 Flow-convergence angle correction

Flow-convergence angle correction replaces the hemispherical collection area assumed by the proximal isovelocity surface area method with an area justified by the actual convergence geometry. If flow is radial and has constant normal speed $v_a$ on a spherical surface of radius $r$ spanning solid angle $\Omega$, thenThe correction concerns a flow surface, not simply the apparent opening of a heart valve in one image. The technical recommendations explicitly distinguish a nonplanar valve surface, persistent flow constraints and nonhemispherical contours.^[ref]

An original geometry comparison shows why a planar angle is insufficient without a three-dimensional model. A spherical cap within a cone of half-angle $\beta$ hasFor $\beta =60{}^{\circ }$, this gives $\Omega =\pi$, or half a hemisphere. A different model that retains a fraction of the azimuthal extent of a hemisphere gives a fraction proportional to that azimuthal angle. A measured angle must therefore be identified as a polar cone angle, an azimuthal sector or another geometric quantity before selecting a formula.

Using the stipulated spherical-cap model with $r=0.6$ cm and $v_a=40$ cm/s gives $Q=45.24$ mL/s, whereas a full hemisphere at the same radius and speed gives 90.48 mL/s. With a matched jet speed of 500 cm/s, the corresponding effective regurgitant orifice area estimates are $0.09048$ and $0.18096\mathrm{c}{\mathrm{m}}^2$. These numbers illustrate geometry, not a correction prescribed for an observed valve.

The velocity measurement adds a separate limitation. Color Doppler measures a beam-directed velocity component; a constant-color boundary need not be a sphere of constant normal flow speed. Changing the assumed collection area cannot repair an incorrectly measured radius, a nonuniform flow field or a jet velocity acquired at a different time.

The apparatus therefore provides an image and a velocity spectrum, while the corrected flow remains a model-based inference. The primary report discusses changing the aliasing contour to reduce constraint and states that a persistently unsuitable geometry may not support a simple angle correction.^[ref]