This is a genuinely time-resolved re-derivation of the same physiology, drawn two ways a real echocardiographer actually looks at the valve — never a flattened 3D render:
Continuity equation: A1·V1(t) = A2·V2(t) = Q(t)
Simplified Bernoulli: ΔP(t) = 4·(V2(t)² − V1(t)²) [mmHg, V in m/s]
Flow waveform: Q(t) = Qpeak·sin(πt/LVET), 0≤t≤LVET (0 otherwise)
Unlike a single peak-flow snapshot, the flow rate Q(t) here is modeled as an actual pulsatile half-sine ejection waveform whose peak, Qpeak = SV·π/(2·LVET), is solved so that its time-integral over one ejection period exactly equals the stroke volume you set — a real constraint, not an approximation. The top strip plots V1(t) and V2(t) live, exactly like a continuous-wave Doppler tracing scrolling across an echo machine; the middle strip plots the instantaneous gradient ΔP(t) with the area under each beat shaded, and the "mean gradient" readout is the actual time-average of that measured curve over the ejection period (not a fixed clinical rule-of-thumb) — for this idealized half-sine profile it converges to exactly half the peak gradient, a testable relationship (real asymmetric ejection profiles run closer to ~0.66).
- En-face planimetry inset (bottom-left) draws the valve orifice and LVOT the way a short-axis 2D echo view does — two circles whose areas are literally A2 = AVA and A1 = π(LVOT/2)², with three leaflet arcs that stiffen and encroach on the orifice as AVA shrinks.
- AVA slider — shrinks the orifice circle and (via continuity) raises Qpeak's velocity through it, so the jet trace V2(t) rises with the square of that velocity in the gradient panel.
- LVOT diameter — sets A1; the single biggest source of error in real echo-derived AVA.
- Stroke volume / heart rate — set Qpeak and the ejection window LVET (shorter at higher heart rates), reshaping both waveforms live.
Clinical severity (2020 ACC/AHA valve guidelines, by AVA): mild ≥1.5 cm², moderate 1.0–1.5 cm², severe <1.0 cm² (critical <0.6 cm²).