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Serum Sodium Concentration and Tonicity in Hyperglycemic Crises: Major Influences and Treatment Implications

2019; Wiley; Volume: 8; Issue: 19 Linguagem: Inglês

10.1161/jaha.118.011786

2047-9980

Antonios H. Tzamaloukas, Zeid Khitan, Robert H. Glew, Maria‐Eleni Roumelioti, Helbert Rondon‐Berrios, Moses Elisaf, Dominic S. Raj, Jonathan Owen, Yijuan Sun, Kostas C. Siamopoulos, Mark Rohrscheib, Todd S. Ing, Glen H. Murata, Joseph I. Shapiro, Deepak Malhotra,

Diet and metabolism studies

HomeJournal of the American Heart AssociationVol. 8, No. 19Serum Sodium Concentration and Tonicity in Hyperglycemic Crises: Major Influences and Treatment Implications Open AccessReview ArticlePDF/EPUBAboutView PDFView EPUBSections ToolsAdd to favoritesDownload citationsTrack citations ShareShare onFacebookTwitterLinked InMendeleyRedditDiggEmail Jump toSupplementary MaterialsOpen AccessReview ArticlePDF/EPUBSerum Sodium Concentration and Tonicity in Hyperglycemic Crises: Major Influences and Treatment Implications Antonios H. Tzamaloukas, MD, Zeid J. Khitan, MD, Robert H. Glew, PhD, Maria‐Eleni Roumelioti, MD, Helbert Rondon‐Berrios, MD, Moses S. Elisaf, MD, Dominic S. Raj, MD, Jonathan Owen, MD, Yijuan Sun, MD, Kostas C. Siamopoulos, MD, Mark Rohrscheib, MD, Todd S. Ing, MD, Glen H. Murata, MD, Joseph I. Shapiro, and MD, and Deepak MalhotraMD, PhD Antonios H. TzamaloukasAntonios H. Tzamaloukas Raymond G. Murphy Veterans Affairs Medical Center, , Albuquerque, , NM University of New Mexico School of Medicine, , Albuquerque, , NM , Zeid J. KhitanZeid J. Khitan Joan C. Edwards School of Medicine, , Marshall University, , Huntington, , WV , Robert H. GlewRobert H. Glew University of New Mexico School of Medicine, , Albuquerque, , NM , Maria‐Eleni RoumeliotiMaria‐Eleni Roumelioti University of New Mexico School of Medicine, , Albuquerque, , NM , Helbert Rondon‐BerriosHelbert Rondon‐Berrios University of Pittsburgh School of Medicine, , Pittsburgh, , PA , Moses S. ElisafMoses S. Elisaf University of Ioannina School of Medicine, , Ioannina, , Greece , Dominic S. RajDominic S. Raj George Washington University School of Medicine, , Washington, , DC , Jonathan OwenJonathan Owen University of New Mexico School of Medicine, , Albuquerque, , NM , Yijuan SunYijuan Sun Raymond G. Murphy Veterans Affairs Medical Center, , Albuquerque, , NM University of New Mexico School of Medicine, , Albuquerque, , NM , Kostas C. SiamopoulosKostas C. Siamopoulos University of Ioannina School of Medicine, , Ioannina, , Greece , Mark RohrscheibMark Rohrscheib University of New Mexico School of Medicine, , Albuquerque, , NM , Todd S. IngTodd S. Ing Stritch School of Medicine, , Loyola University Chicago, , Maywood, , IL , Glen H. MurataGlen H. Murata Raymond G. Murphy Veterans Affairs Medical Center, , Albuquerque, , NM , Joseph I. ShapiroJoseph I. Shapiro Joan C. Edwards School of Medicine, , Marshall University, , Huntington, , WV and Deepak MalhotraDeepak Malhotra *Correspondence to: Deepak Malhotra, MD, PhD, Division of Nephrology, University of Toledo, Health Science Campus Mail Stop +1186, 3000 Arlington Avenue, Toledo, OH 43614‐2598. E‐mail: E-mail Address: [email protected] University of Toledo School of Medicine, , Toledo, , OH Originally published24 Sep 2019https://doi.org/10.1161/JAHA.118.011786Journal of the American Heart Association. 2019;8:e011786IntroductionMaintenance of the volume of all cells, particularly those of the central nervous system, is critical for their function and survival.1, 2, 3, 4, 5, 6 Tonicity (ie, effective osmolarity) of a solution refers to its property to cause osmotic fluid shifts into or out of cells suspended in it. Direct determination of serum tonicity is not readily available for clinical applications.6 Serum sodium concentration ([Na]S) is the main parameter used as a surrogate value for serum tonicity.5, 6, 7 The only direct information provided by [Na]S is whether serum tonicity is normal (the volume of cells exposed to a serum with normal [Na]S is not affected), low (the volume of cells exposed to a serum with low [Na]S increases by osmotic intracellular