(Circulation. 2000;101:765.)
© 2000 American Heart Association, Inc.
Clinical Investigation and Reports |
Assessment of Aortic Valve Stenosis Severity
A New Index Based on the Energy Loss Concept
From the Laboratoire de génie biomédical, Institut de recherches cliniques de Montréal, Montreal (D.G., P.P., F.S., L.-G.D.), and Quebec Heart Institute/Laval Hospital, Laval University, Ste-Foy, Quebec (P.P., J.G.D.), Canada.
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionAppendix 1References |
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Background—Fluid energy loss across stenotic aortic valves is influenced by factors other than the valve effective orifice area (EOA). We propose a new index that will provide a more accurate estimate of this energy loss.
Methods and Results—An experimental model was designed to measure
EOA and energy loss in 2 fixed stenoses and 7
bioprosthetic valves for different flow rates and 2 different
aortic sizes (25 and 38 mm). The results showed that the
relationship between EOA and energy loss is influenced by both flow
rate and aortic cross-sectional area (AA) and that the
energy loss is systematically higher (15±2%) in the large aorta. The
coefficient (EOAxAA)/(AA-EOA) accurately
predicted the energy loss in all situations
(r2=0.98). This coefficient is more closely
related to the increase in left ventricular workload than
EOA. To account for varying flow rates, the coefficient was indexed for
body surface area in a retrospective study of 138 patients with
moderate or severe aortic stenosis. The energy loss index
measured by Doppler echocardiography was
superior to the EOA in predicting the end points, which were defined as
death or aortic valve replacement. An energy loss index 
0.52
cm2/m2 was the best predictor of adverse
outcomes (positive predictive value of 67%).
Conclusions—This new energy loss index has the potential to reflect the severity of aortic stenosis better than EOA. Further prospective studies are necessary to establish the relevance of this index in terms of clinical outcomes.
Key Words: echocardiography • hemodynamics • valves • stenosis
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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Transvalvular pressure gradients (TPG) and valve effective orifice area (EOA) are the parameters currently used for the hemodynamic evaluation of native and prosthetic heart valves.1 2 3 4 5 Recent studies, however, have emphasized the importance of taking into account the pressure recovery phenomenon that occurs downstream from heart valves.6 7 8 9 Indeed, often quite a difference exists between the gradient measured by Doppler echocardiography (TPGmax) and that measured by catheterization. The latter is the net pressure drop (TPGnet), ie, the gradient of pressure between the left ventricular outflow tract and the ascending aorta. The difference between TPGmax and TPGnet is called pressure recovery, and it is due to the conversion of a certain amount of kinetic energy (dynamic pressure) to potential energy (static pressure) downstream from the valve (Figure 1
). Recent studies
suggested that pressure recovery may be clinically relevant in patients
who have moderate or severe aortic stenosis and a small aortic
cross-sectional area.7 10 11 Overall, these observations
suggest that the parameters presently used to assess
the severity of aortic valve stenosis do not always accurately
reflect the energy loss and the increased workload caused by the
stenosis.
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The purpose of this study was to find a Doppler echocardiographic parameter that provides a more accurate estimate of the energy loss across aortic valves and, hence, of the severity of aortic stenosis. To do this, we used an experimental model to derive Doppler and catheterization measurements for 2 stenoses and 7 bioprosthetic heart valves studied at different steady and pulsatile flow rates and for 2 different aortic cross-sectional areas. A second objective was to evaluate the performance of this new index in predicting the adverse clinical outcome of patients with aortic stenosis when compared with the currently recommended parameter for the assessment of the severity of aortic stenosis, ie, the valve EOA.5
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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In the equations, the following symbols,
, P, V, A, and Q,
are used to indicate the density, the static pressure, the velocity,
the cross-sectional area, and the flow rate of the fluid, respectively.
The indexes V, VC, and A represent the
left ventricular outflow tract, the vena contracta, and the
aorta, respectively (Figure 1
). EL is
energy loss expressed in units of pressure.
