= C. Carlhäll
{c}
\b[<C. Carlhäll>] is first author of a 2007 experiment quantifying how <mitral annulus> motion contributes to <left ventricular filling>. The study implanted markers in the ventricular wall and around the annulus in six sheep, then used biplane <fluoroscopy> to reconstruct three-dimensional marker motion.<Contribution of mitral annular dynamics to LV diastolic filling with alteration in preload and inotropic state by C. Carlhäll and others>[Byline; Abstract, marker implantation and biplane reconstruction]{ref} This makes boundary movement an experimentally measured part of chamber filling, rather than treating the valve plane as stationary.
The investigators estimated enclosed volumes using multiple <tetrahedra> defined by the reconstructed markers.<Contribution of mitral annular dynamics to LV diastolic filling with alteration in preload and inotropic state by C. Carlhäll and others>[Abstract, tetrahedral volume estimates]{ref} Changing marker positions can change both the annular area and its excursion. Their contributions cannot generally be recovered from one distance alone.
An original geometric example takes a tetrahedron with one vertex at the origin and the other vertices at $(2,0,0)$, $(0,3,0)$ and $(0,0,4)$ cm. Its <volume> is
$$
V=\frac16\left|\det\begin{pmatrix}2&0&0\\0&3&0\\0&0&4\end{pmatrix}\right|=4\,\mathrm{cm^3}.
$$
Moving only the last vertex to $(0,0,6)$ cm increases this to $6\,\mathrm{cm^3}$. Translating all four vertices by the same vector leaves the volume unchanged, because the relevant vectors are differences between vertices. This illustrates the reconstruction geometry, not measured animal dimensions.
A boundary-swept volume and the amount of blood crossing that boundary are nevertheless distinct observables. Interpreting their relationship requires a consistent moving-boundary model and matching cardiac phases. The primary work compared annular dynamics under altered loading and contractile conditions; its contribution is the quantitative experimental connection between three-dimensional motion and filling. The original initial-only byline is preserved without inferring an expanded identity from a separate profile.
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