= Respiratory-system elastance
{title2=$E_{\rm rs}=1/C_{\rm rs}$}
\b[Respiratory-system elastance] is the local increase in passive elastic <pressure> per increase in respiratory <volume>. It is the reciprocal of local <respiratory-system compliance>:
$$
E_{\rm rs}=\frac{dP_{\rm rs}}{dV}=\frac1{C_{\rm rs}}.
$$
Its units are <pressure> per <volume>, such as $\mathrm{Pa\,m^{-3}}$ or $\mathrm{cm\,H_2O\,L^{-1}}$. A larger elastance means that the same small <volume> increment needs a larger elastic <pressure> increment.
The <lung> and <chest wall> share a <volume> increment while their <pressure> increments add. Thus their elastances add,
$$
E_{\rm rs}=E_L+E_W,
$$
whereas their compliances do not. For stipulated $C_L=0.20$ and $C_W=0.10\,\mathrm{L\,(cm\,H_2O)^{-1}}$, the elastances are 5 and 10, totaling 15 in reciprocal units. Combined compliance is $1/15\approx0.0667$. The underlying <pressure> partition is distinct from attributing all measured stiffness to the lung.<Pulmonary Function Testing by Warren M. Gold and Laura L. Koth>[Lung Elasticity, pressure references and compliance]{ref}
<Elastic work in a pressure-volume model> gives another meaning to stiffness. Around a passive zero-recoil equilibrium, let added <volume> be $v$ and <pressure> $P=Ev$ with constant elastance. The reversible <work> needed to move from zero to $v$ is
$$
W=\int_0^v Ex\,dx=\frac12Ev^2.
$$
For an original SI example, $E=10^6\,\mathrm{Pa\,m^{-3}}$ and $v=5\times10^{-4}\,\mathrm{m^3}$ give final <pressure> 500 Pa and elastic work 0.125 J. Doubling elastance at the same <volume> doubles this work; doubling <volume> at fixed elastance quadruples it. Resistive losses and active muscle work are outside this ideal elastic calculation.
If the pressure-volume curve is nonlinear, local elastance $dP/dV$ can differ from the interval ratio $\Delta P/\Delta V$. Its reciprocal corresponds to the local compliance at that state, not an average across an arbitrary range. A primary ventilator study compared different pressure-volume methods under passive conditions, making this measurement definition operational.<Static and Dynamic Measurements of Compliance and Driving Pressure: A Pilot Study by Pierre Tawfik and others>[Figure 1, methods A–D]{ref} Report <volume> range, passive conditions and whether the value is a derivative or a secant.
Back to article page
