(Circulation. 1995;91:1196-1204.)
© 1995 American Heart Association, Inc.
Articles |
Comparison of Valvular Resistance, Stroke Work Loss, and Gorlin Valve Area for Quantification of Aortic Stenosis
An In Vitro Study in a Pulsatile Aortic Flow Model
Presented in part at the 65th Scientific Sessions of the American Heart Association, November 1992, New Orleans, La.
From the Department of Cardiology (W.V., K.R.K.), Tuebingen University, Tuebingen; and the Helmholtz Institute for Biomedical Engineering (H.R., G.N., T.S., B.S., A.S.), Aachen University of Technology, Aachen, Germany.
Correspondence to Wolfram Voelker, MD, Department of Cardiology, Internal Medicine III, Otfried-Müller-Str 10, 72076 Tübingen, Germany.
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Abstract |
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 Top Abstract IntroductionMethods Results Discussion References |
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Background Valvular resistance and stroke work loss have been proposed as alternative measures of stenotic valvular lesions that may be less flow dependent and, thus, superior over valve area calculations for the quantification of aortic stenosis. The present in vitro study was designed to compare the impacts of valvular resistance, stroke work loss, and Gorlin valve area as hemodynamic indexes of aortic stenosis.
Methods and Results In a pulsatile aortic flow model, rigid
stenotic orifices in varying sizes (0.5, 1.0, 1.5, and 2.0
cm2) and geometry were studied under different hemodynamic
conditions. Ventricular and aortic pressures were measured to determine
the mean systolic ventricular pressure (LVSPm) and the
transstenotic pressure gradient (
Pm).
Transvalvular flow (Fm) was assessed with an
electromagnetic flowmeter. Valvular resistance
[VR=1333 · (Pm/Fm)] and
stroke
work loss
[SWL=100 · (Pm/LVSPm)] were
calculated and compared with aortic valve area
[AVA=Fm/(50
Pm)].
The measurements were performed for a large range of transvalvular
flows. At low-flow states, flow augmentation (100
200 mL/s) increased
calculated valvular resistance between 21% (2.0-cm2
orifice) and 66% (0.5-cm2 orifice). Stroke work loss
demonstrated an increase from 43% (2.0 cm2) to 100% (1.0
cm2). In contrast, Gorlin valve area revealed only a
moderate change from 29% (2.0 cm2) to 5% (0.5
cm2). At physiological flow rates, increase in
transvalvular flow (200300 mL/s) did not alter calculated Gorlin
valve area, whereas valvular resistance and stroke work loss
demonstrated a continuing increase. Our experimental results were
adopted to interpret the results of three clinical studies in aortic
stenosis. The flow-dependent increase of Gorlin valve area, which was
found in the cited clinical studies, can be elucidated as true further
opening of the stenotic valve but not as a calculation error due to the
Gorlin formula.
Conclusions Within the physiological range of flow, calculated aortic valve area was less dependent on hemodynamic conditions than were valvular resistance and stroke work loss, which varied as a function of flow. Thus, for the assessment of the severity of aortic stenosis, the Gorlin valve area is superior over valvular resistance and stroke work loss, which must be indexed for flow to adequately quantify the hemodynamic severity of the obstruction.
Key Words: hemodynamics • aorta • valves • stenosis
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Introduction |
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TopAbstractIntroductionMethods Results Discussion References |
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I t is assumed that in mitral or aortic stenosis the valve orifice remains fixed irrespective of the magnitude of transvalvular pressure gradient or flow.1 Thus, a flow-dependent increase in calculated valve area, which was found in some clinical studies in aortic2 3 and mitral stenoses,1 4 had been interpreted to reflect a flow dependence of the Gorlin formula rather than an actual increase in the orifice area.
