 Diameter versus area stenosis

Diameter versus area stenosis distinguishes two geometric ways to express vascular stenosis relative to a stated reference lumen. A percentage reduction in diameter is generally not the same percentage reduction in area.

For a circular narrowed lumen with diameter $d$ and a circular reference with diameter $d_0$, define the fractional reductionsSince $A=\pi d^2/4$, the conversion isMultiply a fraction by 100 to report a percentage. A diameter change from $4$ to $2\mathrm{mm}$ gives $s_d=0.50$ and $s_A=0.75$. Conversely, a $50\%$ area reduction corresponds to about $29.3\%$ diameter reduction in this circular model. Converting a geometric definition is not the same thing as converting clinical grading systems.

Eccentric lumen stenosis shows why the shape assumption matters. Suppose the reference is a circle of diameter $4\mathrm{mm}$, while the narrowed lumen is an ellipse with full axes $2$ and $4\mathrm{mm}$. Its area is $\pi (2)(4)/4=2\pi \mathrm{m}{\mathrm{m}}^2$, half the reference area. A single view measuring the $2\mathrm{mm}$ axis would show a $50\%$ diameter reduction, but treating that view as a circular lumen would incorrectly infer a $75\%$ area reduction.

The reference also matters. For the same measured narrow diameter $2\mathrm{mm}$, references $4$ and $5\mathrm{mm}$ give diameter reductions $50\%$ and $60\%$. A report should therefore identify the measurement plane or projection, the reference segment, the geometric convention and the imaging method.

For a small uncertainty in $s_d$, the circular-model sensitivity is $\mathrm{d}{s}_A/\mathrm{d}{s}_d=2(1-s_d)$. Uncertainty in the reference and narrow diameters, including shared measurement errors, must be propagated through their ratio rather than treating the percentage as a directly measured primitive quantity.

Ultrasound can supply vessel images and flow-related observations using a probe and coupling gel.^[ref] A geometric stenosis estimate and a flow observation remain distinct measurements. Even a correctly converted lumen area does not determine the pressure loss or tissue perfusion without an appropriate model of the vessel and circulation.