A 45-year-old man is brought to the emergency department after being found unresponsive in… — USMLE Step 3

A $45$ -year-old man is brought to the emergency department after being found unresponsive in a garage. Beside him is a partially empty jug of antifreeze. Upon arrival, he is obtunded. His temperature is $37.0^\circ$ C ( $98.6^\circ$ F), blood pressure is $130/80$ mmHg, heart rate is $112$ /min, and respiratory rate is $24$ /min.

Laboratory studies are obtained and reveal the following:

Test	Result	Reference Range
Serum sodium	$138$ mEq/L	$136-145$ mEq/L
Serum potassium	$4.5$ mEq/L	$3.5-5.0$ mEq/L
Serum chloride	$102$ mEq/L	$98-106$ mEq/L
Serum bicarbonate	$12$ mEq/L	$22-28$ mEq/L
Blood urea nitrogen (BUN)	$14$ mg/dL	$8-20$ mg/dL
Serum creatinine	$1.5$ mg/dL	$0.7-1.3$ mg/dL
Serum glucose	$108$ mg/dL	$70-100$ mg/dL
Serum ethanol	Undetectable	Undetectable
Measured serum osmolality	$315$ mOsm/kg H $_2$ O	$275-295$ mOsm/kg H $_2$ O

Based on these findings, what is the patient's calculated osmolar gap?

Answer: 28 mOsm/kg H2O

Answer

The calculated serum osmolality is determined using the formula:

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

. Plugging in the patient's values yields

2 \times 138 + 14/2.8 + 108/18 = 276 + 5 + 6 = 287 \text{ mOsm/kg H}_2\text{O}

. The osmolar gap is the measured osmolality minus the calculated osmolality, which is

315 - 287 = 28 \text{ mOsm/kg H}_2\text{O}

. An elevated osmolar gap (typically

>10

) alongside a high anion gap metabolic acidosis is a classic presentation for toxic alcohol poisoning, supported here by the presence of antifreeze (ethylene glycol).

Step-by-Step Solution

Calculate the expected serum osmolality using the standard physiological formula.

Calculated osmolality = 287 mOsm/kg H2O

This establishes the baseline osmoles contributed by the major plasma solutes (sodium, urea, and glucose).

Subtract the calculated osmolality from the measured osmolality.

315 - 287 = 28 mOsm/kg H2O

The difference between measured and calculated osmolality (osmolar gap) represents unmeasured osmotically active substances, such as toxic alcohols.

Key Concept

Interpreting Laboratory Results: Osmolar Gap Calculation

Estimated Time:1m 30s

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