Editing Capnography (section)

== Capnogram model ==
The capnogram waveform provides information about various respiratory and cardiac parameters. The capnogram [[Double exponential function|double-exponential]] model attempts to quantitatively explain the relationship between respiratory parameters and the [[Exhalation|exhalatory]] segment of a capnogram waveform.<ref>{{Cite journal|last=Abid|first=Abubakar|date=May 2017|title=Model-Based Estimation of Respiratory Parameters from Capnography, With Application to Diagnosing Obstructive Lung Disease|journal=IEEE Transactions on Biomedical Engineering|volume=64|issue=12|pages=2957–2967|doi=10.1109/TBME.2017.2699972|pmid=28475040|hdl=1721.1/134854 |s2cid=206616144 |hdl-access=free}}</ref> According to the model, each exhalatory segment of capnogram waveform follows the analytical expression:

:<math>p_D(t) = p_A (1 - e ^{-\alpha}e^{\alpha e^{-t/\tau}})</math>

where
* <math>p_D(t)</math>represents the [[partial pressure]] of [[carbon dioxide]] measured by the capnogram as a function of time <math>t</math> since the beginning of exhalation.
* <math>p_A</math>represents the alveolar partial pressure of carbon dioxide.
* <math>\alpha</math>represents the inverse of the [[dead space fraction]] (i.e. the ratio of [[tidal volume]] to [[Dead space (physiology)|dead space]] volume).
* <math>\tau</math>represents the pulmonary time constant (i.e. the product of [[Airway resistance|pulmonary resistance]] and [[Lung compliance|compliance]])

In particular, this model explains the rounded "shark-fin" shape of the capnogram observed in patients with [[obstructive lung disease]].