Mitral Regurgitation PISA Doppler Map 2D

Cardiac Phase

Systole

Valve Pathology

Posterior leaflet prolapse 40%

Annular diameter 32 mm

Heart rate 70 bpm

Live Hemodynamics (PISA)

Coaptation gap

0.0 mm

Flow convergence radius

0.00 cm

Geometric EROA

0.00 cm²

PISA-derived EROA

0.00 cm²

Regurgitant flow

0 mL/s

Regurgitant fraction

0 %

How it works

This is the 2D companion to the 3D mitral-valve-prolapse simulator. Instead of a rendered leaflet mesh and 3D particle jet, it draws the valve as a top-down cross-section at the annular plane and computes the actual clinical PISA (proximal isovelocity surface area) method the 3D sim's own theory box only described in prose:

V(r) = Q / (2πr²)              continuity on a hemispheric shell
r_alias : V(r_alias) = V_alias      solve for the Doppler flow-convergence radius
EROA_PISA = 2π·r_alias²·V_alias / V_max

The same disease-severity sliders drive a geometric orifice (gap × width, exactly as in the 3D sim) which fixes the true flow rate Q = EROA_geom × V_max. That Q is then fed forward through the continuity equation to find the radius r_alias at which velocity drops to the Nyquist limit V_alias = 40 cm/s — the flow-convergence shell a real color Doppler image shows as a color-aliasing boundary. Feeding r_alias back through the clinical EROA formula recovers the same orifice area, which is exactly the identity real echocardiography relies on to measure an orifice it cannot see directly.

Shells — concentric semicircles colored by computed velocity V(r): blue where flow is still slow and laminar, red near the orifice where continuity forces it to accelerate.
Strip chart — regurgitant flow Q(t) plotted over the last several beats, so the systolic burst pattern (not just its geometry) is visible directly, something the 3D particle jet cannot show as a quantity.
Posterior billow — drawn as a hinge-and-tip cross-section: the posterior leaflet tip lifts above the annular plane into the atrium and pulls away from the fixed anterior coaptation point, opening the same gap the 3D mesh computes vertex-by-vertex.

Left atrium Left ventricle PISA shell / jet