title: Derivation and validation of a formula to calculate the contribution of ethanol to the osmolal gap.
abstract: OBJECTIVE
  We sought to evaluate the relationship between osmolal gap and serum ethanol level and derive a formula that can be used clinically to calculate the expected osmolal gap in the presence of ethanol. Some investigators have noted that the residual osmolal gap appears to increase as the ethanol level increases, and thus it is important to determine the exact relationship between these 2 values.
  
  
  METHODS
  In part 1, a convenience sample of emergency department patients undergoing serum ethanol determination had sodium, urea, and glucose levels and osmolality determined on the same blood sample, and values were prospectively recorded. Predicted osmolality excluding ethanol was calculated with the following formula: 2 Na (mEq/L) + (Urea [mg/dL])/2.8 + (Glucose [mg/dL])/18. The osmolal gap was determined by subtracting the calculated serum osmolality excluding ethanol from the measured serum osmolality. Linear regression analysis was then used to derive a formula for the relationship between ethanol and the osmolal gap. This formula was then prospectively validated on a second convenience sample of patients. In part 2, we repeated this experiment in vitro by adding known amounts of ethanol to serum.
  
  
  RESULTS
  We derived the formula to calculate the contribution of ethanol to the osmolal gap by using 98 observations. The mean ethanol level was 197.8 mg/dL (SD 138.5), with a range of 0 to 538.2 mg/dL. The relationship between ethanol and osmolal gap was linear, with a Pearson coefficient of correlation of 0.99. Linear regression analysis generated a model with the following formula: Osmolal gap=(Ethanol [mg/dL])/3.7 - 0.35 or, in SI units: Osmolal gap (mOsm/kg)=1.25 (Ethanol [mmol/L]) - 0.35 The 95% confidence interval (CI) for the multiplicative factor was 1/3.58 to 1/3.80 (or, in SI units, 1.21 to 1.28). The 95% CI for the additive constant was -2.19 to 1.50. We prospectively validated our formula on 128 patients. The mean residual osmolal gap for this group of patients was 0.84 mOsm/L (SD 5.65; range, -18.40 to 17.85 mOsm/L). The results of the in vitro experiments were similar.
  
  
  CONCLUSIONS
  Our data suggest that the best formula for the calculation of the contribution of ethanol to osmolality is as follows: Ethanol (mg/dL)/3.7 or, in SI units: 1.25 (Ethanol [mmol/L])
authors.affiliation: Department of Emergency Medicine, Vancouver Hospital and Health Sciences Centre, British Columbia, Canada. rpurssel@vanhosp.bc.ca
authors.forename: R A
authors.initials: RA
authors.lastname: Purssell
authors.forename: M
authors.initials: M
authors.lastname: Pudek
authors.forename: J
authors.initials: J
authors.lastname: Brubacher
authors.forename: R B
authors.initials: RB
authors.lastname: Abu-Laban
mesh_terms: D000328:Adult; D000435:Alcoholic Intoxication / Q000097:blood / Q000175:diagnosis; D001786:Blood Glucose / Q000378:metabolism*; D004305:Dose-Response Relationship, Drug; D004636:Emergency Service, Hospital; D000431:Ethanol / Q000097:blood*; D006801:Humans; D009994:Osmolar Concentration; D011446:Prospective Studies; D015203:Reproducibility of Results; D012964:Sodium / Q000097:blood*; D014508:Urea / Q000097:blood*
chemical_list: D001786:Blood Glucose; D000431:Ethanol; D014508:Urea; D012964:Sodium