Emergency medical services bring a 52-year-old man to the emergency department after he wa… — USMLE Step 3

Emergency medical services bring a 52-year-old man to the emergency department after he was found unresponsive in a park. He has a known history of severe alcohol use disorder. On physical examination, his temperature is $36.5^\circ\text{C}$ ( $97.7^\circ\text{F}$ ), blood pressure is $110/70 \text{ mmHg}$ , pulse is $98/\text{min}$ , and respiratory rate is $16/\text{min}$ . He is uncooperative and confused but moves all extremities spontaneously.

Initial laboratory studies reveal the following:

Laboratory Test	Result	Reference Range
Sodium ( $Na^+$ )	$140 \text{ mEq/L}$	$136 - 145 \text{ mEq/L}$
Potassium ( $K^+$ )	$4.2 \text{ mEq/L}$	$3.5 - 5.0 \text{ mEq/L}$
Chloride ( $Cl^-$ )	$102 \text{ mEq/L}$	$95 - 105 \text{ mEq/L}$
Bicarbonate ( $HCO_3^-$ )	$20 \text{ mEq/L}$	$22 - 28 \text{ mEq/L}$
Blood urea nitrogen (BUN)	$28 \text{ mg/dL}$	$7 - 18 \text{ mg/dL}$
Glucose	$180 \text{ mg/dL}$	$70 - 110 \text{ mg/dL}$
Creatinine	$1.2 \text{ mg/dL}$	$0.6 - 1.2 \text{ mg/dL}$

A toxicology screen is negative for acetaminophen and salicylates. His blood ethanol level is undetectable. The laboratory reports a measured serum osmolality of $324 \text{ mOsm/kg H}_2\text{O}$ .

Based on the provided laboratory results, what is the patient's calculated osmolar gap?

Cevap: 24 mOsm/kg

Cevap

The patient's osmolar gap is exactly

24

. Calculated serum osmolality is found using the formula:

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

. Substituting the provided lab values yields:

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

. The osmolar gap is the measured osmolality (

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

) minus the calculated osmolality (

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

), which equals

24

. An elevated gap (normal is

\leq 10

) in the context of an uncooperative, confused patient with an alcohol use disorder strongly suggests toxic alcohol ingestion, such as methanol or ethylene glycol, requiring further diagnostic workup and potential treatment with fomepizole.

Adım Adım Çözüm

Calculate the expected serum osmolality using the formula:

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

Calculated osmolality =

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

This formula estimates the total concentration of the major osmotically active solutes in the plasma under normal physiological conditions.

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

Osmolar gap =

324 - 300 = 24

The osmolar gap quantifies the presence of unmeasured osmotically active substances (such as toxic alcohols) in the patient's blood.

Anahtar Kavram

The osmolar gap is determined by subtracting the calculated serum osmolality from the laboratory-measured serum osmolality. A normal gap is typically

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

; an elevated gap suggests the presence of unmeasured exogenous osmoles.

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