The alveolar gas equation is a core FRCA topic, and allows for the estimation of the partial pressure of oxygen within an alveolus, if the inspired pressure of oxygen and the partial pressure of carbon dioxide are known.
Here on TeachMeAnaesthetics, we aim to cover the absolute key details of high yield exam topics, which can then be supplemented with further reading as needed.
In this short article, we will discuss the origin, components and application of the alveolar gas equation.
The Alveolar Gas Equation
The alveolar gas equation is as follows:
Equation 1: PaO2 = PiO2 – PaCO2/R
where PaO2 is the alveolar partial pressure of oxygen, PiO2 is the inspired partial pressure of oxygen, PaCO2 is the alveolar partial pressure of carbon dioxide, and R is the respiratory quotient.
PiO2 is a function of the inspired oxygen fraction, and is also affected by the effect of water vapour ‘displacing’ oxygen from air:
Equation 2: PiO2 = FiO2(Patm – SVPH20)
where PiO2 is the inspired partial pressure of oxygen, FiO2 is the fraction of oxygen, Patm is the atmospheric pressure, and SVPH20 is the saturated vapour pressure of water.
Which means, in totality, the alveolar gas equation can also be given by:
Equation 3: PaO2 = FiO2(Patm – SVPH20) – PaCO2/R
The Respiratory Quotient
The respiratory quotient gives the ratio between VCO2 (carbon dioxide production) and VO2 (oxygen consumption). In a subject with a balanced diet, the value is 0.8. It does, however, vary with diet as follows:
- Fat predominant diet: 0.7
- Protein predominant diet: 0.8
- Carbohydrate predominant diet: 1.0
Derivation of the Alveolar Gas Equation
On first viewing, the above equation makes very little sense. While it is not at all necessary to be able to derive the alveolar gas equation, a superficial understanding of its origin is useful.
By modelling oxygen delivery into the alveolus as an input/output model, the amount of oxygen delivered to the alveolus, which is equal to concentration x volume, can be equated to the oxygen output:
Equation 4: FiO2 x alveolar volume = (FaO2 x alveolar volume) + VO2
where FiO2 is the inspired oxygen fraction, FaO2 is the alveolar oxygen fraction and VO2 is the oxygen uptake of the system
We also know that the respiratory quotient, R, is equal to VCO2/VO2.
Using mathematical manipulation, we can substitute out the unknown VO2, remove the alveolar volume from the equation, and use terms (PaCO2/R) that are more readily available in order to allow us to estimate the alveolar partial pressure of oxygen.
For more details, the E-LFH topic (Anaesthesia – Exam Preparation – Physics – Physiological Models) walks you through the derivation in more detail.
Application of the Alveolar Gas Equation
You may be asking yourself what the relevance of the alveolar gas equation is. Although it appears slightly abstract, it has utility in predicting a subject’s oxygenation in various scenarios.
For example, at altitude, atmospheric pressure is reduced, yet the saturated vapour pressure of water and the fraction of oxygen in air (FiO2) remain constant.
PaO2 = FiO2(Patm – SVPH20) – PaCO2/R
Therefore, as we ascend, alveolar partial pressure of oxygen drops due to a reduction in the first term of this equation.
This can be alleviated by increasing the FiO2 with exogenous oxygen, by hyperventilating to reduce PaCO2, by increasing the respiratory quotient (through a change in diet), or by descending.
Suggested Reading
Chapter 6. The Primary FRCA structured oral examination Study Guide 1. 2nd edition. Wijayasiri and McCombe. 2016.
Chapter 5. West’s Respiratory Physiology. 10th edition. West. 2016.
Page 211. Physics, Pharmacology and Physiology for Anaesthetists. Key Concepts for the FRCA. 2nd edition. Cross and Plunkett. 2014.