(Circulation. 2000;102:1053.)
© 2000 American Heart Association, Inc.
Basic Science Reports |
The Power-Velocity Integral at the Vena Contracta
A New Method for Direct Quantification of Regurgitant Volume Flow
From the Cardiac Ultrasound Laboratory (T.B., R.A.M., M.D.H., R.A.L.), Cardiovascular Surgical Unit (J.L.G.), and Cardiac MRI Unit (G.H.), Massachusetts General Hospital, Harvard Medical School, Boston.
Correspondence to Robert A. Levine, MD, Cardiac Ultrasound Laboratory, Massachusetts General Hospital, VBK 508, Boston, MA 02114. E-mail rlevine{at}partners.org
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Abstract |
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Background—Noninvasive quantification of regurgitation is limited because Doppler measures velocity, not flow. Because backscattered Doppler power is proportional to sonified blood volume, power times velocity should be proportional to flow rate. Early studies, however, suggested that this held only for laminar flow, not for regurgitant jets, in which turbulence and fluid entrainment augment scatter. We therefore hypothesized that this Doppler power principle can be applied at the proximal vena contracta, where flow is laminar before entrainment, so that the power-times-velocity integral should vary linearly with flow rate and its time integral with stroke volume (SV).
Methods and Results—This was tested in vitro with steady and pulsatile flow through 0.07- to 0.8-cm2 orifices and in 36 hemodynamic stages in vivo, replacing the left atrium with a rigid chamber and column for direct visual recording of mitral regurgitant SV (MRSV). In 12 patients, MRSV was compared with MRI mitral inflow minus aortic outflow and in 11 patients with 3D echo left ventricular ejection volume–Doppler aortic forward SV. Vena contracta power in the narrow high-velocity spectrum from a broad measuring beam was calibrated against that from a narrow reference beam of known area. Calculated and actual flow rates and SV correlated well in vitro (r=0.99, 0.99; error=-1.6±2.5 mL/s, -2.4±2.9 mL), in vivo (MRSV: r=0.98, error=0.04±0.87 mL), and in patients (MRSV: r=0.98, error=-2.8±4.5 mL).
Conclusions—The power-velocity integral at the vena contracta provides an accurate direct measurement of regurgitant flow, overcoming the limitations of existing Doppler techniques.
Key Words: echocardiography • regurgitation • mitral valve • blood flow
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Introduction |
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Valvular regurgitation, at times life-threatening, is common in virtually all heart diseases. Accurate regurgitant volumes are critical to guide therapy, especially now that valve repair is widely available and favors early intervention before functional deterioration.1 Current noninvasive techniques cannot measure regurgitant flow rate directly at the lesion,2 3 4 5 6 7 which requires the product of velocity and orifice area: Velocityxarea=flow rate.
Doppler measures velocity, but orifice area is unknown and often varies throughout the regurgitant flow period.8 9
To overcome this limitation, we developed a new approach using the
backscattered acoustic power from the Doppler signal10
to provide the area information we
need: Velocityxpower
flow rate.
Backscattered power returning to the ultrasound transducer
is a nonlinear function of hematocrit, resulting from constructive and
destructive interference of sound waves returning from scatterers
within the Doppler sample volume.11 12 13 For blood of a
given hematocrit, however, flowing through a thin disk-like sample
volume of fixed height, backscattered power in the Doppler spectrum
of flow velocities is linearly proportional to the blood volume of
moving scatterers and therefore will be linearly proportional to the
cross-sectional area (CSA) of flow within the beam14 15 : a
flow with twice the CSA, and therefore twice the volume of
moving scatterers within the sample volume, will return Doppler
signals with twice the power, so long as the areas all lie within the
Doppler beam (Figure 1
).
Backscattered power from nonmoving or stagnant blood within the sample
volume but outside the flow CSA does not contribute to the power in the
Doppler spectrum from rapidly moving blood. Backscattered power
therefore has the potential to provide the CSA information we need to
calculate flow rate.