Theoretical Background
Using the basic concepts of hydraulics, a loss of fluid energy
by dissipation into heat is observed after an abrupt change in flow
geometry. The energy in a fluid (due to gravity, static pressure, and
motion) is often expressed in terms of total pressure.12
Because the contribution of gravity is negligible in the context of
aortic valve flow, the energy of this flow can be defined as
P+(0.5xV2); note that
0.5xV2=4V2 when the
pressure is expressed in mm Hg and the velocity in m/s. The first
term is the potential energy due to static pressure, and the second is
the kinetic energy due to dynamic pressure. When the blood flows
through an aortic valve, it is spatially accelerated from the left
ventricular outflow tract to the vena contracta; then, it
is decelerated within the divergence of the jet downstream from the
vena contracta (Figure 1). During acceleration, a part of static
pressure is converted to dynamic pressure, which is a stable and
low-energy dissipation process.12 More precisely, the
fluid energy loss upstream from the vena contracta is negligible.
During deceleration, a certain amount of dynamic pressure is
reconverted to static pressure. This process is unstable and it
generates turbulence, which means that a part of the initial energy is
dissipated into heat and is, therefore, irreversibly lost after the
vena contracta. Thus, the energy loss between the left
ventricular outflow tract and the ascending aorta can be
shown as follows:
EL=(PV-PA)+
[0.5(VV2-VA2)].
The energy loss includes both static and dynamic pressure gradients,
whereas the TPGnet
(PV-PA) is only the
gradient of static pressure. For normal native valves, the energy loss
is negligible, but for stenotic native valves and many
prosthetic heart valves, it may become significant and generate
mechanical overload to the left ventricle.
By applying the Bernoulli equation between the left ventricle and the
aorta and by combining it with the continuity equation, energy loss
(EL) can be shown as follows:
 | (1) |
(in the Appendix), energy loss can be expressed as
follows by using the flow rate (Q) and the EOA.
 | (2) |
can also be rearranged, taking into account the unit
conversion, as follows:
 | (3) |
In Vitro Study
Description of the Model
The modular mock flow circulation model used in this study is
shown in Figure 2. It was previously
described in detail and validated.14 Blood was mimicked by
using a water/glycerol solution (70%/30%) that contained cornstarch
particles (ultrasound scatterers). Pressure measurements were performed
using fluid-filled side-hole catheters, and flow rate was measured with
an electromagnetic flowmeter. An Ultramark 9 HDI was used for
Doppler velocity measurements.
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Protocol: Steady Flow
All measurements were made in the same flow model, but 2
different aortic cross-sectional areas were used. The cross-sectional
area of the left ventricular section
(AV) was 5.07 cm2
(diameter, 2.54 cm). That of the first aortic section used
(AA1) was also 5.07 cm2
(hence, AV/AA1=1). The
cross-sectional area of the second section (AA2)
was 11.34 cm2 (diameter, 3.80 cm; hence,
AV/AA2=0.45). Seven aortic
bioprosthetic valves (Medtronic Intact 19, 21, 23, and 25
mm and Medtronic Mosaic 21, 23, and 25 mm) and 2 stenoses
(2 plexiglas plates with circular orifices of 75 and 100
mm2, respectively) were tested. The
ventricular pressure was adjusted to 
100 mm Hg.
The bioprosthetic valves and stenoses were tested under
flow rates of 90, 147, 203, 260, 317, 373, and 430 mL/s. The
stenoses could not be tested at 373 and 430 mL/s because of an
excessive increase in ventricular pressure. For each flow
rate, the ventricular pressure was measured 20 mm
upstream from the valve, and the aortic pressure was measured at 0.0,
2.5, 5.0, 7.5, 10, 15, 20, 30, 40, 60, 80, and 100 mm downstream
from the valve. The reference point 0.0 mm corresponded to the
exit of the valve ring. For each flow rate tested, the measurement of
the TPG was repeated 3 times and averaged. The highest jet velocity was
measured by continuous-wave Doppler. In the steady-flow
experiments, the mean ventricular flow velocity was derived
from the continuity equation by dividing the mean flow rate measured
with the electromagnetic flowmeter by the cross-sectional area of the
ventricular section.
