Alveolar gas equation helps to calculate partial pressure of oxygen in alveoli and A-a gradient is the difference between alveolar oxygen pressure and arterial oxygen pressure. These both concepts can be used to study various causes of hypoxemia. In this article, we will discuss in brief about the alveolar gas equation & A-a Gradient and their applications in therapeutics.
Image: “Respira mundo” by Camdiluv ♥. License: CC BY-SA 2.0

Image: “Respira mundo” by Camdiluv ♥. License: CC BY-SA 2.0

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Alveolar Gas Equation

Alveolar gas equation helps to calculate the partial pressure of oxygen in alveoli.

PAO2 = PiO2 – (PaCO2/R)

PAO2 = Partial pressure of oxygen in alveoli
PiO2 = Partial pressure of oxygen in inspired air
PaCO2 = Partial pressure of CO2 in arterial blood
R = Respiratory quotient

This is the simplest form of the alveolar gas equation by Rossier & MeanOther versions of alveolar gas equation are:

  • West: PAO2 = PiO2 – (PaCO2/R) + K

K = FiO2 x PaCO2 x [(1–R)/R]

For most clinical conditions, the value of K is too small to make a difference in the value of PAO2 and hence can be neglected.

  • Riley: PAO2 = PiO2 – (PaCO2/R) x [1 – FiO2 (1–R)]

The difference between values of PAO2 calculated by above two equations is only due to inert gas exchange; hence, they can be used to calculate the concentration effect.

  • Selkurt: PAO2 = PiO2 – PaCO2 x [FiO2 + (1 – FiO2)/R]
  • Filley, MacIntosh & Wright: PAO2 = PiO2 – PaCO2 x [(PiO2 – PĒO2)/PĒCO2]

This equation allows for disequilibria of inert gasses, therefore, it can be used during induction or recovery from anesthesia. Important assumptions for above equation:

  • Metabolic minute production of carbon dioxide is constant.
  • PACO2 = PaCO2, as the alveolar membrane is thin and carbon dioxide is highly diffusible.
  • Alveolar and inspired gasses follow the ideal gas low (PV = nRT).
  • Inspired gas contains no CO2 or water.
  • All other gasses except oxygen in the inspired gas are in equilibrium with their dissolved states in the blood.
  • The alveolar gas is saturated with water.
  • Note that PiO2 = (Patm – PH2O) x FiO2.

Patm = Atmospheric pressure (760 mm Hg at sea level)
PH2O = Water vapor pressure (47 mm Hg at body temperature)
FiO2 = Fraction of inspired oxygen (0.21 in room air)

Thus, at normal body temperature, while breathing room air at sea level,

PiO2 = (760 – 47) x 0.21 = 149.7 mm Hg

Respiratory quotient is the amount of CO2 produced divided by the amount of oxygen consumed by tissue metabolism.

  • Normally, R is 0.8, when cells are using both glucose and free fatty acids as fuel.
  • R is 1.0 when the fuel is only glucose (for example, patient on intravenous glucose).
  • R is 0.7 when the fuel is only free fatty acids (for example, a hypoglycemic or a diabetic patient)

Alveolar-arterial gradient

A-a gradient is the difference between alveolar oxygen pressure and arterial oxygen pressure. A-a gradient can be used study the different causes of hypoxemia.

Hypoxemia is a decrease in arterial PO2, while hypoxia is decreased oxygen delivery to the tissues. PO2 can be calculated using alveolar gas equation (discussed above). The patient may develop hypoxia in the presence of normal PaO2, as in cases of carbon-monoxide poisoning or decreased hemoglobin (anemia).

A-a O2 gradient = PAO2 – PaO2


For a patient with PaCO2 = 40 mm Hg, PaO2 = 97 mm Hg, PAO2 can be derived from alveolar gas equation (Rossier & Mean) as follows:

PAO2 = PiO2 – (PaCO2/R) = 149.7 – (40/0.8) if PaCO2 is 40 mm Hg
= 99.7 mm Hg

Thus, A-a O2 gradient =  PAO2 – PaO2
       = 99.7 – 97 if PaO2 is 97 mm Hg
       = 2.7 mm Hg

Assuming that the patient is breathing room air at sea level, with normal body temperature.

  • Normal A-a O2 gradient suggests normal gas exchange between alveoli and blood. Values < 15 mm Hg are considered normal.
  • Increased A-a O2 gradient (> 15 mm Hg) suggests abnormal gas exchange between alveoli and blood, which may be due to V/Q mismatch, shunting, or thickened diffusion barrier.

