A 48-year-old man with a history of severe alcohol use disorder is brought to the emergenc… — USMLE Step 2 CK

A 48-year-old man with a history of severe alcohol use disorder is brought to the emergency department by paramedics after being found obtunded in a park. His temperature is $36.2^\circ\text{C}$ ( $97.2^\circ\text{F}$ ), blood pressure is $110/70\text{ mmHg}$ , pulse is $105/\text{min}$ , and respiratory rate is $18/\text{min}$ . The patient is unarousable and responds only to painful stimuli.

Initial laboratory studies reveal the following:

Laboratory Parameter	Value
Sodium	$138\text{ mEq/L}$
Potassium	$4.2\text{ mEq/L}$
Chloride	$104\text{ mEq/L}$
Bicarbonate	$22\text{ mEq/L}$
Blood urea nitrogen (BUN)	$28\text{ mg/dL}$
Creatinine	$1.1\text{ mg/dL}$
Glucose	$126\text{ mg/dL}$
Ethanol	$92\text{ mg/dL}$
Measured serum osmolality	$340\text{ mOsm/kg H}_2\text{O}$

Based on the provided laboratory results, what is this patient's serum osmolar gap in $\text{mOsm/kg H}_2\text{O}$ ?

Cevap: 27 mOsm/kg H2O

Cevap

The serum osmolar gap is defined as the difference between the measured serum osmolality and the calculated serum osmolality. The standard formula for calculated serum osmolality in the United States (using

\text{mg/dL}

for glucose and BUN) is

2 \times [\text{Na}^+] + \frac{[\text{Glucose}]}{18} + \frac{[\text{BUN}]}{2.8}

. However, when ethanol is present and measured, its contribution must also be subtracted to isolate the gap caused by other unidentified toxic alcohols (e.g., methanol, ethylene glycol). The conversion factor for ethanol is

4.6

. Therefore, the complete calculation for this patient is

2 \times 138 + \frac{126}{18} + \frac{28}{2.8} + \frac{92}{4.6} = 276 + 7 + 10 + 20 = 313 \text{ mOsm/kg H}_2\text{O}

. Subtracting this from the measured osmolality of

340 \text{ mOsm/kg H}_2\text{O}

gives a gap of

27 \text{ mOsm/kg H}_2\text{O}

Adım Adım Çözüm

Identify the need to calculate the serum osmolar gap.

The patient has altered mental status and a measured serum osmolality of

340 \text{ mOsm/kg H}_2\text{O}

, indicating a potential toxic alcohol ingestion.

Calculating the osmolar gap is essential to unmask the presence of unmeasured osmotically active substances (like methanol, ethylene glycol, or isopropyl alcohol) not accounted for by standard chemistry panels.

Calculate the expected (calculated) serum osmolality.

Using the expanded formula:

2 \times 138 + \frac{126}{18} + \frac{28}{2.8} + \frac{92}{4.6} = 276 + 7 + 10 + 20 = 313 \text{ mOsm/kg H}_2\text{O}

Because ethanol is present in the patient's blood, its osmotic contribution must be included in the calculation. Failure to include it will result in an artificially elevated osmolar gap.

Determine the osmolar gap.

340 \text{ (Measured)} - 313 \text{ (Calculated)} = 27 \text{ mOsm/kg H}_2\text{O}

The osmolar gap is the difference between the measured and calculated osmolality. A normal gap is typically less than

10\text{-}15 \text{ mOsm/kg H}_2\text{O}

. A gap of

27

is elevated, suggesting ingestion of an additional toxic alcohol.

Anahtar Kavram

Calculation of the serum osmolar gap, including the proper osmotic contribution of ethanol.

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Cevap

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