transfer of water), or high (the volume of cells exposed to a serum with high [Na]S decreases by osmotic transfer of water out of the cells).6, 7In a pivotal study, Edelman and coinvestigators identified total body sodium, total body potassium, and total body water as the universal determinants of [Na]S in patients with various states potentially associated with extracellular volume disturbances.8 Abnormalities in [Na]S usually result from changes in the external balance of one of its 3 determinants or a combination thereof. The relations between [Na]S and total body sodium, total body potassium, and total body water have been expressed by various formulas. The original Edelman formula expresses sodium concentration in plasma water.8 The Nguyen and Kurtz formula expresses sodium concentration in plasma, which is essentially equal to [Na]S.9 Nguyen and Kurtz developed their formula by multiplying the components of the Edelman formula by a correction coefficient equal to 0.93, which represents the normal plasma water fraction. The Rose formula, which represents a simplified version of the Edelman formula, expresses [Na]S as the fraction (total body sodium plus total body potassium) over total body water.10 Formulas calculating the tonicity of replacement solutions for correction of dysnatremias applied in clinical practice11, 12, 13, 14 are based on the Rose formula, which will also be the basis of the calculations in this review.The principle that underlies the distribution of body water in the 2 major body‐fluid compartments states that the intracellular/extracellular volume ratio is equal to the intracellular/extracellular solute ratio.15 This relationship is a direct consequence of Peter's osmotic principle, which states that in the steady state, solute concentration (osmolality) is equal in the intracellular and extracellular fluids.16 Total body sodium and potassium represent the major solutes in body fluids: sodium is essentially restricted in the extracellular compartment and potassium in the intracellular compartment. Consequently, total body sodium is a measure of effective extracellular solutes, whereas total body potassium represents the effective intracellular solutes.Hyperglycemic crises create complex disturbances in body water and its distribution between the intracellular and extracellular compartments, in addition to tonicity problems not reflected directly in [Na]S. This review analyzes the pathogenesis and treatment of hyperglycemic hypertonicity.Serum Hypertonicity as an Exclusive Consequence of Development of HyperglycemiaWhen solutes with extracellular distribution, other than sodium salts, do not exceed their normal concentration, the expression 2×[Na]S represents approximately 98% of serum tonicity. Solutes distributed in total body water, such as urea, ethanol, methanol, or propyl alcohol, increase osmolality but do not change this relationship between [Na]S and tonicity because they do not affect the volume of cells. In contrast, gain of solutes restricted in the extracellular compartment, other than sodium salts, causes hypertonicity resulting in osmotic fluid exit from the intracellular compartment and decrease in [Na]S. In this case, [Na]S alone does not indicate the state of tonicity. Hypertonicity may result from gain of exogenous solutes with extracellular distribution, for example, mannitol or low‐molecular‐weight radiographic contrast agents. However, hyperglycemia is the major clinical condition that creates hypertonicity challenges from gain of extracellular solutes other than sodium salts.17Glucose infused as a bolus is distributed in the extracellular compartment.18, 19, 20 After glucose enters the cells, it is metabolized to carbon dioxide and water or compounds with negligible osmotic activity (eg, glycogen). Consequently, regarding internal solute balance, glucose is considered an extracellular solute that contributes to the tonicity of body fluids.5, 6, 7, 21, 22 Gains in glucose raise the effective extracellular solute and result in hypertonicity.21 Serum tonicity in patients with hyperglycemia is calculated as the sum of 2×[Na]S plus the serum glucose