Protocol: Pulsatile Flow
The bioprosthetic heart valves and the stenoses
used for the pulsatile flow study were tested under 3 stroke volumes,
50, 60, and 70 mL, and an ejection time of 300 ms, which corresponded
to mean flow rates of 166, 200, and 233 mL/s. The pulse rate was
maintained at 72 beats/min. The pressure measurements were performed at
the same positions as those used in steady-flow measurements. These
measurements were averaged over 10 cardiac cycles. The valve
parameters were computed at peak systole because the flow
acceleration is negligible at this specific moment. The jet velocity
was assessed by continuous-wave Doppler. The
ventricular flow velocity was obtained by positioning the
sample volume of the pulse-wave Doppler beam 20 mm upstream
from the valve using a sample volume of 15 mm.
Data and Statistical Analysis
The valve EOA was determined by Doppler
echocardiography using the standard continuity
equation and by catheter using a combination of Bernoulli and
continuity equations, as previously described.14 The
energy loss was measured by catheterization using
equation 1 and by Doppler echocardiography
using equation 2. Statistical analysis of the association of
variables was performed with the Pearson correlation coefficient,
and graphs were constructed with the corresponding linear regression
equation.
In Vivo Study
Patients
A retrospective study was performed on 138 consecutive patients
(80 men and 58 women; mean age, 67±14 years) who underwent an
echocardiographic evaluation at the Quebec Heart
Institute between January 1997 and June 1998 and who were considered to
have moderate (valve EOA 1.5 cm2 and >1.0
cm2) or severe (EOA1.0
cm2) aortic stenosis on the basis of the
criteria recommended by the American Heart Association and the American
College of Cardiology.5 End points were
defined as death or aortic valve replacement within 8 months after the
echocardiographic evaluation. To give more clinical
perspective to the study, an echocardiographic
evaluation was also performed on 26 healthy subjects (21 men and 5
women; mean age, 45±11 years) with no evidence of heart disease
(normal group).
Doppler Echocardiography
Measurements were performed using a Sonos 2000, 2500, or 5500
ultrasound system (Hewlett Packard) and included the
transvalvular flow velocity using continuous wave Doppler,
left ventricular outflow tract velocity using pulsed-wave
Doppler, and left ventricular outflow tract diameter,
as previously described.3 Two-dimensionally directed left
ventricular M-mode dimensions and the aortic diameter at
the tip of the valve leaflets were measured in the left parasternal
long-axis view using the recommendations of the American Society of
Echocardiography. With these measurements, we
calculated left ventricular stroke volume and ejection
fraction, left ventricular mass (using the corrected
American Society of Echocardiography formula), peak
and mean TPG (using the modified Bernoulli equation), valve EOA (using
the standard continuity equation), and the energy loss coefficient
(EOAxAA)/(AA-EOA). To
take into account the cardiac output requirements of the patient under
normal resting conditions,3 15 the EOA and the energy loss
coefficient were also indexed for body surface area.
Statistical Analysis
A backward stepwise logistic regression analysis was
performed to identify the independent predictors of adverse clinical
outcomes (ie, death or aortic valve replacement within 8 months of the
echocardiographic study). The relevant variables
tested for this analysis were patient age and sex and the
following Doppler echocardiographic
parameters: peak TPG, mean TPG, valve EOA, indexed valve
EOA, energy loss coefficient, energy loss index, left
ventricular mass, left ventricular mass index,
and ejection fraction. P<0.05 was considered
significant.
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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In Vitro Study
Relationship Between Doppler and Catheter Measurements
A very good correlation between Doppler and catheter measurements was found both with steady and pulsatile flows for TPGmax and EOA (r2>0.97). The fitted lines were very close to the identity lines for TPGmax (slope was 0.96 under steady flow and 1.02 under pulsatile flow). For EOA, the Doppler measurements were slightly underestimated compared with the catheter measurements (slope was 0.93 under steady flow and 0.94 under pulsatile flow). The standard errors of the estimates of TPGmax and EOA were
3.09 mm Hg and 0.05
cm2, respectively.
As shown in Figure 3, a very good
correlation (r2>0.98) and concordance
between Doppler and catheter measurements were also found for
energy loss. These results confirm the validity of the theoretical
assumptions used for the determination of energy loss by Doppler
echocardiography.
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Effects of EOA and Cross-Sectional Aortic Area on Energy
Loss
Figure 4 shows the relationship
between energy loss and the EOA for different levels of flow rate (for
clarity, only 3 flow rates are shown in the figure). This figure
includes the data obtained by Doppler
echocardiography with the small
(AA1) and the large (AA2)
aortic sections. In accordance with the theory (equation 2), the energy
loss increased with increasing flow rate and decreasing valve EOA.
