Clinical background
The A–a gradient serves a specific purpose in the assessment of hypoxaemia: distinguishing hypoxaemia caused by pure hypoventilation from hypoxaemia caused by impaired alveolar gas exchange. In hypoventilation the PaCO₂ rises and the PAO₂ falls proportionately, but the gradient between alveolar and arterial oxygen remains normal. In V/Q mismatch, shunt or a diffusion defect, by contrast, the gradient rises, because the PaO₂ falls more than hypoventilation alone would explain. This is the central clinical distinction: a normal A–a gradient in hypoxaemia points to an extrapulmonary cause (hypoventilation, a low FiO₂), whereas a raised gradient points to intrapulmonary pathology.
The decision the tool supports is therefore not a specific diagnosis but a branch point in the diagnostic tree: does the investigation proceed towards hypoventilation or towards parenchymal disease?
Calculating the A–a gradient
The calculation is based on the alveolar gas equation, a physical derivation from inspired gas and alveolar ventilation [1]:
at sea level:
FiO₂ is entered in the calculator as a percentage (21–100) but is used as a decimal in the formula. Patm is the barometric atmospheric pressure (760 mmHg at sea level), PH₂O is the water vapour pressure in the alveoli (47 mmHg at 37 °C) and R is the respiratory quotient, set to 0.8 as the standard assumption for a mixed diet.
The expected normal value increases with age, approximated as:
This age correction rests on the observation that ventilation–perfusion matching deteriorates gradually with advancing age even in healthy individuals, probably through loss of lung elasticity and increased basal shunt [4]. A 20-year-old therefore has an expected normal value of around 9 mmHg, an 80-year-old around 24 mmHg.
Interpretation in practice
The calculator returns the A–a gradient in mmHg together with the age-corrected expected normal value. Interpretation is governed by whether the gradient falls below or above the expected value.
| Gradient | Interpretation band | Action |
|---|---|---|
| ≤ expected for age | Normal gradient | The hypoxaemia is explained by hypoventilation or a low FiO₂. Identify the cause of hypoventilation (opioids, neuromuscular disease, COPD with hypercapnia). Where pulmonary embolism is suspected, further investigation can generally be foregone in patients without previous venous thromboembolism, see below. |
| > expected for age | Raised gradient | The hypoxaemia is caused by V/Q mismatch, shunt or a diffusion defect. This is the dominant mechanism in parenchymal disease (pneumonia, ARDS, pulmonary oedema, pulmonary embolism, interstitial lung disease). Investigation is directed towards an intrapulmonary cause. |
The practical value of calculating the gradient lies in two specific situations. First, in uncomplicated hypoxaemia where the question is whether the patient has an extrapulmonary cause that can be managed with ventilatory support or respiratory stimulation rather than oxygen therapy. Second, as a decision point in suspected pulmonary embolism, where a normal gradient in a patient without previous thromboembolism substantially lowers the probability of the diagnosis.
Validation and performance
The alveolar gas equation is a physical relationship and is not validated as a risk score in the traditional sense. The clinical value of the A–a gradient, particularly for excluding pulmonary embolism, has however been evaluated in prospective studies.
McFarlane and Imperiale [2] studied 540 patients who underwent ventilation–perfusion scintigraphy for suspected pulmonary embolism and who also had an arterial blood gas on room air. A normal A–a gradient, defined as ≤ age/4 + 4, was present in 57 patients without previous pulmonary embolism or deep vein thrombosis, and only 1 of these (1.8%, 95% CI 0.9–10.7%) had pulmonary embolism. The result was reproduced in a validation cohort of 489 patients, in which 1 of 54 (1.9%, 95% CI 0.1–11.2%) with a normal gradient and no previous thromboembolism had pulmonary embolism. A normal gradient therefore has a high negative predictive value for pulmonary embolism in patients without previous venous thromboembolism.
Specificity is, however, low. Jones et al. [3] studied 123 patients older than 64 years who underwent pulmonary angiography for suspected pulmonary embolism. Of 54 patients with angiographically confirmed pulmonary embolism, three had an A–a gradient normal for their age. The mean A–a gradient did not differ significantly between those with pulmonary embolism (46.6 mmHg) and those without (46.0 mmHg). A raised gradient is therefore non-specific in an older population with suspected pulmonary embolism and cannot distinguish pulmonary embolism from other pulmonary pathology. This is to be expected: the gradient measures impaired gas exchange, not embolism specifically.
Limitations
It requires an FiO₂ of room air. The age-corrected normal value formula applies to patients breathing room air (FiO₂ 21%). At a high FiO₂ the normal A–a gradient itself increases, and the thresholds for normality become invalid. The calculator does accept an FiO₂ up to 100%, but interpretation against age/4 + 4 applies strictly only on room air.
Sea level and RQ. The calculation assumes an atmospheric pressure of 760 mmHg and a respiratory quotient of 0.8. At altitude the Patm and hence the PAO₂ fall, which the calculator does not take into account. The RQ varies with diet and metabolic state (0.7 with pure fat oxidation, 1.0 with pure glucose oxidation), but the deviation is small in practice.
Non-specific when raised. A raised gradient indicates impaired gas exchange but does not point to any specific diagnosis. Pneumonia, pulmonary oedema, ARDS, interstitial lung disease and pulmonary embolism all raise the gradient. The gradient therefore cannot be used as a diagnostic test for an individual disease.
Origin of the age formula. The formula age/4 + 4 is a clinical rule of thumb, not a formal derivation from a defined population. It approximates the age-related increase in basal V/Q mismatch documented in healthy individuals [4], but gives a rough estimate rather than a statistical confidence interval.
References
- Story DA. Alveolar oxygen partial pressure, alveolar carbon dioxide partial pressure, and the alveolar gas equation. Anesthesiology. 1996;84(4):1011. PMID: 8638826
- McFarlane MJ, Imperiale TF. Use of the alveolar-arterial oxygen gradient in the diagnosis of pulmonary embolism. Am J Med. 1994;96(1):57–62. PMID: 8304364
- Jones JS, VanDeelen N, White L, et al. Alveolar-arterial oxygen gradients in elderly patients with suspected pulmonary embolism. Ann Emerg Med. 1993;22(7):1177–1181. PMID: 8517570
- Cardús J, Burgos F, Diaz O, et al. Increase in pulmonary ventilation-perfusion inequality with age in healthy individuals. Am J Respir Crit Care Med. 1997;156(4 Pt 1):1124–1129. PMID: 9279253
