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Vortex Ring Formation in Left Ventricular Flow: An Energy
Mechanism to Quantify Losses
OLGA PIERRAKOS*, DEMETRI TELIONIS**, PAVLOS VLACHOS*
Mechanical Engineering*, Engineering Science and Mechanics**
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061
USA
Abstract: - A new mechanism for energy losses past mechanical heart valves (MHV) is identified and
presented. The energy losses are attributed to vortex formation past MHV leaflets. Recent studies
support the conjecture that the natural healthy left ventricle (LV) performs in an optimum, energypreserving manner by redirecting the flow with high efficiency. Yet to date, no quantitative proof has
been presented. The present work provides both quantitative results and the basics of a theory,
subject to a number of assumptions that support these arguments. The theory is based on the
dynamics of vortex ring formation, which is governed by a critical formation number (FN) that
corresponds to the dimensionless time at which the vortex ring has reached its maximum circulation
content. Digital Particle Image Velocimetry was used to study the ejection of fluid into the LV. The
clinical significance of this study is that a critical FN can serve as a parameter to quantify LV filling
process and aid clinicians to diagnose patients with diseased and defective heart valves.
Key-Words: - DPIV, vortex formation, left ventricular flow, mechanical heart valves.
hemodynamic performance of the LV.
According to Chandran et al., the geometry of
the valve prostheses as well as the orientation of
the valves may significantly affect the flow
development, including vortex formation,
regions of stasis and disturbed flow in the LV
[2]. Orientations of the aortic valve has been
studied by Kleine et al. and Laas et al. revealing
that the optimal orientation of the SJM bileaflet
valve in the aortic position was achieved when
one leaflet directed toward the right cusp [3-4].
Orientations of SJM bileaflet valves in the
mitral position are fewer. The group of
Chandran et al. studied two orientations and
showed that the more favorable of the two was
the one with the tilt axis perpendicular to the
septal wall because it offered a smoother
washout of the fluid near the left ventricular
free wall [2]. Fontaine et al. utilized pulsed
wave Doppler velocity measurements, 2-D
echocardiography, and selected color Doppler
flow mapping to show that the SJM bileaflet
valve oriented in the anti-anatomical position
with chordal preservations is favored over
1 Introduction
Recent quantitative results support the
conjecture that the natural healthy left ventricle
(LV) operates in an optimum, energypreserving manner, by redirecting the flow with
high efficiency [1]. The flow past mechanical
heart valves (MHVs) induces a combination of
flow characteristics, which are clearly
dependent on the specific valve design and
orientation. These induced flow characteristics
give rise to detrimental effects such as
hemolysis, cavitation, platelet aggregation, etc.
All these conditions reduce the efficiency of the
heart, and could result in many pathological
conditions. It is thus apparent that although
MHVs have received universal acceptance and
recognition, they have not reached a level of
performance comparable to the natural valves.
Today, the most commonly implanted
prosthetic heart valve is the mechanical bileaflet
design. Orientation and valve design have a
significant effect on energy losses; therefore,
orienting prosthetic valves so that flow
disturbances are minimized enhances the
1
tilting disc, porcine bioprosthetic, and
pericardial bioprosthetic valves [5].
Kilner et al. employed magnetic resonance
velocity mapping in atrial and ventricular
cavities [1]. Their most intriguing conclusion
was that the atria and the ventricles redirect the
flow with sinous, chirally asymmetric paths,
thereby minimizing dissipative interaction
between entering, recirculating and out-flowing
streams. The implication is significant, as it
appears to show that the heart pumps blood with
the minimum loss of energy. It is thus essential
that we employ a method to quantify the losses
past heart valves—for both healthy and diseased
cases.