Furthermore, for the same valve EOA and the same flow rate, the energy
loss was systematically higher (15±2%) with the larger aorta.
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Figure 5 shows the relationship between
the energy loss and the coefficient
(EOAxAA)/(AA-EOA) for
different flow rates and the 2 cross-sectional aortic areas. In
contrast with Figure 4, the measurements obtained with the small
and the large aortic sections are on the same curves. In accordance
with the theory (equation 3), the energy loss increased markedly with
increasing flow rate and decreasing (EOAx
AA)/(AA-EOA). It is also
clear that the energy loss is determined uniquely by the
(EOAxAA)/(AA-EOA)
coefficient for a given flow rate. Also, the two stenoses had
lower (EOAxAA)/(AA-EOA)
coefficients than did bioprosthetic valves and, therefore, they
resulted in greater energy loss. The small overlap observed between the
normal bioprosthetic valves and the fixed stenotic
orifices is due to the fact that the small porcine bioprostheses are at
least mildly stenotic, although they function normally. For
example, the valve EOA of the 19-mm Medtronic Intact
bioprosthesis was between 0.67 and 0.90
cm2, depending on flow rate, which is close to
the EOA of the largest stenotic orifice: 0.64
cm2.
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In Vivo Study
Among the 138 patients included in this retrospective study, 44
(31.9%) had moderate aortic stenosis and 94 (68.1%) had
severe aortic stenosis. Of these patients, 5 (3.6%) died and
60 (43.5%) underwent aortic valve replacement within 8 months after
the echocardiographic evaluation.
The results of the univariate analysis of potential
predictors of outcome (ie, death or aortic valve replacement) are shown
in the Table. A significant
(P<0.01) association existed between the outcome and
patient age, peak TPG, mean TPG, valve EOA, indexed EOA, energy loss
coefficient, and energy loss index. However, in the
multivariate analysis (Table), the
energy loss index (P<0.0001) and patient age
(P=0.014) were the only independent predictors of outcome.
The best predictor of outcome (sensitivity, 68%; specificity, 67%;
positive predictive value, 67%) was obtained using an energy loss
index 0.52 cm2/m2. Of the
68 patients who had an energy loss index 0.52
cm2/m2, 44 (65%) died or
underwent aortic valve replacement within 8 months after the
echocardiographic evaluation compared with 21 of 70
patients (31%) in the group of patients with an energy loss index
>0.52 cm2/m2 (Figure 6). All normal subjects had an energy
loss index >1.35 cm2/m2,
and no overlap existed between these subjects and the patients with
aortic stenosis.
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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Patients who have aortic stenosis and similar aortic valve EOAs may have different clinical outcomes2 16 ; this observation suggests that factors other than valve area may impact left ventricular workload. The noninvasive estimation of energy loss might be useful for the hemodynamic assessment of patients with aortic stenosis because it more closely reflects the amount of left ventricular energy that is lost during systole due to the obstruction created by the valve. Several investigators suggested studying the hemodynamic performance of stenotic valves by assessing energy loss.9 17 18 19 20 However, to our knowledge, this is the first study that proposes an expression of the energy loss that can be easily and accurately determined by Doppler echocardiography.
As demonstrated, the energy loss caused by an aortic valve depends not
only on flow rate and valve EOA, but also on the aortic cross-sectional
area. Hence, at any given flow rate, the energy loss is dependent on
the coefficient
(EOAxAA)/(AA-EOA) rather
than EOA alone. To illustrate this concept, Figure 7 shows the variation of energy loss as a
function of EOA for different aortic diameters and, thus, different
values of AA (left) and as a function of
AA given different values of EOA (right). These
relationships show that in the context of severe aortic
stenosis (EOA<1.0 cm2), a small decrease
in EOA results in dramatic increases in energy loss (Figure 7, left). In contrast, the energy loss increases markedly when the aortic
diameter increases from 15 to 30 mm; it then reaches a plateau
when the aortic diameter becomes >30 mm (Figure 7, right).
These results agree with those determined in the study of Baumgartner
et al,11 which showed that the pressure recovery
phenomenon is clinically relevant mostly in patients with an aortic
diameter <30 mm.
