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(Circulation. 1995;92:579-586.)
© 1995 American Heart Association, Inc.
Articles |
A New Control Volume Method for Calculating Valvular Regurgitation
From Department of Thoracic and Cardiovascular Surgery and MR Centre, Institute of Experimental Clinical Research, Aarhus University Hospital (S.O., E.M.P., K.H.), Skejby Sygehus, Aarhus, Denmark; and School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Ga.
Correspondence to Peter G. Walker, PhD, Cardiovascular Fluid Mechanics Laboratory, School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0100.
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Abstract |
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 Top Abstract IntroductionMethods Results Discussion References |
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Background The purpose of the present study was to develop a new method of measuring heart valvular regurgitation based on control volume theory and to verify its accuracy in vitro and in vivo. Current methods of quantifying valvular regurgitation rely too much on assumptions about the flow field and therefore are difficult to apply in vivo. In particular, the proximal isovelocity surface area (PISA) method oversimplifies the proximal velocity field by assuming hemispherical isovelocity contours proximal to the orifice. This severely limits the applicability of the PISA method. Use of the basic control volume theory, however, removes the need to assume the manner in which the proximal flow accelerates toward the regurgitant orifice, the shape and size of the orifice, the shape of the orifice plate, and the non-newtonian behavior of the fluid. Apart from a correction that is necessary if the orifice plate is moving, the control volume method assumes only the incompressibility of the fluid and therefore is a potentially more accurate approach. In addition, the use of magnetic resonance imaging (MRI) precludes the need for an acoustic window.
Methods and Results MRI has been used to measure the three-dimensional velocity field proximal to regurgitant orifices, including single and multiple orifices and a cone-shaped orifice plate. Both steady (0 to 7.5 L/min) and pulsatile (2 and 3 L/min) flows were used. By integrating this velocity over a control volume surrounding the orifice, we calculated the flow rate through the orifice. As a validation, the cardiac output of a 50-kg pig also was measured and was compared with thermodilution measurements. It was found that MRI could be used to measure the three-dimensional flow proximal to regurgitant orifices. This enabled the calculation of the flow rate through the orifice by integrating the velocity over the surface of a control volume covering the orifice. This flow rate correlated well with the actual flow rate (0.992; correlation line slope, 1.01). Care had to be taken, however, to exclude from the integration regions of aliased velocity. The cardiac output of the pig measured using MRI was in close agreement with the thermodilution measurements.
Conclusions Our new method of measuring valvular regurgitation has been shown to be very accurate in vitro and in vivo and therefore is a potentially accurate way to quantify valvular regurgitation.
Key Words: valves • regurgitation • magnetic resonance imaging
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Introduction |
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TopAbstractIntroductionMethods Results Discussion References |
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Traditional invasive angiographic methods of quantifying valvular regurgitation grade the disorder on a scale of 1 to 4. Although adequate for some applications, there is a need for a more accurate, truly quantitative, and noninvasive measurement procedure. This has led to the development of the jet momentum1 2 3 4 and proximal isovelocity surface area (PISA) methods,5 6 7 8 9 which are based on basic fluid mechanics principles. The application of these techniques, however, requires a simplification of the flow field to be valid, with the result that their use in the human heart is limited. In particular, a disadvantage of the PISA method is the assumption that the isovelocity contours are hemispherical proximal to the regurgitant orifice. In the complex flow fields that are found in the heart, it is clear that this assumption is severely limiting. Another approach to quantifying regurgitation has been through the use of magnetic resonance imaging (MRI).10 With a cross-sectional image through the aorta and measurement of the through-plane velocity, the flow curve in the aorta can be measured. It has been suggested that integrating the diastolic section of the aortic flow curve over time provides the regurgitant volume through the aorta. Unfortunately, the reverse flow in the aorta during diastole is also dependent on the coronary flow rate and the contraction of the aortic walls, making the regurgitant flow rate measured this way inaccurate. In addition, this method cannot be used to measure mitral regurgitation because the aortic outflow will be included in the regurgitant flow rate integration. We therefore propose a new method to quantify heart valvular regurgitation that is not based on assumptions about the fluid dynamics of the flow and will not be affected by compliant wall motion or secondary blood flow. We present the theory of this new method and demonstrate its accuracy in a simplified in vitro model.
