European Journal of Echocardiography (2008) 9, 578–584
doi:10.1093/ejechocard/jen156
EXPERIMENTAL PAPER
Non-invasive estimation of pressure gradients
in regurgitant jets: an overdue consideration
Alessandro Giardini1 and Theresa A. Tacy2*
1
Pediatric Cardiology and Adult Congenital Unit, University of Bologna, Italy; and 2Division of Pediatric Cardiology,
University of California, 505 Parnassus Avenue, M342A, San Francisco, CA 94943-0214, USA
Received 1 November 2007; accepted 13 April 2008; online publish-ahead-of-print 7 May 2008
KEYWORDS
Doppler;
Regurgitant jet;
Pressure gradient
Aims This investigation sought to discern the relative accuracy of Doppler predictions of pressure drops
in regurgitant jets across a broad spectrum of conditions, using an in vitro pulsatile flow model.
Methods and results We studied the accuracy of Doppler pressure gradients derived from regurgitant
jet peak velocities using the simplified Bernoulli equation (SBE) using an in vitro flow model of atrio-ventricular valve regurgitation. We observed overall a good correlation (r = 0.89, P , 0.0001) with actual
pressure gradient, when there is normal fluid viscosity and the jet is free of wall interaction.
However, we observed various degrees of underestimation of pressure gradient by Doppler when regurgitant chamber size was reduced (P = 0.0003), when fluid viscosity was increased (P , 0.0001), or in the
presence of wall interaction (P , 0.0001). Chamber compliance had no effect on the accuracy of
pressure gradient prediction (P = 0.36). Significant underestimation error in pressure gradient prediction
by Doppler of up to 43.2% was observed.
Conclusion When jet impingement or wall interaction are present, or when viscosity is increased,
caution should be used in applying the SBE to a regurgitant jet, as significant underestimation in
pressure gradient prediction may occur.
Introduction
The prediction of ventricular pressure from the velocity of a
regurgitant jet escaping from that chamber is an important
aspect of the quantitative echocardiographic exam.1 This
prediction is based on an assumed complete conversion
from potential to kinetic energy. The mechanical energy
balance equation says, in essence, that energy is never
lost, only converted, and as applied to flow across a restrictive orifice, it states that potential energy is converted to
kinetic energy. Potential energy is that harnessed by the
high-pressure chamber, whereas kinetic energy is that
within the high-velocity jet. If one assumes perfect conversion from potential to kinetic energy, one can measure the
pressure drop across the restrictive orifice by using the simplified Bernoulli equation [SBE; DP = 4 (Velocity of the
regurgitant jet)2].2 This application assumes that there are
negligent thermal or viscous energy losses. This simple
mathematical relationship is widely accepted and applied
in cardiovascular applications.
* Corresponding author. Tel: þ39 03495877172.
E-mail address: [email protected]
There are, however, many physical factors which impact
flow conditions and result in imperfect transformation of
potential to kinetic energy. In these settings, the accuracy
of the SBE is adversely affected and can result in either an
overestimation or underestimation of a pressure gradient,
depending upon which physical factors are involved.3 Investigations into Doppler accuracy have been plentiful, yet
have been applied exclusively to stenotic jets.4–10 In clinical
practice, the regurgitant jet is often regarded as error-free.
A belief in a fortuitous and perfect cancellation of errors is
often cited as the reason for this belief.
However, the regurgitant jet often experiences conditions
that impact the relation between SBE-predicted and actual
pressure drop. For instance, in atrio-ventricular valve regurgitation, interaction with the atrial wall, alterations in atrial
compliance, and viscosity deviations from normal should all
have an impact on the accuracy of the SBE-predicted gradient by Doppler.
This investigation sought to discern the relative accuracy
of Doppler predictions of pressure drops in regurgitant jets
across a broad spectrum of conditions, using an in vitro pulsatile flow model. We hypothesized that conditions commonly experienced by regurgitant jets, such as regurgitant
chamber size, wall interaction, viscosity, and altered atrial
Published on behalf of the European Society of Cardiology. All rights reserved. & The Author 2008.
For permissions please email: [email protected].
Non-invasive estimation of pressure gradients in regurgitant jets
579
compliance, could result in an inaccurate prediction of
pressure drop when the SBE was employed.
Methods
Model
To address this hypothesis under controlled conditions, a pulsatile
flow model of atrio-ventricular valve regurgitation was used. This
in vitro model provided for varying fluid viscosity, regurgitant
chamber size, interaction between the regurgitant jet and the
lateral wall, and regurgitant chamber compliance. The pulse simulator consisted of the following components (Figure 1).
