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\b[<Nirav R. Bhakta>] is first author of the 2023 European Respiratory Society/American Thoracic Society technical statement standardizing measurement of lung volumes. The report defines lung-volume subdivisions and distinguishes <body plethysmography> from gas-dilution measurements.<Standardisation of the measurement of lung volumes, 2023 update by Nirav R. Bhakta and others>[Primary byline; Definitions and subdivisions of lung volume, Figure 1; Measurement of FRC]{ref} This is a contribution to making physiological measurements comparable across acquisition systems and laboratories.

The relationships among <functional residual capacity>, <inspiratory capacity>, <expiratory reserve volume>, <total lung capacity> and <residual lung volume> are also a useful test of data reduction. For an original accounting example, write
$$
\mathrm{TLC}=\mathrm{FRC}+\mathrm{IC},\qquad
\mathrm{RV}=\mathrm{FRC}-\mathrm{ERV}.
$$
Subtracting gives <vital capacity> $\mathrm{VC}=\mathrm{IC}+\mathrm{ERV}$. At stipulated FRC 3 L, IC 2 L and ERV 1 L, the derived values are TLC 5 L, RV 2 L and VC 3 L. These are illustrative inventories, not clinical reference values.

The same recorded FRC enters TLC and RV with the same coefficient. If independent FRC, IC and ERV estimates each have <standard uncertainty> 0.10 L, the derived TLC and RV each have variance $0.02\,\mathrm{L^2}$, but their <covariance> is $0.01\,\mathrm{L^2}$. Hence
$$
u^2(\mathrm{TLC}-\mathrm{RV})=0.02+0.02-2(0.01)=0.02\,\mathrm{L^2}.
$$
The standard uncertainty is about 0.141 L, matching direct propagation through IC + ERV. Incorrectly treating the two derived capacities as independent gives 0.20 L instead.

Bhakta's technical work helps make the definitions and acquisition conditions behind such comparisons explicit. The algebra does not establish that a gas-dilution estimate and a plethysmographic estimate sample exactly the same accessible gas in every circumstance. A consistent volume identity and an appropriate measurement mechanism are separate requirements.

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{title=Nirav R. Bhakta, named portrait linked from his UCSF Profiles page}
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 Nirav R. Bhakta (source code)