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As pointed out in previous studies,3 21 a valve EOA that
is acceptable for a small, inactive patient may be unsatisfactory for a
larger, physically active individual; it is therefore relevant to index
the valve EOA for body surface area to take into account the cardiac
output requirements of the patient under normal resting conditions. As
suggested by equation 3 and confirmed by experimental in vitro data,
the energy loss is essentially determined by 2 factors: the coefficient
(EOAxAA)/(AA-EOA) and the
transvalvular flow rate, which at rest is mainly related to
body size. Hence, for clinical application, the coefficient
(EOAxAA)/(AA-EOA) was indexed for body surface area.
The resulting energy loss index,
[(EOAxAA)/AA-EOA)]/body surface area, is an estimate
of the energy loss through the physiological system
composed of the valve and the aortic root, assuming a normal
transvalvular flow rate, and it allows one to compare the
severity of aortic stenosis in patients with different body
surface areas and different resting cardiac outputs.
Figure 8 illustrates the theoretical
relationship between energy loss and this index assuming a normal
cardiac index of 3.0
L · min-1 · m-2 at
rest, a heart rate of 65 beats/min, and a systolic ejection
time of 300 ms. This relationship is analogous to the strong inverse
exponential relation that we previously found between the mean TPG,
either at rest or during exercise, and the valve area indexed for body
surface area.3 21 22 However, as stated in the
introduction, the TPG does not necessarily reflect the energy loss in
all situations. By integrating both the valve area and the aortic
cross-sectional area, the new index proposed in the present study
represents an evolution in that it provides a more accurate
estimation of energy loss across the valve.
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The validity of this new index is also confirmed by the results of the
in vivo study, which showed that the energy loss index was superior to
the valve EOA in predicting adverse clinical outcomes in patients with
moderate to severe aortic stenosis. In this context, it is
interesting to note that the critical threshold that we found in the
clinical study (Figure 6) is consistent with the
theoretical relationship shown in Figure 8, whereby the energy
loss increases dramatically when the energy loss index becomes <0.50
cm2/m2. Therefore, an
energy loss index <0.50
cm2/m2 should probably be
considered a critical value below which patients should be closely
monitored for the appearance of symptoms.
Limitations of the Study
Several in vitro and in vivo studies have demonstrated that the
EOA of native or prosthetic valves can increase with increasing
flow rates and in varying degrees depending on valve geometry and
compliance.23 24 A significant increase in the EOA of
bioprosthetic valves with increasing flow was indeed observed
in the present study. In contrast, previous studies suggest that
minimal or no change occurs in the aortic root diameter with increasing
flow.25 Consequently, an increase in valve EOA with flow
rate, such as may occur during exercise, would result in an increase in
the coefficient
(EOAxAA)/(AA-EOA),
meaning that relatively less energy would be lost between the left
ventricle and the ascending aorta. Given the many variables
involved, the changes in EOA and AA occurring
with increasing flow rates cannot be predicted from a resting
parameter, and the use of the energy loss index would,
therefore, not necessarily obviate the need to perform
dobutamine or exercise stress tests in certain clinical
situations. Nonetheless, its use during these tests should provide more
accurate information. Also, the complexity of the
cardiovascular system cannot be rigorously simulated in
vitro.
Conclusions
This study proposes using a new index to estimate the severity of
aortic valve stenosis. This index is more accurate than the
currently used parameters to estimate work loss, and it has
the advantage of being easily measurable using Doppler
echocardiography. Moreover, the results of the in
vivo study clearly suggest that this index is a better predictor of
outcomes than the currently recommended index of severity, ie, the
valve EOA. Prospective studies are now necessary to further document
the validity of this new index in the clinical situation.
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Acknowledgments |
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This work was supported by the Medical Research Council of Canada (MA-10929) and the Heart and Stroke Foundation of Canada. The authors thank Dr Helen Routh of Advanced Technology Laboratories for the loan of the Ultramark 9 HDI system, Medtronic for providing the heart valves, and Isabelle Laforest and Serge Simard for their assistance in data collection and statistical analysis.
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Footnotes |
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Reprint requests to Dr Durand, Institut de recherches cliniques de Montréal, 110 Avenue des Pins, Montreal, H2W-1R7, Quebec, Canada.