(1) An atrial reservoir consisting of a polymethyl methacrylate
crystal-clear box. The material used is particularly suitable for
in vitro studies given the high transparency to ultrasound
waves. The inflow was located on a lateral wall, and the
outflow was located on a wall adjacent to the inflow, at
the same height. A bovine aortic valve was mounted in the
outflow to create an atrio-ventricular valve. A 4.0 mm hole
was punched into one of the valve leaflets to create a regurgitant orifice. A 6 F pressure port was present on the lateral
wall opposite to and at the same level as the inflow.
(2) A ventricular pumping chamber consisting of a compressible
bulb. Ventricular contraction was accomplished by compression
of the bulb using an external air source. Solenoid valves under
computer control opened and closed the inlet and exhaust
ports of the ventricular chamber. The timing of the solenoid
valves was computer-controlled. A 6 F pressure port was
present on the ventricular side of the atrio-ventricular valve,
at the same level as the atrial pressure port.
(3) An aortic flow chamber consisting of a valve and an arterial compliance section. Total aortic flow was measured by an externalclamp Doppler flow-meter (model T110, Transonic Systems Inc.,
NY, USA).
(4) A resistance section distal to the aortic compliance section, consisting of capillary tubing in parallel. By occluding different proportion of the tubes, the peripheral resistance could be varied
in a reproducible fashion.
Figure 2 Modification of regurgitant chamber size and of wall
interaction in the model. Atrial chamber size was modified by
direct immersion of a plastic bulkhead into the atrial chamber 6,
4.5, 3, and 1.5 cm proximally to the regurgitant valve (A). To evaluate the impact of wall interaction on regurgitant jet velocity, an
appropriately shaped plastic bulkhead was placed in continuity
with the valve ring (B). AV, atrio-ventricular.
regurgitant jet velocity, an appropriately shaped plastic bulkhead
was placed in continuity with the valve ring (Figure 2B). Absence
of wall interaction was evaluated by removal of the lateral bulkhead. Two different conditions of atrial compliance were considered: low atrial compliance was modelled by sealing the roof of
the regurgitant chamber, high atrial compliance by leaving the
roof open.
For each experimental condition, the pulse simulator was filled
with a solution of 10, 30, and 50% glycerin by volume, to obtain a
range of fluid viscosities from 1 to 5 cPs. For each condition,
0.5 g of cornstarch was added to the glycerin solution to improve
Doppler velocity profile. Three different and interchangeable sections representing resistance levels of 2, 10, and 20 mmHg/L/min
were fashioned to simulate after-load ranging from pulmonary to
systemic arterial conditions. Filling pressure of the atrial chamber
was between 5 and 7 mmHg for all conditions. A total of 144 different conditions were studied. For each experimental flow condition,
three samples were analysed and the average of these was used in
subsequent analysis.
The pulse rate was 70 bpm, and the flow rate was maintained
between 3 and 5 L/min for all conditions studied.
Data acquisition
Flow conditions
The following conditions were varied: atrial chamber size, atrial
chamber compliance, presence of lateral wall jet impingement,
peripheral resistance, and fluid viscosity. Four different atrial
chamber sizes were studied (6, 4.5, 3, and 1.5 cm of length).
Atrial chamber size was modified by direct immersion of a plastic
bulkhead into the atrial chamber proximally to the regurgitant
valve (Figure 2A). To evaluate the impact of wall interaction on
Figure 1 Fluid loop model. AV, atrio-ventricular; FP, flow probe.
The solenoid valve and pressure transducers were interfaced to a
Macintosh PC running customized software (LabView, National
Instruments, Austin, TX, USA) through a 16 bit analogue-to-digital
converter, which allowed for simultaneous control of ventricular
ejection as well as recordings of atrial and ventricular pressures.
In the atrial and ventricular chambers, instantaneous pressures
were recorded with fluid-filled catheters connected to disposable
pressure transducers (Merit Medical Systems Inc., UT, USA), once a
steady state was achieved. The actual peak atrio-ventricular
pressure gradient was measured from these tracings.
