= Balloon angioplasty
<Balloon angioplasty> enlarges a narrowed vessel segment by inflating a balloon carried on a <catheter> within the lumen. It is a form of <endovascular surgery>. The balloon applies outward pressure to the narrowed region and is subsequently deflated and removed. A <vascular stent>, if used, is a separate retained support; balloon dilation by itself does not leave that scaffold behind.<Angiogram by the Society for Vascular Surgery>[Angiography and balloon/stent interventions]{ref}
The mechanical target is <vascular stenosis>. Increasing lumen radius can strongly reduce resistance, but geometry is only part of the response. Under the ideal assumptions of <Hagen-Poiseuille flow> through a uniform rigid circular tube,
$$
R=\frac{8\mu L}{\pi r^4},\qquad \frac{R_2}{R_1}=\left(\frac{r_1}{r_2}\right)^4.
$$
An illustrative radius increase from $1.0$ to $1.5\,\mathrm{mm}$ would reduce that segment’s model resistance to $1/1.5^4\approx0.198$ of its former value. This is not a predicted patient flow increase: a short irregular narrowing, compliant walls, pulsatility and the rest of the circulation depart from the ideal tube model.
The historical primary report by <A. R. Grüntzig>, <A. Senning> and <W. E. Siegenthaler> describes a catheter system with controlled balloon inflation in a 50-patient coronary series. In the 32 reported successful cases, mean percentage stenosis changed from $84\%$ to $34\%$, while mean pressure gradient changed from $58$ to $19\,\mathrm{mmHg}$. Measuring both anatomy and pressure made the proposed mechanical effect observable. The report also records failures and emergency bypasses and calls for randomized comparison, so the successful-case averages are not a complete treatment-effect estimate.<Nonoperative dilatation of coronary-artery stenosis: percutaneous transluminal coronary angioplasty by A. R. Grüntzig and others>[1979 abstract, apparatus, successful-case measurements and limitations]{ref}
A modern scientific evaluation similarly separates immediate lumen enlargement, the <pressure gradient>, persistent patency and later <clinical outcomes>. A larger lumen on an angiographic image answers an anatomical question at that observation time; it does not establish that narrowing cannot recur or that every downstream tissue problem has been resolved.
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