Factors affecting A-a O2 gradient


A-a O2 gradient increases by 3 mm Hg for each decade over 30 years of age.

Alveolar PO2

As the shape of oxygen dissociation curve is non-linear, greater the PAO2, greater the A-a O2 gradient, provided rest factors are same.

Magnitude of venous admixture

Venous admixture reduces arterial O2 content and increases arterial CO2 content. As PaO2 is usually on hemoglobin dissociation curve, a small reduction in O2 content causes a large reduction in PaO2, therefore increasing A-a O2 gradient.

CO2 dissociation curve being steep and more linear increased arterial CO2 content does not cause a significant increase in PaCO2. In clinical settings, compensatory hyperventilation is more than enough to offset the small increase in PaCO2; therefore, PaCO2 is often reduced rather than increased.

Cardiac output

Provided the same venous admixture, cardiac output is inversely proportional to A-a O2 gradient. However, reduction in cardiac output is associated with reduced venous admixture and reduced shunt fraction, therefore, PaO2 and A-a O2 gradient are almost unchanged.


Hemoglobin concentration does not influence arterial oxygen content, but increased hemoglobin concentration would slightly reduce arterial oxygen tension.

Alveolar ventilation

Increased alveolar ventilation increases both PAO2 and A-a O2 gradient.

Different Causes of Hypoxemia

Hypoxemia is a decrease in arterial PO2, while hypoxia is decreased oxygen delivery to the tissues. There are five important pathophysiological causes of hypoxemia and respiratory failure, which are as follows.


The minute ventilation depends on the respiratory rate and the tidal volume, which is the amount of inspired air during each normal breath at rest.

Minute ventilation = Respiratory rate x Tidal volume

The normal respiratory rate is about 12 breaths per minute and the normal tidal volume is about 500 mL. Therefore, the minute respiratory volume normally averages about 6 L/min.

Hypoventilation occurs when there is a decrease in the respiratory rate and/or tidal volume, so that decreased amount of air is exchanged per minute. There will be decreased oxygen entry within the alveoli and the arteries leading to decreased PaO2. As already described, the PaCO2 is inversely proportional to the ventilation. Hence, the hypoventilation will lead to increased PaCO2. The alveolar-arterial gradient will be normal and less than 10 mmHg as there is no defect in diffusion of gases. In these cases, increasing the ventilation and/or increasing the oxygen concentration will correct the deranged blood gases.

Diffusion impairment

In diffusion impairment, there is a structural problem within the lung. There may be decreased surface area (as in emphysema), or increased thickness of alveolar membranes (as in fibrosis and restrictive lung diseases) that impairs the diffusion of gases across the alveoli leading to increased alveolar-arterial gradient. In increased A-a gradient, the alveolar PO2 will be normal or increased, but arterial PO2 will be decreased. The greater the structural problem is present, the greater the alveolar-arterial gradient will be.

Since diffusion of gases is directly proportional to the concentration of gases, therefore increasing the concentration of inhaled oxygen will correct PaO2 but the increased A-a gradient will be present as long as the structural problem is present.

Pulmonary shunt

In pulmonary shunt, also known as right-to-left shunt, the venous deoxygenated blood from the right side enters the left side of the heart and systemic circulation without getting oxygenated within the alveoli. In simple words, shunt refers to “normal perfusion, poor ventilation”. The lungs are having normal blood supply, but ventilation is decreased or absent that fails to exchange gases with the incoming deoxygenated blood. The ventilation/perfusion ratio is or near to zero.

This happens for example in atelectasis and cyanotic heart diseases. In atelectasis, the collapsed lung is not ventilated and blood within that segment fails to oxygenate. In cyanotic heart diseases, the blood from right side bypasses (shunts) the lungs and enter the left side, causing hypoxemia and cyanosis.


Image: “Atelectasis” by BruceBlaus. License: CC BY-SA 4.0

The A-a gradient is increased as deoxygenated blood enters the arterial (systemic) circulation decreasing the arterial oxygen tension, PaO2.

Since venous blood does not oxygenate in the pulmonary shunt, therefore increasing the oxygen concentration does not correct the hypoxemia. The blood will bypass the lungs, no matter how much increased oxygen concentration is used. This failure to increase PaO2 after oxygen administration is a very important point and helps to differentiate from the impaired diffusion and other causes of hypoxemia that correct with the supplemental oxygen.

Ventilation – perfusion (V/Q) mismatch

It is the ratio of alveolar ventilation (V) to pulmonary blood flow (Q). The matching of ventilation and perfusion is essential to achieve the adequate exchange of oxygen and carbon-dioxide within the alveoli. The V/Q ratio in normal individuals is around 0.8, but this ratio alters in the presence of significant ventilation or perfusion defects.

