Clinical background
Calculated serum osmolality has two main clinical purposes. The first is to provide the calculated term in the osmolal gap, that is, the difference between laboratory-measured and calculated osmolality. A raised osmolal gap suggests the presence of osmotically active substances not captured by the formula, above all the toxic alcohols methanol and ethylene glycol. The second purpose is to estimate the effective osmolality (tonicity) in the assessment of hyper- or hyponatraemia, in which urea is excluded because it is an ineffective osmole that crosses cell membranes freely.
Without a calculated osmolality the osmolal gap cannot be determined, and an important screening tool in suspected toxic alcohol poisoning is therefore lacking. Laboratory measurement of methanol and ethylene glycol by gas chromatography is not immediately available at most hospitals, which makes the osmolal gap a time-critical surrogate marker in the acute setting.
Calculating serum osmolality/osmolarity
The formula the calculator uses is:
where Na is given in mEq/L and glucose and blood urea nitrogen (BUN) in mg/dL. In SI units, with all concentrations in mmol/L, the formula simplifies to:
This formula corresponds to the one Worthley et al. proposed in 1987 as the simplest and most robust calculation method [2]. It rests on the fact that sodium with its accompanying anions (chloride and bicarbonate) accounts for the dominant share of plasma osmolality, so that doubling the sodium concentration approximates their combined contribution. Glucose and urea are added with conversion factors that convert from mg/dL to mOsm/kg. The original formula of Dorwart and Chalmers (1975) used a coefficient of 1.86 for sodium and included a constant [1], but later comparative studies have shown that this more complex formula performs less well than the simplified one with a coefficient of 2 [3,4].
The derivation cohort for the Worthley formula consisted of 300 patients: 100 healthy individuals, 100 hospital patients and 100 intensive care patients, in whom plasma osmolality was measured and compared with values calculated using five different published formulae [2]. The simplest formula gave the smallest difference between measured and calculated osmolality in all three groups.
Interpretation in practice
The calculated value itself has two uses that lead to different clinical conclusions:
| Use | Calculation | Normal range | Clinical action |
|---|---|---|---|
| Total osmolality | 275 to 295 mOsm/kg | Compare with measured osmolality to calculate the osmolal gap | |
| Effective osmolality (tonicity) | 275 to 295 mOsm/kg | Judge whether hyponatraemia is hypotonic or whether the sodium disturbance is driven by ineffective osmoles (urea, ethanol) |
The osmolal gap is calculated as the measured osmolality minus the calculated osmolality. The reference interval is traditionally given as minus 10 to plus 10 mOsm/kg, but several authors have argued that the true interval is narrower, around 0 ± 2 mOsm/kg, when the simplified Worthley formula is used [4]. An osmolal gap above 10 mOsm/kg should raise suspicion of osmotically active substances not covered by the formula: toxic alcohols, ethanol, acetone, or iatrogenic substances such as mannitol.
Effective osmolality is used in hyponatraemia to distinguish hypotonic hyponatraemia (low effective osmolality) from states in which a low sodium is accompanied by ineffective osmoles, for example uraemia or hyperglycaemia with dilutional hyponatraemia. In hyperglycaemia, sodium is corrected by approximately 1.6 mmol/L per 5.6 mmol/L (100 mg/dL) rise in glucose, which is a separate calculation that effective osmolality does not replace but complements.
Validation and performance
Several external validation studies have compared different calculation formulae against measured osmolality. Rasouli and Kalantari analysed 210 serum samples and compared 18 published formulae [3]. Multivariable linear regression showed that sodium, BUN, glucose and potassium were significant predictors of osmolality. The Dorwart–Chalmers formula performed less well than the simplified Worthley formula. The authors recommended the Worthley formula for rapid mental calculation.
In 2016, Rasouli summarised the overall state of the evidence and explicitly recommended that the Dorwart–Chalmers formula be removed from textbooks and autoanalysers and replaced by Worthley's simplest equation [4]. He also proposed that the reference interval for the osmolal gap should be corrected to 0 ± 2 mOsm/L rather than the traditional interval.
As regards the diagnostic performance of the osmolal gap as a screening test for toxic alcohol poisoning, the results have been mixed. Lynd et al. evaluated 131 patients at two tertiary hospitals, 20 of whom had methanol or ethylene glycol concentrations above the threshold for antidote treatment [5]. At an osmolal gap of 10 mOsm/kg the sensitivity for identifying patients requiring an antidote was 0.90, but the specificity was only 0.22. For patients requiring haemodialysis the sensitivity was 1.0. Use of an ethanol coefficient of 1.25 increased specificity without affecting sensitivity.