Valvular resistance3 4 5 6 7 8 and stroke work loss9 10 have been proposed as alternative measures of stenotic valvular lesions that may be less flow dependent than valve area calculations based on the Gorlin formula.11
To determine the validity of valvular resistance and stroke work loss in the quantification of aortic stenosis, we performed a hemodynamic study in a well-controlled pulsatile aortic flow model. Valvular resistance and stroke work loss were assessed under changing hemodynamic conditions and compared with calculations of valve area according to the Gorlin formula.
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Methods |
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TopAbstractIntroductionMethods Results Discussion References |
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Experimental Model
All experiments were performed in an electrohydraulic, computer-controlled pulsatile flow model simulating the left side of the human circulatory system (Fig 1
). This circuit has
been previously
described.12 13 14 15 The
test fluid consisted
of a 60% water–40% glycerol solution (viscosity, 3.6 cP; density,
1.06 g/mL). Heart rate was held constant at 70 beats per minute.
Piezoelectric catheter-tip transducers (Sensodyne) were used to record
the instantaneous pressures in the ventricular apex and aorta. The
aortic pressure was measured 130 mm distal to the aortic valve plane.
Each pressure signal was averaged over 64 consecutive beats to achieve
highly reproducible results. The variation of subsequent measurements
was within 1 mm Hg. The transstenotic flow rate was
measured with an electromagnetic flowmeter (Zapeda Instruments)
positioned in the aorta.
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Different types of stenotic orifices were
mounted in aortic position of
this pulsatile flow circuit (Fig 2): circular central
orifices of 0.5, 1.0, 1.5, and 2.0 cm2,
representing severe to mild aortic stenosis, and stenoses with
identical orifice areas of 0.5 cm2 but with variable
configurations, simulating different types of adult aortic
stenosis16 ; these included circular, slitlike, and
Y-shaped orifices with abrupt narrowing and
circular orifices with a long (2.0 cm) and a short (0.5 cm) nozzle.
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The flow rate was increased stepwise from a basal systolic flow of 50 mL/s to 200 mL/s (0.5 cm2), 300 mL/s (1.0 cm2), and 400 mL/s (2.0 cm2). At each flow rate, pressure and flow data were recorded simultaneously.
Calculations
Mean systolic pressure gradient
(Pm) was
obtained by averaging the integrated differences between the
simultaneously recorded pressure curves over the systolic time period.
Mean systolic flow (Fm) was derived from the
electromagnetic flow curve and expressed in mL/s.
For calculation of
valvular resistance, Pm was divided
by Fm. To express resistance in metric units
(dynes · s · cm-5), the conversion factor for
pressure has to be included (1 mm Hg=1333
dynes · cm-2):
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Stroke work loss (SWL) was calculated as the ratio of the mean transstenotic pressure gradient to the mean systolic ventricular pressure (LVSP)10 :
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Functional aortic valve area (AVAF) was calculated according to a modified version of the Gorlin formula:
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In addition, the effective aortic valve area (AVAEFF) within the vena contracta was calculated as the following:
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where AA is cross-sectional area of the aorta (see "Appendix").
To adopt these experimental results for a valid interpretation of clinical studies in aortic stenosis, the Reynolds number (Re) was determined (see "Appendix"):
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Statistical Analysis
All pooled clinical data were expressed
as mean±SD. The
significance of differences between paired measurements was assessed
with Student's paired t test.
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Results |
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TopAbstractIntroductionMethods Results Discussion References |
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Aortic Valve Area
At a normal cardiac output of 5 L/min, which corresponds to a systolic flow of 200 mL/s, the effective valve areas were 0.37 cm2 (0.5 cm2), 0.69 cm2 (1.0 cm2), 0.90 cm2 (1.5 cm2), and 1.07 cm2 (2.0 cm2). For the 0.5-cm2 orifices, calculated valve area was dependent on the geometry of the stenosis and ranged from 0.35 cm2 (Y-shaped orifice) to 0.42 cm2 (circular orifice with long nozzle) (see Tables 1
and
2).
