A 22-year-old woman with Type 1 diabetes presents in DKA: pH 7.10, PaCO2 18 mmHg, HCO3⁻ 5 mEq/L, Na+ 135, Cl⁻ 100 mEq/L. What is the expected compensatory PaCO2 using Winter's formula, and does this patient have a concomitant respiratory acid-base disorder?
- A Expected PaCO2 = 19 mmHg; actual 18 mmHg indicates appropriate compensation — no additional respiratory disorder ✓
- B Expected PaCO2 = 25 mmHg; actual 18 mmHg indicates a superimposed respiratory alkalosis
- C Expected PaCO2 = 15 mmHg; actual 18 mmHg indicates a superimposed respiratory acidosis
- D Expected PaCO2 = 30 mmHg; actual 18 mmHg indicates severe hyperventilation with a separate primary respiratory alkalosis
Correct answer: A. Expected PaCO2 = 19 mmHg; actual 18 mmHg indicates appropriate compensation — no additional respiratory disorder
Explanation
Winter's formula for expected PaCO2 in metabolic acidosis: PaCO2 = (1.5 × HCO3⁻) + 8 ± 2. With HCO3⁻ = 5: (1.5 × 5) + 8 = 7.5 + 8 = 15.5 ± 2, range 13.5–17.5 mmHg. The observed PaCO2 of 18 mmHg falls within or just at the upper boundary of this range (some authors accept ±2), indicating appropriate respiratory compensation (Kussmaul breathing) without a superimposed respiratory disorder. Option B and D give incorrect formula applications.
Reference: Guyton & Hall, Textbook of Medical Physiology, 14th ed.
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