= Absolute-volume ambiguity in spirometry
\b[Absolute-volume ambiguity in spirometry] is the undetermined volume offset left when <spirometry> measures only air entering or leaving the mouth. If $Q(t)$ is outward <volumetric flow rate>, expelled volume is $E(t)=\int_0^tQ(s)\,ds$, while absolute lung volume is
$$
V_L(t)=K-E(t).
$$
The same measured trace is compatible with every admissible initial volume $K$. Differentiation removes the constant: neither integrating flow nor improving its numerical precision recovers that missing offset.
An original example has 4 L expelled between maximal inspiration and maximal expiration. An initial volume of 6 L leaves 2 L, while an initial volume of 8 L leaves 4 L. Both give the same <forced vital capacity> and can have exactly the same flow-time curve. They differ in <total lung capacity> and <residual lung volume>, which the expelled-volume trace alone does not identify. The pulmonary-function text distinguishes spirometric volume changes from absolute lung-volume measurements.<Pulmonary Function Testing by Warren M. Gold and Laura L. Koth>[Lung Volumes: gas dilution and plethysmographic methods]{ref}
<Helium dilution measurement of lung volume> adds independent information. In an ideal closed circuit, an external reservoir has known volume $V_A$ and initial helium fraction $c_0$, while the communicating lung gas initially contains no helium. After complete mixing to fraction $c_f$, conservation gives
$$
c_0V_A=c_f(V_A+V_L),\qquad
V_L=V_A\left(\frac{c_0}{c_f}-1\right).
$$
For stipulated $V_A=3$ L, $c_0=0.10$ and $c_f=0.04$, the communicating lung volume at connection is 4.5 L. This original calculation assumes no leaks, complete mixing, consistent gas conditions and appropriate accounting for the apparatus volume. The primary textbook describes the closed-circuit mixing apparatus and helium concentration measurement.<Pulmonary Function Testing by Warren M. Gold and Laura L. Koth>[Closed-circuit helium dilution, Figure 25-10]{ref}
<Communicating gas volume versus trapped gas volume> limits this inference: gas that does not communicate with the tracer during the measurement is not counted by the ideal mixing balance. Adding a tracer or another independent measurement breaks one ambiguity only under its own experimental assumptions. A well-resolved spirometric trace and a validated absolute-volume measurement answer complementary questions.
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