of intensive care stay were able to be used in the analysis. The day of admission (66 days) could not be included in the analysis as well as an additional 277 days because of the lack of data for the calculation of the formulae. Furthermore, 10 observation days were excluded from the analysis because of severe diarrhoea.
The following daily measured parameters were recorded for the analysis:
Serum: sodium, potassium, osmolality.
Total daily outputs and inputs of volume and sodium–potassium concentration.
- Urine: daily volume, sodium, potassium and osmolality.
- Drainage tubes: nasogastric suction, wound drains, pleural effusion; volume, sodium and potassium concentration based on empirical data. The fluid of nasogastric suction was calculated with a sodium/ potassium concentration of 110 mmol/l. Pleural effusion and wound drains were calculated as isotonic fluids.
Inputs
The volume and the sodium and potassium concentration of
- intravenous fluid including volume replacement,
- solvent solutions for medications (sodium content of antibiotics was not included) and
- enteral and parenteral nutrition solutions.
To ensure practicability in the daily routine, some assum- ptions had to be made, which potentially may affect the results of the calculations. At normal body temperature, oxidation water formation equals perspiration and therefore no volume change will occur during normal body temperature and adequate nutrition [12]. Any increase in body temperature will lead to an augmentation in perspiration. In the case of fever, perspiration could only be calculated from the standard formula but not measured. Because body temperature often changes (due to fever lowering medication) over 24 h, it is not possible to calculate perspiration per day individually. Therefore, perspiration was not included in the current ongoing losses in all formulae. Moreover, the measurement or calculation of gastrointestinal losses (volume and electrolytes) via stool is not possible to measure in the daily routine. So stool losses were not included in the calculations, and patient-days with documented severe diarrhoea were eliminated from the study (n = 10).
TBW was calculated as body weight x 0.6 for men and body weight x 0.5 for women [12]. Because it is rather difficult to weigh the patients daily on the ICU, daily TBW calculation was done according to the fluid balances (total volume input – total loss volume).
Statistics
The purpose of the study was to analyse the predictive value of four different formulae on longitudinal serum sodium levels in ICU patients with hyper- and normonatraemia. A linear regression analysis was performed to estimate r2 for analysing how much of the variability of the predicted values may be explained by the variability of measured values. The variability of predicted values along the measured range of serum sodium levels is provided as the Bland–Altman plot [13]. Residual statistics of the linear models are provided in a separate supplemental data sheet.
This study was approved by the Ethics Commission of the Medical University of Vienna, Austria.
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Results |
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The demographics of the included patients are given in Table 1. All patients developed hypernatraemia at least once during the ICU stay. The all-cause mortality was 42%. Causes of ICU-acquired hypernatraemia were defined as follows: positive sodium balance, administration of loop diuretics, osmotic diuresis, renal failure, extrarenal water losses and diabetes insipidus (multiple choices were possible). The most common mechanism for the development of ICU-acquired hypernatraemia was an increase in free water loss due to the disturbance of the renal concentration mechanism. Renal concentration defects were defined as a urine osmolality of <800 mmol/l during the rise of serum sodium. The increase in renal free water loss includes administration of furosemide (35%), osmotic diuresis (35%) and renal failure (20%). An exaggerated sodium intake due to the administration of sodium-rich infusions and/or nutritions accounted for 48% of cases of ICU-acquired hypernatraemia and thus was the most important single mechanism for the development of hypernatraemia. Extrarenal water losses due to fever (8%) or via tubes (7%) were rare causes for the loss of free water.
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A single mechanism for hypernatraemia was identified in 50 periods. Two simultaneous mechanisms for hypernatraemia were identified in 20 periods and three mechanisms in 6 periods. Mean central venous pressure was 14.1 (±6.0) indicating that most patients were at least eu- or hypervolaemic during hypernatraemia. The average duration of hypernatraemia was 2 days in our patients. Almost all patients (>90%) developed hypernatraemia during their first 7 days of ICU stay. The mean individual daily changes in serum sodium were
1.5 ± 3.5 mmol/l. According to the serum sodium level on Day 1, we measured ongoing sodium, potassium and water inputs and outputs (for 24 h) and calculated the predicted serum sodium level on Day 2 using different formulae. The calculations were correlated to the real change in the serum sodium level.
