A-a Gradient Calculator

The alveolar-arterial oxygen difference compares the oxygen tension the alveolus should contain with the tension actually delivered to arterial blood, and it is the standard way to decide whether hypoxaemia originates in the lung itself or somewhere upstream of it. The alveolar term cannot be sampled, so it is computed: inspired oxygen fraction multiplied by dry barometric pressure, which is 760 minus the 47 mmHg of water vapour that fully saturates gas at body temperature, minus arterial carbon dioxide divided by the respiratory quotient. The quotient of about 0.8 on a mixed diet accounts for the body consuming more oxygen than the carbon dioxide it produces, so alveolar carbon dioxide displaces slightly more oxygen than a one-to-one substitution. On room air at sea level the alveolar value works out near 100 mmHg. A healthy young adult breathing room air has a gradient of roughly 5 to 15 mmHg, arising from bronchial and thebesian venous drainage and from mild regional ventilation-perfusion inequality. It widens with age as small airways close at higher lung volumes, which is why age-adjusted limits such as 2.5 plus 0.21 times age, or age divided by 4 plus 4, are used instead of a fixed cut-off. A widened gradient points to ventilation-perfusion mismatch, right-to-left shunt, or diffusion limitation, whereas hypoxaemia with a normal gradient points to hypoventilation or a low inspired oxygen fraction, as at altitude. The main caveat is that the gradient loses discriminating power on supplemental oxygen, because the calculated alveolar value grows far faster than the arterial one; the a/A ratio or the P/F ratio is more stable in that setting, and barometric pressure must be corrected for altitude.

The alveolar gas equation grew out of respiratory physiology laboratories working on aviation problems during and after the Second World War. Wallace Fenn, Hermann Rahn, and Arthur Otis at the University of Rochester published their oxygen-carbon dioxide diagram in 1946, a graphical framework that made explicit how alveolar oxygen falls as alveolar carbon dioxide rises for a given inspired mixture and respiratory exchange ratio. That relationship is the substance of the equation still used at the bedside, and the water vapour and exchange-ratio terms in it come directly from that work. The step from alveolar gas to the alveolar-arterial difference as a diagnostic quantity belongs largely to Richard Riley and Andre Cournand, who in the late 1940s described the three-compartment model of the lung as ideal, shunt, and dead-space units, and used measured differences between calculated alveolar and sampled arterial gas to quantify how far a real lung departed from the ideal. Their work depended on the practical arterial puncture and blood gas techniques of the same period, and the difference became routinely measurable only after Leland Clark oxygen electrode of 1956 and the assembled blood gas analysers of the 1960s brought the measurement into clinical laboratories. The age-adjusted normal values in common use derive from studies of healthy volunteers published in the 1960s, notably work by K. Mellemgaard in 1966 describing the size and components of the difference in normal subjects.