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Arthur B. DuBois is first author of the 1956 primary report introducing a rapid plethysmographic measurement of thoracic gas volume and comparing it with a nitrogen-washout measurement of functional residual capacity in normal subjects.^[ref] The experiment turns a gas-compression relation into an observable pressure-volume slope.

The apparatus enclosed the subject in a sealed chamber, used a mouthpiece shutter and recorded chamber and mouth-pressure signals with capacitance manometers on a cathode-ray oscillograph. Chamber calibration related its pressure signal to changes in body volume.^[ref] This supplied simultaneous signals rather than an estimate from one uncalibrated pressure reading.

An original Boyle's law example follows the paper's derivation. For an approximately isothermal closed gas compartment,Here $\Delta V$ is the signed change in gas volume, not a raw chamber-pressure signal. If $|\Delta P|\ll P_0$, the approximation is $V_0\approx -P_0\Delta V/\Delta P$. The original article derives the same exact-to-small-change distinction.^[ref]

For stipulated $P_0=100$ kPa, compression $\Delta V=-0.030$ L and pressure rise $\Delta P=1$ kPa, the exact expression gives 3.03 L and the small-change approximation gives 3.00 L. Their 0.03 L difference is an approximation effect in the chosen gas model, not observed instrument error in the study.

The experiment also depends on the relationship between mouth and alveolar pressure. The paper explicitly discusses failures when that relationship is disrupted.^[ref] DuBois's contribution combines the physical law, pressure sensing, chamber calibration and tests of the assumptions needed to interpret the signal.

Body plethysmography uses pressure and volume changes in an enclosing chamber to measure respiratory mechanics and compressible thoracic gas volume. For lung-volume measurement, a brief closed-airway effort relates gas compression inside the lungs to the chamber signal. The gas volume belongs to the instant of occlusion; it is not automatically residual lung volume.^[ref]

In the original 1956 experiment, Arthur B. DuBois and colleagues used an airtight chamber of approximately 600 L, a mouthpiece shutter, capacitance pressure transducers and a cathode-ray oscillograph. One signal represented mouth pressure and the other chamber pressure, converted to volume change through instrument calibration.^[ref] An open communication between mouth and alveolar gas during the closed-airway effort is essential to interpreting the mouth signal.

For an ideal isothermal gas amount, Boyle's law givesWith stipulated effective absolute gas pressure $P=100$ kPa, compression $\Delta V=-0.006$ L and increase $\Delta P=0.2$ kPa, the exact expression gives 3.006 L. Neglecting the product of small changes gives the first-order result $V\simeq -P\Delta V/\Delta P=3.0$ L. Here $\Delta V$ is the inferred lung-gas change, not an unconverted box-pressure reading.

If the measurement starts at quiet end-expiration, the interpreted lung-volume reference is functional residual capacity; linked inspiratory capacity and vital capacity maneuvers then provide other capacities. The thermal behavior of gas, instrument response and mouth-to-alveolar pressure equilibration remain physical assumptions to assess. A precise algebraic fit cannot repair a pressure signal that represents a different compartment.

Unlike tracer dilution, compression can probe gas that is not freely reached by the tracer during the test. This explains why body plethysmography and nitrogen washout can give different results without being duplicate names for the same observable.^[ref]

Chest-wall relaxation volume is the volume at which the passive chest wall has zero elastic recoil pressure. With pressure across the wall defined as $P_W=P_{\mathrm{pleural}}-P_{\mathrm{body}\mathrm{surface}}$, write that volume as $V_{W,0}$, so $P_W(V_{W,0})=0$. Below it, the wall tends to expand; above it, the wall tends to recoil inward. The zero of pressure and the slope defining chest-wall compliance are different features of the pressure-volume curve.

The coupled lung and chest wall generally settle at another volume. Their elastic pressures add:In a passive, open-airway equilibrium, total recoil is zero even though the individual pressures need not vanish. This balance underlies the relaxed end-expiratory volume, or functional residual capacity, in the ideal passive setting. OpenStax describes the opposed lung and chest-wall recoil and defines the volume remaining after normal expiration.^[ref]

An original linear model makes partitioning passive recoil equilibrium explicit:For positive compliances, the coupled equilibrium lies between the two component zero-recoil volumes. Choose $V_{L,0}=1$ L, $V_{W,0}=4$ L and $C_L=C_W=0.20\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$. Then $V_{\ast }=2.5$ L, with lung pressure $+7.5$ and wall pressure $-7.5$ cm water. Calling 2.5 L the chest-wall relaxation volume would confuse zero total pressure with zero wall pressure.

