= Eccentric lumen stenosis
\b[Eccentric lumen stenosis] concerns a narrowed vessel lumen whose geometry breaks the symmetry of a circular, concentric reference model. Noncircular shape and displacement away from the reference centre are distinct geometric features; neither alone identifies the composition of the surrounding tissue. The practical issue is that one observed diameter may not characterize the remaining lumen area.
For an original noncircular model, take an elliptical lumen with semiaxes $a$ and $b$. Its area and <area-equivalent lumen diameter> are
$$
A=\pi ab,\qquad D_{\rm eq}=2\sqrt{ab}.
$$
If full principal diameters are $D_1=2a$ and $D_2=2b$, then $D_{\rm eq}=\sqrt{D_1D_2}$. This circle has the same area, not necessarily the same flow resistance, as the ellipse.
The width of the ellipse projected onto an axis at angle $\theta$ to its major axis is
$$
w(\theta)=2\sqrt{a^2\cos^2\theta+b^2\sin^2\theta}.
$$
With $a=2$ and $b=1\,\mathrm{mm}$, principal projected widths range from $4$ to $2\,\mathrm{mm}$. Relative to a circular $4\,\mathrm{mm}$ reference, those two widths would suggest diameter reductions $0\%$ and $50\%$, although the model's true area reduction is fixed at $50\%$. The area-equivalent diameter is about $2.828\,\mathrm{mm}$.
This ideal projection calculation explains why observation direction matters. It is not a complete model of a contrast-filled, curved, moving vessel. An observed image also depends on viewing geometry, overlap, resolution and the boundary-reconstruction method. Judkins' primary coronary-arteriography work used selective catheterization with serial and cine recording, providing an apparatus for observing the contrast-filled arterial route.<Selective Coronary Arteriography: Part I: A Percutaneous Transfemoral Technic by Melvin P. Judkins>[1967, Material and Technic, selective catheterization and serial/cine recording]{ref}
<Diameter versus area stenosis> conversions that square one diameter ratio assume a circular model. They should not be applied automatically to a single width of an eccentric or noncircular lumen. Two principal diameters can determine the area of the stated ellipse, but a general irregular outline requires more shape information. Shape, percentage narrowing and the physiological consequence of <vascular stenosis> remain separate questions.
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