Balloon volumetric compliance ($C_V=\mathrm{d}V/\mathrm{d}p$)

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:It has units of volume per pressure. It differs from diameter response $\mathrm{d}D/\mathrm{d}p$ in a balloon pressure-diameter curve and from a fractional volume response $(1/V)\mathrm{d}V/\mathrm{d}p$.

For an illustrative cylindrical region whose length can also change,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 $10\mathrm{atm}$.^[ref] Using those diameters in a chosen fixed-length $10\mathrm{mm}$ cylinder gives the finite-interval estimateThe 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 $C_{\mathrm{measured}}=C_{\mathrm{balloon}}+C_{\mathrm{fixture}}$. 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.

A balloon compliance fixture correction removes the volume response of tubing, connectors, fluid and other apparatus from a measured balloon volumetric compliance. It is a correction to a defined measurement arrangement. The pressure reference and the state of the apparatus must match between characterization and use.

For a quasistatic experiment in which fixture and balloon experience the same pressure increment, writeA separately characterized fixture supplies $C_f$. A rigid termination can provide one control configuration, but changing tubing or trapped gas between the control and balloon runs changes the correction itself.

For an original example, $C_{\mathrm{meas}}=2.00$ and $C_f=0.50\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$ give $C_b=1.50\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$. Assigning the whole measured response to the balloon would overestimate it by one third relative to the corrected value. Independent standard uncertainties $0.05$ and $0.04\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$ give $u(C_b)=\sqrt{0.05^2+0.04^2}\approx 0.0640\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$. Correlated inputs instead require the term $-2\mathrm{Cov}(C_{\mathrm{meas}},C_f)$ in the variance.^[ref]

Trapped gas explains one nonlinear contribution. For an isothermal gas pocket with $p_{\mathrm{abs}}{V}_g$ constant, its local stored-volume response is $-d{V}_g/dp=V_g/p_{\mathrm{abs}}$. A $20\mu \mathrm{L}$ pocket at $100\mathrm{kPa}$ absolute pressure contributes $0.20\mu \mathrm{L}\mathrm{kP}{\mathrm{a}}^{-1}$. Absolute pressure is required here; substituting gauge pressure into the gas law would be wrong.

A manufacturer's diameter-versus-pressure chart, such as Nipro's Thouzer chart, reports a different observable from injected volume.^[ref] Such a chart does not measure the fixture's stored volume. Comparing a measured volume curve with it requires the balloon geometry and apparatus correction, rather than treating diameter compliance and whole-system volume compliance as identical.

During flow, different parts of the fixture can have different pressures. The simple additive quasistatic model then needs a dynamic extension, consistent with the balloon inflation hydraulic time constant. Loading history and hysteresis must also match before two response curves can be subtracted.