Changing the wall's slope can move the coupled equilibrium without moving its own zero. In the same model, increasing $C_W$ to 0.40 while holding everything else fixed gives $V_{\ast }=2.0$ L; $V_{W,0}$ remains 4 L. The more compliant wall supplies a smaller outward pressure at a given volume below its zero. These numbers explain a mechanical distinction rather than state normal human volumes.

A measurement must therefore distinguish passive wall recoil, total respiratory-system recoil and active respiratory-muscle pressure. The relationship between esophageal-balloon pressure and pleural pressure also needs experimental justification when partitioning these components.^[ref] Posture and muscle activity belong to the stated measurement conditions; a measured end-expiratory volume need not equal a purely passive equilibrium.

Expiratory reserve volume, ERV, is the additional gas that can be exhaled after the end of a quiet expiration, down to maximal expiration. It lies between functional residual capacity and residual lung volume:It is distinct from the ordinary tidal volume and does not include the gas left after the maneuver.^[ref]

For stipulated FRC 2.5 L and residual lung volume 1.4 L, ERV is 1.1 L. Beginning instead at the end of a 0.5 L tidal inspiration permits a 1.6 L expiration down to that same residual endpoint. That larger excursion includes tidal volume as well as expiratory reserve volume, so its starting point changes its name and interpretation.

A shift in the ordinary end-expiratory level also changes ERV without necessarily changing residual lung volume. If that lower endpoint stays at 1.4 L while FRC changes from 2.5 to 2.0 L, ERV changes from 1.1 to 0.6 L. This is an original comparison of reference levels, not a claim about a particular disease or posture.

The identity is useful for combining measurements. A measured FRC supplies an absolute gas-volume reference; a linked expiratory maneuver supplies the increment needed to calculate residual lung volume. The technical standard requires consistent linked maneuvers for this calculation.^[ref] An incomplete expiration changes the observed excursion, so a reported ERV should remain attached to its maneuver and endpoints.

Functional residual capacity, FRC, is the volume of gas remaining in the lungs at the end of a passive expiration during quiet breathing. It includes both expiratory reserve volume and residual lung volume:It is an end-expiratory reference level, not the gas expelled in one breath.^[ref]

An original volume ledger uses residual lung volume 1.2 L and expiratory reserve volume 1.0 L, giving FRC 2.2 L. A subsequent tidal volume of 0.5 L raises the represented lung-gas volume to 2.7 L. These stipulated numbers illustrate the relationships; they are not reference limits for an individual.

Helium dilution lung volume measurement supplies an independent gas-volume scale. In a simplified closed, well-mixed system, a known apparatus volume $V_a$ initially contains helium at fraction $c_1$, while the connected lung gas initially contains none. Conservation of the tracer givesFor constructed $V_a=2$ L, $c_1=0.10$ and equilibrated $c_2=0.04$, $V_L=3$ L. This is a model with equal pressure and temperature and no leaks or interfering gas-volume changes. It measures the volume communicating with the tracer; inaccessible gas cannot be recovered by dilution alone. The technical standard distinguishes that limitation from body plethysmography.^[ref]

The phase of connection matters: connecting at a different lung volume changes the volume being estimated. Defining functional residual capacity therefore requires both an anatomical gas-volume estimate and an identified end-expiratory state.

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.^[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 givesStipulated $V_a=2.4$ 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 isAt 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.^[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.

Inspiratory capacity, IC, is the maximum volume that can be inhaled from the end of a quiet expiration to maximal inspiration. Its lower reference is functional residual capacity, and its upper reference is total lung capacity:The last expression combines tidal volume with inspiratory reserve volume.^[ref]

For stipulated total lung capacity 6.0 L and functional residual capacity 2.5 L, IC is 3.5 L. If tidal volume is 0.5 L, the corresponding inspiratory reserve volume is 3.0 L. The two descriptions use the same maximum inspiratory endpoint but different starting points.

The starting point is essential when interpreting a change. In an original comparison, keep total lung capacity at 6.0 L while moving the quiet end-expiratory level from 2.5 to 3.2 L. IC falls from 3.5 to 2.8 L, although the maximum inspiratory volume has not changed. Thus a lower inspiratory capacity need not imply a lower total lung capacity; an independently specified baseline is required to distinguish the possibilities.

Inhalation through a volume-measuring apparatus can determine an inspiratory increment without directly measuring the gas already present in the lungs. A stable starting level and complete endpoint connect that increment to the defined capacity. The technical standard therefore links capacity maneuvers with an identified FRC-level measurement.^[ref] The values in the example illustrate endpoint bookkeeping rather than reference limits for a particular person.

