Paramedics bring a 52-year-old unhoused man to the emergency department after he was found… — USMLE Step 2 CK

Paramedics bring a 52-year-old unhoused man to the emergency department after he was found unresponsive in an alleyway during the winter. He has a known history of alcohol use disorder. On examination, he is obtunded and tachypneic.

Vital signs include a heart rate of $105/\text{min}$ , blood pressure of $115/75 \text{ mmHg}$ , and respiratory rate of $24/\text{min}$ .

Laboratory studies reveal the following:

Test	Result
Sodium	$140 \text{ mEq/L}$
Potassium	$4.5 \text{ mEq/L}$
Chloride	$102 \text{ mEq/L}$
Bicarbonate	$14 \text{ mEq/L}$
Blood urea nitrogen (BUN)	$14 \text{ mg/dL}$
Creatinine	$1.5 \text{ mg/dL}$
Glucose	$90 \text{ mg/dL}$
Serum measured osmolality	$325 \text{ mOsm/kg}$
Blood ethanol level	$0 \text{ mg/dL}$

Arterial blood gas on room air shows a pH of $7.25$ , $\text{pCO}_2$ of $28 \text{ mmHg}$ , and $\text{pO}_2$ of $95 \text{ mmHg}$ .

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

Answer: 35 mOsm/kg

Answer

The calculated serum osmolar gap is

35 \text{ mOsm/kg}

The serum osmolar gap is calculated by subtracting the calculated serum osmolality from the directly measured serum osmolality. The formula for calculated serum osmolality is

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

. For this patient, the calculated osmolality is

2(140) + \frac{90}{18} + \frac{14}{2.8} = 290 \text{ mOsm/kg}

. Subtracting this from the measured osmolality of

325 \text{ mOsm/kg}

yields an osmolar gap of

35 \text{ mOsm/kg}

. An elevated osmolar gap (

> 10 \text{ mOsm/kg}

) in the setting of a high anion gap metabolic acidosis strongly suggests intoxication with an unmeasured osmotically active substance, such as methanol or ethylene glycol.

Step-by-Step Solution

Recognize the need to calculate the osmolar gap.

The patient has an unexplained high anion gap metabolic acidosis and altered mental status, raising suspicion for toxic alcohol ingestion.

Calculating the osmolar gap is an essential diagnostic step when toxic alcohol poisoning (like ethylene glycol or methanol) is suspected.

Calculate the expected serum osmolality.

Calculated osmolality =

2(140) + \frac{90}{18} + \frac{14}{2.8} = 280 + 5 + 5 = 290 \text{ mOsm/kg}

The standard formula estimates the contribution of the major serum osmoles: sodium (and its associated anions), glucose, and urea.

Calculate the osmolar gap.

Osmolar gap =

325 \text{ mOsm/kg} - 290 \text{ mOsm/kg} = 35 \text{ mOsm/kg}

The osmolar gap is defined as the measured serum osmolality minus the calculated serum osmolality. A normal gap is typically less than

10 \text{ mOsm/kg}

Key Concept

Calculation of the serum osmolar gap is used to detect the presence of unmeasured, osmotically active substances (such as toxic alcohols) in the blood.

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