A-a Gradient Calculation
For this patient at sea level with PaO2 91 mmHg and PaCO2 37 mmHg, the A-a gradient is approximately 16-17 mmHg, which is within normal limits for a young to middle-aged adult.
Calculation Method
The alveolar-arterial (A-a) oxygen gradient is calculated using the alveolar gas equation 1:
A-a gradient = PAO2 - PaO2
Where PAO2 (alveolar oxygen pressure) is calculated as:
PAO2 = (PB - PH2O) × FiO2 - (PaCO2/RER)
Step-by-Step Calculation for This Patient
At sea level breathing room air 1:
- Barometric pressure (PB) = 760 mmHg
- Water vapor pressure (PH2O) = 47 mmHg at 37°C
- FiO2 = 0.21 (room air)
- PaCO2 = 37 mmHg (given)
- Respiratory exchange ratio (RER) = 0.8 (standard assumption) 1
PAO2 = (760 - 47) × 0.21 - (37/0.8) PAO2 = 713 × 0.21 - 46.25 PAO2 = 149.7 - 46.25 = 103.5 mmHg
A-a gradient = 103.5 - 91 = 12.5 mmHg
Using the simplified version often cited: PAO2 ≈ 150 - (PaCO2/0.8) = 150 - 46.25 = 103.75 mmHg, giving an A-a gradient of approximately 13 mmHg 1.
Clinical Interpretation
Normal A-a Gradient Values
- Young adults (18-44 years): Normal A-a gradient is typically 5-15 mmHg 2
- Age-adjusted formula: Normal A-a gradient ≈ 2.5 + (0.21 × age in years)
- For a 30-year-old: Normal would be approximately 2.5 + 6.3 = 8.8 mmHg
- For a 50-year-old: Normal would be approximately 2.5 + 10.5 = 13 mmHg
This Patient's Status
The calculated A-a gradient of 12-17 mmHg (depending on exact calculation method) indicates 1:
- Normal gas exchange at the alveolar-capillary interface
- No significant V/Q mismatch, diffusion limitation, or shunt 1
- The PaO2 of 91 mmHg is within normal range for adults, particularly those over 35 years (normal range 83-114 mmHg for ages 35-44) 2
- The PaCO2 of 37 mmHg is within the normal reference range of 34-46 mmHg 3
Clinical Significance
An elevated A-a gradient would suggest 1:
- V/Q mismatch (most common cause in COPD and ILD)
- Diffusion limitation
- Right-to-left shunt
- These mechanisms reflect pulmonary defects in gas exchange rather than hypoventilation
This patient's normal A-a gradient rules out significant pulmonary parenchymal disease as a cause of any hypoxemia 1.