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For all stenotic models, valve area increased with
increasing flow and
Reynolds number. The flow depen-dence of valve area was maximal for the
least severe obstruction (Fig 3). Within the low range
of flow (100200 mL/s), valve area increased by 24% (2.0
cm2), 20% (1.5 cm2), 13% (1.0
cm2), and 6% (0.5 cm2). Further increase in
flow (200300 mL/s) had only a small effect on calculated valve area
(see Table 2
).
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The transition from an increasing to a
nonincreasing phase of valve
area was dependent on the ratio of Reynolds number to the effective
valve area. When Re/AVAEFF exceeded 10 000, calculated
valve area reached a plateau and was independent of the actual flow
(Fig 3).
Valvular Resistance
At a standard cardiac output of 5 L/min,
valvular resistance
ranged from 64 (2.0 cm2) to 639
dynes · s · cm-5 (0.5 cm2). For a
constant orifice size of 0.5 cm2, valvular
resistance was 693 (Y shaped), 635
(slitlike), 546 (short nozzle), and 515 (long nozzle)
dynes · s · cm-5.
Within the low range
of transvalvular flow (100200 mL/s), the
increase in valvular resistance ranged from 21% (2.0-cm2
orifice) to 66% (0.5-cm2 orifice). Flow augmentation from
200 to 300 mL/s resulted in an additional increase in valvular
resistance of 20% (2.0-cm2 orifice) to 51%
(1.0-cm2 orifice) (Fig 4, Table 2).
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Stroke Work Loss
Stroke work loss at 5 L/min was 10% (2.0
cm2), 14%
(1.5 cm2), 22% (1.0 cm2), and 49% (0.5
cm2). This index demonstrated a considerable increase (43%
to 100%) during flow augmentation at low-flow states (100200 mL/s).
The further increase in flow (200300 mL/s) resulted in an additional
increase in stroke work loss: 20% (2.0 cm2) to 43% (1.0
cm2) (Table 2, Fig
5).
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Discussion |
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TopAbstractIntroductionMethods Results Discussion References |
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In several studies,3 4 6 7 8 the accuracy of the Gorlin formula for the assessment of aortic stenosis has been challenged. Thus, stroke work loss has been claimed to be a measure of stenotic valvular lesions that obviates the assessment of transvalvular flow and appears to remain more stable than Gorlin valve area.9 10 Alternatively, valvular resistance, the simple ratio of transvalvular pressure gradient to flow, has been proposed as a valid parameter for quantification of aortic stenosis.3 5 6 7 8 Calculated aortic valve area has been found to increase significantly more than valvular resistance either during exercise2 or after the application of nitroprusside17 or dobutamine.3 With the assumption that in calcific aortic stenosis the anatomic valve area is flow independent and remains unchanged under varying hemodynamic conditions, the stability of valvular resistance has been interpreted as an argument favoring valvular resistance over valve area calculations for assessment of the severity of aortic stenosis.6 7 8 18 However, a flow-mediated increase in true anatomic valve area could also explain why valvular resistance varies less than valve area. Whether a flow-dependent increase in calculated valve area is due to an actual change in anatomic valve area or due to the Gorlin formula cannot be clarified under clinical conditions but requires exploration under well-controlled in vitro conditions.
In the present study, rigid stenotic orifices were mounted in a
pulsatile aortic flow model to evaluate the impacts of valvular
resistance, stroke work loss, and Gorlin valve area as hemodynamic
indicators in aortic stenosis. At low-flow states, flow augmentation
(100200 mL/s) increased valve area less than stroke work loss and
valvular resistance. During further increase in transvalvular flow
(200300 mL/s), calculated aortic valve area remained constant,
whereas valvular resistance and stroke work loss demonstrated a
continuing increase (Fig 6). For all stenotic orifices
used in this setting, a square-law dependence of pressure gradient on
flow was found (Fig 7).
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This supports the concept underlying the Gorlin formula (that pressure gradient is proportional to the square of flow) but is an argument against the assessment of valvular resistance (simple ratio of pressure gradient to flow) or stroke work loss for assessment of aortic stenosis.
