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Exp Fluids (2010) 48:837–850
DOI 10.1007/s00348-009-0771-x
RESEARCH ARTICLE
Assessment of left heart and pulmonary circulation flow dynamics
by a new pulsed mock circulatory system
David Tanné • Eric Bertrand • Lyes Kadem
Philippe Pibarot • Régis Rieu
•
Received: 20 February 2008 / Revised: 2 October 2009 / Accepted: 2 October 2009 / Published online: 4 November 2009
Ó Springer-Verlag 2009
Abstract We developed a new mock circulatory system
that is able to accurately simulate the human blood circulation from the pulmonary valve to the peripheral systemic
capillaries. Two independent hydraulic activations are used
to activate an anatomical-shaped left atrial and a left ventricular silicon molds. Using a lumped model, we deduced
the optimal voltage signals to control the pumps. We used
harmonic analysis to validate the experimental pulmonary
and systemic circulation models. Because realistic volumes
are generated for the cavities and the resulting pressures
were also coherent, the left atrium and left ventricle pressure–volume loops were concordant with those obtained in
vivo. Finally we explored left atrium flow pattern using 2C3D?T PIV measurements. This gave a first overview of the
complex 3D flow dynamics inside realistic left atrium
geometry.
D. Tanné E. Bertrand R. Rieu
Equipe Biomécanique Cardiovasculaire, IRPHE-UMR 6594,
CNRS, Aix-Marseille Université, Marseille, France
D. Tanné P. Pibarot
Quebec Heart and Lung Institute/Laval Hospital,
Laval University, Sainte-Foy, QC, Canada
D. Tanné
Protomed, Marseille, France
Abbreviations
MCS
Mock circulatory system
LA
Left atrium
LV
Left ventricle
PA
Pulmonary arteries
AO
Aorta
PIV
Particle image velocimetry
LV, LA
xx
Vxx(t)
Volume of the cavity in ml
Vaxx ðtÞ
Volume of the residual air inside the activation
box in ml
Vacxx ðtÞ
Volume of the activation fluid in ml
Qacxx ðtÞ
Activation flow in l/min
Qaxx ðtÞ
Residual air flow that is the variation of the air
volume due to compressibility in l/min
Qav(t)
Aortic valve flow in l/min
Qmv(t)
Mitral valve flow in l/min
Qpv(t)
Pulmonary venous flow in l/min
Pxx(t)
Pressure in the cavity in mmHg
Paxx ðtÞ
Pressure in the residual air compliance in
mmHg
Ucxx ðtÞ
Reference voltage signal that actuates the gear
pump in V
hxx ðtÞ
Open loop transfer function of the pump
Caxx ; Eaxx Residual air compliance (Caxx ) and elastance
(Eaxx ¼ 1=Caxx ) in ml/mmHg and mmHg/ml,
respectively
L. Kadem
Department of Mechanical and Industrial Engineering,
Concordia University, Montreal, QC, Canada
R. Rieu (&)
Equipe Biomécanique Cardiovasculaire, ECM,
IMT Technopole de Château-Gombert, 38 Rue Joliot-Curie,
13383 Marseille cedex 13, France
e-mail: [email protected]
1 Introduction
Mitral valve dysfunction includes the following: (1) mitral
stenosis that occurs when the valve orifice is narrowed,
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which leads to an augmentation of the pressure difference
across the valve or (2) mitral regurgitation that occurs
when the valve is leaking during cardiac contraction, which
leads to a volume overload in the left atrium (LA). Both
types of dysfunction will thus cause an increase in the LA
pressure and then to a passive elevation of the pressure in
the pulmonary arteries (PA).
When mitral valve disease and PA hypertension become
severe, it is necessary to perform a surgical correction of
the valve dysfunction. The surgeon generally attempts to
repair the diseased native valve. However, in a substantial
proportion of the patients (10–30%), the valve cannot be
repaired and needs to be replaced by a prosthetic (biological or mechanical) valve. The main goals of mitral valve
replacement are, therefore, to restore normal valvular
hemodynamics and to normalize PA pressure. Unfortunately, the regression of PA pressure after the replacement
may vary extensively from one patient to the other and is
often incomplete (Leavitt et al. 1991; Zielinski et al. 1993).
Moreover, some patients with normal or mildly elevated
PA pressure before operation may develop moderate or
severe PA hypertension after mitral valve replacement
suggesting that the implantation of a prosthetic valve may
cause an elevation in LA and PA pressures. Indeed, the
implantation of an under-sized prosthetic valve (prosthesis–patient mismatch) is associated with persistent PA
hypertension (Leavitt et al. 1991; Li et al. 2005; Zielinski
et al. 1993) and higher mortality (Lam et al. 2007; Magne
et al. 2007).
These findings underline the importance of identifying
and, whenever it is possible, avoiding the factors that
promote the persistence or progression of PA hypertension
following mitral valve replacement. As opposed to in vivo
studies, mock circulatory systems (MCS) are powerful
tools to dissect out the independent contribution of each
prosthesis- and/or patient-related factor to the variation of
LA and PA pressures.
We therefore developed a new MCS able to reproduce
the left heart hemodynamics and the systemic and pulmonary circulatory systems. In the vast majority of the
atrio-ventricular models published in the literature, the LA
shape is very simplified, most likely because these studies
were primarily focused on the intra-ventricular flow
dynamics. Some investigators have used a spherical-shaped
LA with one pulmonary venous inlet (Kadem et al. 2005;
Reul et al. 1981), a rigid box (Balducci et al. 2004; Marassi
et al. 2004; Morsi and Sakhaeimanesh 2000), whereas
others simply used a box-tank as a LA chamber (Akutsu
and Masuda 2003; Cenedese et al. 2005; Kini et al. 2001;
Pierrakos et al. 2004; Steen and Steen 1994). Mouret et al.