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Because backscattered power also depends on round-trip attenuation of sound and backscattering coefficient (backscattered power/volume, a function of hematocrit),12 13 these power measurements must be calibrated in the same individual against power returning from a beam of known CSA that lies entirely within flow at the same depth as the pathological flow of interest: The hematocrit, backscattering coefficient, and attenuation are the same, so that any changes in Doppler power should relate to changes in the CSA of flow within the beam.15
It has long been assumed that this principle holds only for laminar
flow, such as that in blood vessels,15 and cannot be
applied to regurgitant jets because, for a given flow rate,
backscattered power is increased by turbulent
eddies11 13 16 and fluid entrainment into the
jet.17 18 Regurgitant flow, however, is laminar, not
turbulent, at the proximal vena contracta, the smallest jet CSA, where
velocity is highest (Figure 2).5 6 17 19 Therefore, we
proposed the new hypothesis that mitral regurgitant (MR) flow can be
quantified directly at the vena contracta, where flow is laminar before
entrainment. At this site, identified by a narrow velocity spectrum
corresponding to laminar flow, total backscattered power integrated
over the velocity spectrum should be linearly proportional to the vena
contracta CSA: Jet CSA
velocity power (at
velocity v) dv, or the power integral (PI).
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Flow rate Q equals vena contracta area times velocity; therefore,
power times velocity, integrated over the vena contracta velocity
spectrum, should be proportional to regurgitant flow rate:
Qvelocity power (at velocity v) vdv, or
the power-velocity integral (PVI).
Finally, the time integral of power times velocity should be
proportional to regurgitant stroke volume:
RSV=time Q (at each time t) dt, or the
power-velocity-time integral (PVTI).
We tested this method in vitro; in vivo with a new model providing a direct regurgitant volume gold standard; and in initial patient applications, with calibration to provide clinically useful absolute flow values.
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Methods |
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In Vitro Studies
Flow was driven from a Plexiglas left ventricle (LV)-simulating chamber (5.7-cm diameter) through an orifice 10 cm from the ultrasound transducer (typical mitral depth) to a left atrium (LA)-simulating chamber (Figure 2
). Circular orifice areas of 0.2, 0.5, and 0.8
cm2, corresponding to mild to severe clinical
lesions, were studied at 5 steady flow rates from 20 to 60 mL/s from a
piston pump that minimized cavitation (modified Mark IV Power-injector,
Medrad), and with 4 parabolic pulses of 20 to 70 mL from syringe
injections; a 0.07-cm2 orifice was also studied
at 20-mL/s flow. Microbubble generation by the orifice pressure drop in
blood or surfactant-containing analogues was resolved by use of
degassed distilled water and 19% glycerol (specific gravity, 1.043
g/cm3); adding 48 600 polystyrene
microspheres/mL (25.2-µm diameter; Duke Scientific) produced
a backscattering coefficient equivalent to that of human
blood.20
In Vivo Experimental Studies
We developed a new canine model to measure MR volume directly
without flowmeters (Figure 3).21 In adult dogs (20 to
25 kg) anesthetized with 30 mg/kg IV sodium pentobarbital and
ventilated, a nondistensible LA chamber was sutured to the mitral
annulus via a Dacron sewing ring, and the atrial walls were sutured
tightly around it. This chamber was directly attached to a
1.0-cm-diameter column within which MR stroke volume (MRSV) produced a
vertical fluid excursion with each systole that was videotaped and
measured (1.3 cm=1 mL). With right heart bypass, all venous return was
collected, and the oxygenated blood was pumped via a
reservoir and wide-bore cannula into the LV through a 1-way valve. A
total of 36 different hemodynamic stages were
analyzed in 3 dogs with regurgitant orifices of 0.12 to 0.21
cm2 cut into the anterior leaflet, and afterload
was changed by aortic clamping.
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Patient Studies
Initial clinical applications involved 23 patients with MR with
a range of severity and etiologies
(Table), including eccentric jets,
studied from a transthoracic apical approach with at least
fair to good image quality. In 12 patients (age, 52±17 years; 9 male,
3 female), MRSV by Doppler power was compared with mitral inflow
minus aortic outflow MRI (see below) obtained within 30 to 60 minutes
of Doppler.