It is well known from the study of fluid dynamics that the coefficient of velocity, which represents the viscous losses at the inlet of the stenosis, varies with flow at low Reynolds numbers but remains constant at larger Reynolds numbers.19 20 In the present study, the Reynolds number exceeded 2200 in all cases. Under these circumstances, viscous losses can be neglected. Thus, the documented increase in effective valve area at low-flow states cannot be interpreted as a flow-dependent increase in the coefficient of velocity (cV)21 but rather expresses an increase in the coefficient of orifice contraction (cC; the ratio of effective valve area and anatomic valve area) ("improved streamlines of flow as the velocity of pulsatile flow increases"22 ). In contrast to our results, Cannon et al23 noticed a linear relation between transvalvular pressure gradient and flow, supporting the concept of valvular resistance. However, Cannon et al restricted their experimental study to low-flow states because their circulation model did not allow ventricular pressures of >150 mm Hg. In concordance with our results, Flachskampf et al24 found no appreciable change in valve area with flow. However, these authors used a steady-state model and did not specifically address low-flow rates. Finally, Segal et al21 performed an in vitro study to evaluate the effect of flow on Gorlin valve area. They also found a flow dependence of the Gorlin formula at low-flow states and, thus, considered Doppler-determined valve area to be more accurate than Gorlin valve area. However, in this study only very small stenotic orifices—0.06 and 0.34 cm2—were used. In these unphysiological models of aortic stenosis, viscous losses may become significant ("spray phenomenon") and prohibit the application of the simplified Bernoulli equation as a prerequisite of the Gorlin formula.20 25
Our experimental data were adopted to interpret the results of three
clinical studies in aortic stenosis that demonstrated a flow-dependent
increase in calculated valve area either during exercise2
or after administration of dobutamine3 or
nitroprusside.17 The analysis of the pooled data from
these three studies revealed that mean Gorlin valve area increased
significantly, by 17% (0.72±0.260.84±0.31 cm2)
(Table 3). Our experimental data are of help in determining
whether this increase is due to the Gorlin formula or
represents an actual increase in the valve orifice. Calculation
of the Reynolds number (Re) and effective aortic valve area
(AVAEFF) revealed that the ratio of Re to
AVAEFF exceeded 10 000 before flow augmentation in almost
all of these patients (Table 3, Fig 8). Our
experimental results suggest that beyond this flow range, no further
increase in the contraction coefficient can be expected. Thus, it can
be concluded that the flow-dependent increase of valve area, which was
found in these clinical studies, does not represent a
"computational artifact of the Gorlin formula"2 or a
"flow dependence of the Gorlin formula"3 but rather
is due to true further increase in actual valve area in the individual
patients.
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Study Limitations
For the present study, a newtonian fluid
was used,
whereas blood is a nonnewtonian medium with velocity-dependent
viscosity. However, because all flow conditions are in the turbulent
range, nonnewtonian viscosity effects can be neglected.
Pressure measurements within the vena contracta are necessary for calculation of effective aortic valve area according to the Gorlin formula.26 These pressure measurements alter the hemodynamic conditions at the stenosis and thus were abandoned in the present study. Under consideration of pressure recovery,27 28 effective valve area was calculated. It has previously been shown that this calculation is reliable under well-controlled conditions.15 29
Because the jet velocity was not directly measured, the Reynolds number was derived from pressure measurements according to the simplified Bernoulli equation. The simplified Bernoulli equation (ie, Torricelli's law) assumes that there are negligible viscous losses upstream of the vena contracta. This is expected to be valid when the Reynolds number is sufficiently large (>1500). Several experimental studies confirmed the reliability of the Bernoulli equation within this flow range.20 25
In the present study, effective aortic valve area was assessed. No attempt was undertaken to calculate anatomic valve area, which necessitates the inclusion of an empirically derived discharge coefficient. In correspondence, the flow dependence of the true or anatomic valve area, which was found in patients with aortic stenosis,2 3 17 has not been directly measured but rather calculated from the pressure and flow measurements. However, we agree with Dumesnil and Yoganathan30 that the effective area is the more important variable to consider clinically because it is directly related to pressure and flow. It better reflects the patient's clinical and hemodynamic status than the anatomic area.
