= Stent recoil
<Stent recoil> is a reduction in the diameter of an expanded <vascular stent> after the expanding load is removed. For a balloon-expandable device, the relevant acute comparison is commonly the diameter during balloon expansion against the diameter after balloon deflation. It is distinct from later biological tissue growth inside the treated segment.<Non-Clinical Engineering Tests and Recommended Labeling for Intravascular Stents and Associated Delivery Systems by the FDA>[Section IV.B.4, Recoil for Balloon Expandable Stents]{ref}
Using matched diameter measurements $d_e$ during expansion and $d_r$ after release, define
$$
R=100\left(1-\frac{d_r}{d_e}\right).
$$
The denominator is the expanded diameter. An original bench example with $d_e=3.20\,\mathrm{mm}$ and $d_r=3.04\,\mathrm{mm}$ gives $R=5\%$. If the sections are circular, the corresponding area loss is
$$
100\left[1-\left(\frac{3.04}{3.20}\right)^2\right]=9.75\%.
$$
Diameter and area percentages should not be interchanged, and neither alone specifies the resulting change in <blood flow>.
The mechanical distinction is between permanent expansion and recoverable deformation. A loading–unloading test relates <stent recoil> to the device’s material response and geometry. Imaging should compare the same location along the device; averages can hide differences near its ends. The primary FDA engineering guidance consequently asks for diameter-specific measurements and attention to variation with length and position.<Non-Clinical Engineering Tests and Recommended Labeling for Intravascular Stents and Associated Delivery Systems by the FDA>[Section IV.B.4, diameter, length and measurement-location discussion]{ref}
The ratio also has a useful measurement property. Multiplying both diameters by the same scale factor leaves $R$ unchanged, while an equal additive edge-location offset generally does not. For independent diameter standard uncertainties $u_e,u_r$, first-order <uncertainty propagation> gives
$$
u_R^2=\left(\frac{100d_r}{d_e^2}\right)^2u_e^2+\left(\frac{100}{d_e}\right)^2u_r^2.
$$
With $u_e=u_r=0.01\,\mathrm{mm}$ in the example, $u_R\approx0.431$ percentage points. Shared image-scale or fitting errors require a <covariance> term instead of the independent-error formula.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[Section 5.2, correlated input quantities]{ref}
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