= Partitioning passive recoil equilibrium
\b[Partitioning passive recoil equilibrium] separates the elastic pressure contributions of the <lung> and <chest wall> at a shared volume. With <transpulmonary pressure> $P_L=P_{\rm alv}-P_{\rm pl}$ and wall pressure $P_W=P_{\rm pl}-P_{\rm surface}$,
$$
P_{\rm rs}=P_L+P_W=P_{\rm alv}-P_{\rm surface}.
$$
At a passive, open-airway equilibrium the total is zero, but the lung and wall contributions can be equal and opposite rather than individually zero. Their pressure references determine what is being added.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§22.3, pleural pressure and opposing elastic recoil]{ref}
The <component-elastance ambiguity in total recoil measurements> persists away from equilibrium. An original linear family writes
$$
P_L(V)=p_0+\lambda E(V-V_*),\qquad
P_W(V)=-p_0+(1-\lambda)E(V-V_*),
$$
where $E>0$ is total stiffness and $0<\lambda<1$. Every choice of $p_0$ and $\lambda$ produces the identical total curve $P_{\rm rs}=E(V-V_*)$. Measuring that total curve alone cannot identify either the baseline pressure partition or the component slopes.
For stipulated $E=10\,\mathrm{cm\,H_2O\,L^{-1}}$, $V_*=2.5$ L and $p_0=7.5$ cm water, choosing $\lambda=0.5$ gives equal component slopes of 5. Choosing $\lambda=0.8$ gives slopes 8 and 2. At equilibrium both cases even have the same component pressures, $+7.5$ and $-7.5$. After a 0.5 L increase, the pressure increments are either 2.5 plus 2.5 or 4 plus 1 cm water. Both totals equal 5 cm water.
The respective <lung compliances> are 0.20 and $0.125\,\mathrm{L\,(cm\,H_2O)^{-1}}$, while the <chest-wall compliances> are 0.20 and 0.50. The combined compliance is 0.10 in either case. Thus one equilibrium internal-pressure reading, in addition to the total curve, still does not determine both component slopes.
A measurement series with a justified <pleural pressure> estimate supplies the missing partition across volume. The 1959 primary study used an intra-esophageal balloon, a mouthpiece connection and differential pressure recording to obtain such internal mechanical information.<Airway Resistance and Lung Compliance by Ole Storstein and others>[Methods, balloon catheter and Sanborn differential pressure transducer]{ref} The estimate's positioning and relation to pleural pressure require validation. Passive conditions matter as well: respiratory-muscle pressure would add another contribution to an equation intended to describe elastic recoil alone.
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