The authors have a financial interest in the products presented in this work. Medtronic Company (Minneapolis, Minn) provided bioprosthetic valves to the Laboratory of Biomedical Engineering of the Institut de recherches cliniques de Montréal for the in vitro study. The principal investigators of this research project were D. Garcia, P. Pibarot, and L.-G. Durand. Medtronic Company also provides financial support to the Department of Cardiology of the Quebec Heart Institute for the clinical and echocardiographic follow-up of patients receiving Medtronic Intact and Mosaic valves. The principal investigator of this research project is J.G. Dumesnil.
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Appendix 1 |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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We sought an expression for energy loss expressed in units of pressure (mm Hg) in an aortic valve as a function of AA, AV, VV, and VVC. The energy loss was calculated using the following assumptions: flow is incompressible, the velocity profile is uniform, gravity is neglected, the acceleration terms are negligible (because measurements were performed with steady flow or pulsatile flow at peak systole), and the energy loss is negligible upstream from the vena contracta. By projecting the linear momentum equation26 on the flow direction axis using the control volume defined by the gray square in Figure 1
, equation 4
is obtained.
 | (4) |
 | (5) |
, and 5 can be combined to give the following
equation.
 | (6) |
 | (7) |
, the energy loss can be reduced to the
following:
 | (8) |
/2=4.
The energy loss can also be expressed by using the EOA as
follows:
 | (9) |
Received April 1, 1999; revision received September 2, 1999; accepted September 23, 1999.
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References |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
|---|
1. Skjaerpe T, Hegrenaes L, Hatle L. Noninvasive estimation of valve area in patients with aortic stenosis by Doppler ultrasound and two-dimensional echocardiography. Circulation. 1985;7:810–818.
2.
Otto CM, Burwash IG, Legget ME, Munt BI, Fujioka M,
Healy NL, Kraft C, Miyake-Hull CY, Schwaegler RG. Prospective study of
asymptomatic valvular aortic stenosis:
clinical, echocardiographic, and exercise predictors of
outcome. Circulation. 1997;95:2262–2270.
3. Dumesnil JG, Honos GN, Lemieux M, Beauchemin J. Validation and applications of indexed aortic prosthetic valve areas calculated by Doppler echocardiography. J Am Coll Cardiol. 1990;16:637–643.[Abstract]
4. Chambers J, Coppack F, Deverall P, Jackson G, Sowton E. The continuity equation tested in a bileaflet aortic prosthesis. Int J Cardiol. 1991;31:149–154.[Medline] [Order article via Infotrieve]
5.
Bonow RO, Carabello BA, de Leon AC Jr, Edmunds LH Jr,
Fedderly BJ, Freed MD, Gaasch WH, McKay CR, Nishimura RA, O’Gara PT,
O’Rourke RA, Rahimtoola SH. Guidelines for the management of patients
with valvular heart disease: executive summary, a report of the
American College of Cardiology/American Heart
association task force on practice guidelines. Circulation. 1998;98:1949–1984.
6.
Baumgartner H, Khan SS, DeRobertis M, Czer LS, Maurer
G. Discrepancies between Doppler and catheter gradients in aortic
prosthetic valves in vitro: a manifestation of localized
gradients and pressure recovery. Circulation. 1990;82:1467–1475.
7. Voelker W, Reul H, Stelzer T, Schmidt A, Karsch KR. Pressure recovery in aortic stenosis: an in vitro study in a pulsatile flow model. J Am Coll Cardiol. 1992;20:1585–1593.[Abstract]
8. Khan SS. Assessment of prosthetic valve hemodynamics by Doppler: lessons from in vitro studies of the St Jude valve. J Heart Valve Dis. 1993;2:183–193.[Medline] [Order article via Infotrieve]
9. Heinrich RS, Fontaine AA, Grimes RY, Sidhaye A, Yang S, Moore KE, Levine RA, Yoganathan AP. Experimental analysis of fluid mechanical energy losses in aortic valve stenosis: importance of pressure recovery. Ann Biomed Eng. 1996;24:685–694.[Medline] [Order article via Infotrieve]
10.
Niederberger J, Schima H, Maurer G, Baumgartner H.