concentration ([Glu]S) in mmol/L.21Correction of hypertonicity constitutes one of the main aims and challenges of managing hyperglycemic crises.22 Correction of hyperglycemia results in loss of effective extracellular solute23 and osmotic transfer of extracellular water into the cells, leading to a rise in [Na]S.24 Serum tonicity decreases during correction of hyperglycemia because the decrease in osmolarity secondary to the decrease in [Glu]S (Δ[Glu]S) is greater than the corresponding increase in osmolarity secondary to the rise in [Na]S (Δ[Na]S).24 The magnitude of the change in tonicity due to the level of correction of hyperglycemia must be accurately predicted because hyperglycemia causes a second major increase in body fluid tonicity through osmotic diuresis that requires additional measures for its correction.7 This second hyperglycemic influence on tonicity will be addressed later in this report.Table 1 shows formulas expressing the changes in the determinants of tonicity during development or correction of hyperglycemia in patients without changes in the external balances of water, sodium, or potassium (ie, in a closed system). The prediction of the extent of decrement in tonicity consequent to a given Δ[Glu]S requires calculation of the Δ[Na]S in addition to the projected Δ[Glu]S. A key step for this prediction was provided by Katz, who calculated that [Na]S decreases by 1.6 mmol/L for each increase in [Glu]S by 5.6 mmol/L, or by 100 mg/dL (formula (1) in Table 1).25 In the same table, formula (2) by Al‐Kudsi and collaborators, based on the Katz value of Δ[Na]S/Δ[Glu]S, predicts the value of [Na]S after a decrease of [Glu]S from any hyperglycemic level to 5.6 mmol/L.26 The performance of the Al‐Kudsi formula depends on the accuracy of Katz's predicted value of Δ[Na]S/Δ[Glu]S.Table 1. Formulas Expressing Serum Tonicity and Its Indexes in a Closed System of HyperglycemiaKatz formula for Δ[Na]S/Δ[Glu]S25: Download figure ((1)) [Na]S at hyperglycemia corrected to [Glu]S of 5.6 mmol/L using the Al‐Kudsi formula26:Download figure ((2)) Complete Δ[Na]S/Δ[Glu]S formula expressing development of hyperglycemia in a closed system Download figure ((3)) [Na]S in hyperglycemia corrected to any given euglycemic value in a closed system using formula (3):Download figure ((4)) The value Δ[Glu]S as a function of [Glu]A during development of hyperglycemia30:Download figure ((5)) John Wiley & Sons, Ltd[Glu]S, Δ[Glu]S, and [Glu]A are expressed in mmol/L in formulas (1) through (4); formula (3) expresses the ratio Δ[Na]S/Δ[Glu]S in mmol/L per mmol/L. Comparison of its results to the results of formula (2) requires multiplication of its findings by 5.6; formula (2) with the original expression of [Glu]S in mg/dL26 is as follows:Download figure[Glu]A2 has a negative value in formula (4); formula (4) requires prior calculation of Δ[Glu]S3 by formula (5). Subscript numbers indicate stage. α indicates intracellular/extracellular volume ratio; Δ[Glu]S, change in serum glucose concentration; Δ[Na]S, change in serum sodium concentration; [Glu]A, change in glucose concentration per liter of baseline extracellular volume; [Glu]S, serum glucose concentration; [Na]S, serum sodium concentration; [Na]SCorrected, corrected serum sodium concentration. The subscripts 1 and 2 refer to euglycemia and hyperglycemia, respectively.Studies of Katz's Δ[Na]S/Δ[Glu]S FormulaThe Katz formula has been subjected to theoretical analysis and clinical utility and reliability studies in a closed system and to clinical observations in an open system.Closed‐System ObservationsKatz calculated the ratio Δ[Na]S/Δ[Glu]S assuming only an increase in extracellular glucose content and no external changes in body water or monovalent cations (ie, in a closed system). Several theoretical analyses that elaborated on and extended Katz's calculations identified the mathematical determinants of Δ[Na]S/Δ[Glu]S in a closed system.27, 28, 29, 30, 31, 32 The glucose gained per liter of the baseline extracellular volume ([Glu]A) and the ratio of intracellular/extracellular volume at baseline euglycemia (ratio α1) were shown to be the dominant determinants of the magnitude