(2004) used particle image velocimetry (PIV) measurements to explore LA flow dynamics in normal sinus rhythm
and in atrial fibrillation conditions using a more realistic
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LA shape with two symmetrical pulmonary veins. Verdonck et al. (1992) also used this kind of LA shape.
The purpose of this study was to develop a MCS that
accurately simulates the human blood circulation from the
pulmonary valve, i.e., the right ventricular outflow, to the
peripheral systemic capillaries. To this effect, it was
essential to control flows and pressures in each subsystem
(pulmonary circulation, LA, LV, aorta and systemic circulation) to ensure a fluid dynamic behavior close to the
one found in the human circulation. Furthermore, to study
the flow dynamics inside the LV and the LA, an optical
access to the two cavities is required for the acquisition of
velocity fields by PIV. In this paper, we present validation
data for pressures, flows and volumes, harmonic analysis
and PIV measurements in experimental conditions mimicking the physiological situation of a healthy subject
without PA hypertension.
2 MCS design
We enhanced our previous dual activation atrio-ventricular
simulator (Mouret et al. 2000) to study LA and PA flow
dynamics. The LA activation was modified to allow a
complete control of the atrial volume. We added a model of
the pulmonary circulation that simulates the compliance
and the resistance of vessels in the lungs. An additional
gear pump was also incorporated to simulate the right
ventricular ejection into the pulmonary circulation.
Figure 1 shows a schematic representation of this new
MCS and a photo of the atrio-ventricular device.
Two deformable silicon molds are independently compressed or stretched using two gear pumps (Issartier et al.
1978) in order to mimic both LA and LV contractions and
relaxations and to allow the displacement inside the molds
of the fluid of interest, a blood analog named circulatory
fluid. Each mold is enclosed in a rectangular box completely filled with a fluid, named activation fluid, to ensure
adequate atrio-ventricular synchronization and to enable
PIV measurements (see Sects. 2.2.3, 4.3 for more details).
2.1 Silicon mold production
The rationale for using transparent deformable silicon
molds is not only to reproduce the deformation of cardiac
cavities but also to assess the flow patterns within the
cavity using optical techniques such as PIV. The geometry
of the cavity strongly influences the velocity fields. Furthermore, Munson et al. (2005) have reported for orifices a
loss coefficient and differences in flow organization
depending on the shape of the entrance region, i.e., the LA
shape before the mitral prosthesis. We thus elected to
reproduce a human anatomical-shaped LA cavity. Images
Exp Fluids (2010) 48:837–850
839
Fig. 1 a Description of the new left heart and pulmonary circulation
mock circulatory system. Two independent activation fluid circuits
(dash line) allow the circulation of the blood analog fluid (continuous
line). Aortic valve (AV); mitral valve (MV); pulmonary valve (PV);
right ventricle (RV); resistance (R); compliance (C); pump (P); see list
for other abbreviations. b The left atrio-ventricular device
were obtained by multidetector computed tomography
(512 pixels 9 512 pixels) in a healthy subject in sinus
rhythm (heart rate: 66 bpm). The field of view was
250 mm 9 250 mm resulting in a spatial resolution of
0.488 mm. To reconstruct the 3D end-systolic internal
volume of the LA, 190 slices (voxel thickness =
0.625 mm) were used (Fig. 2a). Each slice was segmented
by a simple threshold method, and the resulted contours
were smoothed using cubic splines. We used SolidWorks
(SolidWorks, MA, USA) to slightly modify the shape of
the LA (Fig. 2b). The native oval shape of the mitral orifice
became circular (diameter = 29 mm) to better simulate the
situation of patients with a mitral prosthetic valve. The
shape of the ostial sections of the pulmonary veins were
preserved over a distance of 1 cm and then smoothed to a
10 mm circular section, which were extended by a tube of
length 60 mm to pass through the wall of the activation
box. The LA appendage is a long, hooked and crenellated
structure which length and orifice size vary considerably in
vivo (Ernst et al. 1995). Figure 2a confirms this very
complex shape. We therefore elected to simulate it by a
5 ml volume smoothed cavity with length of 18 mm and a
minimum and maximum orifice size of 14 and 28 mm,
respectively (Fig. 2b). These values are in agreement with
those of Ernst et al. (1995).
Then, an aluminum matrix (Fig. 2c) was manufactured
using a 5-axis milling machine to allow the casting of
external successive layers of silicon (Silopren LSR 2050,
GE Bayer Silicones). We added cylindrical aluminum parts
to the matrix at the end of the pulmonary veins and the
mitral valve to simultaneously mold the atrium and flanges.
These flanges ensure the watertightness and allow an
Fig. 2 a Three-dimensional
atrial volume reconstruction
from images acquired by
computed tomography in a
healthy subject. The mitral
valve (MV) is in the back. Two
of the pulmonary veins are
visible (LLPV left lower
pulmonary vein, RUPV right
upper pulmonary vein), whereas
the two others are hidden by the
atrial body. The atrial
appendage (LAA) is below the
mitral valve. The image also
shows the ascending (in
transparency on the left of the
atrium) and the descending (in
transparency on the right) aorta.
The right (RV) and left (LV)
ventricles are displayed on the
lowest slice while the upper
slice shows the pulmonary
arteries (AP). b Design of the
simplified atrial volume. c The
aluminum matrix. d The final
silicon mold that is inserted in
the atrial activation box
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adequate and reproducible positioning of the cast. The
removal from the mold consisted first in undoing the veins
and then the atrial body (Fig. 2d).
2.2 Numerical model of the LA and LV hydraulic
activation
Recently, Colacino et al. (2007) have developed a numerical
model of pneumatically driven LV mold. In the past, we used
a hydro-pneumatic activation for the LA box (Mouret et al.