Shear layers shedding past heart valves
generate vortex formation that results to energy
losses. It is thus important that we study and
understand this mechanism in LV flows. The
dynamics of vortex ring formation evolved from
the work of Didden, Pullin, Glezer and Coles,
and Saffman [6-9]. Recently, Gharib, Rambod,
and Shariff (referred to as GRS from hereon)
demonstrated that the generation of vortex
rings, using a piston/cylinder arrangement, is
governed by a universal time scale or formation
number (FN) [10]. The FN corresponds to the
dimensionless time at which the vortex ring has
reached its maximum hydrodynamic circulation
content. In other words, the FN corresponds to
the maximum supply rate of angular kinetic
energy to the vortex ring fluid elements. Once
this maximum is reached the vortex ring
pinches off, allowing the surplus of vorticity to
shed into its wake forming a trailing jet. GRS
provided a theoretical proof of the existence of
the FN based on the Kelvin-Benjamin
variational principle for steady axisymmetric
vortex rings.
In all of these studies, a slug flow model was
implicated as it assumed a uniform velocity
profile with constant piston velocity, which
according to GRS is valid for small stroke
ratios. The mathematical derivation for the slug
model is presented in Saffman [9]; however, the
theoretical development of the energy
maximization principle originates with Kelvin.
For a wide range of flow conditions, GRS
showed that the FN lies in the range of 3.6 to
4.5 [10]. Rosenfeld, Rambod and Gharib
(referred as RRG from hereon) showed that
vortex rings generated by impulsively started
motion of the piston had a FN of approximately
4 in agreement with GRS but in non-uniform
velocity profiles, the FN drastically decreased
[11]. RRG concluded that variations in the
velocity profile affect both the evolution of the
total circulation and also the FN. RRG also
concluded that the FN indistinctly depends on
the velocity programme, the Reynolds number
and the configuration geometry. GRS was the
first to recognize the practical significance of
this limiting process principle as they
speculated that the FN in vortex ring formation
plays a significant role in nature, such as in
possibly optimizing cardiac flows, and even
industrial applications.
Vortex formation generated by shear layers
shedding past heart valves (natural or artificial),
Figure 1, results in energy loss and thus a
reduction in the efficiency of smooth flow
redirection. In this paper, we will present
results on the ejection of fluid into the left
ventricle (diastole) by employing time-resolved
Digital Particle Image Velocimetry (DPIV).
We provide the first quantitative in-vitro proof
that validates this maximization principle for
three heart valve configurations, namely two
mechanical and one porcine valve prostheses in
the mitral position.
Furthermore, we will show that orientation
and design of the MHV can affect the
approximate FN. In a similar sense, the
utilization of mitral jet’s formation number
serves to illustrate and quantitatively validate
Kilner’s observation of asymmetric flow
redirection minimizing energy losses.
Aortic
Mitral
Fig. 1: Schematic of vortex ring
formation in the left ventricle.
2 Methods and Facilities
2
To study the hemodynamic characteristics of
blood flow through heart chambers and valves,
we employ a piston-driven, LV simulator
capable of adjusting the heartbeat and the
volume flow rate. The pressure at the exit and
entrance of the LV are hydrostatically
controlled and can be adjusted by the user.
Figure 2 shows a simple schematic of the mock
circulatory loop. Similar LV simulator
machines have been constructed and operated in
the past [12-15]. The system was characterized
in detail using pressure and flow rate
measurements in order to ensure operational
repeatability. The LV model was flexible,
transparent, and made from silicone. During
this experiment, the center plane, which cuts the
ventricle
approximately in
half,
was
interrogated. Additionally, an image calibration
target was used to confirm that the system was
free of optical distortion arising from index of
refraction mismatch.
2mm thickness to illuminate the area of interest.
The flow is seeded with neutrally buoyant
particles, which serve as flow tracers. The
particle diameter is in the order of 10 microns.
A very fast CMOS digital camera (1000
frames/sec, 512 x 256 pixel resolution) is
synchronized with the laser to capture the
instantaneous positions of the particles. In the
present experiment, a sampling frequency of
1000 Hz was used resulting to a total of 4 secs
of data. The task of the velocity evaluation is
carried using conventional cross-correlation
between the particle image patterns of two
consecutive frames. A total of 125x61 vectors
with grid spacing of 300 microns and error in
the order of +/- 0.005m/s are used to describe
the flow field. The current DPIV system
delivers sufficient temporal and spatial
resolution to investigate the turbulent
characteristics of the flow inside the LV.