of the changes induced by development of hyperglycemia in a closed system, including internal osmotic volume shifts, changes in tonicity, [Na]S and [Glu]S, and the ratio Δ[Na]S/Δ[Glu]S.30, 31 The contribution of [Glu]A to the magnitude of osmotic fluid shifts and changes in tonicity, [Na]S, and [Glu]S is intuitive. Its contribution to the Δ[Na]S/Δ[Glu]S ratio will be discussed below.The ratio of intracellular/extracellular volume (ratio α) decreases during expansion of the extracellular volume due to either salt and water retention or osmotic transfer of intracellular water into the extracellular compartment in states of hypertonicity, and it increases during development of hypovolemia from external fluid losses or from transfer of extracellular water into the cells in states of hypotonicity. The contribution of the euglycemic volume ratio to the changes in tonicity, [Na]S, and [Glu]S induced by hyperglycemia is a consequence of the fact that total body water determines the change in tonicity secondary to gain in solute with extracellular distribution along with the amount of solute gained.5 The increase in serum tonicity (ΔTon) after a gain in [Glu]S is expressed as the algebraic sum Δ[Na]S+Δ[Glu]S. Note that Δ[Na]S has a negative sign because [Na]S decreases during development of hyperglycemia.24 ΔTon is determined by the amount of glucose gained divided by total body water, whereas Δ[Glu]S is equal to the amount of glucose gained divided by extracellular volume.5 Therefore, the relationship between extracellular volume and total body water is a major determinant of the ratios ΔTon/Δ[Glu]S and Δ[Na]S/Δ[Glu]S.29, 30, 31 The baseline volume ratio (α1) is the most appropriate expression of the relationship between extracellular volume and total body water.30 For a given degree of hyperglycemia, the rise in tonicity will be lower, and thus the decrease in [Na]S will be greater, when the baseline intracellular volume is very large in comparison to the extracellular volume (ie, in a volume‐depleted state in which the volume ratio α1 has a large value), because the abundance of intracellular volume provides a relative abundance of water for osmotic exchanges. An abundance of extracellular volume in edematous states, characterized by low value of the ratio α1, has effects exactly opposite those of a high value α1 on the rise in tonicity and drop in [Na]S during development of hyperglycemia because the intracellular water available for osmotic exchanges is relatively sparse in this case.Another determinant of changes induced by glucose gain in a closed system is the baseline tonicity, which is composed of the baseline [Na]S ([Na]S1) and the baseline serum glucose concentration ([Glu]S1).30 In Table 1, formula (3) expresses the Δ[Na]S/Δ[Glu]S value as a function of its identified determinants,30 whereas formula (4) expresses the corrected sodium for the degree of hyperglycemia [Na]S, which is calculated using the Δ[Na]S/Δ[Glu]S expression in formula (3).The degree of hyperglycemia characterizes, along with other clinical and laboratory features, the severity of hyperglycemic crises.17, 22 The amount of glucose that needs to be added to the extracellular fluids to produce similar degrees of hyperglycemia depends on the extracellular volume. The value [Glu]A, which is the glucose added—or removed—per liter of initial extracellular volume, was introduced in formulas (3) and (3) because it allows comparable Δ[Glu]S values in patients with varying extracellular volumes. The total amount of glucose gain is the product [Glu]A times the baseline extracellular volume. Note that although [Glu]A and Δ[Glu]S express the same change in body glucose, the values differ because [Glu]A is a measure of the glucose gain or loss per liter of the baseline extracellular volume, whereas Δ[Glu]S expresses the difference between [Glu]S values in 2 different states of extracellular volume: the baseline state and the state after the change in extracellular glucose content. In a closed system, extracellular volume increases during development of hyperglycemia and decreases during its correction. The relationship between [Glu]A and