The method presented in the present study is based on control
volume theory and continuity. A control volume is any three-dimensional
closed imaginary surface in a flow field. Continuity states that matter
cannot be created or destroyed; therefore, the flow into a control
volume must equal the flow out of the control volume. Take, for
example, a simple pipe flow (Fig 1
). With a control
volume outlined by the lines ABCD, it can be seen that the flow through
face AB must equal the flow through face CD because there can be no
loss of fluid from the pipe between these surfaces. The flow rate
through the surface of the control volume is calculated by integrating
the velocity normal to the surface over the entire surface. When
calculating the flow rate, however, it is necessary that the velocity
perpendicular to the surface be integrated because the other velocity
components do not pass through the control volume surface and therefore
cannot contribute to the flow out of or into the control volume. This
is a very important consideration as it is the limiting factor in the
usefulness of the much-touted PISA method. Fig 2
demonstrates this by showing a schematic application of control volume
theory as it applies to the PISA method using Doppler ultrasound. With
the PISA method, the surface of the control volume is defined as a
hemisphere centered on the orifice with the flat side of the hemisphere
coincident with the plate. Control volume theory applied to this
surface dictates that the net flow through the curved part of the
hemisphere is equal to the flow through the orifice and therefore is
the regurgitant flow rate. Doppler ultrasound cannot, however, be used
to measure the velocity normal to this surface, which is needed to
calculate the true flow rate, so the normal velocity is assumed to be
constant over the control volume surface. The surface therefore is an
isovelocity contour. With this assumption, it is only necessary to
measure the velocity at a single location on the control volume surface
to calculate the flow rate. Unfortunately, the velocity over the
control volume surface is not always constant, making this assumption
invalid and the calculated flow rate wrong. From Fig 2, it can
be seen
that this hemispheric isovelocity assumption is made because Doppler
ultrasound can be used only to measure a single velocity component
(toward the transducer), making it impossible to measure the necessary,
perpendicular velocity over the control surface without moving the
ultrasound transducer. To circumvent this limitation, we used MRI phase
velocity encoding to measure the fluid velocity. MRI is more
advantageous in this respect, because it can measure all three
components of the velocity. The MRI signal is obtained from a Fourier
transform as a complex number with the normal, angiographic image that
is commonly used to study anatomy being the modulus of this complex
number. The velocity is obtained by performing a scan by which the
phase of the complex number is proportional to the velocity. In this
way, from a single MRI scan, both the anatomic and velocity images can
be obtained. The velocity is measured in each voxel in the MR image,
and each velocity component is measured individually, so that the
vertical, horizontal, and through-plane velocities are separate images.
In vitro11 12 studies have validated the accuracy of
MRI
velocity measurement by comparison to computational13
results and laser Doppler anemometry.14 The applicability
of MRI velocity measurements in vivo has been demonstrated and the
accuracy of the measurements verified by comparison to
ultrasound.15 16 17 In addition, MRI was
used to measure the
flow in the coronary arteries by taking measurements in the aorta using
a similar MRI technique,18 demonstrating that it is
possible to accurately locate MRI slices in the ascending aorta and
obtain velocity measurements. To account for cardiac motion and the
pulsatility of the flow, a number of MR images are obtained per
heartbeat. These are approximately 20 to 30 milliseconds apart and are
synchronized with the heartbeat by triggering the acquisition of data
from the patient's ECG. The timing is dependent on machine parameters
such as voxel size but remains essentially within this range. With
these MRI data, the need for an assumed shape for the control volume is
removed. Any shaped control volume could be used because the velocity
component normal to the control volume surface can always be calculated
from the three separate velocity components. To simplify the
calculation, however, it is easier to take a control volume that fits
the data structure. Therefore, a rectangular control volume is used
(Fig 3). The flow rate through the control volume now is
simply an integration of the horizontal velocity through the side walls
and the vertical velocity through the top wall. Extending this to three
dimensions (Fig 4), a rectangular control volume is
constructed around the orifice by obtaining a number of adjacent MRI
slices. In this case, the flow through the MRI slices at the ends of
the control volume also must be included in the integration. This final
integration then equals the flow through the regurgitant orifice.
