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Evaluation of 36 formulas for calculating plasma osmolality

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Abstract

Purpose

Measuring or calculating plasma osmolality is of interest in critical care medicine. Moreover, the osmolal gap (i.e. the difference between the measured and calculated osmolality) helps in the differentiation of metabolic acidosis. A variety of formulas for calculating osmolality have been published, most of them relying on sodium, urea and glucose. A novel formula developed by Zander has recently been published, which also takes into account the effects of potassium, chloride, lactate and bicarbonate on osmolality. We evaluate the previously published formulas including the novel formula by comparing calculated and measured osmolality.

Methods

Arterial or venous blood samples from 41 outpatients and 195 acutely ill inpatients (total 236 subjects) were used to compare measured osmolality with calculated osmolality as obtained from 36 published formulas including the new formula. The performance of the formulas was statistically evaluated using the method of Bland and Altman.

Results

Mean differences up to 35 mosmol/kg H2O were observed between measured and calculated osmolality using the previously published formulas. In contrast, the novel formula had a negligible mean difference of 0.5 mosmol/kg H2O. The novel formula also had the closest 95 % limits of agreement ranging from −6.5 to 7.5 mosmol/kg H2O.

Conclusion

Only 4 out of the 36 evaluated formulas gave mean differences between measured and calculated osmolality of less than 1 mosmol/kg H2O. Zander’s novel formula showed excellent concordance with measured osmolality and facilitates a more precise diagnosis based on blood gas analysers. The new equation has the potential to replace separate measurements of osmolality in many cases.

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Acknowledgments

The study was funded by Roche Diagnostics Graz GmbH, Research and Development, Kratkystraße 2, 8020 Graz, Austria. Roche Diagnostics was involved in the design of the study and data collection, and contributed to revision of the manuscript.

Conflicts of interest

A.S.F. and H.J.S. declare no conflicts of interest; G.C.F. receives lecture fees from Roche Diagnostics; R.Z. has previously worked as a consultant for Roche Diagnostics; D.S.K. and I.Z. are current employees of Roche Diagnostics; H.R. is a former employee of Roche Diagnostics.

Author information

Authors and Affiliations

  1. Department of Respiratory and Critical Care Medicine, Otto Wagner Hospital, Sanatoriumstrasse 2, 1145, Vienna, Austria

    Andreas S. Fazekas & Georg-Christian Funk

  2. Ludwig Boltzmann Institute for Chronic Obstructive Pulmonary Disease and Pneumologic Epidemiology, Otto Wagner Hospital, Vienna, Austria

    Andreas S. Fazekas & Georg-Christian Funk

  3. Roche Diagnostics Graz GmbH Research and Development DPGR, Graz, Austria

    Daniela S. Klobassa, Horst Rüther & Ingrid Ziegler

  4. Physioklin, Mainz, Germany

    Rolf Zander

  5. Clinical Institute for Medical and Clinical Laboratory Diagnostics, Medical University Graz, Graz, Austria

    Hans-Jürgen Semmelrock

Authors
  1. Andreas S. Fazekas
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  2. Georg-Christian Funk
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  3. Daniela S. Klobassa
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  4. Horst Rüther
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  5. Ingrid Ziegler
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  6. Rolf Zander
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  7. Hans-Jürgen Semmelrock
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Corresponding author

Correspondence to Georg-Christian Funk.

Appendix

Appendix

The development of Zander’s optimized equation for plasma is described in three steps. The following is the English translation of Zander’s original publication, which can be accessed via the Physioklin website (http://www.physioklin.de/physiopoc/saeure-basen-sauerstoff-elektrolyt-status/optimale-berechnung-der-osmolalitaet.html):

  1. 1.

    Addition of all osmotically active constituents in terms of mosmol per liter of plasma results in the theoretical osmolarity, expressed in mmol/l. Amounts (mmol/l) of 142 Na, 4.5 K, 1.3 ionized Ca, 0.7 ionized Mg, 103 Cl, 24 HCO3, 1.5 lactate, 1 HPO4, 0.5 SO4, 3.0 organic acids plus proteinate, 5 glucose and 5 urea were taken as normal values from the literature [2]. The resulting value amounts to 291.5 mosmol/l.

  2. 2.

    Corresponding to the fact that electrolytes, mainly sodium and chloride, are osmotically active only in part, i.e. only to 92.6 % (the so called osmotic coefficient 0.926; for glucose 1.013) [2], the resulting real osmolarity amounts to only 269.9 mosmol/l.

  3. 3.

    Taking into account the water content of plasma with 94 % the calculated real osmolality of 287.2 mosmol/kg H2O is given a value, which has been lowered by 6 % as a result of the reduced distribution space of all osmotically active substances.

Now, comparison between the measured normal value of plasma osmolality (288 mosmol/kg H2O) and the calculated value (287 mosmol/kg H2O, rounded) leads to the surprising result that the measured real normal value of osmolality is by chance the same as the osmolarity of the plasma. This might be the reason for the confusion within the literature concerning these two values. On this basis, the optimized formula for calculation of osmolality is as follows (the concentrations of calcium and magnesium and those of phosphate, sulphate, organic acids and proteinate are summarized as constants for clinical reasons):

Osmolarity (mosmol/l) = [Na+ (142) + K+ (4.5) + const. Ca++/Mg++ (2.0) + Cl− (103) + HCO3 − (24) + lactate− (1.5) + const. phosphate/sulphate/organic acids/proteinate− (4.5) + glucose (5.0) + urea (5.0)] = 291.5 mosmol/l × 0.926 (osmot. coefficient) = 269.9 mosmol/l.

Osmolality (mosmol/kg H2O) = osmolarity: 0.94 (water content) = 287.1 mosmol/kg H2O.

The calculation of plasma osmolality (mosmol/kg H2O) is now given as:

Plasma osmolality = (Na+ + K+ + Cl− + lactate− + glucose + urea + HCO3 − + 6.5) × 0.985.

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Fazekas, A.S., Funk, GC., Klobassa, D.S. et al. Evaluation of 36 formulas for calculating plasma osmolality. Intensive Care Med 39, 302–308 (2013). https://doi.org/10.1007/s00134-012-2691-0

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