= Spirometry
\b[Spirometry] measures the <volume> of air moved into or out of the <respiratory system> as a function of time. A <spirometer> records displaced gas directly or derives volume by integrating <volumetric flow rate>. The resulting trace describes gas movement at the mouth; it does not independently determine <alveolar pressure>, <pleural pressure> or <lung compliance>.<Standardization of Spirometry 2019 Update by Brian L. Graham and others>[Introduction and Equipment: volume and flow measurements]{ref}
Two important outputs of a forced expiration following maximal inspiration are <forced vital capacity>, the total volume expelled in that maneuver, and <forced expiratory volume in one second>, the volume expelled during its first second. Their ratio compares early emptying with the eventual expelled volume.<Standardization of Spirometry 2019 Update by Brian L. Graham and others>[FVC Maneuver and definitions of FVC and FEV1]{ref} Equal final volumes can accompany substantially different emptying rates.
An original mathematical example sets expelled volume
$$
V_e(t)=4\bigl(1-e^{-t/\tau}\bigr)\,\mathrm L,\qquad
Q(t)=\frac{dV_e}{dt}=\frac{4}{\tau}e^{-t/\tau}\,\mathrm{L\,s^{-1}},
$$
where the numerical time $t$ and <time constant> $\tau$ are in seconds. Both $\tau=1$ and $\tau=2$ give an asymptotic expelled volume of 4 L. Their first-second volumes are instead $4(1-e^{-1})\approx2.53$ L and $4(1-e^{-1/2})\approx1.57$ L. The corresponding ratios to the limiting volume are approximately 0.632 and 0.393. These smooth toy curves explain the measurements; they are not measured traces or diagnostic reference limits.
<Spirometry> measures volume differences. The gas left after maximal expiration is <residual lung volume>, which has not crossed the instrument. Consequently a volume trace alone does not determine <total lung capacity>: different absolute starting volumes can produce the same expelled-volume trace. This is the <absolute-volume ambiguity in spirometry>.
Timing, effort, leaks and early termination can alter what a trace represents. Distinguish an instrumentally repeatable signal from a maneuver that answers the intended physiological question. The primary technical statement treats equipment quality assurance and maneuver acceptability separately.<Standardization of Spirometry 2019 Update by Brian L. Graham and others>[Device Quality Assurance and FVC Maneuver acceptability sections]{ref}
\Image[/spirometry-volume-flow-model.png]
{title=Original exponential <spirometry> models with equal final expelled <volume> and different <time constants>; the first-second volumes and flow histories differ}
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