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The great advantage of this approach to quantifying valvular regurgitation is that the only assumption made is the obviously correct one of incompressible flow. The method is independent of the spacial variation of the proximal velocity, the size and shape of the orifice, the geometry of the orifice surface, and the non-newtonian behavior of the fluid. One problem does arise, however, if the orifice plate is moving, as may be the case in mitral regurgitation. In this case, the velocity of the plate must be subtracted from the measured fluid velocity for the correct flow rate to be calculated. Apart from this adjustment, the only limiting factor in the precision of the control volume method is the accuracy to which the velocity variation over the surface of the control is measured.
The purpose of the present study was to perform in vitro and in vivo testing of this new method using MRI.
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Methods |
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TopAbstractIntroductionMethods Results Discussion References |
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Flow Phantom
The construction of the flow phantom is shown in Fig 5
. Three sets of orifice/plate geometry were used to
create variations in the proximal flow field; these were (1) flat plate
with a single orifice (two diameters of 6.35 and 12.7 mm); (2) flat
plate with three orifices (diameters of 3 mm) placed at the apexes of
an equilateral triangle and designed to create asymmetries in the
proximal flow field; and (3) cone-shaped plate (half-angle of 45°,
height of 22 mm) with a single orifice (diameter of 4 mm) at the apex.
For each of these variations in geometry, a range of steady flow rates
was used (Table), generated by a steady flow pump. In
addition, for the three-hole geometry, two pulsatile flow rates were
used, generated by a Harvard pump at a rate of 62 beats per minute
(Table). Flow rates were measured using either an ultrasonic
transit
time flow probe (T208 Transonic Systems, Inc) placed outside the
magnetic scanner room or the stopwatch-and-bucket method. The orifice
plates were constructed as one side of an open-ended Plexiglas box
placed inside another Plexiglas box (Fig 5). The inlet to the
phantom
was located between the two boxes, behind the orifice plate. This
design was used to provide smooth, disturbance-free flow in the region
close to the orifice. The outlet to the phantom was facilitated by a
pipe connected to the distal side of the orifice plate. The entire
phantom was filled with water containing copper sulfate to provide
sufficient signal strength.
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MRI Parameters
Seven adjacent MR images or slices were
obtained perpendicular
to the orifice plate (Fig 4
). The central slice was centered on
the
orifice. Within each slice, the vertical, horizontal, and through-plane
velocities were measured using the FLAG (flow-adjusted gradient) pulse
sequence running on a 1.5-T Philips Gyroscan S15/HP
system.19 Other MRI parameters were two signal averages,
25.8-millisecond repetition time, 45° flip angle, and 12-millisecond
echo time. The thickness of the slices was 5 mm with a pixel resolution
of 2x2 mm. Like Doppler ultrasound, MRI velocity measurements have an
aliasing velocity, and wraparound can occur. For these experiments, the
maximum velocity was set at ±20 cm/s. For the pulsatile flow
sequences, 31 images or phases were obtained covering the flow
beat.
Animal Experiments
Measurements were performed on a 50-kg pig
(mixed Danish
landrace and Yorkshire) anesthetized with a continuous intravenous
infusion of pancuronium, fentanyl, and ketamin and ventilated with a
nonmagnetic pressure-driven ventilator (frequency, 14
min-1). The pig was placed in the supine position in the
MR scanner, and a surface ECG was attached. Apart from the aliasing
velocity, which was increased to 1.4 m/s to measure the aortic forward
flow, the same MR parameters listed above for the in vitro experiments
were used, with the imaging being triggered from the r wave of the ECG.
Twenty-two images were obtained per heartbeat, with 28 milliseconds
between each image. From initial scout images, the position of the
pig's aorta was located, and the velocity was measured in a slice
perpendicular to the ascending aorta. Thermodilution was performed to
measure the cardiac output before and after MRI. Three measurements
were performed at each time. A Sirecust system (model 961, Siemens)
with a 7F Swan-Ganz catheter was placed in the pulmonary artery and
used to inject a 10-mL bolus of physiological saline at 0°C.