We analysed a total of 681 patient-days in 66 patients. The mean ± SD differences for real sodium levels were 4.56 ± 4.36 for the Adrogué–Madias formula, 3.37 ± 4.41 for the Barsoum–Levine formula, –1.47 ± 5.26 for the new EFWC-based formula and 3.93 ± 4.76 for the Kurtz–Nguyen formula. In hypernatraemic stages (194 patient-days) differences in mean ± SD were even greater: 6.68 ± 4.27 for the Adrogué–Madias formula, 4.98 ± 3.91 for the Barsoum–Levine formula and 5.31 ± 4.3 for the Kurtz–Nguyen formula, whereas the difference was 0.16 ± 3.99 and even smaller for the EFWC formula.
As shown in Table 2, all calculations in the total patient group correlated significantly with the serum sodium level on the next day (r2 0.45–0.51; P < 0.005). In the linear regression analysis of hypernatraemic days the correlations were less good, but still significant (r2 0.1–0.25; P < 0.005). Inclusion of perspiration did not further improve correlation coefficients (data not shown).
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The data are presented graphically using a Bland–Altman plot (Figure 1). Whereas Adrogué–Madias, Barsoum–Levine and Kurtz–Nguyen overestimated, our own EFWC-based formula slightly underestimated the mean change in serum sodium levels.
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Whereas for the whole group there was a rather good correlation between measured and predicted serum sodium concentrations, there were large variations in individual patients (Figure 1), the highest accounting for 10–15 mmol/l with all tested formulae. The predictions of daily serum sodium changes were not statistically different with all used formulae if the serum sodium level either increased/decreased by >3 mmol/l/day or was stable (Table 3).
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Discussion |
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In this investigation, we have conducted for the first time in a systematic manner a comparison of four formulae advocated for guidance of infusion therapy in hyper- and normonatraemic states in the ICU setting. We have shown that in the overall group, there was a good correlation between the predicted and observed changes in serum sodium concentration, but the formulae were absolutely inadequate in predicting serum sodium in the individual patient. A formula taking into account the electrolyte-free water loss allowed the most accurate prediction in hypernatraemia, although it was still not satisfyingly accurate in the individual patient.
Recently, we have shown that hypernatraemia is a frequent electrolyte disorder in the intensive care setting and associated with increased mortality and morbidity [1,3,14]. Most cases of hypernatraemia actually develop during the ICU stay, and hypernatraemia was suggested to be an indicator for the quality of medical care [3,15]. The causes for hypernatraemia in the ICU setting differ from those acquired outside the hospital. Although inadequate fluid prescription, defects in renal concentration mechanisms (i.e. diuretic therapy) and a high sodium load predominate in the hospitalized patient, extrarenal water losses were the main reasons for community acquired hypernatraemia [2]. So it was not surprising that in our study population, the patients were mostly eu- or hypervolaemic (data not shown).
