Paramedics arrive at the emergency room with a 52-year-old man who was discovered unrespon… — USMLE Step 2 CK

Paramedics arrive at the emergency room with a 52-year-old man who was discovered unresponsive in a public park. The patient has a documented medical history of severe alcohol use disorder. Upon initial evaluation, his body temperature is $36.2^\circ\text{C}$ ( $97.2^\circ\text{F}$ ), pulse is $102/\text{min}$ , blood pressure is $110/70\text{ mm Hg}$ , and respirations are $24/\text{min}$ . He is unarousable to painful stimuli. Cardiopulmonary examination is unremarkable. Initial laboratory studies show the following:

Laboratory Parameter	Value
Serum sodium	$137\text{ mEq/L}$
Serum potassium	$4.5\text{ mEq/L}$
Serum chloride	$98\text{ mEq/L}$
Serum bicarbonate	$12\text{ mEq/L}$
Blood urea nitrogen	$56\text{ mg/dL}$
Serum creatinine	$1.8\text{ mg/dL}$
Serum glucose	$162\text{ mg/dL}$
Serum ethanol	$138\text{ mg/dL}$
Measured serum osmolality	$368\text{ mOsm/kg H}_2\text{O}$

Arterial blood gas (room air) shows a pH of $7.22$ and a $\text{PaCO}_2$ of $26\text{ mm Hg}$ .

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

Answer: 35 mOsm/kg

Answer

The correct osmolar gap is 35. The patient presents with an elevated anion gap metabolic acidosis (Anion Gap = 137 - 98 - 12 = 27). In such cases, evaluating the osmolar gap is crucial to identifying toxic alcohol ingestion. The calculated serum osmolality must account for sodium, glucose, blood urea nitrogen (BUN), and any measured ethanol. The full formula is:

2 \times [\text{Na}^+] + \frac{[\text{Glucose}]}{18} + \frac{[\text{BUN}]}{2.8} + \frac{[\text{Ethanol}]}{4.6}

. Plugging in the values gives

2(137) + \frac{162}{18} + \frac{56}{2.8} + \frac{138}{4.6} = 274 + 9 + 20 + 30 = 333\text{ mOsm/kg}

. The osmolar gap is the measured osmolality minus the calculated osmolality (

368 - 333 = 35

). An osmolar gap greater than 10 to 15 mOsm/kg suggests the presence of unmeasured osmotically active substances, such as methanol or ethylene glycol, which require urgent intervention.

Step-by-Step Solution

Recall the formula for calculated serum osmolality.

Calculated Osmolality =

2 \times [\text{Na}^+] + \frac{[\text{Glucose}]}{18} + \frac{[\text{BUN}]}{2.8} + \frac{[\text{Ethanol}]}{4.6}

To determine the osmolar gap, the expected (calculated) osmolality must first be determined, accounting for all major osmotically active substances including ethanol.

Input the patient's laboratory values into the formula.

Calculated Osm =

2(137) + \frac{162}{18} + \frac{56}{2.8} + \frac{138}{4.6}

Standard conversion factors are used to convert mg/dL to mmol/L (mOsm/kg).

Compute the sum of the components.

274 + 9 + 20 + 30 = 333\text{ mOsm/kg H}_2\text{O}

This represents the osmolality expected from the known solutes in the patient's blood.

Calculate the osmolar gap.

Osmolar gap = Measured Osmolality - Calculated Osmolality =

368 - 333 = 35\text{ mOsm/kg H}_2\text{O}

The difference reveals the presence of unmeasured osmotically active substances (e.g., toxic alcohols like methanol or ethylene glycol).

Key Concept

The serum osmolar gap is calculated by subtracting the calculated osmolality from the measured osmolality. When ethanol is present, it must be included in the calculated osmolality formula to accurately assess for the presence of other toxic alcohols.

Estimated Time:1m 30s

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