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Results |
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TopAbstractIntroductionMethods Results Discussion References |
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Qualitative Results
The radial and axial (see Fig 3
for definitions) MRI-measured
velocity images for the central slice, obtained by cutting through the
orifice of the flat plate with a single orifice, are shown in Fig
6 as gray-scale images and in Fig 7 as
contour plots. The axial velocity figures (Figs 6A and
7A) show the
acceleration of the flow from the inlet at the top of the figures
toward the orifice at the bottom. The axial velocity
represented in these images is zero at the orifice plate
(the flow does not flow through the plate). The contour lines therefore
do not extend all the way down to the orifice plate, giving them a
mushroom shape. As mentioned, the MRI velocity aliases in the same way
as Doppler ultrasound. The position of this alias is clearly seen by
the sharp change from white to black in the gray-scale image and the
concentration of lines in the contour plot. Note that only positive,
nonaliased contour lines are shown for clarity. The radial velocity
(Figs 6B and 7B) shows the acceleration of the
fluid from the two sides
of the proximal chamber horizontally toward the orifice. This gives the
figures a double-lobe–like appearance. In this case, as the velocity
is defined as positive from left to right, the lobe on the left of the
orifice is positive (white, Fig 6B) and that on the right is
negative
(black, Fig 6B). Close to the plate, the fluid has an almost
totally
horizontal velocity. As a result, very high magnitudes are reached, and
aliasing occurs in each of the lobes. The two aliased regions are
different colors because the flow on the left aliases from positive to
negative 20 cm/s, whereas the flow on the right aliases from negative
to positive 20 cm/s.
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By combining the two velocity component images, a
vector plot can be
made that provides better visualization of the flow field (Fig
8). For clarity, all aliased velocities have been
excluded from this image. The figure illustrates well the convergence
of the fluid directed toward the orifice and is a good example of
proximal acceleration. The increase in magnitude of the vectors shows
the acceleration of the fluid toward the orifice.
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Quantitative Results
To quantify the flow rate, an imaginary
box or control volume was
placed proximal to the orifice and the normal velocity was integrated
over its surface (Figs 3 and 4). In practice,
this corresponds to no
more than a simple summation. In performing this integration, the
choice of control volume size is arbitrary and in theory should not
affect the resultant flow rate calculation. Fig 9 shows
the calculated flow rate as a function of the size of the control
volume. The figure shows the results for the flat plate, single orifice
at the highest flow rate. The y axis shows the calculated
flow rate, and the x axis shows the height of the control
volume. The figure shows that as long as the control volume is large
enough to not include any regions of aliasing, the correct flow rate is
closely calculated. If, however, the control volume includes regions of
aliased velocity, which occur close to the orifice, then the calculated
flow rate is false. This error will occur if the control volume is too
low or too narrow or there are too few MRI slices. On Fig 6,
the
aliased velocities are indicated and are easy to distinguish by the
sudden change in color from white to black and vice versa. The size of
the control volume is placed to be as close to the regions of aliased
velocity as possible. The height of the control volume is therefore
chosen from the axial velocity image because the axial velocity is
integrated through the `top' of the control volume (Fig
6A). The
control volume width is chosen from the radial velocity image because
the radial velocity is integrated through the `sides' of the
control
volume (Fig 6B). The integration through the other two faces of
the
control volume involves the through-plane velocity. The through-plane
velocity in each MRI slice therefore is examined, and the slices with
aliasing are excluded. In this way, the minimum breadth of the control
volume is chosen. For each flow rate and orifice size, the velocity of
the fluid proximal to the orifice is different. The position of the
alias therefore also is different, making it necessary to adjust the
size of the control volume accordingly.
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After choosing the size of the
control volume in this way for each
experiment, we calculated the flow rate by integrating the normal
velocity through its faces. Fig 10 shows the flow rates
calculated in this way plotted against the actual flow rate. The figure
combines the results from all of the experiments and, as can be seen,
shows that a very good agreement is obtained over a wide range of flow
rates and orifice/plate geometries. The correlation coefficient for
these data is 0.992 with the slope of the line being 1.02 and the
y intercept being 0.137 L/min. The pulsatile data are
represented as a mean flow rate, calculated by integrating
the flow rate over one cycle and dividing by the cycle time. The
temporal variation of one of the pulsatile flow rates, calculated by
the control volume method, is shown in Fig 11.
