A 45-year-old man is brought to the emergency department by his sister due to altered ment… — USMLE Step 2 CK

A $45$ -year-old man is brought to the emergency department by his sister due to altered mental status. She states that he has a history of alcohol use disorder and was found confused in his apartment with an empty bottle of antifreeze nearby. Laboratory studies show:

Lab	Value
Serum sodium	$140 \text{ mEq/L}$
Serum potassium	$4.0 \text{ mEq/L}$
Serum chloride	$102 \text{ mEq/L}$
Serum bicarbonate	$12 \text{ mEq/L}$
Blood urea nitrogen (BUN)	$28 \text{ mg/dL}$
Serum glucose	$180 \text{ mg/dL}$
Measured serum osmolality	$325 \text{ mOsm/kg H}_2\text{O}$

Based on these laboratory results, what is this patient's calculated osmolar gap? (Provide the exact numerical value)

Cevap: 25 mOsm/kg H2O

Cevap

The calculated osmolar gap is 25.

The patient has an elevated measured osmolality due to the ingestion of ethylene glycol (antifreeze). The calculated osmolality is

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

, derived from the formula

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

. Subtracting this calculated value from the measured osmolality of

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

gives an osmolar gap of

25

. An elevated osmolar gap is a hallmark of toxic alcohol ingestion.

Adım Adım Çözüm

Calculate the estimated serum osmolality using the standard formula.

Calculated Osmolality =

2 \times 140 + \frac{180}{18} + \frac{28}{2.8} = 280 + 10 + 10 = 300 \text{ mOsm/kg H}_2\text{O}

The osmolar gap is the difference between measured and calculated osmolality. To find the gap, the calculated osmolality must first be determined from serum sodium, glucose, and BUN.

Subtract the calculated osmolality from the measured osmolality.

325 - 300 = 25

This yields the osmolar gap, which represents the presence of unmeasured osmotically active substances (in this case, ethylene glycol from antifreeze).

Anahtar Kavram

The osmolar gap is calculated by subtracting the calculated serum osmolality (

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

) from the measured serum osmolality. An elevated osmolar gap (

>10 \text{ mOsm/kg H}_2\text{O}

) typically indicates the presence of toxic alcohols.

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