= Chest-wall compliance
{title2=$C_W=dV/dP_W$}
\b[Chest-wall compliance] is the volume response of the passive <chest wall> to pressure across it. For a local static relation,
$$
C_W=\frac{dV}{dP_W},\qquad P_W=P_{\rm pleural}-P_{\rm body\ surface}.
$$
It differs from <lung compliance>, which uses the pressure difference between the alveolar gas and pleural surroundings. Active respiratory-muscle effort must be distinguished from passive elastic recoil when defining the chest-wall relation.
The <chest-wall relaxation volume> is the passive volume at which its recoil pressure is zero. Below that volume, outward recoil corresponds to negative $P_W$ in this convention; above it, inward recoil corresponds to positive $P_W$. Negative recoil pressure is compatible with a positive slope $dP_W/dV$ and positive compliance. OpenStax describes chest-wall elasticity opposing the inward pull of the lungs.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§22.3, The Process of Breathing, pleural coupling and thoracic wall compliance]{ref}
An original linear illustration makes the signs explicit. Over a chosen volume range, suppose
$$
P_L=5(V-1),\qquad P_W=5(V-4),
$$
with volume in litres and pressures in centimetres of water. Both components have compliance $0.20\,\mathrm{L\,(cm\,H_2O)^{-1}}$. At $V=2.5$ L, lung recoil is $+7.5$ and chest-wall recoil is $-7.5$ cm water, so their sum is zero. At $V=3.0$ L, the sum is $10-5=5$ cm water. The same shared half-litre change requires a five-centimetre-water increment even though both component slopes are positive. These are toy relations, not measured normal curves.
Adding pressure drops gives
$$
P_{\rm total}=P_L+P_W,\qquad
\frac1{C_{\rm total}}=\frac1{C_L}+\frac1{C_W}.
$$
The combined compliance in the example is $0.10\,\mathrm{L\,(cm\,H_2O)^{-1}}$. Treating that total as lung compliance alone assigns the chest-wall contribution to the wrong structure.
Pressure partition requires more information than a total volume and airway-pressure measurement. A primary lung-mechanics study's use of an esophageal balloon and differential pressure measurement illustrates the experimental effort to constrain an internal pressure reference.<Airway Resistance and Lung Compliance by Ole Storstein and others>[Methods, balloon pressure and mouthpiece connection]{ref} Its relationship to <pleural pressure>, posture and muscle activity must be accounted for rather than assumed away.
A useful mechanical comparison states whether the wall is passive, which pressure zero is used and whether local or interval compliance is reported. Chest movement, total respiratory-system stiffness and the chest wall's own elastic slope answer distinct questions.
\Image[/lung-chest-recoil-balance.png]
{title=Original linear example of passive <lung compliance>, <chest-wall compliance> and their combined recoil; at volume 2.5 L the pressures cancel}
Back to article page