2000) to attenuate pressure oscillations. Now, we elected to
validate the idea of two independent hydraulic activations
using a lumped model. The two main advantages of
hydraulic activations are the assessment and the control of
the volume of the two cavities and the minimization of the
distance between the LA and the LV by removing the
flowmeter that was inserted in the mitral position in our
previous MCS (Mouret et al. 2000). In counterpart, this
necessitates an optimal synchronization between the two
cavities to prevent high pressure variations. In this context,
the lumped model allowed us to find the relationship between
instantaneous pressures, volumes, flows and the pump voltage signals inside the LA and LV activation circuits.
2.2.1 Lumped model
Figure 3a and b shows a schematic representation of the
two activation boxes. Although these boxes are completely
filled with fluid, some air bubbles may still remain in the
Fig. 3 Schematic
representation of the ventricular
(a) and atrial (b) activation
boxes and the corresponding
deformable control volumes
including the molds (Vxx(t),
Pxx(t): light gray), the activation
fluids (Qacxx ðtÞ, Vacxx ðtÞ: mid
gray), and the residual air
compliances (Qaxx ðtÞ, Paxx ðtÞ,
Vaxx ðtÞ: dark gray)
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circuit. It is therefore important to analyze the effect of a
residual compliance, due to the compressibility of air, on
the activation performance.
We have represented schematically the remaining air
bubbles as a global volume Vaxx ðtÞ at the top of the boxes.
Because the internal total volumes of the LV and LA boxes
remain constant during the cardiac cycle, the first time
derivatives of VLV(t) and VLA(t), the ventricular and atrial
volumes, respectively, are related to the variations of, on
one hand, the volume of the activation fluid Vacxx ðtÞ and, on
the other hand, the volume of air Vaxx ðtÞ:
oVxx ðtÞ
oVa ðtÞ oVacxx ðtÞ
¼ xx where xx ¼ LV; LA
ot
ot
ot
ð1Þ
Vxx ðtÞ; Vacxx ðtÞ and Vaxx ðtÞ are deformable control volumes
defined by their respective control surfaces (fixed walls of the
boxes, moving walls of the molds and moving activation
fluid-air interfaces). Using the Reynolds transport theorem,
the flow Qaxx ðtÞ that crosses the control surface defining
the volume of air Vaxx ðtÞ is proportional to the variations of
Vaxx ðtÞ:
oVaxx ðtÞ
¼ Qaxx ðtÞ where xx ¼ LV; LA
ot
ð2Þ
The volume of air is a Windkessel model characterized
by the compliance Caxx . The related pressure Paxx ðtÞ is
therefore:
oPaxx ðtÞ Qaxx ðtÞ
¼
ot
Caxx
where xx ¼ LV; LA
ð3Þ
Exp Fluids (2010) 48:837–850
841
Since there was no communication between the
activation and the circulatory fluids, the Reynolds
transport theorem applied to the mass leads to:
oVLV ðtÞ
ot ¼ Qmv ðtÞ Qav ðtÞ
ð4Þ
oVLA ðtÞ
¼ Qpv ðtÞ Qmv ðtÞ
ot
where Qav(t), Qmv(t) and Qpv(t) are, respectively, the aortic
valve, mitral valve and pulmonary venous flows. Similarly,
the variation of the volume of the activation fluid is
proportional to activation flow Qacxx ðtÞ:
oVacxx ðtÞ
¼ Qacxx ðtÞ
ot
where xx ¼ LV; LA
ð5Þ
(LV: gain = 10 dB, -3 dB cut-off frequency =
1.7 Hz. LA: gain = 9.2 dB, -3 dB cut-off frequency =
1.8 Hz) using a frequency analysis.
Therefore, one way to compute reference voltage signals
actuating the pumps is simply to define the three flows
Qav(t), Qmv(t) and Qpv(t) either manually or from in vivo
flow echocardiographic or magnetic resonance imaging
data. Furthermore, to increase the rapidity of the pump
response and attenuate the dynamical error between Ucxx ðtÞ
and Qacxx ðtÞ; a standard proportional–integral–derivative
algorithm has been implemented on a CompactRIO real
time servo-controller (National Instrument, Austin, USA).
2.2.2 Determination of the residual compliance Caxx
2.2.4 Mitral prosthetic valve mounting
For the hydraulic activation, Vaxx ðtÞ must be as small as
possible. To determine this residual volume of air after the
complete filling of the boxes, we measured its corresponding
compliance. If Qav(t), Qmv(t) and Qpv(t) are equal to 0, there
are no variations of the ventricular and atrial volumes since
they still remain filled with the circulatory fluid. Using the
Eqs. 1, 3 and 5 and assuming in first approximation that the
pressure inside the box is the same at any location (i.e.,
Paxx ¼ Pxx ), the compliance Caxx verifies:
The prosthetic valve is mounted on a ring, adaptable to the
model and the size of the prosthesis, which is inserted in
the external wall of the LA and LV activation boxes.
Whereas the atrial box is fixed, the ventricular one is
placed on ball-bearing rails. A compression using a rapid
tightening system allows the watertightness between the
two boxes and the valve ring. Only the circulatory fluid has
to be drained to change the prosthesis. Therefore, the mitral
valve can be rapidly and easily changed to perform, for
instance, preclinical evaluation of prosthesis in standardized physiological and pathological conditions.
Another major improvement is that the double hydraulic
activation allows us to avoid the insertion of a flowmeter
probe in the mitral position so that the circulatory fluid
goes directly from the LA through the mitral valve into the
LV. Inserting a flowmeter proximal to the mitral valve
funnels the flow by adding a straight tube, which leads to
unphysiological flow dynamics. However, according to the
numerical model, the mitral flow can be derived by two
ways from the measurement of the aortic, the pulmonary
venous and the two activation flows as described in:
Qacxx ðtÞ
Caxx ¼ oPxx ðtÞ=ot
where xx ¼ LV; LA
ð6Þ
In practice, we will demonstrate in Sect. 3.1.1 that the compliance Caxx is about 0 ml/mmHg so that the LV and LA activations are not hydro-pneumatic (i.e., Vaxx 0 ml). Therefore,
in the future equations, we will assume that Qaxx ðtÞ 0.