Unfortunately, it was not possible to place a flow probe close to the
MRI scanner, so there is no temporal comparison between the actual and
the calculated flow. In addition, the flow rate does not decline to
zero because of the compliance of the flexible tubes connecting the
pulsatile pump to the phantom.
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To calculate the cardiac output for the
animal experiment, we drew the
control volume to cover the cross section of the ascending aorta, and
the flow rate was calculated by integration of the velocity through
this surface. This was performed for each gated image, producing a flow
curve for the ascending aorta (Fig 12). By integration
of this flow curve over the entire cycle, the total flow rate or
cardiac output was calculated and found to be 2.82 L/min. The
corresponding cardiac output measured with the thermodilution method
was 3.2, 3.4, and 3.2 L/min before the MR examination and 2.9, 2.9, and
2.9 L/min after the MR examination, respectively. Note that due to a
change in heart rate (61 beats per minute before and 58 beats per
minute after the examination), cardiac output changed slightly. The
resultant mean thermodilution cardiac output was calculated to be 3.08
L/min.
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Discussion |
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TopAbstractIntroductionMethods Results Discussion References |
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Obtaining a truly quantitative regurgitant flow rate clearly would be an improvement in diagnosing and monitoring regurgitation. Recent developments in Doppler ultrasound have made it possible to noninvasively quantify blood velocity, but limitations in the technique have made it difficult to derive the regurgitant flow rate from these measurements. MRI velocity measurement, on the other hand, is a newer technique that is not yet fully used in blood flow quantification and may provide a different solution. MRI has the advantage of being able to measure in any plane through the body and therefore is not limited to a particular window. MRI also can measure both the velocity magnitude and direction. It is these two features of MRI that allow the application of control volume theory to the quantification of regurgitation. If Doppler ultrasound could be adapted to measure more than one velocity component, then the theory presented here could be used in conjunction with Doppler. This may be possible through the use of correlation techniques that track particles across the ultrasound image and allow a second velocity component to be measured20 or by imaging the proximal flow field from more than one direction. The method presented here therefore should not be judged purely as a MRI method but also as a more fundamental approach to flow quantification. One of the most important aspects is a reevaluation of the control volume method applied to regurgitation. At present, regurgitant quantification appears to be dominated by the PISA method with the assumption of a constant velocity over a predefined control volume surface. This latter assumption is severely limiting in the application of the control volume method. By dropping the assumption of hemispheric or any other isovelocity shape and regarding the more basic approach to control volume use adopted with this method, it may be possible to escape from PISA and develop more flexible quantification methods. This will apply not only to MRI but also to Doppler ultrasound, as suggested by Sun et al.21
These results show that the control volume method in association with
MRI can accurately measure regurgitant flow rate. An excellent
correlation coefficient between the measured and true flow rate is
obtained. Fig 9 shows the variation in the calculated flow rate
as the
size of the control volume is increased. As mentioned, the inclusion of
aliased velocities in the calculation obviously leads to a false
result. However, we have shown that by examining the velocity images,
it is possible to chose a control volume outside the aliased region.
This was found to be true for all of the variations in geometry used in
these experiments. In the case of the in vitro pulsatile flow, the flow
rate changes, and consequently so does the position of the velocity
alias. In this case, we found it sufficient to use the image
corresponding to the largest alias magnitude for placing of the control
volume. Fig 9 also shows clearly that provided the control
volume is
placed outside the regions of aliasing, the correct flow rate is
closely calculated, and that this calculated flow rate then does not
depend strongly on the size of the control volume. There is, however, a
small variation in the calculated value as the size of the control
volume is increased. This is due to the fact that as the control volume
is increased, the magnitude of the measured velocities decreases. The
signal-to-noise ratio of the measured velocity therefore is decreased,
producing a larger error in the velocity integration. Although this
change in calculated flow rate with size of control volume is
relatively small, it is evident that to minimize this error, the
smallest possible control volume that still lies outside the region of
aliasing should be taken (Fig 6). Should the extent of the
aliased
velocity region be too large, as is possible in the case of mitral
regurgitation when the aortic outflow may interfere with the proximal
velocity sufficiently to cause the aliasing contour to extend into the
left ventricular outflow tract, then it will be necessary to increase
the aliasing velocity to reduce the size of the aliased region and
allow the control volume to be drawn outside of the aliased region. In
MRI, the aliasing velocity is easy to change, being an input parameter
to the MRI scanner, and it can be increased up to 2 to 3 m/s. The
disadvantage of doing this is that the accuracy of small velocity
measurements will decrease if the aliasing velocity is too high. In
addition, the MRI velocity becomes inaccurate in turbulent or strongly
accelerating flow, preventing the measurement of the velocity very
close to or downstream of the orifice. It is therefore necessary to
chose an aliasing velocity that is large enough to prevent a large
region of aliased velocities from appearing but small enough to exclude
regions very close to the regurgitant orifice. The present study
shows that an aliasing velocity of 20 cm/s is a good choice. The
experiments have included a range of plate and orifice geometries and
both steady and unsteady flow to simulate different flow conditions.