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A second group of 11 patients (age, 65±13 years; 8 male, 3 female) had MRSV calculated from 3D echo LV ejection volume (see below) minus forward aortic stroke volume derived from LV outflow tract CSA times the integral over time of power-weighted mean velocity to account for the sampled velocity spectrum.22
Doppler Methods
In all studies, the 2.5-MHz transducer (1.8-MHz Doppler) of
a Hewlett-Packard 5500 scanner was used to record velocities up to
800 cm/s with high pulse repetition frequency Doppler from a thin
sample volume (0.35 cm) placed in the vena contracta to record the
narrowest high-velocity spectrum just beyond the orifice. To prevent
signal reduction at low flow rates, a low wall filter (200 Hz, or 
8
cm/s) was used. Compress, reject, transmit power, receive gain, depth,
and velocity range settings were kept constant in the in vitro series
and within each patient and animal.
Power-Velocity Analysis
Digitally recorded Doppler video display intensities,
nonlinearly compressed, were reconverted to their original uncompressed
acoustic amplitudes and power (amplitude squared) on the basis
of the acquisition compress and reject settings. Power and power times
velocity were then integrated over all velocities in the narrow vena
contracta velocity spectrum (Figure 4) at
each time point with MATLAB software (Version 5.1, MathWorks).
Steady-flow power and power-velocity integrals (PI and PVI) were
averaged over the recorded time samples (200 to 350x4.9
ms/line). Pulsatile-flow PVI was integrated over time to obtain the
PVTI.
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Doppler Beam Size
The entire 1.2x2.0-cm transducer aperture produces an estimated
sample volume of 3.1-mm lateralx5.2-mm elevation dimension at 10 cm
based on half-maximum-power beam width.23 To encompass
larger jets, we created a broad distal measuring beam by reducing the
transducer aperture with a Tyvek (Dupont) mask (Figure 5). In vitro, a 7-mm-diameter circular
aperture increased beam width to 6.75 mm (circular
0.36-cm2 CSA); in vivo, a larger (10-mm) aperture
was used to record weaker signals (beam width=5.8 mm, CSA=0.26
cm2).
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Power Calibration
Calibration converts unitless power to absolute areas and
accounts for the variation in backscattered power among individuals for
the same blood volume due to different attenuation and backscattering
coefficients.13 We calibrated power from the broad
measuring beam encompassing the vena contracta using a narrow reference
beam placed within the flow area (Figure 5).15 24
The reference beam provides the ratio between power and area because
its CSA is known. We then applied this calibrating ratio to the power
from the broad measuring beam to determine the CSA of flow within the
beam. Ultrasound attenuation and backscattering coefficient are the
same for both beams and cancel out, compensating for individual
differences.
The power received from the measuring beam
(PImeas), with its reduced transducer aperture,
must be multiplied by a correction factor (CF) to compensate for the
decrease in transmitted and received power compared with the reference
(ref.) beam, which uses the full aperture:
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Magnetic Resonance Imaging
MRSV was obtained as mitral inflow minus aortic outflow with a
1.5-T system (GE Signa). Phase contrast cine acquisitions were obtained
in planes aligned with the mitral annulus and orthogonal to the mid
ascending aorta.25 Phase velocity maps were integrated
over the appropriate flow areas, integrated over time, and
subtracted.
3D Echocardiography
In the second patient group, LV volumes were calculated with a
polyhedral surfacing algorithm26 from reconstructed
endocardial borders in 10 rotated apical views collected with a
transthoracic Omniplane probe (Hewlett-Packard) with ECG
and respiratory gating.
Statistical Analysis
Doppler power results (PI, PVI, and PVTI) were compared with
reference values (CSA, flow rate, and volume) by linear regression.
Agreement was assessed by plotting differences against reference values
(or, in patients, the mean of calculated and reference
values),27 comparing mean differences with zero by
t test.
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Results |
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In Vitro Studies
The PI was linearly proportional to regurgitant orifice area (ROA) up to and including 0.5 cm2 (Figure 6A
, left-hand axis, r=0.99);
the area of 0.8 cm2, which is clinically
extreme,28 was incompletely assessed with current
beam size and was not included in the regression. With dual-beam
calibration of PI to ROA
(ccal=8.9x10-4,
right-hand axis), regression gave
y=0.84x+0.01cm2,
SEE=0.01cm2, with good agreement between
calculated and actual ROA <0.8 cm2 (Figure
6B; mean difference=-0.04±0.03 cm2,
P<0.0001); slight underestimation was evident at 0.2 and
0.5 cm2, as expected for Doppler (effective)
versus anatomic orifice area.29 Figure 6C
shows that the narrow reference beam fit within all the orifices used
and therefore returned the same power regardless of orifice area and
flow rate over 32 combinations studied.