Two types of heart valve prostheses were
studied, mechanical (MHV) and biological
(BHV). We used a St. Jude Medical (SJM)
bileaflet mechanical valves and a SJM Biocor
porcine valve. The SJM MHVs tested in the
mitral and aortic positions were cuffless, having
diameters of 31-mm and 29-mm respectively.
The SJM Biocor porcine valve was cuffed and
the respective valve sizes were the same as
those of the MHVs. We used water as the
working fluid. To satisfy the dynamic flow
similarity between the natural heart and our
experimental model, we operated the simulator
at 1-Hz, with stroke volume of 90-mL resulting
to a mean Reynolds number of 2700, based on
the mitral valve diameter of 31-mm. The SJM
valve was placed in the mitral position for the
two
orientationsanatomical
and
antianatomical. In the anatomical position, the
leaflets of the MHV open similar to the
biological heart valve (HV), while in the antianatomical orientation, the leaflets open at an
angle of 90 degrees with respect to the latter.
The flow patterns generated by the two MHV
orientations were compared with those of the
SJM Biocor porcine valve. The latter was
studied not only to document its hemodynamic
performance but also to serve as a reference
case.
Fig. 2: Schematic of the heart simulator.
Preload
Reservoir
Variable
Resistance
Flow
Meters
Test Fluid
H20
Pressure
Transducers
MV
AV
Piston
DAQ
Board
Measurements of the complex pulsatile flow
in the LV require detailed temporal and spatial
resolution. In the present study, we employ a
Time-Resolved
Digital
Particle
Image
Velocimetry system. The ground of Particle
Image Velocimetry was laid in the early
eighties, but it was the work of Willert and
Gharib, Westerweel, and Huang and Gharib that
established the digital implementation of PIV
[16-18]. Our system uses a powerful pulsing
laser (55 Watts) that delivers a plane sheet of
3 Results
3
The filling phase (diastole) of the heart cycle is
studied in association with vortex ring
formation in the left ventricle. In all the
experiments, the time duration of diastole was
0.55 secs or approximately 50% of the heart
cycle. Although a complete assessment of
vortex ring formation and the time-varying
information can be achieved by animating the
time sequence, one instant at approximately
time equal to 0.1 secs (Figure 3) reveals the
formation of the incoming vortex ring entering
the LV. The three velocity fields, corresponding
to the three valve configurations, reveal the
unique vortex ring formation associated with
each case. It is especially important to notice
that for the porcine valve, a unique phenomenon
of the leaflets fluttering induces not only one
vortex ring but also introduces smaller vortical
structures trailing the initial vortex ring. These
vortical structures are not associated with the
pinch-off trailing wake of the initial vortex ring
and this phenomenon will be further discussed
later on. It must also be noted that there is an
asynchronous opening of the MV leaflets,
which induces an asymmetric vortex ring
formation.
Although this violates the
axisymmetric assumption set forth in the
analysis for vortex ring formation, the flow is
too complicated to assume anything else.
(a)
approximation [10-11]. The non-dimensional
vortex formation number FN is given by
t
L U pt
FN  

D
D
0U p (t )dt
D
(1)
where L is the discharge piston position, Up is
the equivalent to the piston velocity (Ūp refers
to the running mean velocity) and D is a
characteristic length, which for this application
is the mitral valve diameter of 31 mm. The total
theoretical circulation  of the discharged jet
was calculated using
Theory 
1 t 2
U p (t )dt
2 0
(2)
This relationship is again based on the slug flow
model approximation. Additionally, the
experimental total circulation over the entire left
ventricular domain was approximated by
Exp   dA
(3)
A
where A is area and  is vorticity.
Figure 4 shows the instantaneous velocity
upstream of the MV. This velocity distribution
corresponds to the maximal instantaneous
velocity (which assuming a parabolic profile is
at the centerline) as measured from the
ultrasonic flow meter, located upstream of the
MV. These upstream velocity profiles for the
three configurations are consistent, as expected,
because the upstream velocity profile is
independent of the valve design and reveal the
characteristics of the piston waveform driving
the heart simulator. Henceforth, we refer to
these velocity profiles as theoretical-upstream.
