A 45-year-old man is brought to the emergency department after being found obtunded in his… — USMLE Step 3

A 45-year-old man is brought to the emergency department after being found obtunded in his garage. His family reports that he has a history of severe alcohol use disorder and recent major depressive disorder. An empty container of commercial antifreeze was found nearby. Vital signs are temperature $36.5^\circ\text{C}$ ( $97.7^\circ\text{F}$ ), blood pressure $135/85\text{ mmHg}$ , pulse $98/\text{min}$ , and respiratory rate $26/\text{min}$ with deep inspirations (Kussmaul respirations). Physical examination reveals a comatose patient with no focal neurologic deficits.

Initial laboratory results are obtained:

Test	Result
Sodium	$140\text{ mEq/L}$
Potassium	$4.5\text{ mEq/L}$
Chloride	$105\text{ mEq/L}$
Bicarbonate	$10\text{ mEq/L}$
Blood urea nitrogen	$28\text{ mg/dL}$
Creatinine	$1.2\text{ mg/dL}$
Glucose	$108\text{ mg/dL}$
Serum osmolality (measured)	$326\text{ mOsm/kg}$
Arterial blood gas, pH	$7.15$

Based on the provided laboratory data, calculate the patient's serum osmolar gap. What is the value in $\text{mOsm/kg}$ ?

Cevap: 30 mOsm/kg

Cevap

The correct serum osmolar gap is

30\text{ mOsm/kg}

The patient's osmolar gap is determined by subtracting the calculated serum osmolarity from the measured serum osmolality. The calculated osmolarity is

2 \times 140 + \frac{108}{18} + \frac{28}{2.8} = 280 + 6 + 10 = 296\text{ mOsm/L}

. The osmolar gap is

326 - 296 = 30\text{ mOsm/kg}

. An elevated osmolar gap (normal

\leq 10

) combined with a high anion gap metabolic acidosis in a patient found near antifreeze confirms ethylene glycol toxicity.

Adım Adım Çözüm

Extract relevant laboratory values required for the osmolarity equation.

Sodium =

140\text{ mEq/L}

, Glucose =

108\text{ mg/dL}

, BUN =

28\text{ mg/dL}

These three solutes are the primary physiologic determinants of expected serum osmolarity.

Calculate the expected serum osmolarity using the standard formula.

(2 \times 140) + \frac{108}{18} + \frac{28}{2.8} = 280 + 6 + 10 = 296\text{ mOsm/L}

The formula standardizes glucose and BUN from mg/dL to mmol/L, and multiplying sodium by 2 accounts for its accompanying anions (chloride and bicarbonate).

Calculate the final osmolar gap.

326 \text{ (measured osmolality)} - 296 \text{ (calculated osmolarity)} = 30\text{ mOsm/kg}

The gap represents the presence of unmeasured, osmotically active substances in the blood, which in this clinical scenario strongly points to ethylene glycol toxicity.

Anahtar Kavram

The serum osmolar gap is calculated as: Measured Osmolality - Calculated Osmolarity, where Calculated Osmolarity =

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

. A normal gap is

\leq 10\text{ mOsm/kg}

; an elevated gap indicates the presence of unmeasured exogenous osmoles (e.g., toxic alcohols).

Alternatif Yöntem

In patients with suspected mixed ingestions, if an ethanol level is obtained, the calculated osmolarity formula should be expanded by adding

\frac{\text{Ethanol (mg/dL)}}{4.6}

to account for ethanol's osmotic contribution before calculating the final gap.

Tahmini Süre:1m 15s

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