= Balloon compliance fixture correction
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, write
$$
\Delta V_{\rm inj}=\Delta V_b+\Delta V_f,\qquad
C_{\rm meas}=C_b+C_f,\qquad C_b=C_{\rm meas}-C_f.
$$
A 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, $C_{\rm meas}=2.00$ and $C_f=0.50\,\mathrm{\mu L\,kPa^{-1}}$ give $C_b=1.50\,\mathrm{\mu L\,kPa^{-1}}$. 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 $0.04\,\mathrm{\mu L\,kPa^{-1}}$ give $u(C_b)=\sqrt{0.05^2+0.04^2}\approx0.0640\,\mathrm{\mu L\,kPa^{-1}}$. Correlated inputs instead require the term $-2\operatorname{Cov}(C_{\rm meas},C_f)$ in the variance.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[Section 5.2, correlated-input propagation]{ref}
Trapped gas explains one nonlinear contribution. For an isothermal gas pocket with $p_{\rm abs}V_g$ constant, its local stored-volume response is $-dV_g/dp=V_g/p_{\rm abs}$. A $20\,\mathrm{\mu L}$ pocket at $100\,\mathrm{kPa}$ absolute pressure contributes $0.20\,\mathrm{\mu L\,kPa^{-1}}$. 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.<Thouzer semi-compliant balloon catheter product information by Nipro>[Compliance chart, pressure rows and balloon-diameter columns]{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.
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