The Corrected Serum Sodium Concentration in Hyperglycemic Crises: Computation and Clinical Applications

In hyperglycemia, hypertonicity results from solute (glucose) gain and loss of water in excess of sodium plus potassium through osmotic diuresis. Patients with stage 5 chronic kidney disease (CKD) and hyperglycemia have minimal or no osmotic diuresis; patients with preserved renal function and diabetic ketoacidosis (DKA) or hyperosmolar hyperglycemic state (HHS) have often large osmotic diuresis. Hypertonicity from glucose gain is reversed with normalization of serum glucose ([Glu]); hypertonicity due to osmotic diuresis requires infusion of hypotonic solutions. Prediction of the serum sodium after [Glu] normalization (the corrected [Na]) estimates the part of hypertonicity caused by osmotic diuresis. Theoretical methods calculating the corrected [Na] and clinical reports allowing its calculation were reviewed. Corrected [Na] was computed separately in reports of DKA, HHS and hyperglycemia in CKD stage 5. The theoretical prediction of [Na] increase by 1.6 mmol/L per 5.6 mmol/L decrease in [Glu] in most clinical settings, except in extreme hyperglycemia or profound hypervolemia, was supported by studies of hyperglycemia in CKD stage 5 treated only with insulin. Mean corrected [Na] was 139.0 mmol/L in 772 hyperglycemic episodes in CKD stage 5 patients. In patients with preserved renal function, mean corrected [Na] was within the eunatremic range (141.1 mmol/L) in 7,812 DKA cases, and in the range of severe hypernatremia (160.8 mmol/L) in 755 cases of HHS. However, in DKA corrected [Na] was in the hypernatremic range in several reports and rose during treatment with adverse neurological consequences in other reports. The corrected [Na], computed as [Na] increase by 1.6 mmol/L per 5.6 mmol/L decrease in [Glu], provides a reasonable estimate of the degree of hypertonicity due to losses of hypotonic fluids through osmotic diuresis at presentation of DKH or HHS and should guide the tonicity of replacement solutions. However, the corrected [Na] may change during treatment because of ongoing fluid losses and should be monitored during treatment.

In hyperglycemia, hypertonicity results from solute (glucose) gain and loss of water in excess of sodium plus potassium through osmotic diuresis. Patients with stage 5 chronic kidney disease (CKD) and hyperglycemia have minimal or no osmotic diuresis; patients with preserved renal function and diabetic ketoacidosis (DKA) or hyperosmolar hyperglycemic state (HHS) have often large osmotic diuresis. Hypertonicity from glucose gain is reversed with normalization of serum glucose ([Glu]); hypertonicity due to osmotic diuresis requires infusion of hypotonic solutions. Prediction of the serum sodium after [Glu] normalization (the corrected [Na]) estimates the part of hypertonicity caused by osmotic diuresis. Theoretical methods calculating the corrected [Na] and clinical reports allowing its calculation were reviewed. Corrected [Na] was computed separately in reports of DKA, HHS and hyperglycemia in CKD stage 5. The theoretical prediction of [Na] increase by 1.6 mmol/L per 5.6 mmol/L decrease in [Glu] in most clinical settings, except in extreme hyperglycemia or profound hypervolemia, was supported by studies of hyperglycemia in CKD stage 5 treated only with insulin. Mean corrected [Na] was 139.0 mmol/L in 772 hyperglycemic episodes in CKD stage 5 patients. In patients with preserved renal function, mean corrected [Na] was within the eunatremic range (141.1 mmol/L) in 7,812 DKA cases, and in the range of severe hypernatremia (160.8 mmol/L) in 755 cases of HHS. However, in DKA corrected [Na] was in the hypernatremic range in several reports and rose during treatment with adverse neurological consequences in other reports. The corrected [Na], computed as [Na] increase by 1.6 mmol/L per 5.6 mmol/L decrease in [Glu], provides a reasonable estimate of the degree of hypertonicity due to losses of hypotonic fluids through osmotic diuresis at presentation of DKH or HHS and should guide the tonicity of replacement solutions. However, the corrected [Na] may change during treatment because of ongoing fluid losses and should be monitored during treatment.
Keywords: sodium concentration, hyperglycemia, dysnatremia, hypertonicity, diabetic ketoacidosis, hyperosmolar hyperglycemia INTRODUCTION Imbalances that develop in patients with severe hyperglycemia and preserved renal function include extracellular gain of solute (glucose) and deficits of water, sodium, potassium, and other ions resulting from glycosuria. These imbalances, which cause extracellular and intracellular volume deficits, changes in the concentrations of key serum ions, and hypertonicity, constitute major treatment targets (1).

