## Abstract

Background: There are several methods for calculating serum osmolality, and their accordance with measured osmolality is the subject of controversy.

Methods: The concentrations of sodium, potassium, glucose, blood urea nitrogen (BUN) and osmolalities of 210 serum samples were measured. Two empirical equations were deduced for the calculation of serum osmolality by regression analysis of the data. To choose the best equation, chemical concentrations were also used to calculate osmolalities according to our formulas and 16 different equations were taken from the literature and compared with the measured osmolalities. Correlation and linear regression analyses were performed using Excel and SPSS software.

Results: Multiple linear regression analysis showed that serum concentrations of sodium (β=0.778, p≤0.000), BUN (β=0.315, p≤0.000), glucose (β=0.0.089, p≤0.007) and potassium (β=0.109, p≤0.008) are strong predictors of serum osmolality. The data were also analyzed by manual linear regression to yield the equations: osmolality=1.897[Na
^{+}]+glucose+BUN+13.5, and osmolality=1.90[Na
^{+}+K
^{+}]+glucose+BUN+5.0. The osmotic coefficient for sodium and potassium solutes was deduced to be 0.949 from the slope of the curves of measured osmolality vs. [Na
^{+}] and [Na
^{+}+K
^{+}], respectively. The inclusion of a BUN value in the equation for osmolality increased the correlation coefficient by approximately 450% and decreased the SD of difference by approximately 35% (p≤0.002). Inclusion of the osmotic coefficient for sodium solutes caused an underestimation of measured osmolality and positive osmolal gap unless an appropriate coefficient, constant value and/or the potassium value were included in the equation. The agreement was not improved when molal chemical concentrations were used instead of molar values. The formula presented by Dorwart and Chalmers gave inferior results to those obtained with our formulas.

Conclusions: Our data suggest use of the Worthley et al. formula Osm=2[Na
^{+}]+glucose+BUN for rapid mental calculation and the formulas of Bhagat et al. or ours for calculation of serum osmolality by equipment linked to a computer.

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