Respiratory Physiology - The Alveolar Gas Equation

Question 1

What are the components of the alveolar gas equation?

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Answer 1

The alveolar partial pressure of oxygen is equal to the inspired oxygen fraction (FiO2), multiplied by atomspheric pressure, but minus the partial pressures of water and of alveolar CO2, divided by the respiratory quotient.

PAO2 = FiO2 x (Patm-PH2O)-(PaCO2/RQ)

PAO2 - Alveolar partial pressure of O2
FiO2 - Inspired fraction of O2
Patm - Atmospheric pressure
PH2O - Saturated vapour pressure of water at 37C - deducted from Patm before multiplication, as the vapour cannot hold any oxygen
PACO2 - Alveolar partial pressure of CO2 - often replaced with PaCO2 (arterial), as it is easier to measure and assumed to be equal)
RQ - Respiratory quotient - Rate of production of CO2 divided by the rate of consumption of O2.
1:1 for pure carbohydrate metabolism
0.6:1 for pure fat metabolism
0.8:1 is taken as an accepted average value

Worked example:
21% O2, standard pressure (101kPa), PACO2 of 5, and R = 0.8
PAO2 = 0.21 x (101.3 - 6.3) - 5/0.8
PAO2 = 19.95 - 6.25
PAO2 = 13.7 kPA

Question 2

What assumptions are required for the alveolar gas equation?

Answer 2

• Steady state (No accumulation or loss of CO2 or O2)
• Adequate FiO2 to maintain steady state - Dangerously hypoxic FiO2 or very high PACO2 may give an impossible negative answer.
• All gases obey Dalton’s law of partial pressures
• CO2 diffuses across the alveolar capillary membrane instantaneously
• There is no rebreathing of CO2 (FiCO2 is 0)
• FiO2 is maximally saturated with H2O in the upper airways.

Question 3

How does PaCO2 affect PAO2?

Answer 3

PAO2 decreases linearly with an increase in PaCO2

The alveolar gas equation demonstrates that as PaCO2 increases, so does PaCO2/R, which is then deducted from the first term of the equation

Clinically, this means that hyperventilating a patient to reduce CO2 will increase the PAO2

Question 4

How does FiO2 affect PAO2?

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Answer 4

Increasing FiO2 increases PAO2 in a linear fashion.
PAO2 = PiO2 - PaCO2/R
PiO2 = FiO2 x (pAtm-pH2O)
This is in the format y = mx + c, which produces a linear graph

Question 5

How does altitude affect the PAO2?

Answer 5

PAO2 = FiO2(Patm-PH2O)-PACO2/0.8

Despite FiO2 still being 21%, the Patm drops, reducing the inspired PO2.

The PH2O is independent of atmospheric pressure, and only affected by temperature

Question 6

What is the PAO2 of a persion in an aircraft with cabin pressure of 80kPA?

Assuming 21% FiO2, normal PACO2 of 5 kPA, R = 0.8

Answer 6

PAO2 = FiO2(Patm-PH2O)-PACO2/0.8
PAO2 = 0.21*(80-6.3)-5/0.8
PAO2 = 15.5 - 6.25
PAO2 = 9.25 kPA

The vapour pressure of water is independent of atmospheric pressure.

Question 7

How can the respiratory quotient help manage COPD

Answer 7

In patients known to retain CO2, reduction of PaCO2 can be helpful.
By encouraging fat metabolism, and reducing the RQ, less CO2 is produced per unit of oxygen consumed, therefore reducing retention of CO2.

Question 8

What is Hypoxic Pulmonary Vasoconstruction?

Answer 8

An automatic response to low PAO2 in poorly ventilated alveoli, resulting in vasoconstriction, and diverting blood to better ventilated lung units

This improves V/Q matching, reducing shunt

This process may be disrupted or overactive in disease states. In COPD, delivering high FiO2 can worsen hypercapnia, even without affecting a patient’s hypoxic drive.

Question 9

How can increasing FiO2 worsen acidosis?

Answer 9

By artificially increasing PAO2 in poorly ventilated lung areas, reducing hypoxic pulmonary vasoconstriction, and thus leading to CO2 build up in those lung units.