For each flow condition, continuous wave Doppler recordings of
regurgitant jet flow velocity were obtained with the use of an ultrasound machine (Acuson Sequoia, Siemens Medical Solutions, USA),
equipped with a 3.0 MHz transducer. The continuous wave Doppler
beam was aligned parallel to flow to avoid error in velocity measurements. Continuous wave Doppler was preferred to pulsed wave
Doppler for the high flow velocities to be measured, and because
of the independence of peak velocity measurement from the position of the sample volume along the pathway of the regurgitant
jet. The spectral Doppler image was digitally transferred to a personal computer running Acuson KinetDx DS3000 software (Siemens
Medical Solutions), for analysis and storage purposes. With the use
of KineticDx software, the predicted peak gradient of the Doppler
signal was calculated using the SBE.
The difference between the actual and the Doppler predicted
peak atrio-ventricular pressure gradient was calculated for each
condition. The percentage of error of over- or underestimation of
580
A. Giardini and T.A. Tacy
Doppler-estimated pressure gradient was calculated as: error% ¼
[(SBE 2 predicted
pressure
gradient/actual
pressure
gradient)21] 100.
Data analysis
The per cent error in Doppler prediction of the actual pressure gradient was calculated. The logarithm of the per cent error (LPE) data
was calculated to transform the data to a normal distribution. The
LPE therefore is the outcome variable.
The impact of each of the four variables (wall interaction,
chamber compliance, fluid viscosity, and chamber size) on LPE was
assessed. The Mann–Whitney test was used to assess the impact of
each dichotomous variable (wall interaction and chamber compliance) on LPE; the variables for each were coded as 0 (no wall interaction, low compliance) or 1 (wall interaction, high compliance).
Viscosity conditions of 1, 3, and 5 cPs were coded as 1, 3, and 5;
the four chamber sizes were coded as 1.5, 3, 4.5, and 6, and each
treated as continuous variables. The Kruskal–Wallis test with
Dunn’s multiple comparison post-test was used to analyse the
impact of these continuous variables on LPE.
The impact of the four variables on LPE was further evaluated by
multiple linear regression. The variables were coded as described
above. The regression analysis calculated a P-value, an r value,
and coefficient for each independent variable. To assess the
impact of each condition tested on accuracy of Doppler pressure
gradient prediction, the fold effect was calculated for each independent variable as: exp (coefficient).
Percentage effect of each independent variable was calculated
as=100 [exp (coefficient)21]. The interaction between two
factors was calculated as net effect, using the equation=100 [exp (coefficienta coefficientb)21]. To analyse the possible interaction between different parameters, multiple linear regression
analysis was repeated using a model considering multiplicative effects. A P-value of ,0.05 was considered statistically
significant.
Figure 3 Correlation between actual and Doppler-predicted
pressure gradient across the regurgitant valve. PG, pressure
gradient.
Results
Actual pressure gradients measured across the atrioventricular valve ranged from 70 to 182 mmHg for different
flow conditions. Pressure drops predicted by the SBE ranged
from 40 to 204 mmHg. As expected, there was a significant
correlation between actual and Doppler-predicted pressure
gradients (r = 0.89, P , 0.0001; Figure 3).
We observed a progressive underestimation of pressure
gradient by Doppler when regurgitant chamber size was
reduced from 6 to 1.5 cm (P = 0.0003; Figure 4), when fluid
viscosity was increased (P , 0.0001; Figure 5), or in the presence of wall interaction (P , 0.0001; Figure 6). No significant difference in LPE was observed when chamber
compliance was reduced (P = 0.36; Figure 7). The progressive Doppler underestimation of pressure gradient following
decrease in regurgitant chamber size was particularly
evident when physiologic viscosity (3 cPs) was considered
(P = 0.0048; Figure 8).
Multiple linear regression also showed a significant negative association between fluid viscosity and LPE
(P , 0.0001; Table 1). Wall interaction resulted in underestimation of the pressure gradient by Doppler (P , 0.0001),
whereas atrial compliance (P = 0.26), and regurgitant
chamber size (P = 0.29) did not appear to be relevant.
Independently, chamber size had no effect; however,
when its effect was considered with fluid viscosity or with
wall interaction, atrial size seems to have an impact
on the Doppler pressure gradient estimation. Indeed, the
Figure 4 Effect of chamber size on log error % in the overall study
conditions. Values were compared with the Kruskal–Wallis test with
Dunn’s multiple comparison post-test.
interaction between wall impingement and chamber size
was significant (r = 20.46, P , 0.0001), as was the combination of fluid viscosity and chamber size (r = 20.26,
P = 0.003), both of which appeared to be significantly associated with an underestimation effect.
