This chapter is most relevant to Section F4(i) from the 2017 CICM Primary Syllabus, which expects the exam candidates to be able to "explain the measurement of lung volumes and capacities and factors that influence them". This has appeared a couple of times in the primary exam:

• Question 24 from the second paper of 2017
• Question 4  from the second paper of 2015

Both of these questions asked specifically about the FRC, and how it is measured. Consequently, to maintain some attachment to an exam focus, the measurement of the FRC is discussed in most detail here. The measurement of the other volumes is mentioned in passing wherever it appears relevant.

In summary:

For this topic, the single best resource is probably Wanger et al (2005). Coates et al (1997) do an excellent job of explaining the measurement of lung volumes by plethysmography, and Newth et al (1997) are the go-to source for the nitrogen washout technique. 

Measurement of the FRC by nitrogen dilution

Measurement of lung volumes by the measurement of nitrogen washout was probably the first clinically relevant method, described by Darling et al (1940). 

The technique is as follows:

• The subject, whose lungs ought to be full of nitrogen-rich air, is commenced on 100% FiO₂.
• The subject therefore begins to exhale nitrogen, with every breath, and the nitrogen content in their exhaled gas mixture decreases with every breath.
• This nitrogen content is measured, as are the exhaled volumes.
• As all the gas in their chest ends up being replaced by oxygen, the expired nitrogen concentration ends up at zero. Thus, this continues for some period of time, which is long enought to ensure the complete washout of all nitrogen in the chest, and is classically about seven minutes (i.e. 70-80 tidal volumes)
• Over the course of these seven minutes, all of the nitrogen concentrations and tidal volumes are measured for each breath. Under ideal circumstances, this ends up looking like an exponential curve:
  
  Because of this, it is possible to calculate the total exhaled volume of nitrogen.
• From this total content of nitrogen and the first measured breath's nitrogen concentration it is possible to determine the total lung volume. For example, if the initial N₂ concentration was 79% and the final total nitrogen volume was 4L, the total lung volume would have to have been around 5L.

There are various inaccuracies and caveats involved in this process:

• The nitrogen washout is an exponential, which means that practically one never ends up at a point where the expired N₂ concentration is zero, and theoretically the concentration curve approaches zero asympttically and stretches into infinity.
• The accurate measurement of nitrogen concentration is obviously crucial here, but often nitrogen concentration is extrapolated from the measurement of oxygen and carbon dioxide in expired gas (i.. whatever's left must be nitrogen), which increases the inaccuracy. 
• Leaks in the system (tiny cracks, even perforated eardrums) can let atmospheric nitrogen into the circuit, befouling the result.
• Some nitrogen exhaled during measurement comes not from the lung volume but from the body fluids and tissues (there's approximately 250ml of this in a normal sized person), which needs to be corrected for.
• If there is gas trapping, eg. in asthma or in old age, the trapped gas will never escape to be measured, and the nitrogen washout method will underestimate the lung volume.

Measurement of lung volumes by tracer gas dilution

This method also relies on the measurement of an exhaled gas concentration, except this time one administers a known volume of this gas, and measures the exhaled concentration. Though strictly speaking any gas could be used for this, realistically one would prefer to use some non-toxic gas which has minimal blood solubility and which is cheap enough to use clinically. The blood solubility thing is very important, as the concentration of exhaled tracer gas will be lower if any of it managed to get out into the pulmonary circulation. Nunn's mentions helium (it ticks all the boxes), but others have used various weird gases such as sulfur hexafluoride and argon.

The theory is similar to the concept of measuring the volume of distribution. In this diagram, the volume of tracer is comically exaggerated to make the maths easier; in reality one would usually give 50ml of helium, much less that is required to make your voice sound funny.

In short, the process is as follows:

• You have a patient with an unknown volume of lung  in which there is a known (zero) concentration of tracer gas.
• You then give the subject a bolus of tracer gas, with a known volume which contains a known concentration (say, 100%) of the tracer gas. The subject inhales this volume, and it is distributed widely and evenly in their lung volume.
• The subject then exhales of their intrathoracic gas.
• The concentration of the tracer in their exhaled gas is measured
• From this concentration, the volume of distribution of that gas can be calculated, which represents the intrathoracic as volume.

So, in the diagram above, the exhaled gas concentration is 20g/m³, whereas previously it was 100g/m³. in 1L. It is as if the gas was diluted by 5 times. Thus, the intrathoracic "volume of distribution" must have been 5L. The equation for calculating this is:

C₁  × V₁ = C₂  × (V₁ + V₂)

where:

• C₁ is the initial tracer concentration in the bolus
• V₁ is the volume of the bolus
• C₂ is the tracer concentration in the exhaled gas
• V₂ is the volume of the lung

This obviously has some problems:

• The tracer may not mix "widely and evenly" in the intrathoracic gas volume
• Gas trapping will result in regions of alveoli which do nt articipate in tracer mixing
• No gas is perfectly insoluble and some of the tracer will be lost, dissolved, tissue bound, and so forth 
• The sampled expiratory gas may not be a volume with representative tracer concentration (eg. tracer-rich anatomical dead space)

Measurement of the FRC by body plethysmography

This method is also ancient. It was first devised by DuBois et al (1956). The principles of this method are as follows:

• The subject and the equipment are all confined in a rigid box which contains a known gas volume.
• The measurement equipment is totally enclosed and so the total amount of gas in there is constant.
• The pressure in the patient's lung and in the box are measured. 
• Now, let's say the the subject exhales against a closed airway.
  
• As the subject exhales,
  • Intrathoracic volume decreases, which means the volume of the box increases (as the walls are rigid and there is a finite volume shared by the chest and the box).
  • Intrathoracic pressure increases, and therefore box pressure decreases proportionally.
• Though the amount of the gas in the chest is unknown, we know that (according to Boyle's law) the product of pressure and volume in the chest should be the same as the product of volume and pressure in the box.
• The volume in the box, the pressure in the box and the pressure in the chest are all known variables at this point, leaving the volume of intrathoracic gas as the last unknown

This methods of measurement has the distinct advantage of being able to measure all of the gas in the chest, including the gas which is trapped behind a bunch of collapsed airways. The disadvantages are fairly benign; the main risk is that the patient's bowel gas (however much of it there is) ends up being compressed by the expiratory effort, which affects the measurement somewhat. Unless one is performing plethysmography on a particularly gassy patient, this should not be a major influence.