A 38-year-old man is brought to the emergency department by emergency medical services aft… — USMLE Step 3

A $38$ -year-old man is brought to the emergency department by emergency medical services after being found lethargic and confused in his unheated garage during winter. Beside him was an unlabeled jug containing a brightly colored liquid. His blood pressure is $110/70$ mm Hg, pulse is $102$ /min, and respirations are $26$ /min and deep. Physical examination reveals a somnolent patient who localizes to painful stimuli. Cardiopulmonary examination is unremarkable, and he has no focal neurologic deficits. Laboratory results are as follows:

Laboratory Test	Result	Reference Range
Sodium	$142$ mEq/L	$136$ - $145$ mEq/L
Potassium	$5.0$ mEq/L	$3.5$ - $5.0$ mEq/L
Chloride	$104$ mEq/L	$95$ - $105$ mEq/L
Bicarbonate	$10$ mEq/L	$22$ - $28$ mEq/L
Blood urea nitrogen (BUN)	$14$ mg/dL	$7$ - $18$ mg/dL
Creatinine	$1.2$ mg/dL	$0.6$ - $1.2$ mg/dL
Glucose	$198$ mg/dL	$70$ - $110$ mg/dL
Measured serum osmolality	$332$ mOsm/kg H $_2$ O	$275$ - $295$ mOsm/kg H $_2$ O

Based on the provided laboratory results, calculate the patient's osmolar gap. Enter only the numerical value.

Cevap: 32 mOsm/kg

Cevap

This patient presents with altered mental status and deep respirations (Kussmaul breathing) in the setting of wintertime exposure to a brightly colored, unlabelled fluid, raising strong suspicion for ethylene glycol (antifreeze) toxicity. The laboratory results show a high anion gap metabolic acidosis (Anion gap =

142 - (104 + 10) = 28

). To evaluate for the presence of toxic alcohols, an osmolar gap should be calculated. The formula for calculated serum osmolality is

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

. Using the patient's values, this yields

2(142) + \frac{198}{18} + \frac{14}{2.8} = 284 + 11 + 5 = 300

mOsm/kg. The osmolar gap is the measured osmolality minus the calculated osmolality (

332 - 300 = 32

mOsm/kg). A normal gap is typically

< 10

mOsm/kg; a gap of

32

strongly supports the presence of an unmeasured osmotically active substance, confirming the suspicion of toxic alcohol ingestion.

Adım Adım Çözüm

Extract the relevant values required for the calculated osmolality formula.

Sodium =

142

, Glucose =

198

, BUN =

14

The calculated serum osmolality depends on the primary osmotic drivers in the serum.

Apply the calculated osmolality formula:

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

2 \times 142 + \frac{198}{18} + \frac{14}{2.8} = 284 + 11 + 5 = 300

mOsm/kg.

This formula estimates the total particle concentration normally present in the blood. The divisors convert mg/dL to mmol/L.

Calculate the osmolar gap by subtracting the calculated osmolality from the measured osmolality.

Osmolar gap =

332 - 300 = 32

mOsm/kg.

The difference between measured and calculated osmolality reveals the presence of unmeasured osmotically active substances (e.g., toxic alcohols).

Anahtar Kavram

Calculation of the osmolar gap is an essential step in diagnosing toxic alcohol ingestions (such as ethylene glycol or methanol) in patients presenting with altered mental status and a high anion gap metabolic acidosis.

Tahmini Süre:1m 30s

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