PAO2 - PaO2 = P(A-a)O2
The Alveolar-arterial gradient (A-a gradient) is a mathematical equation that calculates how difficult it is for oxygen to cross the alveolar-capillary membrane.
The equation utilizes two pressures;
- The partial pressure of oxygen in the alveolus; PAO2 (an estimated measurement)
- The partial pressure of oxygen in the arterial blood; PaO2 (a direct measurement from an arterial blood gas (ABG) analysis).
Oxygen is transported either as oxygen dissolved in the blood or as oxygen bound to hemoglobin. Only a small percentage (about 1/5%) of oxygen is dissolved in the blood. This is measured as the partial pressure of oxygen in arterial blood (PaO2) from an ABG. The much larger portion of oxygen (approximately 98.5%) is bound to hemoglobin and can be measured on the pulse oximeter as SpO2 or calculated from the ABG as SaO2.
What is the difference between hypoxia and hypoxemia?
Before discussing oxygenation, it is important to review the difference between hypoxia and hypoxemia. Although the two words are often used interchangeably, it is important to remember that they are not the same. Hypoxia is a more subjective term that describes a pathophysiologic state in which the body does not receive or is not able to use adequate oxygen for aerobic metabolism. This can occur as an overall condition (generalized hypoxia) or in a specific part of the body (regional hypoxia). On the other hand, hypoxemia is a reduction in the concentration of oxygen in arterial blood and is measured objectively through arterial blood gas analysis.
Hypoxia can be caused from various etiologies. These include hypoxemia, anemia, dyshemoglobinemia, histotoxic hypoxia. Hypoxemia, a lack of adequate oxygen in the blood, can result in the peripheral tissues not receiving the amount of oxygenation that is required for aerobic metabolism. Severe anemia, a reduction in hemoglobin, can cause hypoxia because without a sufficient amount of hemoglobin not enough oxygen will be delivered to the tissues. Certain types of hemoglobin, such as carboxyhemoglobin and methemoglobin, if present in the blood in sufficient amounts these dyshemoglobinemias can impede the delivery of oxygen to the tissues. Lastly, hystotoxic hypoxia refers to a somewhat rare pathophysiologic event in which the mitochondria malfunction leading to tissue hypoxia (as seen in cases of cyanide poisoning).
The Alveolar-arterial Gradient Formula
The A-a gradient subtracts the PaO2 from the result of the Alveolar Gas Equation (PAO2):
PAO2 – PaO2 = P(A-a)O2 (mmHg)
The PAO2 calculation is an estimated value using the following equation:
PAO2 = FiO2 (PB-PH2O) – PaCO2 /RQ
FiO2 = concentration of oxygen the patient is breathing
PB = barometric pressure (usually kept at 760 mmHg)
PH2O = partial pressure of water vapor (assumed to be 47 mmHg)
PaCO2 = partial pressure of arterial carbon dioxide (measured via ABG)
RQ = respiratory quotient (A ratio between CO2 production and O2 consumption in relation to the patients diet. Clinicians use the constant of 0.8 unless in extreme nutritional circumstances.)
What is a normal A-a gradient?
It is generally accepted that a healthy person breathing room air will have an A-a gradient of 5 – 15 mmHg due to ventilation and perfusion (V/Q) mismatching, and right-to-left pulmonary shunting of blood. The A-a gradient increases with age, as well as, higher FiO2’s. It is expected that a patient breathing 100% oxygen would have an A-a gradient of 100 – 150 mmHg. For age specific valuations of the A-a gradient normal are required, the equation below can be used:
Normal A-a gradient (mmHg) = (Age/4) + 4
Determining the cause of hypoxemia using the A-a gradient:
Once the normal value and the A-a gradient are calculated, the cause of the hypoxemia can be determined.
If the A-a gradient is within normal range, the cause of the hypoxemia is due to hypoventilation (elevated PaCO2) or a low barometric pressure (high elevations). Remember, since the A-a gradient uses PaCO2 as a part of the Alveolar air equation, if PaCO2 is high, the result can be a reduction in the A-a gradient. In contrast, if the PaCO2 is below the normal range, the A-a gradient can become elevated.
If the A-a is above the normal range, then the hypoxemia is due to a V/Q mismatch, shunt or impaired diffusion across the alveolar-capillary membrane.
To estimate of the percentage of physiologic shunt using the A-a gradient one can use the following rule: for every 50 mmHg difference in A-a gradient, a 2% shunt is approximated. For example, a 300 mmHg A-a gradient would be estimated as a 12% shunt (200/50 = 4 4 x 2% = 8%).
Experienced clinicians utilizing calculations at the bedside can provide better care for patients who are experiencing difficulty with gas exchange. Knowing how to calculate and use the A-a gradient to determine what the source of the patient’s hypoxemia is vital in providing the best care and is an integral part of monitoring the patient in the intensive care.
Chang, D.W. Respiratory Care Calculations. 3rd Ed. Clifton Park, NY: Cengage Learning; 2012. Section 2 pp 11-13.
Kacmarek, R.M., Stoller, J.K., Heuer, A.J. Egan’s Fundamentals of Respiratory Care, 11th Ed. St. Louis, MI: Elsevier; 2017. Chapter 46 pp: 1024-1025.