CORRECTED SODIUM LEVEL, GLUCOSE CONCENTRATION, AND TONICITY
In experimental studies, tonicity of a fluid can be measured directly by rapid photographic recordings of changes in the volume of cells, usually red blood cells, suspended in the fluid of interest (8). In clinical practice, tonicity is evaluated by surrogate biochemical measurements, including serum osmolality and sodium concentration ([Na]) (8). In the absence of solutes with extracellular distribution other than sodium salts (e.g., glucose), [Na] represents the index expressing tonicity (8).
In hyperglycemia, glucose accumulation in the extracellular compartment contributes to tonicity (Ton), which is expressed by the formula (9): where the serum glucose concentration ([Glu]) is in mmol/L (1 mmol/L = 18 mg/dL). Formula 1 provides accurate information on tonicity in hyperglycemia, except when high levels of plasma solids lower plasma water content (e.g., in hyperlipidemia) causing falsely low measurement of [Na] by indirect potentiometry (10). However, this formula should not be used to guide the composition of the replacement solution. Hypertonicity in hyperglycemia results from gain of extracellular solute (glucose) and osmotic diuresis (2,5). Correction of hyperglycemia results in extracellular solute loss (11) and decrease in tonicity (12). The tonicity of the replacement solutions should correct the component of hypertonicity resulting from osmotic diuresis (2,5).
[Na] rises during correction of hyperglycemia as water is transferred osmotically from the extracellular into the intracellular compartment (12). The tonicity of replacement solutions should be based on the projected value of [Na] after normalization of [Glu] (2,6,8 value stemmed from the faulty premise that osmotic transfer of intracellular water into the extracellular space as a result of extracellular glucose gain was not associated with an increase in intracellular tonicity. As a matter of fact, the increase in total body effective solute (baseline solute plus glucose gain) causes equal rises in both intracellular and extracellular fluid tonicities. The glucose-induced gain in extracellular solute causes water exit from the cells (19) to bring about hypertonic hyponatremia (20). Katz's coefficient computes tonicity increase ( Ton) of 2.4 (5.6 -2 × 1.6) mOsm/L for every 5.6 mmol/L increase in [Glu] (2).
The ICVF/ECVF volume ratio α increases during development of hypovolemia or correction of hyperglycemia and decreases during development of hypervolemia or of hyperglycemia. Total glucose gain during development of hyperglycemia is the product of ECFV 1 and [Glu] A . [Glu] A , which is not a glucose concentration encountered clinically because ECFV increases during development of hyperglycemia, was entered in the calculations because the same [Glu] A leads to comparable [Glu] 2 values in hypothetical subjects with widely different euglycemic volume ratio α 1 (17). Table 1 shows general formulas used by Katz for computation of tonicity-related and volume-related parameters. Total intracellular and extracellular solutes in this Table are the total solutes determining tonicity (14). Solutes with body water distribution, e.g., urea, do not contribute to tonicity (8,9) and are not included in the calculations of the tonicity-related variables (9,14). The formula for calculating the hyperglycemic ICFV 2 /ECFV 2 ratio α 2 in Table 1 as the corresponding ratio of effective intracellular-to-extracellular solute is based on the principle asserting that body water is apportioned between the intracellular and extracellular compartments in proportion to the amount of solute in each compartment (41). The calculations for the various [Na]/ [Glu] coefficients in hyperglycemia (37)(38)(39)(40) and for the following examples were based on the formulas of Table 1. Theoretical examples will show the effects of the ICFV 1 /ECFV 1 volume ratio α 1 and of the degree of Ton  In addition to the degree of hyperglycemia and the volume ratio α 1 , the following potential sources of variations in [Na]/ [Glu] and therefore in corrected [Na] have been discussed: (a) differences in the apparent volumes of distribution of glucose and sodium due to intracellular entry of sodium ions, which is larger in some chronic illnesses than in the normal state (17) , but this effect will be small in hyperglycemia developing in a closed system (17). (d) Sodium exchanges between sodium stores in proteoglycans (mainly glycosaminoglycan) in skin, bones and cartilage (42) and sodium in the extracellular compartment, which could influence [Na]/ [Glu], but have not been studied in hyperglycemia (17). Finally, both definition and methods of measurement of ECFV encounter difficulties (43,44). Nevertheless, the average normal ECFV is in the order of 40-45% of TBW, not 33% as in Katz's calculations (43,44), and therefore at euvolemia the ICFV 1 /ECFV 1 volume ratio α 1 should be between 1.50 and 1.

