A stiffened, calcified aortic valve no longer opens fully — the same stroke volume must now cross a smaller orifice. Two coupled principles, both used at the bedside during Doppler echocardiography, explain what happens next:
Continuity equation: A1·V1 = A2·V2
Simplified Bernoulli: ΔP = 4·(V2² − V1²) [mmHg, V in m/s]
A1 is the LVOT cross-sectional area (from the LVOT diameter), V1 the pre-valve LVOT velocity, A2 the stenotic valve area (AVA), and V2 the peak jet velocity through the orifice. Because the same volumetric flow Q = stroke volume ÷ ejection time must pass through both cross-sections, shrinking A2 forces V2 — and therefore the pressure the ventricle must generate — sharply higher.
- AVA slider — the effective valve orifice area. Below ~1.0 cm² the pressure cost rises steeply because ΔP scales with V2², not V2.
- LVOT diameter — sets A1 = π(d/2)²; a measurement error here is the single biggest source of error in real echo-derived AVA.
- Stroke volume / heart rate — set the flow rate Q. Ejection time is estimated from heart rate (faster rates leave less time to eject, so instantaneous flow — and the gradient — rises for the same stroke volume).
- The 3D scene renders the actual duct geometry (LV → LVOT → valve orifice → post-stenotic jet → aorta), and the flow particles' own local velocity is computed from local cross-sectional area via the same continuity equation — watch them accelerate and thin out through the narrow orifice, then decelerate and spread as the jet disperses into the aorta.
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). The mean gradient shown is estimated as ≈0.66 × peak gradient, a commonly cited ratio for a typical AS flow-velocity profile. This is a simplified quasi-steady model of peak systolic flow, not a full time-resolved pulsatile simulation — real Doppler tracings integrate velocity across the whole ejection period.