The Doppler equations the calculator solves

Twenty-three modules build from the physics. One compares pulsed-wave, continuous-wave, color and tissue Doppler, and why PW aliases above Nyquist. The simplified Bernoulli equation, ΔP = 4·V², turns a peak velocity into a gradient; the velocity-time integral gives the stroke distance behind stroke volume. From those: Doppler cardiac output; the continuity equation for aortic valve area, with the dimensionless index; PISA for EROA and regurgitant volume; the Hatle pressure half-time, MVA = 220 / PHT; PASP as 4·(TR Vmax)² plus IVC-derived right atrial pressure; dP/dt from the MR jet; the Abbas equation for pulmonary vascular resistance; and Qp/Qs from paired RVOT and LVOT stroke volumes.

Diastolic function and left atrial pressure

Two algorithms follow the 2025 ASE update (Nagueh, JASE 2025). In sinus rhythm the tool scores three main parameters, reduced e′, elevated E/e′, and TR velocity ≥ 2.8 m/s, then falls back on supplemental parameters when one or two are abnormal: left atrial reservoir strain, pulmonary vein S/D, LAVi and IVRT. Reservoir strain ≤ 18% is the main addition over 2016. A second covers atrial fibrillation, where cutoffs differ: mitral E ≥ 100 cm/s, septal E/e′ > 11, TR > 2.8 m/s, deceleration time ≤ 160 ms.

Constrictive pericarditis versus restrictive cardiomyopathy

Both give small ventricles, high filling pressures and biatrial enlargement, so the module shows only the discriminators: respirophasic mitral inflow variation above 25%, annulus paradoxus with medial e′ ≥ 8 cm/s, expiratory hepatic vein diastolic flow reversal, and a septal notch on M-mode.

Valve lesion atlases

Seven atlases pair three severity panels each: aortic, mitral and pulmonary stenosis and regurgitation, plus tricuspid regurgitation. AR and PR grading begins at mild, since trace regurgitation there is physiologic. Severe AS is Vmax ≥ 4.0 m/s, mean gradient ≥ 40 mmHg, AVA ≤ 1.0 cm², though a late-peaking dagger contour argues severe at borderline velocity. Severe mitral stenosis is MVA ≤ 1.5 cm² with PHT ≥ 150 ms per 2020 ACC/AHA staging. Tricuspid regurgitation is graded by vena contracta ≥ 0.7 cm, EROA ≥ 0.40 cm² and regurgitant volume ≥ 45 mL, not by TR Vmax, the RV-to-RA gradient, which falls once torrential TR equalizes the chambers, so velocity grading reads the worst lesions as mildest.

Strain, hypertrophic cardiomyopathy and amyloidosis

The strain module covers speckle tracking, the AHA 17-segment bull's-eye and its regional patterns: apical sparing in amyloidosis, reduced basal septal strain in hypertrophic cardiomyopathy, globally reduced strain in dilated cardiomyopathy, and LAD, RCA and LCx infarct territories. Normal global longitudinal strain is at or below −18%. HCM and amyloidosis get their own modules; obstructive HCM is a peak LVOT gradient ≥ 30 mmHg at rest or with provocation.

Pitfalls attached to each module

Every module lists how its number fails. Pressure half-time is invalid for about 72 hours after balloon mitral valvuloplasty, and significant aortic regurgitation falsely shortens it. LVOT diameter is squared, so a 1 mm error shifts stroke volume ~10%. Right atrial pressure comes from IVC size and collapse together, never size alone: 3 mmHg small and collapsing, 15 mmHg dilated and non-collapsing, 8 mmHg when discordant.