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For the 0.07-, 0.2-, and 0.5-cm2 orifices,
steady flow rates calculated from PVI correlated and agreed well with
actual values (Figure 7;
y=0.95x+0.21 mL/s, SEE=2.5 mL/s), with a mean
difference of -1.6±2.5 mL/s (P=0.001 versus 0); as before,
there was underestimation for the 0.8-cm2
orifice. Similar correlations and agreement were observed for the 72
pulsatile stroke volumes studied (Figure 8; y=0.92x+1.3 mL,
SEE=2.6 mL, mean difference=-2.44±2.9 mL, P<0.0001).
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The results, for example, showed that the PI remained virtually constant (1.5x104 to 1.6x104 in unitless values) for a constant ROA of 0.2 cm2 as flow rate varied from 20 to 40 and 60 mL/s; conversely, the PVI increased from 1.8x106 to 3.6x106 to 5.3x106 in proportion to flow rate.
In Vivo Experimental Studies
Calculated MR stroke volume correlated and agreed well with
directly measured values of 4 to 21 mL (Figure 9; y=0.98x+0.28 mL,
r=0.98, SEE=0.89 mL, mean difference=0.04±0.87 mL,
P=0.79 versus 0). Because Ref. Beam CSA was known and CF was
determined in vitro, only reference and measuring beam powers needed to
be measured in vivo to obtain absolute flow values.
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Patient Studies
In all patients, a satisfactory high-velocity narrow-spectrum
Doppler signal could be recorded. In the primary 12 patients
studied by MRI, calculated regurgitant stroke volume correlated and
agreed well with MRI values (Figure 10;
r=0.98, y=0.70x+3.5 mL, SEE=2.4 mL,
mean error=-3.6±5.1 mL, P=0.03); calculated values, in
fact, lay close to the line of identity for regurgitant stroke volumes
up to 40 mL (r=0.99, y=0.87x+1.2 mL,
SEE=1.3 mL, mean error=-1.0±1.8 mL, P=0.13
[P=NS versus 0]), with mild underestimation only at higher
values (ROA>0.5 cm2), consistent with
the mild potential underestimation due to currently limited beam size,
as shown in vitro (Figures 6 to 8). Results were
comparable when the secondary patient group (MRSV from LV ejection
volume minus aortic forward flow) was added (n=23; r=0.98,
y=0.71x+3.5 mL, SEE=1.9 mL, mean error=-2.8±4.4
mL, P=0.01); for MRSV up to 40 mL (ROA<0.5
cm2), values lay close to the line of identity
(n=19, r=0.97, y=0.81x+2.1 mL, SEE=1.6
mL, mean error=-1.1±2.2 mL, P=0.05). Figure 11 (top) shows an example of the
high-velocity spectral recording in a patient.
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Discussion |
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Many noninvasive ultrasound measures of regurgitant volume are limited by indirect measurements,30 31 multiple steps prone to error,7 32 and limiting assumptions about regurgitant flows.3 4 33 34 35 To overcome these limitations, we introduced the new concept of integrating Doppler power times velocity at the proximal vena contracta, directly measuring regurgitant flow at the lesion itself. The results demonstrate that at the vena contracta, where flow is laminar before entrainment, jet CSA is linearly proportional to the Doppler PI, regurgitant flow rate to the PVI, and regurgitant stroke volume to the power-velocity time integral. A dual-beam approach compensates, in each individual studied, for attenuation and variations in hematocrit, providing clinically useful absolute values.
This approach has the major advantage of integrating the contribution
of scatterers at all velocities within the vena contracta without
simplifying assumptions about its shape or velocity distribution. It
also simplifies measurement by obviating the need to measure CSA by 2D
echo. Unlike other, single-time-point methods, power-velocity directly
assesses and integrates dynamic variations in ROA and flow rate, as
shown in Figure 11, bottom left: a patient with a dilated LV
shows the characteristic midsystolic decrease in ROA described
in such patients,8 and this variation is automatically
incorporated into the PVI to give flow rate and volume. Finally, this
approach should be relatively immune to variations in the Doppler
beam–to-flow angle 
: the cos decrease in measured velocity is
canceled by a reciprocal increase in CSA relative to the beam, and any
variations in attenuation with angle are dealt with by the dual-beam
calibration (T.B., unpublished data, 1999).