All of the used formulae for the prediction of serum sodium levels are based on the same assumption, i.e. that all daily inputs and outputs of sodium/potassium and water determine the change in serum sodium. The various formulae differ only in the degree of simplification of the original formula proposed by Edelman (see the Appendix) [16]. For the total group, all currently available formulae correlated well with the measured change in serum sodium. Three of the four formulae overestimated the changes in serum sodium levels and predicted sodium levels higher than measured, whereas the new formula of EFWC underestimated the changes slightly (Figure 1). These constant over (or under) estimations could theoretically be eliminated by introducing a correction factor for each formula. But the scattering of the results is too high to make safe predictions in the individual case. In the linear regression model, we calculated an r2 of 0.5 for all formulae, indicating that only 50% of the variability of the predicted values may be explained by the variability of measured values. For patients with hypernatraemia, the formulae are even less predictive than those for the normonatraemic patients (r2 0.2). Because a maximal day-to-day deviation of <5 mmol/l should be demanded for the recommended correction rate of 8–10 mmol/day, currently available formulae were not accurate enough and actually could lead to severe electrolyte derangements [4]. Deviations between calculations and the observed concentrations as large as 15 mmol/l were observed, and they illustrated a range of error by which serious complications can be induced during infusion therapy. So the recommended formulae can give the physician in care a false impression of being on the safer side [4,11].
The Adrogué–Madias formula is the most frequently recommended formula in different reviews as a guide for therapy in hyper- and hyponatraemia [4,17,18]. It is quite surprising that this formula was just recently assessed for reliability in clinical practice for the first time [11]. Even more astonishing, the Barsoum–Levine and Kurtz–Nguyen formulae were assessed in hypothetical cases only. In the study of Liamis, the Adrogué–Madias formula was used to calculate the necessary volume of a sodium chloride solution to achieve a defined change in the serum sodium level. In contrast to our observation, the predicted change in serum sodium was definitely lower than the measured change 24 h after the start of therapy (151.1 ± 6.4 versus 153 ± 8.3). The patient population in this study was different from ours because most subjects were hypovolaemic (62.8%), whereas our study population was mainly eu- or hypervolaemic. The authors concluded that necessary volume for infusion therapy could be adequately calculated using the Adrogué–Madias formula, but in single cases deviations of >4 mmol/l during time periods of <24 h could be observed [11].
Why are the various formulae so inaccurate in predicting serum sodium? All mathematical calculations of water metabolism are based on major simplifications [10]. The formulae are based on the same principles that were published by Edelman in 1958 and differ only in minor aspects [16]. The formula proposed by Adrogué and Madias was designed to predict the changes of serum sodium after the infusion of 1 litre of sodium (and potassium)-containing solution [7]. Although ongoing renal or extrarenal fluid and electrolyte losses or the change in TBW (if >1 litre was given) was ignored in this formula, the predicted sodium levels were similar to those observed with other calculations. This is surprising since the strength of the formula is the short-time prediction of serum sodium after giving a defined fluid load because losses are less relevant during such short observation periods.
Barsoum and Levine proposed an extended Adrogué–Madias formula, which includes the ongoing losses and the net change in TBW and should predict the change in serum sodium after the infusion of a defined solution [8]. To make the formula comparable with the Nguyen–Kurtz formula, we included all the calculated sodium/potassium and volume balances (oral, intravenous, etc.) as described in the original publication. The approach to hypernatraemia by Nguyen and Kurtz avoids the simplification of the original Edelman formula made by Barsoum–Levine and uses empirical evaluated correction factors (slope and 
-intercept). The authors mentioned that these correction factors were necessary for accurate prediction of serum sodium changes. But the reliability of the slope and -intercept determination was recently criticized [19]. Furthermore, Nguyen and Kurtz proposed that all ongoing inputs and losses of volume and sodium/potassium via perspiration, wound drains, stool, nasogastric suction, etc. were necessary for an exact calculation [9]. This theoretical approach is correct, but not usable in the daily routine where stool collections and exact calculations of perspiration are impossible. Therefore, in our calculations, the only difference to the Barsoum–Levine formula was the slope and the -intercept at least.