Closed System of Hyperglycemia: Clinical Observations
Hyperglycemia in patients with advanced renal failure allows study of the theoretical predictions in a closed system because it can be treated with insulin infusion and with no or minimal changes in the external balance of sodium, potassium and water (45,46). One report analyzed 43 episodes of severe hyperglycemia ([Glu] > 33.3 mmol/L or 600 mg/dL), treated with insulin and no other interventions, in patients on chronic dialysis with no or minimal fluid intake and urine loss and no change in body weight during treatment (47). Mean ± standard deviation values at presentation and end of observation, respectively, were as follows: [Glu] 50.7 ± 10.9 mmol/L (913 ± 197 mg/dL) and 9.4 ± 4.3 mmol/L (170 ± 78 mg/dL); [Na] 125 ± 5 and 136 ± 5 mmol/L; and Ton 300 ± 13 and 282 ± 11 mOsm/L. [Na]/

Open System of Hyperglycemia: Theoretical Calculations
Severe hyperglycemia in patients with preserved renal function causes deficits in body sodium, potassium, and water, which are the key determinants of [Na] at euglycemia (50). Balance abnormalities specific to hyperglycemia develop from water gain in the gastrointestinal tract and losses of water, sodium and potassium from the urinary tract. Thirst is caused by hyperglycemic hypertonicity and hypovolemia from urinary losses. Hyperglycemic hypertonicity caused thirst in animal experiments (51). Polydipsia is a prominent clinical manifestation of hyperglycemic crises (7,52,53). Water intake from hyperglycemia led to hyponatremia after correction with insulin of approximately one-third of the hyperglycemic episodes in dialysis patients (47).
A major rise in tonicity in hyperglycemia results from osmotic diuresis, in which water loss is relatively greater than loss of sodium plus potassium (5,17,54). Thus, in hyperglycemic crises occurring in patients with preserved renal function, who represent an open system, [Na] receives influences from three pathophysiologic processes: rise in [Glu] and water gain cause [Na] decreases, while osmotic diuresis causes [Na] increase. In these patients, quantitating the isolated effect of glucose gain is imperative because this effect is predictable with a reasonable degree of certainty, as shown in the previous section, and more importantly, it will disappear with correction of hyperglycemia without requiring additional measures.
Prediction of the quantitative effects of water intake and particularly of osmotic diuresis, which is the dominant effect on tonicity in severe hyperglycemic episodes (2, 3), is difficult because the magnitude of these processes varies greatly (2,17). The effects of osmotic diuresis on [Na] require correction by fluid infusion. One report calculated the effects of osmotic diuresis on tonicity-related values in a hypothetical subject with extreme hyperglycemia ([Glu] of 137.9 mmol/L or 2,483 mg/dL) by using the average reported values of urinary water loss (25% of baseline body water) and urinary sodium plus potassium concentration (60 mmol/L) in severe hyperglycemia (17). In this hypothetical subject, [Na] after correction of hyperglycemia calculated from the body contents of water, glucose, sodium, and potassium at baseline and after their changes from osmotic diuresis, was 167 mmol/L, while corrected [Na] calculated by the Al-Kudsi formula was 169 mmol/L. This finding suggests that the corrected [Na] by the Al-Kudsi formula provides a reasonable prediction of the part of hypertonicity that is due to osmotic diuresis.

Open System of Hyperglycemia: Clinical Observations
Accounting for changes in external balances of water, sodium, and potassium during development and treatment of hyperglycemia is necessary for any evaluation of the corrected [Na] in patients with renal function. There is a paucity of studies in this area. In a prospective study, hyperglycemia was produced in normal volunteers by infusion of somatostatin and 20% dextrose in 0.45% saline and the relation between

Clinical Application of the Corrected [Na]: Definition of the Hyperglycemic Syndromes
The guidelines for hyperglycemic crises address diabetic ketoacidosis (DKA) and hyperosmolar hyperglycemic state (HHS) (1,(21)(22)(23)(24). The diagnostic features of DKA include low arterial blood pH and serum bicarbonate, presence of ketone bodies in serum and urine, a wide serum anion gap, and variable tonicity (1).