Previous Work
Previous studies used backscattered power to average
amplitude-weighted velocities over a CSA, multiplying by area to
estimate flow.22 36 37 38 39 Other studies used the PVI but
only in low-velocity laminar flows, precluding direct assessment of
regurgitation.24 40 Continuous-wave
Doppler studies of the entire regurgitant jet, including turbulent
and entrained flow, demonstrated highly variable relations between
regurgitant volume and signal intensity.41 42 43 The
present approach, in contrast, examines only the laminar vena
contracta to evaluate regurgitant flow most directly.
Current Limitations and Future Application
Although the technique requires some understanding of flow through
a restrictive orifice, this is similarly required for application of
the simplified Bernoulli equation, part of routine clinical practice.
This approach simplifies the measurement process because no separate 2D
echo measure of CSA is required, and dynamic variations in ROA are
incorporated automatically. The approach lends itself to the simplified
application we envision in Figure 11: First, the Doppler
sample volume is placed just beyond the regurgitant orifice, which can
be guided by visualizing the narrowest point of the jet by use of
Doppler color flow mapping; the narrowest high-velocity signal is
then optimized. This requires skills comparable to those for localizing
the highest jet velocities for the simplified Bernoulli equation, which
sonographers routinely do. Second, the spectrum can be analyzed
automatically on board the machine itself, without the offline
analyses we performed with the available system: power within
the high-velocity Doppler spectrum can be directly extracted before
conversion to display intensities to calculate PI, PVI, and PVTI and
output regurgitant area, flow rate, and volume.
Although we had to vary transducer apertures manually to provide measuring and calibrating beams, that can be achieved more easily with electronic aperture variation. Indeed, both beams can in principle be generated simultaneously by connecting the transducer elements to 2 independent digital beam-forming processors, providing measurement and calibration in a single cardiac cycle. Also, because calibration, for a given patient and depth, relates power to the CSA of moving blood independent of velocity, the calibration beam can be formed only in diastole, with the measuring beam in systole (T.B., unpublished data, 1999).
The main limitation, then, would be that currently available beams are not wide enough to sample the most severe regurgitant jets (>0.5 cm2); however, that reflects current basic transducer design, which optimizes spatial resolution and can be remedied with newer transducers under development.
It should be emphasized that although calibration corrects for attenuation and backscattering coefficient for each patient, the correction factor relating calibrating and measuring beam power on the basis of their different apertures is fundamentally a physical result of transducer design and therefore needs to be determined only by the manufacturer in vitro for each system design, not for each patient. Our results support this, because 1 aperture-correction factor provided consistent agreement between power-velocity and actual values across several animals, with similar results for the transducer apertures and correction factor used across multiple patients.
Finally, although this approach was tested in MR, it should potentially be applicable to a wide range of regurgitant, stenotic, and shunt lesions.
Conclusions and Clinical Implications
The integral of Doppler power times velocity at the
regurgitant vena contracta is a new, noninvasive approach that for the
first time accurately measures regurgitant flow directly at the lesion
itself. Because only information contained in the Doppler spectrum
itself is required, this approach can potentially be readily automated
for future routine clinical application. Such quantification
would improve our evaluation of lesion severity and progression to
guide patient interventions and test their ability to preserve
ventricular function.
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Acknowledgments |
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This study was supported in part by grants HL-38176 and HL-57302, National Institutes of Health, Bethesda, Md. Dr Buck was supported by grant Bu1097/1-1, Deutsche Forschungsgemeinschaft, Bonn, Germany. The Mark IV Powerinjector was provided by Geoff A. Morris, Medrad, Inc, Indianola, Pa. We thank Randall Grimes, MD, PhD, for his invaluable fluid dynamics comments and Iain D. Wright and Arnold J. George (Biomedical Engineering) for constructing the flow model.
Received December 31, 1999; revision received March 23, 2000; accepted March 29, 2000.
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