Δ[Glu]S is expressed by formula (4) in Table 1.30Figure 1 shows [Glu]S changes for widely varying values of the volume ratio α1 and [Glu]A.Download figureDownload PowerPointFigure 1. Plasma glucose concentrations at various levels of extracellular glucose gain and different ratios of euglycemic intracellular/extracellular volume (ICFV/ECFV ratio).Regardless of the status of extracellular volume, as [Glu]S rises, the value Δ[Glu]S becomes progressively lower than the value [Glu]A because extracellular volume increases progressively as [Glu]S rises in a closed system. However, the same [Glu]A produces comparable Δ[Glu]S values at different states of extracellular volume even in extreme hyperglycemia. For example, if baseline [Na]S and [Glu]S values are 140 and 5.6 mmol/L, respectively, and [Glu]A is 112 mmol/L (2016 mg/dL), Δ[Glu]S by formula (4) will be 92.1 mmol/L (1659 mg/dL) in euvolemia (α1=1.50), 87.2 mmol/L (1567 mg/dL) in severe hypovolemia (α1=3.00), and 95.4 mmol/L (1717 mg/dL) in severe hypervolemia (α1=1.00). Figure 2 shows the ratio Δ[Na]S/Δ[Glu]S for widely varying values of the volume ratio α1 and [Glu]A.Download figureDownload PowerPointFigure 2. Change in serum concentrations of sodium over glucose (Δ[Na]S/Δ[Glu]S), in mmol/L per mmol/L, at different extracellular glucose gains and ratios of euglycemic intracellular/extracellular volume (ICFV/ECFV ratios) during development of hyperglycemia. ΔNa/ΔGlucose indicates Δ[Na]S/Δ[Glu]S.The numerical values of the ratio Δ[Na]S/Δ[Glu]S calculated by formula (3) (Table 1) decrease progressively at progressively lower values of the volume ratio α1 (ie, at progressively higher gains in extracellular volume) 30 and at progressively higher values of [Glu]A (progressive degree of hyperglycemia).28, 29, 30, 31 The numerical values of the ratio Δ[Na]S/Δ[Glu]S decrease progressively in progressive hyperglycemia because of the progressive decrease in the volume ratio α.31 Values of the ratio Δ[Na]S/Δ[Glu]S numerically <1.6 mmol/L per 5.6 mmol/L result in higher values of hyperglycemic [Na]S and serum tonicity than the values computed from the Katz formula.25Figure 3 shows changes in [Na]S for widely varying values of the volume ratio α1 and [Glu]A. The values of hyperglycemic [Na]S computed by formula (4) differ substantially from the values computed by formula (2) (Table 1) in states of extreme extracellular volume excess or deficit. For example, if baseline [Na]S and [Glu]S values are 140 and 5.6 mmol/L, respectively, and [Glu]A is 112 mmol/L (2016 mg/dL), [Na]S at hyperglycemia will be 113.7 mmol/L by the Katz formula (formula (1) in Table 1) and 116.3 mmol/L by formula (3) (Table 1) in euvolemia (α1=1.5), 115.1 mmol/L by formula (1) and 110.7 mmol/L by formula (3) in severe hypovolemia (α1=3.0), and 112.8 mmol/L by formula (1) and 120.2 mmol/L by formula (3) in severe hypervolemia (α1=1.0).Download figureDownload PowerPointFigure 3. Plasma sodium concentrations at different extracellular glucose gains and different ratios of euglycemic intracellular/extracellular volume (ICFV/ECFV ratios).Finally, hyperglycemia causes potassium egress from cells because of lack of insulin, hypertonicity, and probably ketoacidosis.33 Transfer of potassium from the intracellular into the extracellular compartment causes a decrease in total intracellular solute and an increase in total extracellular solute resulting in osmotic transfer of intracellular water into the extracellular compartment and a decrease in the volume ratio. A decrease in the numerical value of the Δ[Na]S/Δ[Glu]S ratio will result from potassium exit from the cells.29 Although clinically critical, potassium transfers have minimal effects on the ratio Δ[Na]S/Δ[Glu]S and the internal osmotic fluid shifts in oligoanuric patients because of the potentially lethal consequences of hyperkalemia from even a small potassium exit from cells in a closed system. The effect of potassium exit from the cells on the ratio Δ[Na]S/Δ[Glu]S and the internal osmotic fluid shifts become significant in patients with preserved renal function and loss of potassium through osmotic diuresis. This last effect will be discussed