For calculation of valve area, the square root of the mean pressure
gradient was used instead of the more correct root-mean-square
gradient. Although this simplification may lead to an underestimation
of effective valve area by 
10%,31 we adopted the
original version of the Gorlin formula to make a valid comparison of
the experimental data and the clinical results.
Conclusions
Within the physiological range of transvalvular
flow, valvular
resistance and stroke work loss were flow dependent, whereas calculated
aortic valve area remained constant. This is due to the squared
relation between pressure gradient and flow, which was confirmed in
this pulsatile flow model.
In aortic stenosis, calculation of valve area according to the Gorlin formula is superior over valvular resistance or stroke work loss, which must be indexed for flow to quantify the hemodynamic severity of the obstruction.
Calculation of the Reynolds number and valve area revealed that the flow-dependent increase in calculated valve area, which has been described in the cited clinical studies in aortic stenosis, does not represent a computational error of the Gorlin formula but is generally due to an actual increase of orifice size.
In low-flow, low-gradient situations, the Gorlin formula may overestimate the actual severity of aortic stenosis. Because the effect of increasing flow on actual orifice area cannot be predicted by the measurements at rest,32 maneuvers to increase cardiac output may be necessary to fully characterize the severity of aortic stenosis.
Calculation of Reynolds Number
The Reynolds
number (Re) is calculated as follows:
 | (1) |
where
v is cross-sectional averaged fluid velocity, d is
diameter of the vena contracta, and kinematic viscosity
=3.4 · 10-2 cm2/s.
The continuity equation yields:
 | (2) |
Under the assumption that the orifice is circular, AVAEFF can be calculated as follows:
 | (3) |
Thus,
for calculation of the Reynolds number, v and d (Equation 1)
are
replaced:
 | (4) |
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Calculation
of Effective Aortic Valve Area
For the valid assessment of valve area
according to the Gorlin
formula, the maximal transstenotic pressure gradient
(PV-PX) is necessary.26 However,
in the present study, pressure was not measured within the vena
contracta at the site of minimal aortic pressure X but rather at the
site A distal to the region of pressure recovery. Thus, the maximal
pressure gradient (PV-PX) has to be derived
from the measured pressure gradient or total pressure loss
(PV-PA). The difference between PX
and PA corresponds to the amount of pressure recovery,
which can be calculated according to the simplified Bernoulli equation
and the momentum
equation15 :
 | (5) |
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With
the simplified Bernoulli equation (Equation 6) of
 | (6) |
can be rearranged:
 | (7) |
It yields the relation between the maximum pressure gradient (PV-PX) and the total pressure loss (PV-PA):
 | (8) |
The
Gorlin formula is a special version of the continuity
equation (Equation 2), which uses the simplified Bernoulli
equation to
replace the velocity term (in mL/s):
 | (9) |
The combination of Equations 8 and 9 gives:
 | (10) |
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 | (11) |
Thus, when the Gorlin formula is calculated using (PV-PA) instead of (PV-PX), a functional aortic valve area (AVAF) will be assessed. Between AVAEFF and AVAF, the following relation exists:
 | (12) |
C
is replaced according to Equation 5, and thus Equation
12 can
be rearranged as
follows:
 | (13) |
Under
the assumption AVAEFF<<AA, the
equation yields:
2 · AVAEFF2/AA2
AVAEFF2/AA2.
Thus, Equation 13 can be simplified as
follows:
 | (14) |
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Thus, AVAEFF can be calculated from AVAF and AA (6.15 cm2 in this circuit):
 | (15) |
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 | (16) |
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Received April 12, 1994; revision received August 12, 1994; accepted September 23, 1994.
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References |
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TopAbstractIntroductionMethods Results Discussion References |
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