(b)
Fig. 4: Instantaneous velocity upstream of the
mitral valve for the three configurations.
(c)
Fig. 3: Instantaneous velocity fields downstream of
the mitral valve at time equal to 0.1 secs, (a)
anatomical, (b) anti-anatomical, and (c) porcine
configurations [19].
The velocity profiles downstream of the MV
were calculated via DPIV. The mean velocity
The vortex ring formation analysis presented
here is based on the slug flow model
4
profiles were extracted at a location proximally
downstream and parallel to the valve. Figure 5
shows the instantaneous maximal velocity
immediately downstream of the MV and
parallel to it during diastole for the three
configurations.
According to RRG, the
maximal instantaneous velocity should be used
because of the one-dimensional approximation
of the axial velocity profile being at the center
of the orifice for internal boundary layer flows
[11]. In other words, a parabolic profile is
assumed where the maximal velocity is at the
center. Henceforth, this velocity programme
will be referred as theoretical-downstream.
Figure 5 shows the two orientations of the
mechanical valve to have a more parabolic
velocity programme when compared to the
porcine configuration.
accomplish this. Jeong and Hussain proposed a
new definition and approach to identify
coherent structures and in particular a vortex in
an incompressible flow field [20]. The method
defines a vortex in terms of the eigenvalues of
the symmetric and anti-symmetric parts of the
velocity gradient tensor. For two-dimensional
flows, the discretely determined eigenvalues, 1
and 2, at each point must both be negative for a
vortex to exist. More specifically, 2 > 1and
contours of 2 will reveal the vortices. This
vortex identification approach was employed in
better approximating the circulation associated
to the formation of the vortex ring and also to
approximate the time of pinch-off, as will be
discussed further later.
Figure 6 shows the theoretical-upstream and
experimentally calculated circulation for the
three valve cases as functions of the formation
number (FN). For this figure and the ones that
follow, the FN used was derived using Equation
(1) and the theoretical-upstream velocity
programme. The theoretical circulation was
derived using Equation (2) whereas the
experimental circulation was calculated using
Equation (3) over the entire LV domain
utilizing the vortex identification scheme
mentioned above. Although not shown, the
theoretical-downstream circulation exhibited a
linear trend, similar to the theoretical-upstream
values except with higher slopes, especially for
the two orientations of the MHV. Therefore,
both theoretical-upstream and theoreticaldownstream circulation values are below the
corresponding measured (DPIV) circulation in
the LV. This observation was anticipated,
considering that the slug flow model assumes a
uniform profile. This is also in agreement with
Krueger, Dabiri, and Gharib who concluded that
“the slug model consistently underestimates
vortex ring circulation, especially for small
stroke ratios and the slug model should serve as
at least an approximate guide for determining
the scaling relevant to measurements of the
formation number” [21]. The interesting
observation from Figure 6 is how well the
theoretical circulation correlates with the
experimental porcine circulation. On the other
hand, the experimental circulation for the
anatomical and anti-anatomical orientations is
Fig. 5: Maximal instantaneous velocity downstream
of the mitral valve for the three valve configurations.
It is also important to note the differences in
the theoretical and experimental velocity
programmes (Figures 4 and 5). The theoreticaldownstream peak velocity is approximately
double the theoretical-upstream peak velocity
for the two mechanical valve orientations but
consistent with the porcine case. Although not
shown here, the instantaneous velocity profiles
exhibited very close to parabolic velocity
distributions and this is in agreement with
clinical observations.
