= Anatomical dead space
{title2=$V_D$}
\b[Anatomical dead space] is the volume of the conducting <airways> that transports gas without providing the pulmonary <alveolus> surface for <gas exchange>. It includes passages such as the <trachea> and <bronchi>. It is one component of <respiratory dead space>, distinct from <alveolar dead space> associated with ineffective exchange in ventilated alveolar regions.<Pulmonary Function Testing by Warren M. Gold and Laura L. Koth>[Single-Breath Nitrogen Test; The Bohr Equation for Respiratory Dead Space]{ref}
A single-breath tracer experiment makes the conducting volume observable. Following an oxygen inspiration, expired gas initially contains little nitrogen, then passes through a transition as airway and alveolar gas mix, and finally approaches an alveolar plateau. Recording gas fraction against expired volume distinguishes those phases.<Pulmonary Function Testing by Warren M. Gold and Laura L. Koth>[Single-Breath Nitrogen Test, phases I–III]{ref} A 1954 primary study explicitly compared single-breath measurements using different gases.<The Respiratory Dead Space Measured by Single Breath Analysis of Oxygen, Carbon Dioxide, Nitrogen or Helium by J. Bartels and others>[Title and opening page 41]{ref}
An original idealized calculation uses expired volume $V_E$ and a normalized tracer fraction $g(V)$ that rises from zero to an alveolar value of one. Replacing a gradual transition with an equal-area step gives
$$
V_D=V_E-\int_0^{V_E}g(V)\,dV.
$$
Suppose $V_E=0.50$ L, $g=0$ over the first 0.10 L, rises linearly to one over the next 0.10 L, and remains one for the last 0.30 L. The integral is $0.05+0.30=0.35$ L, giving $V_D=0.15$ L. Simply taking the first detectable tracer at 0.10 L would discard the mixing transition.
This is an operational estimate from a gas-transport record, not a direct anatomical scan. Mixing, the selected reference plateau and apparatus volume affect the interpretation. Identifying that measurement convention prevents a tracer-defined boundary from being mistaken for a sharp physical partition in every breath.
\Image[/single-breath-dead-space.png]
{title=A mixing transition changes the single-breath dead-space estimate}
{description=Original idealized normalized tracer curve with an equal-area step at 0.15 L expired volume. The initial zero-tracer interval is only 0.10 L; accounting for the transition supplies the remaining 0.05 L. The curve and numbers are constructed, not measured patient data.}
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