The multiple-orifice plate was designed to produce an asymmetric
proximal flow field; the accurate calculation of both the steady and
unsteady flow rates in this case demonstrates the independence of the
method on this variation of the proximal flow convergence. In addition,
the calculation of the flow rate through the cone-shaped plate
demonstrates the applicability of the method to complex geometries and
the independence of the method on angle-correction techniques. The in
vivo animal study shows that it is possible to locate the MR image in
the ascending aorta and obtain a measurement of the aortic flow
waveform. The corresponding cardiac output was within 8.4% of the
cardiac output measured with thermodilution. However, because it was
located above the level of the coronary ostia, the MRI measurement did
not include the coronary flow. This may account for the small
underestimation of the cardiac output. These results clearly show that
this technique is a possible new method of valvular regurgitation
quantification and warrants further investigation.
Study Limitations
The following limitations and provisos
apply to the present
study.
The velocity measured by MRI is a spatially averaged velocity within each finite voxel. For these experiments, the voxels had dimensions of 5x2x2 mm; each velocity therefore is an average over this volume and is subject to errors if a large spatial acceleration is present. For the proximal convergence region, there are high spatial accelerations present, although these are limited to a region very close to the orifice because the velocity changes approximately with the square of the distance from the orifice. Data from very close to the orifice should not be used, therefore, as an error in the measurement may result due to this averaging effect. It is possible to reduce the size of the voxel, and therefore reduce the effects of spatial velocity changes, by simply changing the input parameters to the MRI scanner. As the voxel is smaller, however, the magnitude of the signal is less and therefore the signal-to-noise ratio is worse, making the velocity measurement less accurate. Our experience with in vivo MRI imaging suggests that the parameters used for these experiments are a sufficient choice. To a certain extent this problem is self-regulated, however, in that the control volume is placed outside the region of aliased velocities and therefore excludes the regions of high spatial acceleration close to the orifice. By setting the aliased velocity to a low value, 20 cm/s in this case, regions of high acceleration are avoided. Another limitation with MRI data is that the data are acquired over a number of heartbeats and represent a temporally averaged measurement. The beat-to-beat variations in flow rate therefore cannot be obtained, and it is very hard to make measurements in patients with arrhythmias, which cause major changes in heart frequency during the measurements.
Transfer to an In Vivo Environment
Our flow phantom is a
simplification of the in vivo situation and
should be discussed with respect to the feasibility of applying this
method clinically. A suggested in vivo procedure would be as follows.
First, use fast angiographic imaging to locate the position of the
regurgitant lesion. These images are very quick to obtain and can be
performed to provide a large number of slices covering most of the
heart. On these images, the regurgitant lesion can be identified by the
signal loss immediately proximal to the orifice and by the signal loss
in the turbulent jet distal to the orifice in a similar manner as the
location of regurgitant orifices can be found using Doppler ultrasound.
Second, use the angiographic slice that best shows the location of the
regurgitant orifice to orientate an image slice through the orifice
center, roughly perpendicular to the orifice. Finally, the velocity is
then measured in this slice and in neighboring slices on either side.
In this way, a rectangular box of velocity data is obtained proximal to
the orifice, and the control volume procedure, which we described, is
used to calculate the flow rate.
