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Departments of 1 Cardiology and 2 Thoracic and Cardiovascular Surgery, Cardiovascular Imaging Center, The Cleveland Clinic Foundation, Cleveland, Ohio 44195
The simplified
Bernoulli equation relates fluid convective energy derived from flow
velocities to a pressure gradient and is commonly used in clinical
echocardiography to determine pressure differences across stenotic
orifices. Its application to pulmonary venous flow has not been
described in humans. Twelve patients undergoing cardiac surgery had
simultaneous high-fidelity pulmonary venous and left atrial pressure
measurements and pulmonary venous pulsed Doppler echocardiography
performed. Convective gradients for the systolic (S), diastolic (D),
and atrial reversal (AR) phases of pulmonary venous flow were
determined using the simplified Bernoulli equation and correlated with
measured actual pressure differences. A linear relationship was
observed between the convective (y) and actual
(x) pressure differences for the S (y = 0.23x + 0.0074, r = 0.82) and D
(y = 0.22x + 0.092, r = 0.81) waves, but not for the AR wave (y = 0.030x + 0.13, r = 0.10). Numerical modeling resulted in similar slopes for the S (y = 0.200x
0.127, r = 0.97), D
(y = 0.247x
0.354, r = 0.99), and AR (y = 0.087x
0.083, r = 0.96) waves. Consistent with numerical modeling,
the convective term strongly correlates with but significantly
underestimates actual gradient because of large inertial forces.
pulmonary veins; echocardiography; fluid dynamics; numerical modeling
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