2.2.3 References for the pump voltage signals
As opposed to pneumatic or hydro-pneumatic activation
where the compressibility of air acts as a smooth filter on the
pressures, the use of two independent hydraulic activations
implies an optimal synchronization between the two pumps
to avoid, for instance, an atrial contraction which is more
pronounced than the ventricular relaxation and consequently
the occurrence of LA and LV high pressures. If hxx(t) is the
pump open loop transfer function, the combination of
Eqs. 1, 4 and 5 leads for a hydraulic activation to:
U ðtÞ ¼ h ðtÞ Q ðtÞ ¼ h ðtÞ ½Q ðtÞ Q ðtÞ
cLV
LV
acLV
LV
av
mv
UcLA ðtÞ ¼ hLA ðtÞ QacLA ðtÞ ¼ hLA ðtÞ Qmv ðtÞ Qpv ðtÞ
ð7Þ
where Ucxx ðtÞ is the reference voltage signal, i.e., the
voltage signal that control the pump, and is the convolution product. hxx(t) has been found to be a low-pass filter
Qmv ðtÞ ¼ Qav ðtÞ QacLV ðtÞ ¼ Qpv ðtÞ þ QacLA ðtÞ
ð8Þ
2.2.5 LA and LV volume computation
Finally, the numerical model predicts that the instantaneous volume of each cavity can be accessed from the
measurement of the activation flows by integrating Eq. 1
and replacing the third term by Eq. 5:
Z
Vxx ðtÞ ¼ Qacxx ðtÞ þ Vxx0 where xx ¼ LV; LA
ð9Þ
t
The initial volume is the volume of each mold at rest. It
is equal to 76 ml for the LA and 93 ml for the LV.
The reference voltage signals Ucxx ðtÞ can thus be also
derived from reference LA and LV volumes defined
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Exp Fluids (2010) 48:837–850
manually or by in vivo imaging (magnetic resonance or
echocardiography). We differentiate these volumes to
assess the aortic, mitral and pulmonary venous flows
(Eq. 4). Then, we compute the reference signals for optimal synchronization using the Eq. 7. In case of pulmonary
hypertension, the left atrium is generally dilated with
reduced contractility (Otto 2004). The high percentage of
elongation of the Silopren LSR2050 allows us to simulate
spherical-like atrial shape by further modifying the LA
pump reference voltage signal.
2.3 Similitude
Designing a pulsed cardiac simulator that adequately
mimics the circulatory physiology of the human being is a
complex task. As underlined by Cenedese et al. (2005), the
fluid has strong structure interactions with the valvular
prosthesis and the wall of the cavities such that the most
reliable scale is 1:1. As the design of the MCS is based on
an anatomical-shaped LA and we use commercially
available mechanical or biological valve prostheses, this
scale 1:1 is mandatory.
For a confined unsteady flow, the two dimensionless
numbers that govern fluid dynamic phenomena are the
Reynolds number Re and the Strouhal number St (Marassi
et al. 2004):
Re ¼
qUD
D
and St ¼
l
UT
where D is the diameter of the mitral valve, U is the mitral
E-wave peak velocity and T is the cardiac period. The density q and the dynamic viscosity l are dependent on the
choice of the circulatory fluid. There are two Newtonian
fluids typically used: water and a mixture of glycerol and
water. We used the latter fluid because its viscosity is similar
to the one of blood (4.10-3 N s m-2) by adjusting the proportion of glycerol (around 40%) in the mixture (Kadem
et al. 2005; Marassi et al. 2004; Nguyen et al. 2004). We
favoured the matching for the refractive index and the viscosity at the expense of the density. The mixture density is
nevertheless close to the one of blood (1,130 kg m-3 and
1,060 kg m-3, respectively). Thus, the factor of similitude
is 1 for all the dimensions as opposed to Cenedese et al.
(2005) and Marassi et al. (2004) who increased the cardiac
period by threefold since their circulatory fluid was simply
water. Salt was added to the mixture (concentration: 1 g/L)
for the use of the electromagnetic flowmeter.
composed of a compliance, which accounts for the capacity
of arteries and veins to accumulate and release some
energy during the cardiac cycle, and a resistance, which
models the total pressure loss.
For the pulmonary circulation, we used a third pump to
simulate the systolic right ventricular ejection, i.e., the pulmonary valve flow. The pump is inserted in the physiological
circuit without addition of an activation box. The reference
voltage signal is calculated so as the pump carries the same
stroke volume as the LV does. To allow the diastolic decline
of the PA pressure, a bioprosthetic valve (model Perimount,
size 21, Carpentiers Edwards) is placed between the pump
and the pulmonary compliance and resistance. As opposed to
the systemic model, we added a second compliance between
the resistance and the LA to mimic the pulmonary veins and
capillaries compliance. Finally, the pulmonary vascular load
results in a p-filter, which we also used in previous numerical
simulations (Tanné et al. 2008).
3 Validation of the MCS
We first verified the control and the application of the
numerical model. Harmonic analysis was also performed to
validate the pulmonary and systemic circulations.
