Appendix E. Measurements and Calculations

Fractional shortening (%) =

Velocity of circumferential fiber shortening (circ/sec) =

fractional shortening × ejection time

Fractional area change (%) =

Ejection fraction (%) =

Volume by Simpson's method of disks where the LV is modeled as a series of stacked cylindrical disks capped by an elliptical disk apex

Volumecylindrical disks = (π × D1/2) × D2/2) × H

where D1 and D2 are orthogonal diameters of the cylinder, and H is the height of the cylinder

and

Volumeelliptical disk = Ah/2 + a2/b2 × π × h3/6

where A is the area of the ellipsoid segment, h is the height of the ellipsoid segment, and a and b are radii of the total ellipsoid.

Volume by the area-length method where the LV is modeled as acylinder–hemi-ellipsoid

Volume = (5 × area × major-axis length)/6

where the area is planimetered by using a short-axis view at the level of the mitral valve

Volume by the diameter-length method where the LV is modeled as a prolate-ellipsoid

Volume = (π × D1 × D2 × major-axis length)/6

where D1 and D2 are orthogonal short-axis diameters

Stroke volume (ml) =

(end-diastolic volume – end-systolic volume)

Cardiac output (liters/min) = (stroke volume × heart rate)

Cardiac index (liters/min/m2) =

Meriodinal wall stress

where P represents LV peak pressure, Ac is LV cavity area, and Am represents LV myocardial area (area of the muscle in the short-axis view)

Circumferential wall stress

where L represents the LV long-axis length

Strain (%) =

where length0 is the initial length

Strain rate (s–1) =

LV mass (g) =

(1.04 × [(LVID + PWT + IVST)3 – LVID3]) × 0.8 + 0.6

dP/dt (mm Hg/s) =

32 × 1000/dt

where dt (in msec) is the time for velocity to rise from 1 m/s to 3 m/s on a continuous wave Doppler tracing of mitral regurgitation

Myocardial performance index =

Fractional area change (%) =

Ejection fraction (%) =

using Simpson's method of disks

Tricuspid annular plane systolic excursion (mm) From the transgastric RV inflow view and using M-mode, the movement of the leading edge of the lateral tricuspid annulus attachment is tracked during systole, and its excursion measured

Myocardial performance index =

dP/dt (mm Hg/s) =

12 × 1000/dt

where dt (in msec) is the time for velocity to rise from 1 m/s to 2 m/s on a continuous wave Doppler tracing of tricuspid regurgitation

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