= Mitral annular excursion
\b[Mitral annular excursion] is displacement of the <mitral annulus> over a specified part of the <cardiac cycle>. A commonly used longitudinal observation follows an annular landmark along the <cardiac long axis> during ventricular <systole>. The reference position, direction and endpoints are part of the measurement; displacement is distinct from annular area or leaflet <coaptation>.
The measurement question can be written explicitly. For a fixed unit axis $\widehat{\boldsymbol e}$ and landmark position $\boldsymbol x(t)$, define
$$
\Delta s=\bigl(\boldsymbol x(t_1)-\boldsymbol x(t_0)\bigr)\mathbin{\cdot}\widehat{\boldsymbol e}.
$$
An original 10 mm displacement viewed along an axis tilted by $30^{\circ}$ projects to $10\cos30^{\circ}\simeq8.66$ mm. Thus changing the observation direction changes the reported excursion even for the same motion. A single landmark also need not represent every part of a deforming <mitral annulus>.
A primary human study used cine <magnetic resonance imaging>, measuring longitudinal displacement in long-axis views and <stroke volume> in short-axis views. Its model combined displacement with a ventricular short-axis area.<Atrioventricular plane displacement is the major contributor to left ventricular pumping in healthy adults, athletes, and patients with dilated cardiomyopathy by Marcus Carlsson and others>[Abstract, Methods]{ref} In an original rigid-piston approximation, area $A$ moving axially by $\Delta s$ sweeps volume $A\Delta s$. Areas 20 and 40 cm$^2$ paired with displacements 1 and 0.5 cm both give 20 mL. Smaller excursion need not imply a smaller geometric swept volume when area differs; this model area is not automatically the mitral opening area.
A complementary experiment by <C. Carlhäll> and colleagues implanted markers around the <mitral annulus> and ventricular wall in six sheep. Biplane <fluoroscopy> reconstructed three-dimensional marker motion, and <tetrahedron>-based estimates assessed annular contributions to filling while loading and contraction were varied.<Contribution of mitral annular dynamics to LV diastolic filling with alteration in preload and inotropic state by C. Carlhäll and others>[Abstract, experimental methods]{ref} This connects a displacement measurement to moving-chamber geometry. The changing boundary, surrounding deformation and <blood flow> must be distinguished when relating <mitral annular excursion> to filling or ejection.
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