= Lung compliance
{title2=$C_L=dV/dP_L$}
\b[Lung compliance] measures how much lung <volume> changes for a change in distending pressure. For a static pressure-volume relation, the local value is
$$
C_L=\frac{dV}{dP_L},\qquad P_L=P_{\rm alveolar}-P_{\rm pleural}.
$$
The relevant pressure is <transpulmonary pressure>, not <alveolar pressure> or airway-opening pressure alone. The <pleural pressure> reference separates the lung's elastic behaviour from that of the surrounding <chest wall>.
OpenStax connects lung expansion to pressure changes, elastic recoil and <pulmonary surfactant>, which modifies surface-tension effects.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§22.3, The Process of Breathing: pressure relationships, surface tension and compliance]{ref} A compliant lung needs a smaller pressure increment for the same small volume increment, but that statement alone does not describe recoil, airway patency or overall respiratory function.
A finite pressure-volume ratio is a secant slope, while $dV/dP_L$ is a local slope. In an original nonlinear example, set $x=V-V_0$ and $P_L-P_{L,0}=5x+5x^3$ when volume is measured in litres and pressure in centimetres of water. Local compliance is $1/(5+15x^2)$. It falls from $0.20$ at $x=0$ to $0.05\,\mathrm{L\,(cm\,H_2O)^{-1}}$ at $x=1$ L. Across that entire one-litre interval, however, the secant compliance is $1/10=0.10$ in the same units. These are constructed values, not clinical reference ranges.
<Static versus dynamic lung compliance> distinguishes elastic behaviour from measurements during airflow. A simplified lumped dynamic model adds an <airway resistance> term proportional to volume-flow rate: pressure depends on both $V$ and $R\dot V$. A pressure ratio obtained while air is moving can therefore differ from the static elastic slope. Inflation history and <hysteresis> also require the direction and volume interval to be specified.
In a 1959 primary study, researchers used an intra-esophageal balloon connected to a differential pressure transducer, with a mouthpiece pressure connection, to obtain pressure differences relevant to lung mechanics.<Airway Resistance and Lung Compliance by Ole Storstein and others>[Methods, intra-esophageal balloon and Sanborn differential pressure transducer; Yale Journal of Biology and Medicine 31, 387–396]{ref} Such a surrogate pressure measurement has its own positioning and calibration assumptions. <Spirometry> supplies volume information; volume measurement alone does not establish lung compliance.
Report the pressure references, volume range, flow conditions and measurement history alongside a compliance value. A single number is a property of the specified experiment and state, not an invariant description of every breath.
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