Importance of pressure recovery for the assessment of aortic
stenosis by Doppler ultrasound: role of aortic size, aortic
valve area, and direction of the stenotic jet in vitro.
Circulation. 1996;94:1934–1940.
11.
Baumgartner H, Steffenelli T, Niederberger J, Schima H,
Maurer G. "Overestimation" of catheter gradients by Doppler
ultrasound in patients with aortic stenosis: a predictable
manifestation of pressure recovery. J Am Coll Cardiol. 1999;33:1655–1661.
12. Miller DS. Internal Flow Systems. Bedford, UK: BHRA (Information Services); 1990:1–396.
13. Dumesnil JG, Yoganathan AP. Theoretical and practical differences between the Gorlin formula and the continuity equation for calculating aortic and mitral valve areas. Am J Cardiol. 1991;67:1268–1272.[Medline] [Order article via Infotrieve]
14. Durand LG, Garcia D, Sakr F, Sava H, Cimon R, Pibarot P, Fenster A, Dumesnil JG. A new flow model for Doppler ultrasound study of prosthetic heart valves. J Heart Valve Dis. 1999;8:85–95.[Medline] [Order article via Infotrieve]
15. Rahimtoola SH. Perspective on valvular heart disease: an update. J Am Coll Cardiol. 1989;14:1–23.[Medline] [Order article via Infotrieve]
16.
Carabello BA, Green LH, Grossman W, Cohn LH, Koster JK,
Collins JJ Jr. Hemodynamic determinants of prognosis of
aortic valve replacement in critical aortic stenosis and
advanced congestive heart failure. Circulation. 1980;62:42–48.
17. Clark C. The fluid mechanics of aortic stenosis, I: theory and steady flow experiments. J Biomech. 1976;9:521–528.[Medline] [Order article via Infotrieve]
18. Clark C. Energy losses in flow through stenosed valves. J Biomech. 1979;12:737–746.[Medline] [Order article via Infotrieve]
19. Sprigings DC, Chambers JB, Cochrane T, Allen J, Jackson G. Ventricular stroke work loss: validation of a method of quantifying the severity of aortic stenosis and derivation of an orifice formula. J Am Coll Cardiol. 1990;16:1608–1614.[Abstract]
20. Fisher J. Total energy loss in prosthetic valves. J Heart Valve Dis. 1994;3:666.[Medline] [Order article via Infotrieve]
21. Dumesnil JG, Yoganathan AP. Valve prosthesis hemodynamics and the problem of high transprosthetic pressure gradients. Eur J Cardiothorac Surg. 1992;6:S34–S38.
22.
Pibarot P, Dumesnil JG, Jobin J, Cartier P,
Lemieux M, Honos G, Durand LG. Hemodynamic and physical
performance during maximal exercise in patients with an aortic
bioprosthetic valve: comparison of stentless versus stented
bioprostheses. J Am Coll Cardiol.. 1999;34:1609–1617.
23.
Baumgartner H, Khan SS, DeRobertis M, Czer LS, Maurer
G. Doppler assessment of prosthetic valve orifice area: an
in vitro study. Circulation. 1992;85:2275–2283.
24.
Shively BK, Charlton GA, Crawford MH, Chaney RK. Flow
dependence of valve area in aortic stenosis: relation to valve
morphology. J Am Coll Cardiol. 1998;31:654–660.
25.
Rassi A, Crawford MH, Richards KL, Miller JF. Differing
mechanisms of exercise flow augmentation at the mitral and aortic
valves. Circulation. 1988;77:543–551.
26. Munson BR, Young DF, Okiishi TH. Viscous flow in pipes. In Munson BR, Young DF, Okiishi TH, eds. Fundamentals of Fluid Mechanics. New York: John Wiley & Sons; 1990:465–5‘60.