Importance of the Corrected [Na] in Hyperglycemic Syndromes
Preventing cerebral edema is a key concern during treatment of hyperglycemic crises. Tonicity-related parameters have received attention in the studies of the pathogenesis of this complication. In 100 cases of cerebral edema developing during treatment of DKA, weighed means at presentation were as follows: [Glu] 34 mmol/L (612 mg/dL), [Na] 132.4 mmol/L, tonicity 299 mOsm/L, and corrected [Na] 140.6 mmol/L (72, 73, 94-96, 98, 102, 106, 109, 112, 117, 123, 124, 126, 131, 138). These values do not differ substantially from the mean values of all DKA cases in Table 2. However, factors related to tonicity statistically associated with brain edema during treatment of DKA include decrease in tonicity, large early infusion volumes, very high [Glu] at presentation, rapid decline in [Glu], very low [Na], and administration of large doses of insulin (102,106,118). The change in corrected [Na] during treatment of DKA was the best discriminator for the development of severe coma in one study (126). Deterioration of neurological manifestations associated with substantial rises of the corrected [Na] has been reported during treatment of both DKA (2,126) and HHS (205,223,231).
Other reported factors associated with cerebral edema in DKA include the degree of acidosis (96,106,118,278), high levels of blood urea at presentation (118,277), and vasogenic factors (112). One study found no effect of the rate of replacement fluid infusion (138). The PECARN study found no significant differences in neurological manifestations during and following treatment of DKA between using 0.9% saline and 0.45% saline as replacement solutions and between fast and slow initial infusion rates (163). Vascular endothelial changes caused by elevated blood levels of cytokines and chemokines secondary to inflammatory status associated with DKA were proposed by the authors of the PECARN study as the main mechanism for the development of cerebral edema.

Tonicity Targets During Treatment of Hyperglycemic Crises
Attention to tonicity plays a role in prevention of severe neurological manifestations during treatment of hyperglycemic emergencies. Decrease in tonicity from extracellular solute loss leads to osmotic entry of fluid into cells and could contribute to the development of cerebral edema (278). For this reason, one report proposed a very slow decrease in tonicity during the early stages of treatment (280). The optimal rate of decline in tonicity, however, has not been clarified. The proposed guideline for the maximal rate of decline in osmolality (tonicity should be targeted instead of total osmolality) during treatment of hyperglycemia is 3 mOsm/kg hourly (22,23). One set of guidelines proposed a 3-8 mOsm/L range in hourly rate of decrease in tonicity (31).
The change in tonicity due exclusively to correction of hyperglycemia has two components, a fall in [Glu] and a rise in [Na]. Guidelines propose hourly rates of 2.8-4.2 mmol/L (50-75 mg/dL) for the decrease in [Glu] (1) and of 0.5 mmol/L for the commensurate rise in [Na] (30)