The formula using electrolyte-free water losses (EFWC-based formula) designed by ourselves is based on the assumption that the kidney is the main regulator in water metabolism and that the primary fluid administrated on the ICU often contains no electrolyte-free water (i.e. sodium chloride 0.9%). This means that it is the response of the kidney to such a fluid load, and not the infused volume itself, that affects serum sodium levels. Obviously, these simplifications are appropriate only if major extrarenal losses of sodium and water are not present. Renal sodium/potassium and water handling was calculated by obtaining the electrolyte-free water clearance as described by Rose [20]. The EFWC depicts the loss of pure water by using the ratio of the concentration of urine sodium and potassium to serum sodium. For the EFWC-based formula, total sodium body content was assumed to be constant in relation to TBW (if no EFW was put in) and the EFWC was subtracted from the TBW to predict the change in serum sodium levels. It can be criticized that the input of electrolyte-free water also contributes to the change in serum sodium. But the insertion of the electrolyte-free water input in our formula was associated with major deviations (>15 mmol/l) in the predicted serum sodium from the measured values (data not shown). This observation was surprising because the total electrolyte-free water intake was even high (2000–3000 ml/day; for reasons to avoid/treat hypernatraemia) in our patients. So the electrolyte-free water intake maybe balanced by the unmeasured free water losses.
Our EFWC calculation is only partly comparable to the tonicity balance, another method for the calculation of serum sodium changes. Halperin and co-workers have shown that the calculation of EFWC offers comparable results for changes in serum sodium levels as the tonicity balance if the admitted fluid contains no electrolyte-free water [21]. Nevertheless, some information on pathophysiology will be lost by calculation of EFWC compared to the tonicity balance, which deals with total sodium/potassium and volume inputs and outputs. Our formula predicted the daily serum sodium changes equally well to the other formulae. In hypernatraemic states, the calculations were even more accurate. This may be due to the fact that the major reason for evolution of hypernatraemia in our patient group was a disturbance of the urinary concentration mechanisms. It has to be stated clearly that the EFWC-based formula was not created to have a new tool for the prediction of serum sodium changes, but to show the importance of EFWC in the pathogenesis of hypernatraemia in the ICU. Except for the Adrogué–Madias formula, all other formulae are less useful in the prediction of serum sodium, because the change in urinary composition after the introduction of a fluid therapy could not be predicted. So for the prediction of serum sodium, the former urinary composition has to be used. We recommend the calculation of EFWC in the daily routine to measure the impact of the kidney on the changes in serum sodium. If the kidney is the main contributor to hypernatraemia, it could therefore be recognized even before hypernatraemia develops.
Besides the necessary mathematical simplifications, further physiological reasons imply the inability to predict serum sodium changes by the various formulae proposed in the literature. The causes as well as the maintenance factors of hypernatraemia often change very rapidly and cannot be assessed prospectively. For instance, the impact of fluid therapy on renal sodium and water handling or the non-osmotic stimulation of vasopressin secretion presents unpredictable factors. Recent investigations have shown that sodium can be stored in the skin in an osmotically inactive form. It is not possible to predict under which circumstances how much of the infused sodium will be stored in these pools [22–24].
This retrospective analysis has some obvious methodological limitations that were necessary to simulate the daily routine. We used two major simplifications: we excluded data from severe calculable factors, such as perspiration or stool losses. Moreover, TBW was calculated using the body weight on admission. Concise evaluations of daily changes of TBW are nearly impossible in the ICU setting even if body weight is measured daily. We estimated the change of TBW by the calculation of the total daily volume balance. Additionally, formulae to guide infusion therapy in dysnatraemias remain to be tested for accuracy in a hyponatraemic collective. Because of the totally different pathophysiology of hyponatraemia, we cannot make any assumptions on the validity of the formulae in the hyponatraemic state.
We conclude that the various formulae recommended for guidance of infusion therapy for the correction of hypernatraemic states are inaccurate in the clinical setting for different reasons. Although there is a good correlation between the predicted and actual changes for the whole group, the formulae were unable to predict changes in the serum sodium level in the individual patient and thus are not without risk in practice. The analysis of major pathophysiological mechanisms (extrarenal and renal losses of electrolyte-free water, volume status, etc) that contributes to hypernatraemia was more important for therapy guidance than all the proposed formulae [21]. Integration of electrolyte-free water clearance into the calculation might improve the predictive power. However, for the daily clinical practice, as all reviews that discuss the tested formulae state, regular measurements of serum sodium and electrolyte balances are mandatory to correct dysnatraemias, to maintain normonatraemia and to avoid complications of infusion therapy.
