Doppler shift

Δf = Difference between the transmitted frequency (ft) and received frequency
v = Velocity of red blood cells
θ = Angle between the Doppler beam and the direction of blood flow
c = Speed of ultrasound in blood (1540m/sec)
Stroke volume (ml) =
Stroke Distance × Cross Sectional Area (CSA)
where
Stroke Distance = LVOT or RVOT Velocity Time Integral (VTI)
CSA = 0.785 × (LVOT or RVOT Diameter)2
Shunt ratios
Qp/Qs = SVRVOT / SVLVOT (for atrial or ventricular septal defects)
Qp/Qs = SVLVOT / SVRVOT (for patent ductus arteriosus)
Valve area by conservation of flow

Mitral valve area by pressure half-time

where
Pressure half-time is measured or calculated as 0.29 × Deceleration time
Valve area by flow acceleration

where
r = PISA radius
Regurgitant volume (ml)
Regurgitant VolumeMitral Valve = SVMitral Valve – SVLVOT
= (CSAMitral × VTIMitral) – (CSALVOT × VTILVOT)
Regurgitant VolumeAortic Valve = SVLVOT – SVMitral Valve
= (CSALVOT × VTILVOT) – (CSAMitral × VTIMitral)
Regurgitant fraction (%) =

Effective Regurgitant Orifice Area (EROA) =

OR

where
r = PISA radius
Bernoulli Equation
Pressure Difference = Convective Acceleration + Flow Acceleration + Viscous Friction
or

P1 – P2 = Pressure difference between the two locations
ρ = Mass density of blood (gm/cm3)
V1 = Velocity proximal to stenosis (m/sec)
V2 = Velocity at vena contracta (m/sec)

s = Distance over which flow accelerates
R = Viscous resistance
μ = Viscosity
v = Velocity of blood flow (m/sec)
Modified Bernoulli equation
ΔP = 4(V22 – V21)
Simplified Bernoulli equation
ΔP = 4V22
Peak instantaneous gradient =
4 × (VPeak)2
Intracardiac pressure measurements
POC = 4v2 + PRC
PRC = POC – 4v2
where
POC = pressure in the origination chamber
PRC = pressure in the receiving chamber
Right ventricular systolic pressure (RVSP) using tricuspid regurgitant (TR) jet
RVSP = 4 (VPeakTR)2 + right atrial pressure (CVP)
In the absence of pulmonic stenosis or right ventricular outflow tract obstruction, RVSP is equal to pulmonary artery systolic pressure.
Right ventricular systolic pressure in the presence of a ventricular septal defect (VSD)
RVSP = Left ventricular systolic pressure – 4 (VPeak VSD)2
Pulmonary artery mean pressures (PAMP) using pulmonary regurgitant (PR) jet
PAMP = 4 (VPeak PR)2 + right atrial pressure (CVP)
Pulmonary artery diastolic pressures (PADP) using pulmonary regurgitant (PR) jet
PADP = 4 (VEnd-diastolic PR)2 + right atrial pressure (CVP)
Pulmonary artery systolic pressure (PASP) in the presence of a patent ductus arteriosus (PDA)
PASP = Systolic blood pressure – 4 (VPeak PDA)2
Left atrial pressure (LAP) from a mitral regurgitant (MR) jet
LAP = Left ventricular systolic pressure – 4 (VPeak MR)2
In the absence of aortic stenosis or left ventricular outflow tract obstruction, systolic blood pressure can be substituted for left ventricular systolic pressure.
Left atrial pressure in the presence of a patent foramen ovale (PFO).
LAP = 4 (VPeak PFO)2 + right atrial pressure (CVP)
Left ventricular end-diastolic pressure (LVEDP) from an aortic regurgitatant (AR) jet.
LVEDP = Diastolic blood pressure – 4 (VEnd-diastolic AR)2