In order to accurately quantify the
experimental circulation of the vortex ring from
the DPIV data, we needed to distinguish
between the overall vorticity present inside the
left ventricle and the vorticity associated with
the vortex ring only. Therefore, a vortex
identification scheme was employed to
5
Thus,  = 0.5 was used and this is also in
agreement with Shusser and Gharib [22]. Hill’s
spherical vortex theory assumes axisymmetric,
unbounded, incompressible flow with no swirl
[9]. These assumptions evidently do not hold
true in the present case, but considering the
complexity of the flow field, this is the closest
approximation that could be applied. As we
anticipated, Hill’s spherical vortex ring energy
relationship underestimates the energy of the
vortex ring. This is shown in Figure 7, which
illustrates that the energy for the anatomical and
anti-anatomical orientations is respectively five
and three times higher than the theoretical
energy. Similar trends to the circulation plot
also exist; namely, the energy curves for the two
mechanical valve orientations steadily increase
with increasing formation time except at the end
of diastole (L/D higher than 2) but, in the case
of the porcine valve the energy curve is fairly
flattened and low.
respectively four times that of the porcine
configuration. Additionally, for the anatomical
and
anti-anatomical
orientations,
the
experimental circulation curves show a steadily
increasing circulation with increasing formation
time. On the other hand, the porcine valve
appears to contain a fairly constant circulation
value of 40 cm2/s. What implication does this
observation have on vortex formation and the
formation number? This will be more closely
analyzed in the discussion section.
Fig. 7: Experimental and theoretical energy for the
three valve configurations.
Fig. 6: Experimental and theoretical circulation for
the three valve configurations.
Figure 7 shows the energy of the vortex ring
as a function of the formation time. The
theoretically derived energy (based on the slug
flow model approximation and on the velocities
upstream of the MV) was calculated using the
following relationship:
t
1
3
ETheory  R 2  U p (t) dt
0
2
(4)
where R is the vortex ring radius.
The
experimentally derived energy was calculated
using Hills’ spherical vortex energy relationship
[9], which is a function of the circulation. The
relationship is
1
8 7 3
8
E Exp  R 2 [ln    2 ln ] (5)
2
 4 8

where E is the energy per unit density and  is
the dimensionless core radius /R where  is
the vortex core radius. The circulation in
Equation (5) is the measured circulation from
DPIV results over the entire left-ventricular
domain that is plotted in the Figure 6. We
assumed the vortex ring radius R to be one-half
the MV diameter and the corresponding vortex
core radius to be one-fourth the MV diameter.
It is also important to approximate the time
of pinch-off for the three valve configurations.
This point in time corresponds to the maximum
circulation that the initial vortex ring can attain,
at which time pinch-off occurs leading to a
trailing jet. It has been shown that for a broad
range of flow conditions, the time of pinch-off
referred as the formation number ranges from
0.9 to 4.5 and depends on the velocity
programme, velocity profile, and Reynolds
number [10-11] To approximate the formation
number for the three valve configurations, we
analyzed the instantaneous DPIV data. Using
the vortex identification scheme mentioned
6
previously, we were able to investigate the
vortical structures present in the LV
instantaneously. This was accomplished by
plotting contours of the 2 eigenvalue. Figures
8, 9, and 10, corresponding to the three valve
configurations, show 2 contours for two time
instants (one before pinch-off and one after).
For the two orientations of the MHV, the first
time instant (prior to pinch-off) corresponds to
FN equal to 0.25 and it is evident from the 2
contours, Figures 8a and 9a, that the initial
vortex ring has formed but the trailing jet has
not, therefore pinch-off has not occurred yet.
By FN of 0.60 and 0.80, respectively for the
anatomical and anti-anatomical orientations,
pinch-off has occurred. Although it cannot be
seen here, analysis of the instantaneous data has
shown that the critical FN for the two
orientations of the MHV is approximately 0.35
and 0.6.
occurred. Instead, we observed that the critical
FN for the porcine case is about 1.0 (Figure
10b). It may also be that there truly is not a
critical FN for the porcine valve but rather
appears that way because of the fluttering
phenomenon present. This hypothesis would in
fact correlate with the circulation and energy
analysis (Figures 6 and 7), which reveals values
below theoretical. This implying that a critical
FN does not exist, because pinch-off does not
occur. In either case, it is clear from this
analysis that the porcine configuration has the
highest FN, followed by the anti-anatomical
orientation and lastly the anatomical one.