Inspiratory reserve volume, IRV, is the additional gas that can be inhaled after the end of an ordinary tidal inspiration, up to maximal inspiration. It is the portion of inspiratory capacity beyond tidal volume:The starting point is end-inspiration, rather than the quiet end-expiratory level used for inspiratory capacity.^[ref]

For a stipulated total lung capacity of 6.0 L, functional residual capacity 2.5 L and tidal volume 0.5 L, end-tidal inspiration reaches 3.0 L and leaves IRV 3.0 L. The full 3.5 L inspiratory capacity includes both the ordinary 0.5 L breath and this additional excursion.

A deeper ordinary breath changes the subdivision even if the absolute endpoints remain fixed. Holding functional residual capacity at 2.5 L and total lung capacity at 6.0 L while increasing tidal volume to 1.0 L reduces IRV to 2.5 L. Thus a change in inspiratory reserve volume need not imply that maximum inspiratory volume changed.

The name describes an available volume increment, not a separate anatomical compartment sealed off from tidal gas. In the ideal volume ledger, boundaries between subdivisions are reference states on the same gas-volume coordinate. A useful measurement consequently states the ordinary breathing level and the maximum endpoint, rather than interpreting IRV independently of the preceding breath.

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.^[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, writeSubtracting 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 $0.01{\mathrm{L}}^2$. HenceThe 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.

Nitrogen washout is a lung-gas measurement method that follows removal of resident nitrogen while the inspired gas contains little or no nitrogen. Gas analysis and expired volume are combined over multiple breaths to estimate the communicating gas volume.^[ref] It differs from adding helium and waiting for equilibration in helium dilution measurement of lung volume.

A conservation argument supplies the basic calculation. In an ideal compartment with unchanged gas volume $V$, initial and final nitrogen fractions $f_0$ and $f_T$, and net nitrogen volume $W$ removed,For stipulated $W=2.10$ L, $f_0=0.78$ and $f_T=0.01$, $V\simeq 2.73$ L. This is a simplified bookkeeping model with gas volumes compared at consistent conditions. Real equipment space and physiological gas exchange need their defined treatment.

The removed tracer is a volume-weighted quantity. For a nitrogen fraction $f(t)$ and positive expiratory volumetric flow rate $Q(t)$, an interval contributes $\int f(t)Q(t)dt$, with any inspired tracer subtracted for net removal. Two constructed expired parcels of 1 L at fraction 0.4 and 3 L at fraction 0.1 contain 0.7 L nitrogen in total. Multiplying their unweighted mean fraction 0.25 by total volume 4 L would instead give 1.0 L. Correct synchronization of gas and flow signals is therefore fundamental.

A long tail need not imply one uniformly slow compartment. In an original two-compartment model,the late signal is increasingly dominated by the slow component even if its initial amount $b$ was small. A finite stopping interval can consequently miss slowly communicating material. The washout curve, its integral and the functional residual capacity estimate describe different aspects of the same transport measurement.

Residual lung volume, RV, is the gas remaining in the lungs after maximal expiration. It is smaller than the quiet end-expiratory functional residual capacity by the expiratory reserve volume:Thus residual gas is not the tidal volume or a direct measurement of gas exchanged in one breath.^[ref]

For stipulated FRC 2.5 L and expiratory reserve volume 1.1 L, RV is 1.4 L. Since spirometry records changes rather than an absolute lung-gas baseline, exhaling into a spirometer cannot by itself identify the gas still inside.

The 1956 experiment by Arthur B. DuBois and colleagues made that hidden volume accessible through body plethysmography. Their apparatus combined an airtight chamber, a mouthpiece shutter, capacitance pressure transducers and an oscillograph. Respiratory efforts against the closed shutter related mouth-pressure changes to changes in chamber volume.^[ref]

The physical idea follows Boyle's law. For a fixed gas amount at approximately fixed temperature, writeTo first order in the small changes,An original ideal calculation uses effective gas pressure 100 kPa, pressure increase 0.2 kPa and volume decrease 4 mL, giving $V\simeq 2000$ mL. This estimates the gas volume at the instant of airway closure. If closure occurs at quiet end-expiration, the result corresponds to an FRC-level measurement; expiratory reserve volume must still be subtracted to obtain residual lung volume. Pressure equilibration, thermal assumptions and correct volume conventions are part of the physical measurement, not consequences of the algebra alone.

