A 22-year-old woman with type 1 diabetes presents with DKA: pH 7.10, PaCO2 18 mmHg, HCO3 5 mEq/L, Na 132, Cl 94. Using Winter's formula, is the respiratory compensation appropriate?

• A Expected PaCO2 = 13 mmHg; respiratory compensation is inadequate, suggesting concurrent respiratory acidosis
• B Expected PaCO2 = 15 mmHg; respiratory compensation is inadequate
• C Expected PaCO2 = 21 mmHg; respiratory compensation is excessive
• D Expected PaCO2 = 17 mmHg; respiratory compensation is appropriate ✓

Explanation

Winter's formula for expected PaCO2 in metabolic acidosis: PaCO2 = 1.5 × HCO3 + 8 ± 2 = 1.5 × 5 + 8 = 7.5 + 8 = 15.5 ± 2, giving a range of 13.5–17.5 mmHg. The measured PaCO2 of 18 mmHg is just at the upper boundary of this range, consistent with appropriate (or very slightly insufficient) respiratory compensation — clinically, this is accepted as adequate compensation without an additional respiratory acidosis. AG = 132 − (94 + 5) = 33 mEq/L, confirming high-AG metabolic acidosis.

Reference: Guyton & Hall, Textbook of Medical Physiology, 14th ed.

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