Fig. 10: Contours of 2 (left column) and vorticity
(right column) during formation times (a) T=0.50
Fig. 8: Contours of 2 (left column) and vorticity
(a)
(b)
and (b) T=1.0 for the porcine configuration.
(a)
(b)
3 Discussion
Although the present analysis of ventricular
flow violates some of the assumptions of the
slug flow model approximations, the results do
suggest that valve orientation and design affect
the critical FN. For our purpose, the slug flow
model was appropriate, even if it presented an
underestimated approximation of circulation
and energy of the vortex ring. The results
showed that the critical formation number for
the porcine valve was at least twice that of the
two orientations of the MHV. This suggests
that for the porcine valve there is a delay in
vortex ring pinch-off, which thus implies less
energy losses and a better overall performance.
In comparing theoretical and experimental
circulation and energy among the three
configurations, several differences were
observed.
The experimentally derived
circulation was highest for the anatomical
(right column) during formation times (a) T=0.25
and (b) T=0.60 for the anatomical orientation.
Fig. 9: Contours of 2 (left column) and vorticity
(right column) during formation times (a) T=0.25
(a)
(b)
and (b) T=0.80 for the anti-anatomical orientation.
For the porcine valve, though, Figure 10a
shows that by FN=0.5, pinch-off has still not
7
orientation followed by the anti-anatomical and
then by the porcine valve. Considering the
valve design alone, one would expect the two
bileaflet orientations of the MHV to generate
more vorticity due to the presence of sharp solid
edges that correspond to a three jet orifice. On
the other hand, the flexible tri-leaflet design of
the porcine valve produced a single jet orifice
with less overall surface area.
Moreover, an observation that was not
anticipated was the character of the circulation
and energy curves (Figures 6 and 7).
Interestingly, with increasing formation time,
circulation and energy gradually and
continuously increase for the two mechanical
valve orientations. On the other hand, for the
porcine valve, circulation and energy remain
fairly constant, on average, for the duration of
diastole. The implication is that there is no
extra vorticity shed from the BHV leaflets and
that perhaps vortex ring pinch-off is nonexistent. The flexibility of the porcine valve
leaflets introduces a fluttering phenomenon in
the flow field and it is believed that this
mechanism aids in limiting the vorticity shed,
thus limiting circulation and energy losses. It
seems that this mechanism is the heart’s optimal
design for limiting energy losses past a healthy
heart valve.
Instantaneous DPIV data investigation
allowed us to approximate the critical FN. For
the two orientations of the MHV, namely
anatomical and anti-anatomical, this critical FN
was observed to be 0.35 and 0.6 respectively. A
more detailed examination of Figures 6 and 7
also reveals the same result. More specifically,
the experimentally calculated circulation and
energy curves (Figures 6 and 7) show a drastic
increase at approximately the FN that we
defined earlier. After that FN, the values appear
to level off. This observation is more apparent
in the anatomical case.
According to RSG, for a wide range of flow
conditions, the FN lies in the range of 3.6 to 4.5
but a non-uniform velocity profile drastically
decreases the FN. For example, in the case of a
parabolic velocity profile, the FN turned out to
be close to 1. From these conclusions alone and
considering our velocity programmes, Figures 4
and 5, we would also anticipate a drastically
reduced FN. Additionally, a sudden decrease in
the FN is also to be expected when a jet is
entering a space with co-flow [21]. This
suggests that there is agreement with our
experimentally derived critical FN when
compared to previous studies.
4 Conclusion
Optimal vortex formation in cardiac flows was
first speculated by the work of Gharib et al.
[10]. In this paper we provide quantitative
evidence in support of this idea. The work of
RRG and GRS examined the formation of
vortex rings assuming a slug flow model
approximation and showed that a formation
number occurs at a universal time where the
vortex ring cannot sustain extra circulation. So,
once this critical FN is reached, pinch-off
occurs and a trailing jet follows the initial
vortex ring. In this effort, we applied a similar
analysis to investigate vortex ring formation
during the diastolic phase of a heart cycle past
heart valves and inside the LV. DPIV was
utilized to study vortex formation in left
ventricular flow past mechanical and porcine
mitral valve prostheses.
