How to calculate the Aa gradient

Accurate assessment and management of oxygenation disorders is critical to optimal patient outcomes. Alveolar to arterial oxygen gradient (Aa), i.e. the difference between the quantity of oxygen within the alveoli (alveolar oxygen tension [PAO₂]) and the quantity of oxygen dissolved within the plasma (PaO₂), is a vital measurement to assist narrow down the reason for hypoxemia. It describes the general efficiency of oxygen uptake from alveolar gas into the capillary blood of the lungs.

Calculations

The basic formula is: PaO₂ is measured by arterial blood gasometry, while PAO₂ is calculated using the bubble gas equation:

In this equation FiO₂ is the fraction of inhaled oxygen (0.21 in room air), Patm is the atmospheric pressure (760 mm Hg at sea level), PH₂O is the partial pressure of water (47 mmHg at 37⁰C), PaCO₂ is the arterial carbon dioxide pressure, and R is the respiratory quotient (about 0.8 at regular state, but varies with the relative utilization of carbohydrates, protein, and fat).

Furthermore, the Aa gradient changes with age and could be estimated by the next equation:

Important notes

• In healthy patients, the difference between PAO is usually small₂ and PaO₂ because PAO₂ is roughly 100 mm Hg and PaO₂ is roughly 95 mm Hg.
• Correct determination of the Aa gradient requires accurate measurement of FiO₂that is easiest to do when the patient is respiration room air or is mechanically ventilated. FiO₂ The variety of patients receiving supplemental oxygen via nasal cannula or mask could be estimated, but this limits the usefulness of the Aa gradient.
• The Aa gradient increases with increasing FiO₂. When the patient receives high FiO₂each PAOs₂ and PaO₂ increase. However, PAO₂ increases disproportionately, causing an increasing Aa gradient.

Clinical implications

Measuring the Aa gradient helps narrow down the reason for hypoxemia as extrapulmonary (outside the lungs) or intrapulmonary (contained in the lungs); in other words, to tell apart hypercapnic respiratory failure brought on by global hypoventilation (extrapulmonary respiratory failure) from respiratory failure brought on by abnormal gas exchange from intrinsic lung disease. Aa gradient in the traditional range (< 20 mm Hg) with increased PaCO₂ highly suggestive of worldwide hypoventilation, whereas a widened gradient (>20 mm Hg) suggests that underlying pulmonary disease could also be contributing to the measured hypercapnia.

Consider two patients…

A young, healthy patient is available in with a drug overdose and his respiratory rate is 8. The results of arterial blood gases (ABG) in room air indicate respiratory acidosis with hypoxemia of seven.31/55/65/24/88%. Assuming PatmPH₂O and R are constant, we calculate its gradient Aa:

Hantzidiamantis, P. & Amaro, E. (2019, August 3). Physiology, alveolar to arterial oxygen gradient (Aa gradient). StatPearls. https://www.ncbi.nlm.nih.gov/books/NBK545153/

Kopman, D. and Schwartztein, R. (2020, April 1). Evaluation, diagnosis, and treatment of the adult patient with acute hypercapnic respiratory failure. https://www.uptodate.com/contents/measures-of-oxygenation-and-mechanisms-of-hypoxemia

Theodore, A. (2020, March 4). Oxygenation measures and mechanisms of hypoxemia. https://www.uptodate.com/contents/the-evaluation-diagnosis-and-treatment-of-the-adult-patient-z-ostra-hiperkapnica-respiratory-failure