below.Hyperglycemia developing in oligoanuric patients offers the opportunity to study the closed‐system predictions because it can be treated only with insulin infusion.32 Studies of oligoanuric patients with severe hyperglycemia treated with insulin confirmed Katz's prediction overall.24, 34, 35, 36 Comparisons of [Na]S and [Glu]S values of patients on chronic dialysis at presentation with hyperglycemia with the corresponding values at euglycemia were also in broad agreement with Katz's predicted value of the ratio Δ[Na]S/Δ[Glu]S.26, 37, 38, 39, 40Although the average computed Δ[Na]S/Δ[Glu]S values were very close to Katz's predicted value in oligoanuric hyperglycemic patients treated with insulin, the range of computed individual Δ[Na]S/Δ[Glu]S values was wide.24, 34, 36 For example, in a study of 43 hyperglycemic episodes treated with insulin in patients on chronic dialysis with minimal water intake and minimal or absent urine output during treatment, the calculated Δ[Na]S/Δ[Glu]S ratio as mean±SD was −1.50±0.22 mmol/L per 5.6 mmol/L.34 The variation in the values of the ratio Δ[Na]S/Δ[Glu]S in this study was mainly attributed to variation in the volume ratio α1. The numerical value of the ratio Δ[Na]S/Δ[Glu]S was significantly lower in edematous compared with euvolemic oligoanuric patients.34 This observation confirmed the theoretical calculations from formula (3) in Table 1. An effect of the degree of hyperglycemia on the Δ[Na]S/Δ[Glu]S ratio was not found in these studies, probably because of the prediction that only extremely high [Glu]S values will produce values of the Δ[Na]S/Δ[Glu]S ratio substantially lower numerically than the estimate from the Katz formula.28, 30, 36Open‐System ObservationsPatients with preserved renal function represent an open system. The development of hyperglycemia in these patients is complicated by 2 processes not accounted for in Katz's formula: water intake secondary to thirst and osmotic diuresis.6, 22 The concept of water intake during development of hyperglycemia was supported by 3 studies that concluded hyperglycemia accounts for part of the interdialytic weight gain.41, 42, 43 A fourth study disputed this finding.44 However, the finding of hyponatremia in approximately a third of the patients on dialysis after correction of hyperglycemia with insulin infusion34 provided strong support for the concept of water intake in this patient group. Osmotic diuresis exerts a major influence on body‐fluid tonicity in hyperglycemic crises in patients with preserved renal function.22 Retrospective observational45, 46, 47 and prospective48 studies that specifically assessed the validity of Katz's formula in patients with preserved renal function reported widely varying Δ[Na]S/Δ[Glu]S ratio values. These variations were attributed to varying water intake and volume and composition of urine in patients with severe hyperglycemia.6Katz's formula computes a rate of increase in tonicity during development of hyperglycemia (ΔTon/Δ[Glu]S) equal to 2.4 (=5.6−2×1.6) mOsm/L per 5.6 mmol/L.24 In a review article that analyzed tonicity issues in published reports of large numbers of severe hyperglycemic episodes, computed average ΔTon/Δ[Glu]S ratio values (in mOsm/L per 5.6 mmol/L) were 1.9 in dialysis‐associated hyperglycemia, 3.5 in diabetic ketoacidosis, and 8.1 in nonketotic hyperglycemic syndrome.36 The average value of the ΔTon/Δ[Glu]S ratio in patients on dialysis was slightly lower than the value predicted using Katz's formula, reflecting fluid intake and retention during development of hyperglycemia in this patient group. However, average ΔTon/Δ[Glu]S values were 1.5‐fold higher than Katz's value in episodes of diabetic ketoacidosis occurring in patients with preserved renal function and 3.4‐fold higher than Katz's value in patients with preserved renal function who developed profound nonketotic hyperglycemia.36 The source of the high ΔTon/Δ[Glu]S ratio values in severe hyperglycemic episodes developing in patients with preserved renal function is the development of osmotic diuresis.22Losses of water, sodium, and potassium through hyperglycemic osmotic diuresis can be profound. These