The slug flow model approximation greatly
underestimates the experimental results because
some of the assumptions of the model are
violated; however, the results do suggest that
valve orientation and design affect the critical
FN. The analysis of the present study revealed
that the FN for the anatomical and antianatomical orientations was 0.35 and 0.6
respectively. For the porcine valve, it appeared
that vortex ring pinch-off was never reached.
Clinically, it is well known that the porcine
valve, with a design much closer to the natural
valves, offers a better performance than the
mechanical valves.
Yet, the level of
performance was not quantified. Kilner’s work
qualitatively showed that the natural heart
yields a smooth redirection of the flow inside
the LV but the basis and reasoning on why this
was happening has not really been addressed. It
is our belief that studying the nature of vortex
formation in the LV can quantitatively offer an
explanation to Kilner’s hypothesis. The delay or
absence of vortex ring pinch-off in the natural
8
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[20] Jeong J., Hussain F., “On the Identification of a
Vortex,” J. Fluid Mech., 285, 1995, pp. 69-94.
[21] Krueger P., Dabiri J., Gharib M., “Vortex Ring
Pinch-off in the Presence of Simultaneously
Initiated Uniform Background Co-flow,” Physics
of Fluids, 15(7), 2003, pp. 49-52.
[22] Shusser M., Gharib M., “Energy and Velocity of
a Forming Vortex Ring,” Physics of Fluids, 12(3),
2000, pp. 618-622.
heart would result in smooth flow redirection.
It stands clear that the higher the FN the better
the efficiency of the heart. The implication is
that this pinch-off delay would ensure limiting
energy losses. On the other hand, the flow past a
mechanical valve deviates from the ideal and
alters the coherent flow redirection because the
design itself decreases the FN. In fact, from our
results we observe that there is an almost
immediate initiation of the pinch-off process
drastically altering the flow characteristics in
the LV.
We propose that the critical FN, which is
specific to the valve design, orientation,
structural and physical flow characteristics,
serve as a parameter to quantify the incoming
jet and thus the efficiency of a heart valve. MRI
or ultrasound based velocimetry methods can be
developed and employed to provide to the
clinicians the means to quantitatively determine
the FN in-vivo. This would aid clinicians to
diagnose patients with diseased and defective
heart valves or even LVs. It is also our
speculation that the presence of chordae
tendenae in the natural heart are another of
nature’s great designs which help in redirecting
the flow and delaying pinch-off, thus increasing
the FN and minimizing energy loss.
References:
[1] Kilner P.J., Yang G., Wilkes A.J., Mohladin R.H.,
Firmin D.N., Yacoub M.H., “Asymmetric
Redirection of Flow Through the Heart,” Nature,
404, 2000, pp. 759-761.
[2] Chandran B., Schoephoerster R., Dellesperger C.,
“Effect of Prosthetic Mitral Valve Geometry and
Orientation on Flow Dynamics in a Model of
Human Left Ventricle,” J. Biomechanics, 22(1),
1989, pp. 51-65.
[3] Kleine P., M. Perthel, J.M. Hasenkam, H. Nygaard,
S. Hansen, J. Laas, “High-Intensity Transient
Signals as a parameter for Optimum Orientation of
Mechanical Aortic Valves,” Thorac. Cardiov.
Surg., 48, 1999, pp. 360-363.
[4] Laas J., Kleine P., Hasenkam M., Nygaard H.,
“Orientation of Tilting Disc and Bileaflet Aortic
Valve Substitutes for Optimal Hemodynamics”,
Annals Thorac. Surg., 68, 1999, pp. 1096-9.
[5] Fontaine A., Shengqiu, Stadter, Ellis, Levine,
Yoganathan, ``In Vitro Assessment of Prosthetic
Valve Function in Mitral Valve Replacement with
Chordal Preservation Techniques,'' J. Heart Valve
Dis., 5(2), 1996, pp. 186-198.
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