3.1 Validation of the numerical model
3.1.1 Residual compliance measurement
We have closed the LA and LV cavities by six quarter turn
valves. In this context, the pumps are excited by a random
disturbance. The activation flow is in that case a limitedbandwidth white noise (Eq. 7). The transfer function
between the input Qacxx ðtÞ and the output P0xx ðtÞ ¼
oPxx ðtÞ=ot is therefore in the frequency domain:
P^0 xx ðf Þ
E^axx ðf Þ ¼ where xx ¼ LV; LA
Q^acxx ðf Þ
where ^ represents the Fourier transform. The Fourier
transform of Eq. 6 implies that the compliance Caxx is the
inverse of E^axx ðf Þ; so that, in the bandwidth, Caxx is equal to
the inverse of the low frequency gain E^axx ð0Þ. We found
that CaLV ¼ 0:061 ml/mmHg and CaLA ¼ 0:096 ml/mmHg:
Compared to the systemic (2 ml/mmHg) or the pulmonary
compliance (40 ml/mmHg), the residual air compliance
can be neglected. Consequently, the flow Qaxx ðtÞ is about
0 ml and Eqs. 7–9 are, therefore, valid.
2.4 Systemic and pulmonary circulations
3.1.2 Mitral valve flow
Regarding the aortic and pulmonary pressures, they are not
only determined by the flows ejected by the ventricles but
also by the vascular load. The systemic circulation is
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In order to further validate the numerical model, we verified the suitability of Eq. 8. We have used our previous left
Exp Fluids (2010) 48:837–850
heart simulator (Mouret et al. 2000) to measure simultaneously the aortic flow, the mitral flow and the LV activation flow. As opposed to the MCS reported in this article,
this simulator includes an electromagnetic flowmeter
(model SR670, Carolina Medical) between the atrium and
the mitral prosthetic valve. Figure 4 depicts the mitral flow
measured with our previous left heart simulator and that
calculated from Eq. 8. During the diastole, there is a very
good agreement between measured and calculated mitral
flows. The residual air compliance has no significant effect,
thus validating the Eq. 8. However, at the opening and
closing of the valve, i.e., at high amplitude pressure drops,
the remaining air is highly compressed or dilated and the
flow Qaxx ðtÞ is then not null. Our previous simulator was
not designed to easily remove air from the activation box
and the pump so that an amount of air stayed inside the
activation circuit. In the new circulatory system, particular
efforts have been done to eliminate the residual air in the
activation system. The pumps have been positioned vertically. All the connections have been machined to avoid
stagnation region, and a dome has been hollowed out in the
top of the ventricular box.
We cannot verify the second part of the Eq. 8 because of
the hydro-pneumatic atrial activation used in our previous
simulator. However, as CaLA CaLV 0 ml/mmHg, we
assume that the mitral flow can also be measured from the
pulmonary venous and atrial activation flows.
3.2 Harmonic analysis
Because the heart is a periodic pump, instantaneous flows
and pressures can be decomposed in the frequency domain
843
using Fourier series. In particular, the ratio of the Fourier
coefficients of pressure to those of flow describes the input
impedance, which is in the aorta and the pulmonary arteries
a measure of the left and right ventricle afterload, respectively (Nichols and O’Rourke 1998). The input resistance
is the impedance at 0 Hz (ratio between the mean values)
and the characteristic impedance is the mean value of the
impedance for frequencies [2 Hz. Instead of analyzing the
temporal variation of the measurements, the in vitro harmonic analysis is an efficient way to verify that the artificial arterial system operates in conditions similar to the
human circulation (Westerhof et al. 1971).
3.2.1 Pressure spectrum
Patel et al. (1965b) have described in vivo normal values
for the pressure spectrum modulus. For each harmonic, we
plot in Fig. 5a, the range of these normal values that we
have normalized to the mean pressure. We have also
plotted the spectrum of the AO, LV, LA and PA pressures
measured with the MCS.
The AO and PA moduli are in very good agreement with
in vivo data suggesting that these in vitro simulated pressures are representative of the human circulatory
physiology.
The fundamental and the first harmonic of the LV
spectrum modulus are also in the physiologic range.
However, the amplitude of the other harmonics is too
high. The amplitude variations of the instantaneous diastolic (time 0.45–0.85 s) ventricular pressure are too high
compared to the systolic phase inducing high amplitude of
the high-ranked harmonics (Fig. 5a). The phenomenon is
more pronounced in the LA spectrum so that we have to
normalize with the harmonic of higher amplitude. Nonetheless, if we scale (factor 1/20 to describe normal pressure amplitudes) our measured LA pressure, the relative
amplitudes of each harmonic (spectrum modulus) come
close to the normal values of Patel et al. (1965b), therefore, validating the shape of the LA pressure waveform
(see Sect. 4.1 for more details). The high amplitude of the
LA pressure does not significantly influence the mean
value and waveform of the PA pressure because the mean
LA pressure is within the normal range and the fluctuations in the LA pressure are damped by the pulmonary
model.
3.2.2 AO and PA input impedances
Fig. 4 Comparison between the measured (dash line) and the
calculated (continuous line) mitral valve flow in our previous mock
circulatory system (Mouret et al. 2000). Important differences are
seen at the onset of valve closing and opening where the effect of the
residual compliance is maximal, due to the sub optimal de-airing of
the activation box in this previous simulator. This aspect has now
been corrected in the new simulator
We also measured the AO input impedance (Fig. 5b). The
modulus and the phase are in accordance with previous
published in vivo data (Patel et al. 1965a) or in vitro
measurements (Cornhill 1977; Mouret et al. 2000). The
input resistance is 1,680 dyn s cm-5. The characteristic
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Fig. 5 a Normalized spectrum
modulus (bold line) of the
respective aortic, ventricular,
atrial and pulmonary arterial
pressures. Normal lines indicate
the range of in vivo data from
Patel et al. (1965b).
