= Chest-wall relaxation volume
{title2=$V_{W,0}$}
\b[Chest-wall relaxation volume] is the volume at which the passive <chest wall> has zero elastic recoil pressure. With pressure across the wall defined as $P_W=P_{\rm pleural}-P_{\rm body\ surface}$, write that volume as $V_{W,0}$, so $P_W(V_{W,0})=0$. Below it, the wall tends to expand; above it, the wall tends to recoil inward. The zero of pressure and the slope defining <chest-wall compliance> are different features of the pressure-volume curve.
The coupled <lung> and <chest wall> generally settle at another volume. Their elastic pressures add:
$$
P_{\rm rs}(V)=P_L(V)+P_W(V).
$$
In a passive, open-airway equilibrium, total recoil is zero even though the individual pressures need not vanish. This balance underlies the relaxed end-expiratory volume, or <functional residual capacity>, in the ideal passive setting. OpenStax describes the opposed lung and chest-wall recoil and defines the volume remaining after normal expiration.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§22.3, pressure relationships, thoracic wall compliance and Respiratory Volumes and Capacities]{ref}
An original linear model makes <partitioning passive recoil equilibrium> explicit:
$$
P_L=\frac{V-V_{L,0}}{C_L},\qquad
P_W=\frac{V-V_{W,0}}{C_W},\qquad
V_*=\frac{C_WV_{L,0}+C_LV_{W,0}}{C_L+C_W}.
$$
For positive compliances, the coupled equilibrium lies between the two component zero-recoil volumes. Choose $V_{L,0}=1$ L, $V_{W,0}=4$ L and $C_L=C_W=0.20\,\mathrm{L\,(cm\,H_2O)^{-1}}$. Then $V_*=2.5$ L, with lung pressure $+7.5$ and wall pressure $-7.5$ cm water. Calling 2.5 L the chest-wall relaxation volume would confuse zero total pressure with zero wall pressure.
Changing the wall's slope can move the coupled equilibrium without moving its own zero. In the same model, increasing $C_W$ to 0.40 while holding everything else fixed gives $V_*=2.0$ L; $V_{W,0}$ remains 4 L. The more compliant wall supplies a smaller outward pressure at a given volume below its zero. These numbers explain a mechanical distinction rather than state normal human volumes.
A measurement must therefore distinguish passive wall recoil, total respiratory-system recoil and active respiratory-muscle pressure. The relationship between esophageal-balloon pressure and <pleural pressure> also needs experimental justification when partitioning these components.<Airway Resistance and Lung Compliance by Ole Storstein and others>[Methods, balloon and mouthpiece pressure measurements]{ref} Posture and muscle activity belong to the stated measurement conditions; a measured end-expiratory volume need not equal a purely passive equilibrium.
Back to article page
