# Alveolar Gas Equation

### What is the alveolar gas equation?

It’s very difficult to measure the partial pressure of oxygen in an alveolus, so instead the alveolar gas equation is used to estimate it, using values that are much easier to directly measure.

The values that we use are:

• Inspired oxygen fraction (FiO2)
• Atmospheric pressure
• Saturated vapour pressure of water at 37°C – 47 mmHg or 6.3 kPa
• Arterial partial pressure of CO2
• Respiratory Quotient (R) (The ratio of CO2 production to oxygen consumption)

The Equation looks like this:

PAO2 = [FIO2 × (Patm − PH2O)] − (PACO2 /R)

Note that the humidification effect is applied before multiplying by the FiO2, because the vapour cannot hold any oxygen itself.

Also note that instead of the alveolar partial pressure of CO2 (PACO2), the equation uses the arterial partial pressure of CO2 (PaCO2). This is purely because it is assumed that these two values are essentially the same. In reality there will always be a slight difference, but CO2 diffuses so quickly across between capillary and alveolus that it is deemed an acceptable substitution, and PaCO2 is vastly easier to measure.

## Worked example

Assuming 21% oxygen, atmospheric pressure of 101.3kPa and a normal PACO2 of 5 kPa and R = 0.8

PAO2 = FiO2(Patm – PH2O) – PACO2/R

PAO2 = 0.21(101.3 – 6.3) – 5/0.8

PAO2 = 19.95 – 6.25

PAO2 = 13.7 kPa

## What’s the respiratory quotient R?

This is the ratio of carbon dioxide production to oxygen consumption.

R = vCO2/vO2

Carbohydrate metabolism releases one carbon dioxide molecule for each oxygen molecule consumed, so the respiratory quotient (R) = 1. Fat, however, consumes a lot more oxygen for each CO2 molecule produced, so the R = 0.7. It is assumed that for a normal individual, the R is usually around 0.8 for the purposes of this equation.

#### How does the respiratory quotient change in COPD?

In patients known to retain CO2, it is helpful to try and reduce arterial CO2 by any means possible. So why not have them produce less CO2 in the first place?

By encouraging fat metabolism, and reducing the respiratory quotient, in theory less CO2 is produced per unit of oxygen consumed, and therefore the retention of CO2 can be reduced.

### What assumptions are required for the alveolar gas equation?

• Steady state, so no accumulation or loss of CO2 or oxygen
• All gases obey Dalton’s law of partial pressures
• CO2 diffuses across the alveolar capillary membrane essentially instantaneously
• There is no rebreathing of CO2, so FiCO2 is zero
• FiO2 is maximally saturated with water

### How is the alveolar gas equation affected by altitude?

The FiO2 remains constant at 21% as altitude increases, however atmospheric pressure decreases. Therefore the term (FiO2(Patm-PH2O) will decrease, resulting in reduced PAO2.

What will be the PaO2 of a person in an aircraft with a cabin pressure of 80kPa?

Assuming 21% oxygen and a normal PACO2 of 5 kPa and R = 0.8

PAO2 = FiO2(Patm – PH2O) – PACO2

PAO2 = 0.21(80 – 6.3) – 5/0.8

PAO2 = 15.5 – 6.25

PAO2 = 9.25 kPa

### What is hypoxic pulmonary vasoconstriction (HPV)?

Hypoxic pulmonary vasoconstriction is an automatic response within the lungs, wherein the blood vessels supplying poorly ventilated alveoli, with a lower partial pressure of oxygen, will vasoconstrict, to divert blood to better ventilated lung units

This improves ventilation-perfusion matching and the efficiency of the respiratory system as a whole. It is important in disease states, where HPV may be disrupted or overactive

An example is in COPD, where giving high FIO2 to a patient can worsen hypercapnoea. This is because the high FiO2 artificially increases the partial pressure of oxygen in poorly ventilated lung units, diminishing the HPV response and causing the blood vessels to relax. This results in more blood being supplied to poorly ventilated areas, where the CO2 accumulates, leading to worsening hypercapnoea.

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