Normal A–a gradient by age, and what a raised gradient means

What is a normal A–a gradient by age?

A normal A–a gradient on room air at sea level is below 10 mmHg in a young adult, according to Sarkar and colleagues' 2017 review of hypoxemia in Lung India, and it rises steadily with age. The usual bedside estimate of the normal value is (age ÷ 4) + 4 mmHg: 9 mmHg at 20, 14 mmHg at 40, 19 mmHg at 60 and 24 mmHg at 80. A measured study gives slightly lower figures. Mellemgaard measured the alveolar–arterial oxygen difference in 80 healthy seated subjects aged 15 to 75 in 1966 and found a regression line of 2.5 + 0.21 × age mmHg, which is 6.7 mmHg at 20 and 15.1 mmHg at 60. The bedside rule therefore sits 2 to 4.5 mmHg above the average healthy value across that age range and works as a generous expected value. Both figures apply only to room air; on added oxygen the normal gradient is wider.

Values are worked out from each formula; kPa use 1 kPa = 7.50062 mmHg. To compare a patient's own gradient with the estimate for their age, enter the blood gas in the A-a gradient calculator, which shows both lines.

Where the (age ÷ 4) + 4 rule comes from

The (age ÷ 4) + 4 rule is a bedside approximation, and we could not trace it to a single original derivation, so it should be read as an estimate rather than a reference interval. A measured basis for age-adjusted values is Mellemgaard's 1966 study in Acta Physiologica Scandinavica, which Murray and Nadel's Textbook of Respiratory Medicine cites for the regression 2.5 + 0.21 × age in 80 healthy seated subjects aged 15 to 75. The rule was also used in published research: Stein, Goldhaber and Henry, analysing the PIOPED cohort in Chest in 1995, tested three definitions of a normal gradient, namely 20 mmHg or less, (age ÷ 4) + 4 or less, and age-related values from the literature. Sarkar's review explains why the gradient widens with age: the rise is mainly due to an age-related fall in PaO2 as V/Q mismatch increases. The review puts the fall in PaO2 after age 70 at about 0.43 mmHg per year.

Two practical points follow. First, a gradient a few mmHg above the bedside estimate in an older adult is a weak signal on its own, so look at it with the PaO2, the PaCO2 and the clinical picture. Second, both the rule and Mellemgaard's line describe healthy people breathing room air near sea level, so they cannot be applied to a gradient measured on supplemental oxygen.

How the A–a gradient sorts the causes of hypoxemia

The A–a gradient sorts hypoxemia by asking whether the lung is transferring oxygen normally. Sarkar's review lists five mechanisms of hypoxemia: V/Q mismatch, right-to-left shunt, diffusion impairment, hypoventilation and low inspired PO2. The review states that hypoxemia due to V/Q mismatch, diffusion limitation and shunt has a widened gradient, whereas hypoxemia due to hypoventilation has a normal gradient, because the alveolar–capillary membrane is intact. In hypoventilation the PaCO2 rises, the alveolar gas equation gives a lower PAO2, and the PaO2 falls with it, so the gap between them stays normal. A low inspired PO2, as at altitude, also lowers PAO2 itself; the equation accounts for it through FiO2 and barometric pressure. A raised gradient in a hypoxemic patient therefore points to disease of the lung's gas exchange, and a normal gradient with a high PaCO2 points to hypoventilation, the one mechanism that leaves the membrane intact.

Telling V/Q mismatch, shunt and diffusion limitation apart

Once the A–a gradient is raised, the three lung mechanisms behave differently, and Sarkar's review gives the features that separate them. V/Q mismatch is the most common mechanism of hypoxemia; it corrects easily with supplemental oxygen, and the review lists asthma, COPD, bronchiectasis, cystic fibrosis, interstitial lung disease and pulmonary hypertension among its causes. Shunt is the extreme of V/Q mismatch, where blood passes unventilated lung units; poor response to oxygen is the feature that separates it from the other mechanisms, and hypercapnia is uncommon until the shunt fraction reaches about 50%. Causes include pneumonia, pulmonary edema, ARDS, alveolar collapse and pulmonary arteriovenous communication. Diffusion limitation comes from a smaller surface area or a thickened alveolar–capillary membrane, as in emphysema and interstitial lung disease; its hallmark is hypoxemia that appears or worsens with exercise, which shortens capillary transit time (normally 0.75 seconds, against the 0.25 seconds needed to complete gas exchange).

Worked examples: reading the gradient against age

Four patients on room air at sea level show how the same A–a gradient can be normal at one age and raised at another. Each uses barometric pressure 760 mmHg, water vapor 47 mmHg and a respiratory quotient of 0.8, so PAO2 = 149.7 − 1.25 × PaCO2. A 40-year-old with PaO2 55 mmHg and PaCO2 70 mmHg has a PAO2 of 62.2 mmHg and a gradient of 7.2 mmHg, within the estimate of 14: hypoventilation alone explains the hypoxemia. A 60-year-old with PaO2 70 and PaCO2 40 has a PAO2 of 99.7 and a gradient of 29.7, well above the estimate of 19, pointing to lung disease. A 70-year-old with PaO2 82 and PaCO2 38 has a gradient of 20.2: above 10 and above the estimate for a 40-year-old, but within the 21.5 expected at 70. A 65-year-old with PaO2 50 and PaCO2 60 has a gradient of 24.7, above the estimate of 20.3 despite the high PaCO2, so hypoventilation is not the whole story.

Enter any of these in the A-a gradient calculator to see the same numbers, in mmHg or kPa.