A patient with diabetic ketoacidosis has pH 7.15, PaCO2 18 mmHg, HCO3⁻ 6 mEq/L, Na⁺ 135 mEq/L, Cl⁻ 98 mEq/L. What is the calculated anion gap and the expected respiratory compensation (PaCO2)?

• A AG = 31 mEq/L; expected PaCO2 = 1.5×6 + 8 ± 2 = 17 ± 2 mmHg; actual PaCO2 of 18 mmHg is within the expected range, indicating pure high-AG metabolic acidosis with appropriate respiratory compensation ✓
• B AG = 31 mEq/L; expected PaCO2 = 40 − (24−6) = 22 mmHg; actual 18 mmHg indicates superimposed respiratory alkalosis
• C AG = 25 mEq/L; expected PaCO2 = 1.5×6 + 8 = 17 mmHg; actual 18 mmHg indicates adequate compensation
• D AG = 25 mEq/L; expected PaCO2 = 40−1.2×(24−6) = 18.4 mmHg; actual 18 mmHg confirms pure metabolic acidosis with complete compensation

Explanation

Anion gap = Na⁺ − (Cl⁻ + HCO3⁻) = 135 − (98 + 6) = 31 mEq/L (elevated, normal 8–12). Winter's formula for expected respiratory compensation in metabolic acidosis: PaCO2 = 1.5 × [HCO3⁻] + 8 ± 2 = 1.5 × 6 + 8 ± 2 = 9 + 8 ± 2 = 17 ± 2 mmHg. The actual PaCO2 of 18 mmHg falls within this range (15–19 mmHg), confirming appropriate (expected) Kussmaul breathing compensation without a superimposed respiratory disorder. Option D uses a different formula (1.2 × delta HCO3) applicable for a quick estimate but Winter's formula is the standard for confirming adequacy of compensation.

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

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