Validation of a pre-existing formula to calculate the contribution of ethanol to the osmolar gap

Purpose. The aim of this study was to validate the formula derived by Purssell et al. that relates blood ethanol concentration to the osmolar gap and determine the best coefficient for use in the formula. The osmolar gap is often used to help diagnose toxic alcohol poisoning when direct measurements are not available. Methodology. Part I of the study consisted of a retrospective review of 603 emergency department patients who had a concurrent ethanol, basic metabolic panel and a serum osmolality results available. Estimated osmolarity (excluding ethanol) was calculated using a standard formula. The osmolar gap was determined by subtracting estimated osmolarity from the actual osmolality measured by freezing point depression. The relationship between the osmolar gap and the measured ethanol concentration was assessed by linear regression analysis. In Part II of this study, predetermined amounts of ethanol were added to aliquots of plasma and the estimated and calculated osmolarities were subjected to linear regression analysis. Results. In the cases of 603 patients included in Part I of the study, the median ethanol concentration in these patients was 166 mg/dL (Q1: 90, Q3: 254) and the range ethanol concentrations was 10-644 mg/dL. The mean serum osmolality was 338 mOsm/kg (SD: 30) and a range of 244-450 mOsm/kg. The mean osmolar gap was 47 (SD: 29) and a range of - 15 to 55. There was a significant proportional relationship between ethanol concentration and osmolar gap (r ² = 0.9882). The slope of the linear regression line was 0.2498 (95% CI: 0.2472-0.2524). The slope of the linear regression line derived from the data in Part II of the study was 0.2445 (95% CI: 0.2410-0.2480). Conclusions. The results of our study are in fairly close agreement with previous studies that used smaller samples and suggest that an accurate conversion factor for estimating the contribution of ethanol to the osmolar gap is [Ethanol (mg/dL)]/4.0.