Furthermore, we have added the
ventricular and atrial spectrum
modulus (dotted line) of our
previous duplicator (Mouret
et al. 2000). We have also
simulated lower amplitude atrial
pressure. Its modulus (bold
dashed line) is in accordance
with in vivo data suggesting that
the variations of the atrial
pressure are correct.
b Normalized aortic and
pulmonary input impedance
modulus and phase (bold lines).
These data are compared to
aortic (Patel et al. 1965a) and
pulmonary (Milnor et al. 1969)
in vivo impedances. The results
of Mouret et al. (2000) are also
plotted (dotted line) for the
aortic impedance
impedance is 125 dyn s cm-5, representing 7% of the
resistance and is smaller than the characteristic impedance
measured on our previous MCS (Mouret et al. 2000). The
shared property of all phase curves is the negative values
up to 3 Hz, meaning that the flow leads in phase the
pressure.
In turn, we compared the PA input impedance (Fig. 5b)
with the in vivo data of Milnor et al. (1969). The measured
PA resistance and characteristic impedance are 369 and
35 dyn s cm-5, respectively, which is similar to the normal
range of 160–430 dyn s cm-5 for the resistance and 18–
30 dyn s cm-5 reported in humans. In the case of PA
hypertension, Huez et al. (2004) found that these values
reach 1,506 ± 138 and 124 ± 18 dyn s cm-5, respectively. In this new MCS, values of pulmonary resistance
and compliances can be changed easily to simulate PA
hypertension.
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4 Fluid dynamics analysis
4.1 Pressures, volumes and flows
The AO, LV, LA and PA pressures are measured using
Millar catheters (model MPC 500, accuracy 0.5% full
scale). They are calibrated against a water column. Electromagnetic flowmeters (Gould Statham SP2202, accuracy
within 10% full scale) are used to acquire the AO, pulmonary venous and valve flows whereas the two activation
flows are measured using ultrasonic flowmeters (model
28A, accuracy 2% full scale with in situ calibration,
Transonic System Inc., Ithaca, USA). The probes are
clamped on homemade supports that limited acoustic
impedance mismatches. They further allow in situ calibrations which have consisted in randomly distributed
repeated measures of the time to fill a calibrated test-tube.
Exp Fluids (2010) 48:837–850
845
The linearity of the calibration curve is assessed over the
whole flow range of interest [0–35 L/min]. The volume of
each cavity is calculated from the respective activation
flow according to Eq. 9. The analog signals are sampled at
1 kHz using the CompactRIO controller (National Instrument). Figure 6a, b and c shows typical pressure, flow and
volume waveforms obtained at a heart rate of 70 bpm.
These waveforms are very similar to those obtained in
humans (Braunwald et al. 2001; Klein and Tajik 1991).
The small oscillations (harmonics [6) visible on the ventricular and aortic pressures are due to the vibration of the
aortic mold wall which is presently too rigid.
The major improvement offered by our MCS is that the
synchronization of the LV and LA cavities allows the
simulation of physiological variations of the LA pressure.
Despite too high amplitude, the shape of the pressure
waveform is very realistic (Neema et al. 2008): at the
beginning of the ventricular systole, there is a decrease in
LA pressure (A–x wave), which corresponds to the atrial
relaxation, which is followed by the filling of the LA cavity
by the pulmonary venous flow (S-wave). During this latter
phase, the LA pressure therefore increases until aortic
valve closure (V-wave) in late ventricular systole. At the
beginning of the diastole, the mitral valve opens and the
LV is filled rapidly, which translates into a decay in the LA
pressure (V–y wave). During the diastasis, the atrium acts
as a conduit and the flow goes directly from the pulmonary
veins to the ventricle. At the end of the diastole the mitral
flow increases (A wave) because of the atrial contraction,
which in turn induces a LA pressure rise (A) and a reversal
flow in the pulmonary veins (RevA wave).
The good concordance between the shape of the LA
pressure waveform and in vivo data has been already evidenced in Fig. 5a when a 1/20 scaling LA pressure spectrum has been found coherent with clinical data. Although
a servo-controller was designed to ensure the optimal atrioventricular synchronization, a residual error persisted for
the difference Qav ðtÞ QacLV ðtÞ Qpv ðtÞ QacLA ðtÞ; which
theoretically should be 0. This is probably the main cause
of high LA pressure variations. Since mathematically
correct reference voltage signals were generated, the minimization of this error should be achievable by improving
the servo-control algorithm by determining and correcting
the nonlinearities in the system.
Fig. 6 a Left ventricular (solid line) and left atrial (dotted line)
volumes. b Aortic (dashed line), left ventricular (dotted line), left
atrial (solid line) and pulmonary arterial (dot-dashed line) pressure.
A–x and V–y are the two nadirs of the atrial pressure. V and A are the
two specific peaks of atrial pressure. Despite the higher amplitude, the
variations of the atrial pressure are in very good accordance with
physiologic waveforms. c Aortic valve (solid line) and mitral valve
(dot-dashed line) flows. E and A correspond to the rapid filling of the
ventricle and the atrial contraction, respectively. d Pulmonary venous
(dotted line) and pulmonary valve (dashed line) flows. S, D and RevA
are the systolic, the diastolic and the reversal waves of the pulmonary
venous flow. The dots correspond to the instant of the PIV
measurements
4.2 Pressure–volume loops
Another way to characterize the cardiac cavity is to plot the
pressure–volume relationship. An excellent review of
possible applications of these loops, mainly in the LV can
123
846
be found in (Burkhoff et al. 2005). Figure 7a and b report
the ventricular and atrial pressure–volume loops obtained
with our MCS. Because realistic volumes are generated for
the cavities using hydraulic activations and the resulting
pressures are also coherent, the in vitro pressure–volume
loops are concordant with those obtained in vivo (Alter
et al. 2008; Braunwald et al. 2001). In particular, the
LA pressure–volume loop is composed of the two typical
A- and V-loops (Dernellis et al. 1998; Hoit et al. 1994;
Matsuda et al. 1983) corresponding, respectively, to the
atrial contraction and relaxation. Due to the high LA and
diastolic LV pressures variations, some parameters such as
pressure–volume area and stroke work (Suga 2003) are
over-estimated. Nonetheless, the end-systolic (Sensaki
et al. 1996) and the effective arterial (Kelly et al. 1992)
elastances remain quite close to normal values (2.4 and
1.7 mmHg/ml, respectively). The acquisition of such
realistic experimental LA pressure–volume loops confirms
the efficacy of our MCS to simulate human atrial flow
dynamics.
