A-a Gradient Calculator

How does this A-a gradient calculator work?

This tool assesses the alveolar - arterial gradient and determines the possible existence and the source of hypoxemia. This gradient is the difference between the alveolar concentration of oxygen and the arterial concentration of oxygen. For your convenience, you can input the pressures required in either mmHg or kPa. The following lines are a guide to how you should use this A-a gradient calculator:

- O₂ Arterial pressure – P_aO₂ is the partial arterial pressure of the oxygen in the arteries; its range is between 75-100 mmHg. Low levels are indicator of hypoxia, a level of 60 mmHg requires additional oxygen and anything dropping below 30mmHg is life threatening.
- CO₂ Arterial pressure – P_aCO₂ is the partial arterial pressure of carbon dioxide in the arteries. It ranges between 35-45 mmHg and is the main indicator of CO2 production and elimination. High values are suggestive for impaired ventilation while low values indicate hypocapnia or overventilation.
- Age – the age of the subject is required in order to determine the estimated normal A-a gradient based on the following formula: (Age + 4) / 4
- Atmospheric pressure – is set default at 760 mmHg, the value for above sea level.
- Fraction of Inspired Oxygen (F_iO₂) – is set default at 21% as the concentration in room air.
The other two variables used are the water vapor pressure pH2O (mmHg) = 47 mm Hg at 37 degrees Celsius and the respiratory quotient RQ (VCO2/VO2) = 0.8.

A-a gradient = [F_iO₂ (P_atm – P_H20) – P_aCO₂ /0.8 ] – P_aO2

Example calculation

Let’s take the example of a patient aged 34, P_aO₂ = 86 mmHg, P_aCO₂ = 45 mmHg and P_atm = 760 mmHg, F_iO₂ = 21%. The result is:

■ A-a Gradient is 7.48 mmHg or 1 kPa.

■ Expected (normal) A-a Gradient for the specified age is 9.5 mmHg or 1.27 kPa.

■ Usually A-a Gradient increases 5 to 7 mmHg for every 10% increase in F_iO₂.

Medical implications of the A-a gradient:

- The normal range is between 5 to 20 mmHg up to middle age and increases as we get older in a rhythm of 1 mmHg for every decade. 
- It is used to determine whether the source of hypoxemia is intra or extra pulmonary.
- A normal gradient accompanied by hypoxemia (low P_aO₂) indicates hypoventilation by decreased respiratory drive or neuromuscular impairment or the possibility of a low fraction of oxygen inspired.
- The gradient is elevated when the alveolar function is impaired and ventilation issues appear such as in pulmonary embolism or right to left shunt.
- An elevated gradient accompanied by hypoxemia indicates V/Q mismatch – ventilation perfusion imbalance that is met in respiratory diseases such as asthma or COPD) or a cardiac right to left shunt, intraalveolar filling such as that in pulmonary edema.

Other pulmonary function tests

These are examples of other tests performed to evaluate the respiratory system beside the arterial blood gas analysis used for P_aO₂ and P_aCO₂.

- Peak expiratory flow (PEF).
- Total lung capacity (TLC)
- Expiratory reserve volume (ERV)
- Forced vital capacity (FVC)
- Forced expiratory volume (FEV)
- Forced expiratory flow 25% to 75%
- Maximum voluntary ventilation (MVV)
- Residual volume (RV)

Reference

Helmholz HF Jr. (1979) The abbreviated alveolar air equation. Chest; 75(6):748.