losses can be indirectly estimated by computing the volume of water and the amounts of sodium and potassium retained from the replacement solutions during correction of hyperglycemic crises. For example, treatment of severe nonketotic hyperglycemia in the balance study of Arieff and Carroll resulted in average net gains of 9.1 L water, 407 mmol sodium, and 137 mmol potassium.49 A characteristic feature of osmotic diuresis caused by various solutes other than sodium salts is that the sum of the urinary concentrations of monovalent cations (sodium plus potassium) is routinely lower than the normal [Na]S.50Figure 4 shows average urinary sodium and potassium concentrations in patients with hyperglycemic osmotic diuresis reported in Arieff and Carroll's study49 and 3 studies reporting urine volume plus urine sodium and potassium concentrations in patients with hyperglycemia.51, 52, 53 The highest reported average value of the sum of urinary sodium and potassium concentrations was <120 mmol/L.51 In the 3 studies allowing calculation of urinary cation concentrations in individual patients,51, 52, 53 all sums of urinary monovalent cation concentrations were substantially 143 mmol/L) in the presence of markedly elevated [Glu]S in 7 studies reporting 250 episodes of nonketotic hyperglycemia.49, 54, 55, 56, 57, 58, 59 In these studies, average [Na]S, weighed for the number of patients in each study, was 150.2 mmol/L, whereas average weighed [Glu]S was 48.7 mmol/L (877 mg/dL). Assuming baseline values of 140 mmol/L for [Na]S and 5.6 mmol/L for [Glu]S before the development of hyperglycemia in these episodes, weighed average [Na]S at presentation with hyperglycemia should be equal to 127.6 [=140−1.6×(48.7−5.6)/5.6] mmol/L using the Katz formula, whereas the weighed average corrected [Na]S using the Al‐Kudsi formula should be 162.5 [=150.2+1.6×(48.7−5.6)/5.6] mmol/L, indicating a 14% [=(1−140/162.5)×100] weighed average deficit of body water in excess of the deficit in sodium and potassium. In the presence of severe hyperglycemia, even normal, let alone elevated, [Na]S values are associated with moderate to profound neurological manifestations of hypertonicity.60, 61, 62Treatment of hyperglycemia with insulin administration reverses the hypertonicity due to extracellular glucose excess. Reversal of the hypertonicity caused by external losses of water and monovalent cations requires infusion of large volumes of hypotonic fluids.17, 22 Consequently, determination of the tonicity (the sum of sodium and potassium concentrations) of the replacement solutions requires knowledge of the parts of hypertonicity contributed by glucose excess and by excess fluid loss through osmotic diuresis.22 The corrected value of [Na]S by the formula of Al‐Kudsi and coauthors (formula (2) in Table 2), which is based on Katz's formula of the Δ[Na]S/Δ[Glu]S ratio, has been proposed as an estimation guide of the tonicity of replacement solutions.22 To our knowledge, the reliability of Katz's formula in patients with profound hyperglycemic osmotic diuresis has not been tested. The next section of this report presents a mathematical analysis of changes in tonicity and its determinants in hyperglycemia complicated by osmotic diuresis.Table 2. Solute and Volume Expressions in the Baseline Euglycemic Stage (Stage 1)NaECF1:Download figure ((6)) GluECF1:Download figure ((7)) SoluteECF1:Download figure ((8)) SoluteICF1:Download figure ((9)) α1:Download figure ((10)) John Wiley & Sons, Ltd[Glu]S1 is expressed in mmol/L. Subscript numbers indicate stage. α indicates intracellular/extracellular volume ratio; ECFV, extracellular volume; GluECF, total extracellular glucose; [Glu]A, change in glucose concentration per liter of baseline extracellular volume; [Glu]S, serum glucose concentration; ICFV, intracellular volume; NaECF, total extracellular sodium; SoluteECF, total effective extracellular solute; SoluteICF, total effective intracellular solute.Calculation of the Δ[Na]S/Δ[Glu]S Ratio and the Tonicity of Replacement Solutions in Hyperglycemia Complicated by Osmotic DiuresisThe corrected [Na]S value is used to calculate the appropriate tonicity of so