No effect of atrial compliance was noted when its interaction with fluid viscosity or with wall interaction was considered (r = 0.26, P = 0.23; and r = 20.11, P = 0.3,
respectively).
Wall interaction showed a fold effect on LPE of 0.76, and a
percentage effect equal to –24.3% (Table 1). Fluid viscosity
showed a fold effect on LPE of 0.57, and a percentage effect
of –43.2%, meaning that as viscosity increases, so does
Doppler underestimation of the pressure gradient.
Non-invasive estimation of pressure gradients in regurgitant jets
Figure 5 Effect of increasing fluid viscosity on log error %. Values
were compared with the Kruskal–Wallis test with Dunn’s multiple
comparison post-test. cPs, centipoises.
Figure 6 Effect of wall interaction on log error %. Values were
compared with Mann–Whitney test.
581
Figure 7 Effect of atrial compliance on log error % in the overall
study conditions. Values were compared with Mann–Whitney test.
Figure 8 Effect of chamber size on log error % in the 3 cPs simulation only. Values were compared with the Kruskal–Wallis test
with Dunn’s multiple comparison post-test. cPs, centipoises.
Table 1 Results of multiple linear regression between log % error and different flow conditions
Flow variable
Wall interaction
Chamber compliance
Chamber size
Fluid viscosity
r
20.278
0.073
0.142
20.566
Discussion
Our study demonstrates that flow conditions that could be
encountered in clinical practice impact the accuracy of
P-value
,0.0001
0.26
0.29
,0.0001
Fold effect
0.76
1.1
1.1
0.57
% effect
224.3%
+7.6%
+15.3%
243.2%
Doppler-derived estimation of pressure gradients in regurgitant jets. In an in vitro model of atrio-ventricular valve
regurgitation, significant pressure gradient underestimation
582
occurred when fluid viscosity was high and when wall
interaction with the jet was present.
Much is known about the factors that impact the accuracy
of Doppler estimation of gradients in stenotic jets. These
include: the relative importance of terms neglected in simplifying the Bernoulli equation, pressure recovery
effects,7,11 fluid viscosity,3 jet eccentricity,12 and others.13
Although there are differences between stenotic and regurgitant jets, many fluid dynamics principles apply to both
kinds of jets. Yet, in clinical practice, the Doppler prediction
of the peak gradient of a regurgitant jet has been widely
assumed to be accurate, possibly due to an assumed cancellation of error. However, this accuracy has not been empirically tested under a variety of flow conditions.
As expected, in our model, we observed an overall correlation between actual and Doppler-predicted pressure gradients (P , 0.0001), with a coefficient of 0.95, suggesting the
presence of an overall underestimation of 5%. This finding
is in accordance with data from clinical studies.14 However,
a favourable correlation does not translate into accurate
pressure gradient prediction for various conditions seen in
clinical practice.
Effect of wall interaction and atrial size
Our data demonstrate that when there is an interaction
between the regurgitant jet and the atrial wall, Dopplerpredicted pressure gradient seems to underestimate the
actual pressure gradient, especially when the size of the
atrial chamber is small. Doppler-catheter discrepancies
under these flow conditions appear to particularly evident
in the case of increased fluid viscosity. Similar haemodynamic conditions are commonly encountered in the echocardiographic examination of children with congenital heart
disease who typically have small cardiac structures and who
may have eccentric regurgitant orifices and increased
haematocrit.
Limitations relative to the Bernoulli principle itself can
explain the underestimation of pressure drop by Doppler
observed for the conditions characterized by small atrial
chamber size and presence of wall interaction, especially if
fluid viscosity is increased. In clinical practice, regurgitant
jets from atrio-ventricular valves are usually considered as
free jets. A free jet is defined as a jet issuing into a relatively
stagnant environment where the cross-sectional area of the
jet is less than one-fifth of the cross-sectional area of the
region of chamber into which it is flowing, and it develops
free from influence of external or chamber boundaries (i.e.