Thoracic gas volume, $V_{\mathrm{TG}}$, is the compressible intrathoracic gas volume assessed by body plethysmography at the instant of airway occlusion. It is not the volume of the entire thorax, which also contains tissues and fluid, and it does not identify a respiratory phase by itself.^[ref]

The phase matters when assigning a named capacity. In a constructed record, suppose the plethysmographic gas estimate is 3.2 L at an occlusion 0.4 L above the preceding quiet end-expiratory volume. If the measured increment and gas conditions are consistent, the corresponding functional residual capacity is $3.2-0.4=2.8$ L. Calling the unadjusted 3.2 L an FRC measurement would change the reference state without changing the observation.

The original experiment linked gas volume to pressure and inferred volume changes through Boyle's law.^[ref] In the small-change model,Thus a pressure-amplitude error can mimic extra gas volume. For an original illustration, let the actual gas volume be 2.8 L but the mouth signal represent only $7/8$ of the relevant alveolar pressure change. With all other terms unchanged, the inferred volume is $2.8/(7/8)=3.2$ L.

A second model can instead contain 2.8 L readily communicating with a tracer plus 0.4 L of compressible gas not reached during the tracer test. It can yield the same apparent 3.2 versus 2.8 L comparison. The numerical difference alone does not prove which model applies.

This is why comparison with helium dilution measurement of lung volume or nitrogen washout needs both compartment definitions and measurement assumptions. The technical standard describes the different accessible gas pools and potential pressure-equilibration errors.^[ref] Thoracic gas volume is a specific physical measurement, not a direct label for trapped gas or a substitute for every lung-volume definition.

Tidal volume, $V_T$, is the volume of gas inhaled or exhaled during one respiratory cycle. It is a per-breath increment, distinct from the gas remaining at functional residual capacity or the maximum total lung capacity.^[ref]

A flow measurement becomes a volume by integration. If $Q(t)$ is positive during inspiration, thenA stipulated triangular inspiratory flow pulse lasting 1 s with peak 1 L/s has area $\frac{1}{2}\times 1\times 1=0.5$ L. Integrating a signed flow over an entire balanced breath instead gives approximately zero, because expiration cancels inspiration; that signed net transfer is not tidal volume.

Multiplying by respiratory rate $f$ gives minute ventilation, ${\dot{V}}_E=f{V}_T$. Two constructed patterns, 0.5 L at 12 breaths/min and 0.25 L at 24 breaths/min, both move 6 L/min. They need not deliver the same gas exchange. In an ideal fixed-respiratory dead space model,where $V_D$ is the per-breath volume not participating in the modeled exchange. For stipulated $V_D=0.15$ L, the two patterns give alveolar ventilation 4.2 and 2.4 L/min. This comparison assumes each breath exceeds the modeled dead-space volume; it is an accounting example, not an individual breathing prescription.

A spirometry or flow trace therefore needs an identified interval and sign convention before its integral is interpreted. The illustration places a quiet tidal volume within a full lung-volume excursion: it shows increments on a constructed absolute scale rather than claiming that ordinary spirometry directly observes the residual offset.

Total lung capacity, TLC, is the volume of gas in the lungs after maximal inspiration. It combines residual lung volume with vital capacity, or equivalently functional residual capacity with inspiratory capacity:The equivalent subdivision is $\mathrm{TLC}=\mathrm{RV}+\mathrm{ERV}+V_T+\mathrm{IRV}$, using expiratory reserve volume, tidal volume and inspiratory reserve volume.^[ref]

A constructed example assigns 1.2 L to residual lung volume, 1.0 L to expiratory reserve volume, 0.5 L to tidal volume and 3.3 L to inspiratory reserve volume. Their sum gives TLC 6.0 L. The vital capacity is 4.8 L, functional residual capacity is 2.2 L, and inspiratory capacity is 3.8 L. Each identity gives the same total because the compartments share consistent endpoints.

A spirometry trace alone measures changes at the mouth; it does not establish the volume remaining after complete expiration. Adding an arbitrary constant to the entire gas-volume trace leaves every observed inhaled and exhaled increment unchanged. An independent estimate of residual lung volume or functional residual capacity is therefore needed to fix that offset. The measurement standard obtains capacities by combining an FRC measurement with linked volume maneuvers.^[ref]

This distinction also explains why vital capacity and total lung capacity are not interchangeable descriptors. Two hypothetical systems can both have a 4 L vital capacity, while having residual lung volume 1 and 2 L respectively. Their total capacities are then 5 and 6 L. The arithmetic separates the amount that can be exchanged during the maneuver from the amount present at full inspiration.