4.3 Particle image velocimetry measurements
4.3.1 Methods
We have designed the present MCS to have an optical
access to both the LV and LA chambers. Furthermore, the
silicon molds have been cured at ambient temperature,
which provides a refractive index (n = 1.42) very close to
the circulatory fluid (n = 1.38). They are also very thin
(0.4 mm) so that the optical distortions are elusive despite
the large deformations of the wall. To illustrate potential
applications of our new MCS, we therefore describe results
from two-components multi-planes (2C-3D?T) PIV in the
left atrium under normal hemodynamic conditions (heart
rate = 70 bpm, no pulmonary hypertension, no atrial
dilatation). A double pulsed mini-YAG laser (120 mJ,
15 Hz, above the top wall of the LA activation box) and a
CCD PIVCAM 10–30 camera (8 bits, 1,000 pixels 9 1,016 pixels, 30 Hz, at right angle with the laser
Fig. 7 a Left ventricular
pressure–volume loop. b Left
atrial pressure–volume loop.
The two physiologic A- and
V-loops are well simulated
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Exp Fluids (2010) 48:837–850
sheet on the rear side of the LA activation box, TSI Inc.,
Shoreview, MN, USA) are both mounted on a z-traverse
micrometric displacement system. Twenty-two planes
(z-axis resolution = 3 mm) slice the whole atrial body and
the ostia of the pulmonary veins. The plane z = 0 mm
coincides with the center of the mitral valve. For each
plane, image pairs are acquired every 0.02678 s (32 phases
per cardiac cycle) and repeated 30 times, which has been
found sufficient to reach a statistical convergence for the
velocities (Kadem et al. 2005). The circulatory fluid is
seeded with Nylon polyamide particles (mean size:
15–20 lm, mean density: 1,130 kg/m3, Goodfellow, Huntingdon, England). The PIV system is synchronized with
the pressure-flow measurements using an external trigger
delivered by the CompactRIO controller. To decrease the
total time of acquisition (some 6 h for the acquisition and
the storage of 21 220 image pairs/41.9 GB), eight pairs are
acquired per cardiac cycle (frequency = 9.3 Hz) with a
constant pulse separation time equal to 300 ls. This time is
calculated from the classical one-quarter displacement rule
and from the measurement of the peak pulmonary venous
flow rate stored by the electromagnetic flow-meter.
Ensemble-averaged recursive cross-correlation is performed (Insight3G, TSI Inc.) starting from a 64 pixels 9 64 pixels interrogation area to a 16 9 16 spot size. A
Nyquist FFT correlator algorithm is used. The calibration
procedure consists in aligning a calibrated target with the
laser sheet and acquiring one image per plane. The resulting x-axis and y-axis resolution varies from 98.6 lm/pixel
(first plane near the camera, z = -24 mm) to 91.6 lm/
pixel (last plane far the camera, z = 39 mm). The center of
the coordinate system (x- and y-axis) is assigned to the
center of the mitral valve (see the coordinate system in
Fig. 3). Vorticity maps are computed using the eight-points
method.
4.3.2 Comparisons with magnetic resonance visualizations
Figure 8 shows six instants using three-dimensional isosurfaces of the two-components velocity vector magnitude.
Exp Fluids (2010) 48:837–850
847
Fig. 8 Iso-surfaces of the
velocity magnitude, from
0.03 m/s (dark blue, e, f) to
0.6 m/s (green blue, b) passing
through 0.41 m/s (a), 0.3 m/s
(a, b, c, d), 0.16 m/s (c, d, e, f)
and 0.08 m/s (e, f), measured by
two-components multi-plane
PIV at mid-systole
(a, t = 0.187 s), at end-systole
b, t = 0.321 s), at mitral valve
opening (c, t = 0.455 s), at
D-wave peak (d, t = 0.589 s),
at mid-diastole (e, t = 0.696 s)
and at atrial contraction
(f, t = 0.776 s). The contour of
the atrial silicon mold is colored
in pale yellow. The two inserts
(a, b) display two acquisition
planes (z = 0 mm and
z = -9 mm) to help for the
visualization. Note the
regurgitation jet located at the
central strut of the mono-leaflet
prosthetic valve. Mitral valve
(MV); left upper pulmonary vein
(LUPV); left lower pulmonary
vein (LLPV); right upper
pulmonary vein (RUPV)
The flows from the left pulmonary veins are not clearly
seen because these two veins are almost orthogonal to the
acquisition plane so that their projections measured by
2C-3D?T PIV are largely under-estimated and almost
equal to 0. Nevertheless, the iso-surfaces of the two right
pulmonary veins, which are almost collinear to the acquisition plane, depict short and large jets with a ball-like
surface at the end due to the formation of small asymmetric
vortices (vortex rings) at mid-systole (Fig. 8a). Indeed, the
jets enter into the atrium where no residual structures
remain after the closing of the mitral valve. At the end of
the systole, the two jets have progressed toward the valve.
They are thinner and longer than at mid-systole while the
atrial volume increases (Fig. 8b). The jet from the right
upper pulmonary vein strikes the wall and seems to be
widened. At the mitral valve opening (Fig. 8c), the flow
converges and slightly accelerates toward the valve.