no wall effects).13,15 From engineering studies, we know
that as a free jet leaves a nozzle into a receiving chamber, a
turbulent shear layer develops between the receiving
chamber fluid and the inflow jet stream boundary.16–18 The
shear layer will eventually consume the core of the jet,
from which point the jet becomes fully developed or freely
turbulent.16,18 All sides of the jet are equally affected, and
although the width of the jet experiences instantaneous
changes, the jet expands symmetrically and mean jet width
will also grow over time in a balanced fashion, resulting in a
symmetrical jet flow.13,18 It is also known that as the jet
intrudes into the receiving chamber, vortex motion entrains
surrounding fluid.18 These vortices envelope and drag in
pockets of stagnant fluid, increasing jet mass, and decreasing
flow velocity, and jet kinetic energy transforms into jet
A. Giardini and T.A. Tacy
stream expansion.18–20 Under these flow conditions, viscous
losses related to boundary layers are minimal and pressure
drop across the regurgitant valve can be described by the
reduced form of the Navier–Stokes equations, known as
SBE. However, under experimental conditions, as in clinical
practice, a regurgitant jet might experience significant
lateral or distal interaction with chamber walls. When a
surface is placed beside the nozzle, stagnant flow entrainment through the jet0 s large-scale vortex structures is inhibited on the surface side of the jet, creating an asymmetrical
shear layer between the jet stream and the surface.18–21
Viscous forces acting from the surface in the direction opposite to the jet flow retard the flow adjacent to the
surface.18,22 Because mass entrainment is retarded on the
surface side, and because flow momentum must be conserved
throughout the jet, flow velocities on the surface side of the
jet will be higher than the velocities on the free side.18
However, since flow velocity at the surface must be zero
because of viscosity and the no-slip condition, spatial transverse velocity gradients will be significant, leading to high
shearing forces and increased viscous effects that ‘pull’ the
jet flow towards the surface.18,23 Under these conditions,
viscous losses not accounted for by Bernoulli equation will
lead to underestimation of pressure drop by Doppler ultrasound, especially if fluid viscosity is increased. Such jet–
wall interactions have been extensively studied in different
settings and represent the fluido-dynamic bases of the
Coanda effect.18 In the present experiment, when atrial
chamber size was increased or wall interaction was
removed, the pressure gradient predicted by the SBE
appeared to estimate well the actual PG. Indeed, under
these conditions, no interaction between regurgitant jet
and boundary layers can develop, viscous losses are negligible, and the SBE is applicable.
Effect of fluid viscosity
The range of fluid viscosities studied in the present experiment ranged from 1 cPs (simulating anaemia) to 5 cPs (simulating polycythaemia). An intermediate fluid viscosity of
3 cPs was used to simulate the normal blood viscosity. In
the present study, increased fluid viscosity was associated
with a Doppler underestimation of actual pressure gradient,
whereas reduction of viscosity to 1 cPs was associated with
an overestimation error by Doppler. Fluid viscosity of 3 cPs
was associated with the most accurate Doppler prediction
of actual pressure drop. The SBE is derived from the more
general Navier–Stokes equations, assuming viscous/turbulent losses to be negligible. Therefore, when viscous losses
are not negligible, because of increased fluid viscosity or
jet interaction with boundary layers, SBE-predicted pressure
drop is expected to underestimate actual pressure gradient.13 However, the Bernoulli equation, even in its extensive
form, does not explain the occurrence of overestimation by
Doppler. Therefore, to account for the Doppler overestimation of actual pressure gradient observed during low fluid
viscosity conditions, additional fluid-dynamic phenomena
must be considered, in particular a pressure recovery
effect. Pressure recovery has been extensively studied in
aortic valve stenosis to explain the common occurrence of
Doppler overestimation of actual pressure drop.3,5–8
Both stenotic and regurgitant jets are characterized by a
laminar core just distal to the orifice from which the jet
Non-invasive estimation of pressure gradients in regurgitant jets
emanates. In a stenotic jet, the region where the laminar core
is at its smallest diameter is referred to as the vena contracta,
which is also the location of highest velocity, and the site of
the Doppler detection of peak jet velocity. After the vena contracta, the jet expands into the receiving chamber, some of
the kinetic energy of the jet is dissipated, and some is
returned to potential energy (pressure). Thus, the overall
pressure drop becomes less than the one predicted by
Doppler, since some pressure was ‘recovered’ distal to the
vena contracta site. The magnitude of pressure recovery in
stenotic jets is impacted by the anatomy of the orifice and
the receiving chamber. There is less pressure recovery (and
therefore more accurate Doppler prediction of gradients),
when there is a large receiving chamber, and/or a small stenotic orifice.10 A regurgitant jet is usually defined in fluid
dynamics as a ‘free jet’ with a regurgitant orifice crosssectional area ,20% of the cross-sectional area of the receiving chamber.13 Thus, one expects less pressure recovery
(more accuracy) of Doppler-predicted pressure gradient in
regurgitant jets when compared with stenotic jets.
