A 48-year-old man is brought to the emergency department by emergency medical services aft… — USMLE Step 2 CK

A 48-year-old man is brought to the emergency department by emergency medical services after his neighbor found him unresponsive in his garage. An open, empty container of automotive antifreeze was found nearby. On examination, he is deeply lethargic and responds only to painful stimuli. His vital signs show a blood pressure of $110/70 \text{ mmHg}$ , heart rate of $105/\text{min}$ , and respiratory rate of $24/\text{min}$ .

Laboratory testing reveals the following:

Parameter	Value
Serum sodium	$142 \text{ mEq/L}$
Serum potassium	$4.5 \text{ mEq/L}$
Serum chloride	$104 \text{ mEq/L}$
Serum bicarbonate	$10 \text{ mEq/L}$
Blood urea nitrogen	$28 \text{ mg/dL}$
Serum glucose	$126 \text{ mg/dL}$
Measured serum osmolality	$345 \text{ mOsm/kg H}_2\text{O}$
Blood ethanol	Undetectable

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

Answer: 44 mOsm/kg

Answer

The patient's osmolar gap is calculated by subtracting the calculated serum osmolality from the measured serum osmolality. Calculated osmolality is found using the formula:

2 \times Na + \frac{BUN}{2.8} + \frac{Glucose}{18}

. Plugging in the values yields:

2 \times 142 + \frac{28}{2.8} + \frac{126}{18} = 284 + 10 + 7 = 301 \text{ mOsm/kg H}_2\text{O}

. The measured osmolality is

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

. The osmolar gap is therefore

345 - 301 = 44

. A normal osmolar gap is

\leq 10

. In a patient with an unexplained high anion gap metabolic acidosis and altered mental status, an elevated osmolar gap strongly suggests toxic alcohol ingestion, such as ethylene glycol (which is found in antifreeze).

Step-by-Step Solution

Recall the formula for calculated serum osmolality.

Calculated Osmolality =

2 \times Na + \frac{BUN}{2.8} + \frac{Glucose}{18}

This formula estimates the osmolal contribution of the major endogenous serum solutes (sodium, urea, and glucose).

Substitute the provided laboratory values into the formula.

2 \times 142 + \frac{28}{2.8} + \frac{126}{18}

Accurate substitution of sodium, BUN, and glucose is required to find the expected baseline osmolality.

Perform the mathematical calculation.

284 + 10 + 7 = 301 \text{ mOsm/kg H}_2\text{O}

These values represent the standard milliosmoles per kilogram of water contributed by normal solutes.

Subtract the calculated osmolality from the measured serum osmolality to find the osmolar gap.

345 - 301 = 44

An elevated osmolar gap (>10) suggests the presence of unmeasured osmotically active substances, such as toxic alcohols (e.g., ethylene glycol).

Key Concept

The serum osmolar gap is used to detect the presence of unmeasured, osmotically active agents (like ethylene glycol or methanol) and is found by subtracting calculated osmolality from measured osmolality.

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