Figure 8d occurs at the D-wave onset. Four new jets come
into the left atrium. However, at the opposite of the
S-wave, the mitral valve is now opened and the flow passes
directly from the pulmonary veins to the left ventricle.
Indeed, Fig. 8e shows iso-velocities contours mimicking
two tubes, one from each group of two pulmonary veins.
Finally, Fig. 8f shows a nearly uniform low amplitude field
directed toward the mitral valve. The left atrial contraction
acts, at the end of the diastole, as a booster pump which
completely vanishes all vortical structures (Mouret et al.
2000; Zhang and Gay 2008).
Figure 9 describes the evolution of a vortical structure
within the left atrium (z = 12 mm) during systole. The
vorticity magnitude is the highest where the jets from the
right pulmonary veins are located (Fig. 9a, b, c). An anticlockwise structure is forming while the flow from the right
veins continues to circulate according to a clockwise
rotation (Fig. 9d and e). Figure 9f confirms that the jet
from the right upper pulmonary vein passes along the wall
and the periphery of a vortical structure located at the
center of the left atrium, near the mitral valve and the left
pulmonary veins. This is very relevant since Fyrenius et al.
(2001) have described such flow organization in vivo using
123
848
Exp Fluids (2010) 48:837–850
Fig. 9 Two-components
velocity fields (arrows, third
vectors represented) and z-axis
vorticity magnitude
(background) at the plane
located at z = 12 mm at
different phases: t = 0.187 s
(S-wave, a), t = 0.214 s
(b), t = 0.241 s (c), t = 0.268 s
(d), t = 0.295 (e), t = 0.321 s
(f), t = 0.402 s (g), t = 0.509 s
(E-wave, h). During the
ventricular end-systole
(t = [0.268–0.509] s), the
vorticity maps show the
presence of a large systolic
vortex
magnetic resonance phase contrast imaging in healthy
subject. Indeed they support the idea that the left pulmonary venous flows recirculate in vortices at the center
of the atrium whereas the flow from the right upper pulmonary vein passes along the vortex periphery with
123
minimal entrainment (Fyrenius et al. 2001). The formation
of this vortex cannot be really observed in our study
because of very important drop-out velocities which are not
acquired by 2C-3D?T PIV measurements. However, the
Figs. 8 and 9 strongly corroborate a flow organization such
Exp Fluids (2010) 48:837–850
as reported in the literature. The vortex vanishes at the
onset of mitral valve opening (Fig. 9h) resulting in a vortex
duration of 0.24 s, which is very closed to the value
reported by Fyrenius et al. (0.28 ± 0.077 s).
Furthermore, according to Kilner et al. (2000), the
eccentricity of the pulmonary veins avoids the collision of
the four jets by allowing swirling flows such as observed in
our MCS. This justifies the choice of an anatomical-shaped
left atrium and underlines the fact that oversimplified
geometries, as previously used in the past, cannot accurately mimic the cardiac flow dynamics.
However, three components PIV measurements are
necessary in the future to explore the full velocity fields in
the atrium. Apart from another way of validating our MCS,
stereoscopic PIV measurements are necessary to calculate
three-dimensional based vortex identification criteria (such
as k2, Q, D or more complex methods) that will enable a
better understanding of the left atrial flow organization.
Therefore, they may be useful to identify the prosthesis- or
patient-related factors that may alter the normal blood flow
pattern within the left atrium and therefore predispose to
thromboembolism in patients with mitral prosthetic valves
with atrial dilatation and pulmonary hypertension.
5 Summary
We constructed a novel mock circulatory system to assess
the left heart and pulmonary circulation flow dynamics.
A lumped model allows us to derive the correct references
for voltage signals to control the pumps ensuring a synchronization between ventricular and atrial contractions
and relaxations. The main distinctive feature of our MCS is
the two independent hydraulic activations so that the ventricular and atrial volumes are completely controlled. The
harmonic analysis has validated the models of the pulmonary and systemic circulations since their respective
input impedance are similar to those measured in vivo. The
shape of the measured pulmonary arterial and aortic pressure waveforms is therefore realistic. The ventricular and
atrial pressure–volume loops can be used to study the
dynamics of the two cavities. Finally, the MCS allows PIV
measurements to assess flow velocity fields both in the LV
and LA. Two-components three-dimensional PIV measurements in normal hemodynamic conditions depict a
flow organization very closed to the one described in vivo
by magnetic resonance, providing a strong validation of the
duplicator. Mainly, a large vertical structure at the center of
the left atrium during systole is described as previously
reported in the literature.
The MCS described in this article is able to accurately
reproduce the atrioventricular function, the mitral valve flow
dynamics, and the systemic and pulmonary circulations.
849
Hence, this new simulator provides a powerful tool to
explore in vitro the main prosthesis- and patient-related
factors that determine the evolution of LA and PA pressures
and the LV and LA flow patterns following mitral valve
replacement. The main advantage of this in vitro approach is
that each factor can be modified separately, which is difficult
or impossible to achieve in vivo. Moreover, the MCS provides a realistic environment that is highly relevant to the
clinical situation. Most of the hemodynamic factors are
acquired using techniques that are currently used in the
clinical setting, which will facilitate the transposition of the
results acquired in vitro to the in vivo situation.
Acknowledgments We thank Dr. Vhernet and Dr. Mario-Goulart
from the University Hospital Center of Montpellier for their collaboration and their assistance in the acquisition of the cardiac images in
humans. We also thank Frederic Mouret for his collaboration in the
MCS design. This work was supported by a grant from the Canadian
Institutes of Health Research (Dr. Pibarot, MOP 67123), Ottawa,
Canada. Dr. Pibarot holds the Canada Research Chair in Valvular
Heart Diseases, Canadian Institutes of Health Research, Ottawa, ON,
Canada.
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