However, when regurgitant chamber size is reduced, free
jet conditions that apply to the regurgitant jet may be lost,
and the jet becomes a confined jet.
As previously reported in stenotic jets,3 an approach
based on the Reynolds number may be able to reconciliate
discrepancies due to simplification of the Bernoulli equation
and those related to pressure recovery. The Reynolds
number is a dimensionless quantity representing the ratio
of inertial to viscous forces.3 The Reynolds number embodies
viscous forces in its denominator, so that when the Reynolds
number is low (viscosity is high), viscous forces are important by definition. Therefore, at low Reynolds numbers, the
viscous term, which is deleted from the SBE, would be an
important cause of underestimation. With increasing Reynolds numbers, viscous forces would be less important
whereas inertial forces would increase, and pressure recovery effects would be relatively predominant, resulting in
overestimation. Intermediate Reynolds numbers (intermediate viscosity) would lead to an accurate Doppler estimate of
pressure drop by reciprocal cancellation of viscous and
pressure recovery effects.3
These general considerations seem to apply also to regurgitant jets under particular haemodynamic conditions, like
the one observed for small atrial chamber size and wall
interaction. Under these circumstances, the regurgitant
jet becomes ‘confined’. For a ‘confined’ jet, Dopplercatheter discrepancies in the estimation of pressure drops
are regulated by Reynolds number and can be represented
by the following equation:
SBE-predicted pressure drop ¼ actual pressure drop
þ pressure recovery viscous losses
As described above, for high fluid viscosity (5 cPs), inertial
forces responsible for pressure recovery are negligible,
whereas viscous losses become prevalent and lead to
Doppler underestimation of actual pressure gradient. For
low fluid viscosity conditions (1 cPs), viscous losses become
negligible, inertial forces increase, leading to the occurrence of a pressure recovery effect and overestimation of
actual pressure drop by Doppler. For intermediate fluid viscosity (3 cPs), reciprocal cancellation of viscous and
583
pressure recovery effects would lead to an accurate prediction of actual pressure drop by the SBE.
Clinical implications
Doppler ultrasound has become a widely used method for
non-invasive estimation of pressure gradient in regurgitant
atrio-ventricular valves, especially for the estimation of
right ventricular systolic pressures trough Doppler interrogation of tricuspid regurgitant jets. The results of the
present study suggest that particular attention has to be
paid in the estimation of right ventricular systolic pressure
in neonates and infants. Indeed, all the flow conditions
found to alter the accuracy of SBE in the estimation of
actual pressure drops, like abnormal fluid viscosity related
to polycythaemia and small regurgitant chambers (atria)
with great potential for wall interaction, can be encountered in the paediatric age group. The SBE underestimation
related to these flow conditions might be even more significant in paediatric patients with right ventricular outflow
tract obstruction or those with pulmonary hypertension.
Indeed, the observed 43.2% underestimation of the actual
pressure drop by Doppler would magnify the absolute underestimation (in mmHg) in those patients who have high right
ventricular systolic pressure.
Study limitations
In vitro flow modelling is well suited to this type of investigation due to the ability of the investigator to control and
vary flow conditions in order to determine the effects of
various parameters, such as chamber compliance, regurgitant chamber size, and wall interaction in the present
study. However, studies employing in vitro flow modelling
are only as applicable as the modelling is physiologic. In
this investigation, the model analysed extreme conditions
regarding atrial compliance (very low compliance and high
compliance), and wall interaction (wall interaction absent
or present). Regurgitant chamber size and fluid viscosity
could, however, be modulated across a range of physiologic
values. Intermediate values of atrial compliance and of wall
interaction may be present in vivo; therefore, any potential
effect observed between different patients is directly
related to their individual differences.
In the present in vitro model of atrio-ventricular valve
regurgitation, a single circular regurgitant orifice of 4 mm
in diameter was studied. In vivo characteristics of the
regurgitant orifice in terms of size, shape, and number
may vary. Previous computational models have shown
that the haemodynamic behaviour of a double orifice
regurgitant valve does not differ from that of a valve
with a single orifice of same total area and that pressure
drops are not influenced by the configuration of the
valve.24 However, for the same flow conditions, different
sizes of the regurgitant orifice might have produced slightly
different results. Indeed, a larger size of the regurgitant
orifice would directly increase the Reynolds number,
leading to an increase of inertial forces and enhancement
of pressure recovery effects.13
Conflict of interest: none declared.
584
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