The regular shape of the walls in the phantom using the flat plates makes it easy to perform integration of the control volume surface. In vivo, the irregular shape of the wall in the region of the orifice may make this somewhat more difficult as the location of the wall in each image will have to be found. More care will have to be taken in choosing the boundary of the control volume, ensuring that it is extended to the orifice wall. In calculating the cardiac output in the animal experiment, the boundary of the aorta had to drawn by hand. Although this is quite easy to perform, there is an element of subjectivity in this procedure that may affect the accuracy of the results. Note that the control volume does not have to coincide with the regular shape of the data structure but can take any shape. As the three components of velocity are measured, the velocity normal to any surface can be calculated. It therefore is not necessary to align the MRI slices normal to the orifice. This was done so in these experiments only for simplicity. The use of water as the working fluid will not affect the applicability of the method. Although it may be true that the higher viscosity and non-newtonian behavior of blood can change the flow field proximal to the orifice, this will not affect these results as no assumptions were made about the proximal flow field. This method measured the actual fluid velocity and can do so regardless of whether the fluid is blood or water. This is a large advantage of this method because it allows its application to the regurgitant flow through an orifice in any region of the heart. Complex proximal flow fields, which may be found with mitral regurgitation and transeptal defects, will not invalidate the method as they would with the PISA and jet momentum methods, as long as the control volume surrounds the orifice and connects to the orifice surface. It has recently been shown that the mitral outflow and the confinement of the flow close to the proximal septum influence the flow proximal to regurgitant orifices.22 23 Strong flows into one side of the control volume and out the other will not affect the results as they will cancel out in the integration. The same argument will validate the use of a rigid instead of a compliant phantom. The compliance of the surrounding walls may affect the proximal flow field, but as the true flow is measured this will be incorporated in the integration. One possible limitation of our phantom is the stationary nature of the orifice as in vivo orifices may move with time. To account for this, it would be necessary to move the control volume in time with the orifice by drawing a different control volume at each time step and to subtract the velocity of the orifice from the measured velocity. This would be done by measuring the orifice plate velocity either from velocity measurements with MRI or by measuring the displacement of the orifice from one image to the next and dividing by the time difference between images. This type of correction has been described by Cape et al,24 who used it in association with Doppler ultrasound measurements. Other limitations due to the nature of MRI are the relative expense and the phobia of some patients regarding the MRI scanner. As mentioned, however, the control volume method could also be applied using the velocity measured with any device as long as the velocity normal to the control surface is available.
Future
developments in MRI will undoubtedly improve the accuracy of MRI
velocity measurements. The development of short echo time imaging will
decrease the noise of the measurements and reduce errors from
disturbances in the flow. Faster imaging methods and quicker hardware
will also speed up the data acquisition, which takes 
15 to 25
minutes per image slice. In particular, breath-hold techniques
are being implemented that will allow the acquisition of a single
velocity component image in 20 seconds. These methods will also
remove any variation in the measured velocity due to breathing. At
present, there is a significant amount of postprocessing and data
analysis involved in this method. This is largely due to the
non–application-specific software used for the process. The
development of application-specific software, combined with interactive
graphics, would make the data analysis much faster and more user
friendly, making the method justifiable clinically.
Conclusions
The present study demonstrates the validity of a
new method
for quantifying valvular regurgitation. By removing constraints in the
nature of the distal or proximal regurgitant flow field, it is possible
to construct a technique based on the use of a generalized shape for a
proximal control volume. By integration of the velocity normal to the
control volume surface, it is theoretically possible to calculate the
regurgitant flow through an orifice of any shape and under any proximal
flow conditions. The accuracy of the calculation therefore is dependent
only on the accuracy and resolution of the velocity measured proximal
to the orifice. This basic theory is applicable by using a velocity
measured with Doppler ultrasound, MRI, or any other method as long as
the velocity normal to the control volume surface is measured. At
present, this is best performed with MRI, which can measure
multiple velocity components; in the future, however, Doppler
ultrasound may also be capable of this.20 We present
the validation of the method using MRI and find that the flow rate
through simulated regurgitant orifices and the cardiac output in vivo
could be measured very accurately.
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Acknowledgments |
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This work was supported by the Karen Elise Jensen Foundation, Denmark; National Institutes of Health (grant HL-45485); and the American Heart Association, Georgia Affiliate.
Received December 7, 1994; accepted January 3, 1995.
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