Within lung, all the alveoli do not have uniform ventilation and perfusion. They tend to vary due to the effects of gravity. At the apex of lung, alveoli are large and completely inflated, while they are small at the bases. Similarly, the blood supply is more at the base of the lung than at the apex. This creates physiological ventilation (V) – perfusion (Q) mismatch between different alveoli.

The decreased V/Q ratio (< 0.8) may occur either from decreased ventilation (airway or interstitial lung disease) or from over-perfusion. The blood is wasted in these cases and fails to properly oxygenate. In extreme conditions, when ventilation is significantly decreased and V/Q approaches to zero, it will behave as a pulmonary shunt.

The increased V/Q ratio (> 0.8) usually occurs when perfusion is decreased (pulmonary embolism preventing the blood flow distal to obstruction) or over-ventilation. The air is wasted in these cases and is unable to diffuse within the blood. In extreme conditions, when perfusion is significantly decreased and V/Q approaches to 1, the alveoli will act as dead space and no diffusion of gases occur.

Therefore the increased mismatch in ventilation and perfusion within the lung impairs the gas exchange processes and ultimately will lead to hypoxemia and respiratory failure.

High altitude

At high altitudes, the barometric pressure (PB) is decreased, which will lead to decreased alveolar PO2 as in the equation:

PAO2 = FIO2 × (PB – PH2O) – PACO2/R

The decreased alveolar PAO2 will lead to decreased arterial PaO2 and hypoxemia but the A – a gradient remains normal as there is no defect within the gas exchange processes. In these conditions, supplementing with additional oxygen (increasing the FIO2) increases the PAO2 and corrects the hypoxemia.

When a person suddenly ascends to the high attitude, the body responds to the hypoxemia by hyperventilation causing respiratory alkalosis. The concentrations of 2, 3-diphosphoglycerate (DPG) are increased, shifting the oxygen-hemoglobin dissociation curve to the right.

Chronically, the acclimatization takes place and body responds by increasing the oxygen carrying capacity of the blood (polycythemia). The kidneys excrete bicarbonates and maintain the pH within normal limits.

Causes of Hypoxemia
Cause PaO2 A-a gradient Response of PaO2 to supplemental oxygen
Hypoventilation Decreased Normal Increases
Diffusion Impairment Decreased Increased Increases
Shunt Decreased Increased Does not increase
V/Q Mismatch Decreased Increased Increases usually (depends on V/Q mismatch type)
High Altitude Decreased Normal Increases

Conditions associated with increased A-a O2 gradient

  • Pulmonary atelectasis
  • Pulmonary consolidation/infection/neoplasm
  • Alveolar destruction
  • Extrapulmonary shunting
  • Drugs such as vasodilators and volatile anesthetics
  • Hepatic failure
  • Pregnancy

Popular Exam questions

The correct answers can be found below the references.

1. Which of the following alveolar gas equations allows for disequilibria of inert gases?

  1. PAO2 = PiO2 – (PaCO2/R)
  2. PAO2 = PiO2 – (PaCO2/R) + K                    K = FiO2 x PaCO2 x [(1 – R)/R]
  3. PAO2 = PiO2 – (PaCO2/R) x [1–FiO2 (1–R)]
  4. PAO2 = PiO2 – PaCO2 x [FiO2 + (1– FiO2)/R]
  5. PAO2 = PiO2 – PaCO2 x [(PiO2 – PĒO2)/PĒCO2]

2. Which of the following best describes effects of venous admixture on arterial blood gases and A-a O2 gradient in clinical settings?

  1. ↓ O2 content, ↓ PaO2, ↑ CO2 content, ↑ PaCO2, ↑ A-a O2 gradient
  2. ↓ O2 content, ↓ PaO2, ↑ CO2 content, ↓ PaCO2, ↑ A-a O2 gradient
  3. ↑ O2 content, ↑ PaO2, ↑ CO2 content, ↓ PaCO2, ↑ A-a O2 gradient
  4. ↓ O2 content, ↓ PaO2, ↑ CO2 content, ↑ PaCO2, ↓ A-a O2 gradient
  5. ↓ O2 content, ↓ PaO2, ↑ CO2 content, ↓ PaCO2, ↓ A-a O2 gradient

3. Which of the following is least commonly associated with an increased A-a O2 gradient?

  1. Lobar pneumonia
  2. Liver failure
  3. Renal failure
  4. Pregnancy
  5. Use of vasodilators
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