= Helium dilution measurement of lung volume
= Helium dilution lung volume measurement
{synonym}
\b[Helium dilution measurement of lung volume] estimates communicating lung-gas volume by mixing it with a known apparatus volume containing <helium>. The gas concentration changes as the tracer distributes through the connected space. Connection at the quiet end-expiratory level makes the result an estimate associated with <functional residual capacity>.<Standardisation of the measurement of lung volumes, 2023 update by Nirav R. Bhakta and others>[Measurement of FRC using helium dilution, Introduction and theory]{ref}
In an ideal closed system with equal pressure and temperature, let $V_a$ be the known apparatus volume and $c_1$ its initial helium fraction. If the lung initially contains negligible helium and equilibration gives fraction $c_2$, conservation gives
$$
c_1V_a=c_2(V_a+V_L),\qquad V_L=V_a\left(\frac{c_1}{c_2}-1\right).
$$
Stipulated $V_a=2.4$ L, $c_1=0.10$ and $c_2=0.04$ give $V_L=3.6$ L. If that unknown space includes 0.2 L of external mouthpiece volume, the represented lung volume is 3.4 L. Instrument space and lung space must therefore be distinguished before naming the reported volume.
Equilibration also matters quantitatively. Stopping at an apparent fraction 0.05 instead of the modeled final 0.04 would give 2.4 L, an underestimate of 1.2 L in the uncorrected model. The sensitivity is
$$
\frac{\partial V_L}{\partial c_2}=-\frac{V_ac_1}{c_2^2}.
$$
At the stated values, a small positive fraction error 0.001 changes the estimate by approximately $-0.15$ L. Correct concentration measurement and the stopping definition are thus parts of the volume measurement.
The technical apparatus includes a mixing circuit, helium analysis, <carbon dioxide> absorption and replacement of consumed <oxygen>.<Standardisation of the measurement of lung volumes, 2023 update by Nirav R. Bhakta and others>[Equipment; Figures 6–8]{ref} These features keep other gas changes from masquerading as tracer dilution. Leaks, incomplete mixing and gas not communicating with the circuit violate different assumptions. <Body plethysmography> asks a complementary question about compressible <thoracic gas volume>; the two methods need not sample identical gas compartments.
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