 Proximal isovelocity surface area method

The proximal isovelocity surface area method estimates instantaneous flow towards a leaking heart valve from the upstream convergence field. Color Doppler supplies a contour at a chosen aliasing speed $v_a$. If that contour represents a hemisphere of radius $r$, flow approximately normal to it giveswhere the matched jet speed $u_j$ comes from continuous-wave Doppler echocardiography. The inferred effective regurgitant orifice area is a flow-equivalent area, not the area of the colored region or necessarily the anatomical hole.^[ref]

The physical idea is conservation of mass. More generally, $Q={\int }_S\mathbf{u}\cdot \mathbf{n}dS$. Replacing that integral by one speed times a surface area requires an appropriate velocity component and geometry. Doppler ultrasound measures a component along the beam, so an apparent constant-color contour is not automatically a measured three-dimensional surface of constant normal speed.

For an original hemispherical example, let $r=0.6$ cm and $v_a=40$ cm/s. The modeled backward flow is $90.48$ mL/s. With matched $u_j=500$ cm/s, the effective area is $0.1810\mathrm{c}{\mathrm{m}}^2$. If this area remains constant and the velocity-time integral is 140 cm, the modeled regurgitant volume is 25.33 mL. These are stipulated inputs, not severity thresholds.

Geometry and timing can each change that inference. In an ideal radial model restricted to a known solid angle $\Omega$, $Q=\Omega r^2{v}_a$; a hemisphere uses $\Omega =2\pi$. Thus a stipulated $\Omega =\pi$ gives half the flow at the same radius and speed. This illustrates flow-convergence angle correction; a real nonhemispherical or confined flow needs a justified geometric model rather than an arbitrary numerical adjustment.

Likewise, a radius observed at one instant must be paired with the jet speed at that instant. A peak effective area multiplied by a full-cycle velocity integral can overstate transported volume when the leak occupies only part of systole. The technical report explicitly discusses matching times, nonplanar convergence and changing regurgitant duration.^[ref] The apparatus observes an aliased velocity pattern and a jet spectrum; the flow and area are derived through the stated model.