= Aortic root measurement-plane dependence
{title2=$D_{\rm oblique}=D_\perp/\cos\theta$}
\b[<Aortic root measurement-plane dependence>] is the change in a reported dimension caused by selecting a different anatomical level or imaging direction. Basal, sinus and <sinotubular junction> measurements describe different structures. Even at a fixed level, an oblique observation need not equal a dimension obtained in a plane perpendicular to the local vessel direction.
The anatomical exposition illustrates separate root measurement levels in an <echocardiography> view and distinguishes the basal and sinotubular boundaries.<Surgical anatomy of the aortic valve and root—implications for valve repair by Ruggero De Paulis and Andrea Salica>[Figure 1 and General considerations]{ref} The three-dimensional crown of leaflet attachments also differs from a single flat ring.<The surgical anatomy of the aortic root by Robert H. Anderson>[Abstract, attachment geometry and annulus terminology]{ref}
An original ideal <circular cylinder> example isolates obliquity. Let the true perpendicular radius be $R$. A plane whose normal is tilted by angle $\theta$ from the cylinder axis cuts an <ellipse> with semiaxes
$$
b=R,\qquad a=\frac{R}{\cos\theta},\qquad 0\le\theta<\frac\pi2.
$$
The longest apparent diameter is $2R/\cos\theta$. For a stipulated perpendicular diameter 30 mm and tilt 30 degrees, it is approximately 34.64 mm, 15.5% larger despite unchanged material geometry.
The ellipse's area is $\pi R^2/\cos\theta$. If the longest diameter were instead inserted into a circular-area formula, the estimate would be $\pi R^2/\cos^2\theta$, 33.3% above the true perpendicular area at 30 degrees. Measuring the area of the oblique cut and assuming a circular area from its longest diameter introduce different geometric factors.
An actual <aortic root> is curved, sinus-bearing and time-dependent; it is not a uniform circular cylinder. The example demonstrates one source of measurement dependence rather than providing a universal correction for patient images. Anatomical asymmetry, selected landmarks and phase of the <cardiac cycle> must also be recorded.
A reproducible comparison therefore identifies the root level, imaging plane, direction of the reported dimension and cardiac phase. Two numbers should not be treated as a growth observation until their measurement definitions are compatible; a change in plane can change a number without an underlying change in root size.
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