Echocardiography formulas

Every equation used for derived echo values, with assumptions and sources.

Body surface area (Du Bois)

BSA = 0.007184 × W^0.425 × H^0.725

W in kg, H in cm. All indexed values in this platform use Du Bois.

LV mass (linear, Devereux)

LVM = 0.8 × 1.04 × [(IVSd+LVIDd+PWd)³ − LVIDd³] + 0.6

Dimensions in cm, result in g. Index to BSA. Normal ≤115 (M) / ≤95 (F) g/m².

Relative wall thickness

RWT = 2 × PWd / LVIDd

>0.42 = concentric geometry.

Ejection fraction

EF = (EDV − ESV) / EDV × 100

Biplane method of discs. 2D inter-observer variability ±5–8 points.

Stroke volume

SV = π × (LVOT D / 2)² × LVOT VTI

The diameter is squared: 1 mm error ≈ 10% error.

Cardiac output / index

CO = SV × HR / 1000 ; CI = CO / BSA

Normal CI 2.5–4.0 L/min/m².

Simplified Bernoulli

ΔP = 4V² (full: 4(V₂² − V₁²))

Use the full form when the proximal velocity is >1.5 m/s.

Aortic valve area (continuity)

AVA = LVOT area × VTI(LVOT) / VTI(AV)

Severe <1.0 cm² or <0.6 cm²/m².

Dimensionless velocity index

DVI = VTI(LVOT) / VTI(AV)

<0.25 severe AS. Independent of LVOT diameter.

Mitral valve area (PHT)

MVA = 220 / PHT ; MVA ≈ 759 / DT

Invalid immediately after PMC, with significant AR, or with abnormal LV compliance.

PISA — EROA

EROA = 2πr² × Va / Vmax

Hemispheric assumption. Overestimates in eccentric or late-systolic MR.

Regurgitant volume & fraction

RVol = EROA × VTI(jet) ; RF = RVol / (RVol + forward SV)

Severe primary MR: RVol ≥60 mL, RF ≥50%.

Systolic PA pressure

SPAP = 4 × TRVmax² + RAP

Subtract any RVOT/pulmonary valve gradient.

Mean PA pressure

mPAP ≈ 0.61 × SPAP + 2 ; = 4 × PR(early)² + RAP

Chemla formula, or from the PR jet.

mPAP from acceleration time

mPAP ≈ 90 − 0.62 × AcT (AcT <120 ms)

Otherwise 79 − 0.45 × AcT.

PVR (Abbas)

PVR ≈ (TRVmax / RVOT VTI) × 10 + 0.16

Screening only; unreliable above about 6 WU.

RV–PA coupling

TAPSE / SPAP (mm/mmHg)

<0.55 uncoupled; <0.31 severely uncoupled.

Qp/Qs

Qp/Qs = [π(RVOT D/2)² × RVOT VTI] / [π(LVOT D/2)² × LVOT VTI]

≥1.5 = haemodynamically significant shunt.

Effective arterial elastance

Ea = ESP / SV ; ESP ≈ 0.9 × SBP

Net arterial load (resistance + compliance + reflection). Normal ≈ 2.2 mmHg/mL.

End-systolic elastance (simplified)

Ees ≈ ESP / (ESV − V₀), V₀ ≈ 0

Slope of the ESPVR: load-independent contractility. The single-beat method (Chen) is more exact.

Ventricular–arterial coupling

Ea / Ees ≈ ESV / SV

Optimal efficiency 0.5–1.0. >1.36 is associated with worse outcome in HF.

Valvulo-arterial impedance

Zva = (SBP + MG) / SVi

Global LV afterload in AS. ≥3.5 mmHg·m²/mL is associated with adverse outcome.

Systemic arterial compliance

SAC = SVi / pulse pressure

<0.6 mL/m²/mmHg = stiff arterial tree.

End-systolic meridional wall stress

σ = 0.334 × P × LVIDs / [PWs × (1 + PWs/LVIDs)]

×10³ dyn/cm². The LV afterload the myocyte actually experiences.

LV dP/dt (from MR jet)

dP/dt = 32 mmHg / Δt(1→3 m/s)

>1200 mmHg/s normal; <800 mmHg/s markedly reduced contractility.

Cardiac power output

CPO = MAP × CO / 451 (W)

<0.6 W is the strongest haemodynamic predictor of death in cardiogenic shock.

Stroke work

SW = SV × (MAP − PCWP) × 0.0136 (g·m)

The area of the PV loop, in clinical units.

Systemic vascular resistance

SVR = 80 × (MAP − RAP) / CO

dyn·s·cm⁻⁵; normal 800–1200.

LA pressure estimate

PCWP ≈ 1.24 × (E/e′) + 1.9

Population regression; wide limits of agreement. Use as a direction, not a number.

LA stiffness index

LA stiffness = (E/e′) / LA reservoir strain

>0.26 is associated with HFpEF.

PA compliance & PAPi

Cpa = RV SV / (SPAP − PADP) ; PAPi = (SPAP − PADP) / RAP

Cpa <1 mL/mmHg predicts mortality in PAH. PAPi <0.9 predicts RV failure.

Fluid responsiveness

ΔVTI (PLR) >10–15% ; IVC distensibility (PPV) >18%

PLR is valid in spontaneous breathing and AF. Distensibility applies only to passive ventilation with tidal volume ≥8 mL/kg.

Myocardial work (pressure–strain loop)

GWI = ∫ LV pressure dε (LV pressure from cuff SBP, template-shaped)

Global work index and efficiency (GWE = constructive/(constructive + wasted)); vendor-specific. NORRE GWI 1270–2428 mmHg%, GWE ≥≈91%.

Stroke volume from LVOT

SV = 0.785 × LVOTd² × LVOT VTI ; SVi = SV / BSA

Serial VTI tracks SV within a patient even if the diameter is imprecise.

PLR fluid-responsiveness test

ΔVTI = (VTI after PLR − VTI before) / VTI before

≥10–15% predicts a rise in cardiac output with fluid; assess within 60–90 s.