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Appendix |
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All of the used formulae were based on the Edelman approach that defines that the relation of the total body exchangeable sodium and potassium content to total body water determines the serum sodium level (A.7):
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| (A.1) |
Therefore, 
, where Nae and Ke represent the total exchangeable sodium and potassium content of the body, respectively. According to that only a change in Nae + Ke or in TBW can influence the serum sodium level:
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| (A.2) |
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A.1. Adrogué–Madias formula (1) |
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 TopAbstractIntroductionSubjects and methodsResultsDiscussionAppendix A.1. Adrogue-Madias formula (1) A.2. Barsoum-Levine formula [4]A.3 Nguyen-Kurtz formula [16]A.4. Electrolyte-free water...References |
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The original equation proposed by Adrogué and Madias was designed to estimate the change in serum sodium after the infusion of 1 litre of infusate:
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| (A.3) |
To predict the effect of a certain infusion on serum sodium concentration, we used the original formula and substitute only for a variable volume of the solution [1]:
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| (A.4) |
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A.2. Barsoum–Levine formula [4] |
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TopAbstractIntroductionSubjects and methodsResultsDiscussionAppendixA.1. Adrogue-Madias formula (1)A.2. Barsoum-Levine formula [4]A.3 Nguyen-Kurtz formula [16]A.4. Electrolyte-free water...References |
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The formula proposed by Barsoum and Levine is derived from the Adrogué–Madias formula. It additionally contributes to ongoing fluid and sodium/potassium gains and losses. It was designed to predict the change (
Na) in serum sodium concentration:
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| (A.5) |
To derive the formula for predicting the new serum sodium concentration, we just have to solve the formula for Na. This will result in the following equation:
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| (A.6) |
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A.3 Nguyen–Kurtz formula [16] |
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In comparison to the other formulae, the Nguyen–Kurtz formula is based on the original (not simplified) formula by Edelman:
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| (A.7) |
Two important factors (slope and -intercept) of water metabolism were included in the formula. The physiological and pathological effect of the slope (1.11) and the -intercept (–25.6) are discussed in detail elsewhere [15,16]. In short, the effect of the Gibbs–Donnan equilibrium and the osmotic coefficient of sodium salts were responsible for the slope of 1.11; the -intercept consists of the osmotically inactive exchangeable sodium and potassium, the plasma water potassium concentration and the non-sodium/non-potassium osmotically active osmoles. For the calculation of Naplasma (instead of Naplasma-water), the slope is 1.03 and the -intercept is 23.8.
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| (A.8) |
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A.4. Electrolyte-free water clearance formula |
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Our formula is based on the assumption that the loss of electrolyte-free water in the urine is the major determent for the new serum sodium concentration. In the nominator, the serum sodium concentration is multiplied by TBW to calculate the total body sodium content. The denomi- nator consists of the subtraction of the electrolyte-free water clearance (EFWC) in the urine from TBW. The impact of the slope and the
-intercept on the serum sodium levels was not included in the formula (see the Discussion section). The EFWC is used in contrast to the other formulae instead of the change in total exchangeable sodium and potassium as well as the change in TBW (A.8). In comparison to the Adrogué–Madias formula that ignores all outputs, our formula ignores all sodium/potassium and water inputs. This is further discussed in the main text:
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| (A.9) |
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| (A.10) |
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Acknowledgments |
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The study was performed at the Critical Care Unit 13H1, Clinic for Internal Medicine III, Medical University of Vienna.
Conflict of interest statement. None declared.
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Notes |
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* Both authors contributed equally to this study.
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Accepted in revised form: 26. 6.08
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