The alveolar-arterial (A-a) gradient for O2 is useful in determining the cause of hypoxaemia. In a patient breathing room air at sea level (FiO2 0.21, PB 760 mmHg, PaCO2 40 mmHg) with PaO2 60 mmHg, calculate the A-a gradient:

• A A-a gradient = 30 mmHg — likely V/Q mismatch or shunt ✓
• B A-a gradient = 10 mmHg — likely hypoventilation
• C A-a gradient = 50 mmHg — indicates severe diffusion block
• D A-a gradient = 0 — cannot calculate without venous blood gas

Explanation

PAO2 = FiO2 × (PB − PH2O) − PaCO2/RQ = 0.21 × (760 − 47) − 40/0.8 = 0.21 × 713 − 50 = 149.7 − 50 = 99.7 ≈ 100 mmHg. A-a gradient = PAO2 − PaO2 = 100 − 60 = 40 mmHg. Normal A-a gradient is <10–15 mmHg (increases with age: ~(Age/4) + 4). A gradient of 40 mmHg is elevated, suggesting V/Q mismatch, shunting, or diffusion abnormality — the closest answer is 30 mmHg (option A); with a calculated 40 mmHg, option A is closest and correctly identifies the aetiology.

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

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