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 C. W. Akins, B. Travis, and A. P. Yoganathan Energy loss for evaluating heart valve performance. J. Thorac. Cardiovasc. Surg., October 1, 2008; 136(4): 820 - 833. [Abstract] [Full Text] [PDF]
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 M.-A. Clavel, C. Fuchs, I. G. Burwash, G. Mundigler, J. G. Dumesnil, H. Baumgartner, J. Bergler-Klein, R. S. Beanlands, P. Mathieu, J. Magne, et al. Predictors of Outcomes in Low-Flow, Low-Gradient Aortic Stenosis: Results of the Multicenter TOPAS Study Circulation, September 30, 2008; 118(14_suppl_1): S234 - S242. [Abstract] [Full Text] [PDF]
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R. El Oakley, P. Kleine, and D. S. Bach Choice of Prosthetic Heart Valve in Today's Practice Circulation, January 15, 2008; 117(2): 253 - 256. [Full Text] [PDF]
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 S. H Little, K.-L. Chan, and I. G Burwash Impact of blood pressure on the Doppler echocardiographic assessment of severity of aortic stenosis Heart, July 1, 2007; 93(7): 848 - 855. [Abstract] [Full Text] [PDF]
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Z. Hachicha, J. G. Dumesnil, P. Bogaty, and P. Pibarot Paradoxical Low-Flow, Low-Gradient Severe Aortic Stenosis Despite Preserved Ejection Fraction Is Associated With Higher Afterload and Reduced Survival Circulation, June 5, 2007; 115(22): 2856 - 2864. [Abstract] [Full Text] [PDF]
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C. R. Bridges, S. M. O'Brien, J. C. Cleveland, E. B. Savage, J. S. Gammie, F. H. Edwards, E. D. Peterson, and F. L. Grover Association between indices of prosthesis internal orifice size and operative mortality after isolated aortic valve replacement J. Thorac. Cardiovasc. Surg., April 1, 2007; 133(4): 1012 - 1021. [Abstract] [Full Text] [PDF]
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 L. Kadem and D. Garcia Are We Using the Right Fluid Mechanics Principles? Ann. Thorac. Surg., January 1, 2007; 83(1): 354 - 354. [Full Text] [PDF]
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K. Yoshida, S. Tobe, and M. Yamaguchi Reply Ann. Thorac. Surg., January 1, 2007; 83(1): 354 - 355. [Full Text] [PDF]
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 C. M. Otto Valvular Aortic Stenosis: Disease Severity and Timing of Intervention J. Am. Coll. Cardiol., June 6, 2006; 47(11): 2141 - 2151. [Abstract] [Full Text] [PDF]
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M. Briand, J. G. Dumesnil, L. Kadem, A. G. Tongue, R. Rieu, D. Garcia, and P. Pibarot Reduced Systemic Arterial Compliance Impacts Significantly on Left Ventricular Afterload and Function in Aortic Stenosis: Implications for Diagnosis and Treatment J. Am. Coll. Cardiol., July 19, 2005; 46(2): 291 - 298. [Abstract] [Full Text] [PDF]
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 D. Garcia, P. J. C. Barenbrug, P. Pibarot, A. L. A. J. Dekker, F. H. van der Veen, J. G. Maessen, J. G. Dumesnil, and L.-G. Durand A ventricular-vascular coupling model in presence of aortic stenosis Am J Physiol Heart Circ Physiol, April 1, 2005; 288(4): H1874 - H1884. [Abstract] [Full Text] [PDF]
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L Kadem, J G Dumesnil, R Rieu, L-G Durand, D Garcia, and P Pibarot Impact of systemic hypertension on the assessment of aortic stenosis Heart, March 1, 2005; 91(3): 354 - 361. [Abstract] [Full Text] [PDF]
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D. Garcia, J. G. Dumesnil, L.-G. Durand, L. Kadem, and P. Pibarot Discrepancies between catheter and Doppler estimates of valve effective orifice area can be predicted from the pressure recovery phenomenon: practical implications with regard to quantification of aortic stenosis severity J. Am. Coll. Cardiol., February 5, 2003; 41(3): 435 - 442. [Abstract] [Full Text] [PDF]
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R. A. Levine and E. Schwammenthal Stenosis is in the eye of the observer: impact of pressure recovery on assessing aortic valve area J. Am. Coll. Cardiol., February 5, 2003; 41(3): 443 - 445. [Full Text] [PDF]
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P. Pibarot and J. G. Dumesnil Hemodynamic and clinical impact of prosthesis-patient mismatch in the aortic valve position and its prevention J. Am. Coll. Cardiol., October 1, 2000; 36(4): 1131 - 1141. [Abstract] [Full Text] [PDF]
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