= Balloon volumetric compliance
{title2=$C_V=\mathrm dV/\mathrm dp$}
\b[Balloon volumetric compliance] is the local change in balloon volume per change in a specified pressure difference, with the mechanical state and other conditions defined:
$$
C_V=\frac{\mathrm dV}{\mathrm dp}.
$$
It has units of volume per pressure. It differs from diameter response $\mathrm dD/\mathrm dp$ in a <balloon pressure-diameter curve> and from a fractional volume response $(1/V)\mathrm dV/\mathrm dp$.
For an illustrative cylindrical region whose length can also change,
$$
V=\frac{\pi D^2L}{4},\qquad
C_V=\frac{\pi LD}{2}\frac{\mathrm dD}{\mathrm dp}
+\frac{\pi D^2}{4}\frac{\mathrm dL}{\mathrm dp}.
$$
The second term vanishes only when length is held fixed. A diameter-only observation does not otherwise determine the whole volume response.
The Nipro chart gives $2.00$ and $2.16\,\mathrm{mm}$ for its nominal $2.00\,\mathrm{mm}$ balloon at labeled rows $6$ and $10\,\mathrm{atm}$.<Thouzer semi-compliant balloon catheter product information by Nipro>[Compliance chart, 2.00 mm column]{ref} Using those diameters in a chosen fixed-length $10\,\mathrm{mm}$ cylinder gives the finite-interval estimate
$$
\frac{\Delta V}{\Delta p}=\frac{\pi(10)}4\frac{2.16^2-2.00^2}{10-6}
=0.416\pi\simeq1.307\,\mathrm{\mu L\,atm^{-1}}.
$$
The assumed cylinder is not a measured manufacturer balloon volume. The calculation illustrates why a finite volume change differs from substituting one endpoint diameter into a local derivative.
A <balloon compliance fixture correction> separates the balloon from the measurement apparatus. In a simple quasistatic model where both experience the same pressure increment, measured injected-volume response can be $C_{\rm measured}=C_{\rm balloon}+C_{\rm fixture}$. A blank or independently characterized fixture is needed before assigning the entire response to the balloon.
Pressure reference, external constraint, loading history, temperature and equilibration also belong to the definition. <Hysteresis> can give different paths on inflation and deflation. Compliance describes a response in the stated regime; it does not alone supply a rupture pressure or a failure probability.
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