Use of the Corrected [Na] During Treatment of Hyperglycemic Crises
The corrected [Na] predicts the relation between effective body solute and total body water after decrease of [Glu] to its desired level (2,17) and should be used as a guide for the composition of replacement solutions in the same fashion as actual [Na] values are used to guide fluid management of dysnatremias (7,(281)(282)(283)(284)(285). Evidence presented earlier supports the use of the Al-Kudsi formula for calculation of the corrected [Na]. Two limitations of the corrected [Na] should be addressed during treatment: First, the corrected [Na] using the Al-Kudsi formula is not accurate in some conditions, mainly in advanced extracellular volume disturbances. Second, and more importantly, the corrected [Na] reflects the relation between effective body solute and body water at the moment of blood sampling (2,17,36). Correction of the extracellular volume deficit improves renal function and in the face of persistent hyperglycemia leads to large volume osmotic diuresis, which causes further water deficit and rises in the corrected [Na] (2).
We propose the following scheme for use of the corrected [Na] during treatment of hyperglycemic crises: The initial measurement of serum values should include osmolality in addition to basic metabolic panel. In the absence of an exogenous solute (e.g., ethanol) an osmol gap, that is the difference between measured osmolality and osmolarity calculated as 2 × [Na] + [Glu] + serum urea, where [Glu] and urea are in mmol/L, exceeding 10-12 mOsm/L indicates either presence of another non-dissociated compound in the serum (e.g., acetone) or a condition causing decrease in the water fraction of the serum (e.g., hyperlipidemia, hyperproteinemia). In the second case, falsely low [Na] values are reported when this measurement is performed in an autoanalyzer that requires dilution of the samples measured (286). If there is a large osmol gap, [Na] should be measured again in an apparatus that does not require dilution of the measured specimen, e.g., a blood gas machine, to obtain an accurate estimate of the presenting tonicity.
The tonicity of replacement solutions should be based on repeated calculations of the corrected [Na]. If the corrected [Na] at presentation is in the eunatremic range, infusion of isotonic saline should be started at a rate dictated by clinical manifestations of hypovolemia. Prevention of either decline or rise in the corrected [Na] is critical. Patients with corrected [Na] values within the normal range of [Na], like the average patient with DKA ( Table 2), do not have relatively larger deficit of water compared to monovalent cations. In these patients, use of isotonic solutions as initial treatment of DKA and slow decline of [Glu], as proposed in the guidelines (1), leads to rapid correction of severe extracellular volume deficits and prevents sharp changes in the corrected [Na].
In subjects with initial corrected [Na] in the eunatremic range, tonicity should decline at a low rate. Maintenance of the corrected [Na] at the same level and decrease in [Glu] at the rate proposed in the guidelines (2.8-4.2 mmol/L hourly), will lead to a 0.8-1.2 mmol/L per hour rate of increase in [Na] and, from Equation (1), to a 1.2-1.8 mOsm/L per hour rate of decrease in tonicity. This conservative rate of decline in tonicity, which is slower than the hourly rate of 3 mOsm/L proposed in guidelines, may assist in preventing cerebral edema. In the rare instance of low presenting corrected [Na], or for treatment of cerebral edema, hypertonic saline infusion may be used (111). During treatment, urine volume should be monitored and [Glu], [Na], serum potassium concentration, and other relevant parameters should be measured frequently, initially every 1-2 h. The corrected [Na] should be calculated after each measurement of [Glu] and [Na] and should guide changes in the tonicity of the infusate. Development of large osmotic diuresis may lead to increases in the corrected [Na] and the need for hypotonic infusions later in the course of treatment.
A corrected [Na] in the hypernatremic range at presentation with hyperglycemia indicates excessive water deficit that must be corrected. Initially, infusion of isotonic fluids will correct rapidly volume deficits and will also decrease the level of hypertonicity. However, the subsequent development of large volume osmotic diuresis may lead to rise in the corrected [Na]. Monitoring urine volume, frequent measurement of the relevant serum biochemical values, and repeated calculation of the corrected [Na] after each measurement of [Glu] and [Na] is imperative.
The corrected [Na] should not rise further; however, deciding whether it should remain at the same level at least early during the decrease in [Glu] or it should decrease at a slow rate (e.g., by 0.5 mmol/L every 1 or 2 h) from the start of the treatment requires prospective studies. Infusion of hypotonic solutions will eventually be needed regardless of whether the early phase of treatment aims at maintaining or decreasing the corrected [Na]. Addition of potassium salts to the infused saline should be guided by repeated measurements of the serum potassium concentration. In deciding the concentration of sodium in the replacement solutions, it is important to take into account the concentration of potassium salts in the infusate (2).

CONCLUSIONS
The corrected [Na] calculated by the Al-Kudsi formula should guide the tonicity of replacement solutions. This use should be tempered by the knowledge that rarely encountered extreme volume disturbances can cause [Na] changes substantially different from those predicted by the corrected [Na] and, more importantly, that the corrected [Na] can vary greatly during treatment depending on changes in the external balances of water, sodium and potassium. For these reasons, frequent measurements of [Glu] and [Na], repeated calculation of the corrected [Na] after each measurement, and changes in the tonicity of replacement solutions based on the corrected [Na] are critical steps in the management of tonicity issues in hyperglycemia.

DATA AVAILABILITY STATEMENT
Publicly available datasets were analyzed in this study. This data came from tables of publications cited in the text.