= Balloon pressure-diameter curve
A \b[balloon pressure-diameter curve] relates the pressure applied to a specified <balloon catheter> to its measured diameter under stated conditions. It is a device response curve, not a universal law assigning the same diameter to every balloon at one pressure. External constraint, fluid conditions, loading history and the location at which diameter is measured can matter.
The manufacturer chart for a nominal $2.00\,\mathrm{mm}$ Thouzer balloon lists diameters $2.00\,\mathrm{mm}$ at the row labeled $6\,\mathrm{atm}$ and $2.16\,\mathrm{mm}$ at $10\,\mathrm{atm}$.<Thouzer semi-compliant balloon catheter product information by Nipro>[Compliance chart, 2.00 mm column, 6 and 10 atm rows]{ref} From those chart entries, the secant diameter response is
$$
\frac{\Delta D}{\Delta p}=\frac{2.16-2.00}{10-6}=0.040\,\mathrm{mm\,atm^{-1}}.
$$
That interval slope does not establish a constant slope outside the tabulated interval or the diameter achieved in a constrained living vessel.
Diameter response and <balloon volumetric compliance> have different units. For an illustrative cylindrical balloon region of fixed length $L$,
$$
V=\frac{\pi D^2L}{4},\qquad
\frac{\mathrm dV}{\mathrm dp}=\frac{\pi LD}{2}\frac{\mathrm dD}{\mathrm dp}.
$$
Using chosen local values $D=2\,\mathrm{mm}$, $L=10\,\mathrm{mm}$ and $\mathrm dD/\mathrm dp=0.040\,\mathrm{mm\,atm^{-1}}$ gives about $1.257\,\mathrm{mm^3\,atm^{-1}}$, or $1.257\,\mathrm{\mu L\,atm^{-1}}$. This fixed-length cylinder is a model, not the manufacturer's full balloon geometry.
A pressure-size measurement should state its pressure reference, loading direction, temperature, surrounding constraint and equilibration rule. Inflation and deflation need not retrace one curve when <hysteresis> or permanent deformation is present. A pressure-diameter curve also differs from a rupture result: measured expansion over an interval alone does not identify a safe maximum or a failure probability.
The <hoop stress> relation $\sigma_\theta\simeq\Delta p\,r/h$ for a thin cylindrical wall supplies a force balance, but a material and geometric response model is still required to predict diameter. A wall can carry increasing tensile stress with relatively little further enlargement. Thus pressure, size, wall loading and failure are related measurements requiring their own definitions.
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