Krahn and Khajuria found that under controlled conditions the osmolal gap had high sensitivity and specificity for predicting toxic volatile substances, but that the mean value of the gap was not constant over time [6]. In a retrospective analysis from 1996 to 2004 the mean gap increased by 12 mOsm/kg, which meant that the traditional reference interval gave poor diagnostic accuracy when data from several years were pooled. The authors advised against bedside calculation and stressed the need for laboratory-specific reference intervals.
Sutter et al. combined the osmolal gap, the anion gap and serum calcium in a predictive model in 102 patients with suspected ethylene glycol poisoning, 45 of whom had confirmed poisoning [7]. The model had a c-index of 0.81, a sensitivity of 78 per cent and a specificity of 89 per cent. The authors emphasised that clinical judgement remains decisive and that no single laboratory parameter is sufficient.
Limitations
The most important limitation is that the calculator gives only the calculated osmolality. To determine the osmolal gap, a laboratory-measured osmolality is required, preferably determined by freezing point depression. Measurement by vapour pressure osmometry misses volatile substances such as methanol and ethanol and must not be used for gap calculation in suspected toxic alcohol poisoning.
With significant ethanol intoxication, the contribution of ethanol to osmolality must be added to the calculated osmolality, otherwise the gap is incorrectly overestimated. The calculator's pitfalls section gives the factor ethanol/3.7 (mg/dL), based on Purssell et al., who validated the ethanol coefficient [8]. Khajuria and Krahn found that a coefficient of 1.20 was needed for ethanol and 1.15 for glucose to optimise the gap calculation [9], indicating that no single coefficient is perfect under all conditions.
The osmolal gap may be normal or low in late presentation of toxic alcohol poisoning, because the parent alcohol is metabolised to acids that instead drive the anion gap upwards. A normal osmolal gap therefore does not exclude toxic alcohol poisoning if metabolism has already occurred [10]. Conversely, a raised osmolal gap may have causes other than toxic alcohols: ketoacidosis, lactic acidosis, chronic renal failure with accumulation of osmotically active metabolites, or iatrogenic substances.
The formula applies to adult patients with normal plasma protein and lipid concentrations. In marked hyperlipidaemia or hyperproteinaemia, pseudohyponatraemia can give misleadingly low sodium values if measurement is by indirect ion-selective electrode, which in turn gives a falsely low calculated osmolality. Direct measurement of sodium (point-of-care or direct ISE) is not affected by this.
References
- Dorwart WV, Chalmers L. Comparison of methods for calculating serum osmolality. Clin Chem. 1975;21(2):190-4. PMID: 1112024
- Worthley LI, Guerin M, Pain RW. For calculating osmolality, the simplest formula is the best. Anaesth Intensive Care. 1987;15(2):199-202. PMID: 3605570
- Rasouli M, Kalantari KR. Comparison of methods for calculating serum osmolality: multivariate linear regression analysis. Clin Chem Lab Med. 2005;43(6):635-40. PMID: 16006260
- Rasouli M. Basic concepts and practical equations on osmolality: Biochemical approach. Clin Biochem. 2016;49(12):936-41. PMID: 27343561
- Lynd LD, Richardson KJ, Purssell RA et al. An evaluation of the osmole gap as a screening test for toxic alcohol poisoning. BMC Emerg Med. 2008;8:5. PMID: 18442409
- Krahn J, Khajuria A. Osmolality gaps: diagnostic accuracy and long-term variability. Clin Chem. 2006;52(4):737-9. PMID: 16455871
- Sutter ME, Al-Khameess WA, Abramson JL et al. Predictors of ethylene glycol ingestion cases called into a regional poison center. J Med Toxicol. 2012;8(2):130-4. PMID: 22231275
- Purssell RA, Pudek M, Brubacher J et al. Derivation and validation of a formula to calculate the contribution of ethanol to the osmolal gap. Ann Emerg Med. 2001;38(6):653-9. PMID: 11719745
- Khajuria A, Krahn J. Osmolality revisited: deriving and validating the best formula for calculated osmolality. Clin Biochem. 2005;38(6):514-9. PMID: 15885229
- Kraut JA. Diagnosis of toxic alcohols: limitations of present methods. Clin Toxicol (Phila). 2015;53(7):589-95. PMID: 26114345
