Download Investigation of blood flow through the mitral valve

Journal of Engineering Science and Technology
EURECA 2013 Special Issue August (2014) 68 - 78
© School of Engineering, Taylor’s University
INVESTIGATION OF BLOOD FLOW
THROUGH THE MITRAL VALVE
YVONNE LIM*, MUSHTAK AL-ATABI
School of Engineering, Taylor’s University, Taylor's Lakeside Campus,
No. 1 Jalan Taylor's, 47500, Subang Jaya, Selangor DE, Malaysia
*Corresponding Author: [email protected]
Abstract
The mitral valve is a heart valve located in between the left atrium and
ventricle. Mitral valve failure occurs due to various reasons resulting in
backflow of blood from the ventricle to the atrium. Severe failure requires
surgical repair. Medical professionals have different opinions on surgical repair
methods. This paper describes the development of an in vitro platform to test
effectiveness of a surgical repair method. The study is done experimentally
using flow visualisation and numerically using computational fluid dynamics.
From the experimental results, it is seen that the flow through an open mitral
valve produces two vortices. The set-up can be used as a testing protocol for the
testing of surgical repair methods. The numerical results mimic the results from
the experimental testing and can be further developed for future testing of the
mitral valve failures and repairs.
Keywords: Mitral valve, Surgical repair methods, flow visualisation, CFD.
1. Introduction
The mitral valve is located in the heart between the left atrium and the left
ventricle. It has four basic components, the mitral annulus, the anterior and
posterior mitral valve leaflets, and the subvalvular apparatus which consists of the
chordae tendineae and the papillary muscles. The mitral annulus is the opening in
which the blood flows through; the mitral valve leaflets control the flow of blood
into the mitral valve; the chordae tendineae are the fibres which hold the mitral
valve leaflets in place and the papillary muscles connect the chordae to the
ventricular walls.
The mitral valve allows the blood flow from the left atrium to the left ventricle
during diastole (when the heart relaxes) and prevents blood from flowing back to
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Investigation of Blood Flow through the Mitral Valve
69
the atrium during diastole (when the heart contracts). In this way, it mimics the
function of a check valve by preventing backflow from the ventricle to the atrium
at all times. However, due to various medical reasons, mitral valve failure, either
prolapse or stenosis may occur, this reduces the heart’s efficiency as a pump. This
causes the heart to work harder as a pump to displace the same amount of blood
from the heart to the rest of the body when compared to a healthy heart.
There are two major ways to correct mitral valve failure due to mitral
prolapse, surgical replacement and surgical repair. Surgical replacement involves
replacing the damaged valve with a mechanical valve. Recipients of these
mechanical valves have to take anticoagulants to prevent blood clots formed from
blood adhering to the walls of the artificial valve. Surgical repair involves
repairing the damaged section of the mitral valve without replacement with a
mechanical device. In this study, the focus is on the surgical repair of mitral valve
prolapse. Surgical repair is considered a better option compared to surgical
replacement as there is a better survival rate after the procedure as the patient is
not required to take anticoagulants and the mechanical valve used has a limited
life-span. There are various types of surgical repair to repair anterior and posterior
leaflet prolapse. The most common repair methods are edge-to-edge repair,
chordal replacement and chordal transposition [1].
Medical professionals have different opinions of which surgical repair method
is the most effective. Surgeons cannot test these methods on patients due to
ethical reasons. According to the Hippocratic Oath which states that as medical
professionals, they are obliged first and foremost not to do any harm [2].
Furthermore, surgeries are expensive. Mistakes are costly, not just financially; a
wrong move might cost the patient his or her life. Therefore, surgeons are not to
treat patients with any method that they do not consider the best. Other than that,
success rates of various repair methods are not as reliable due to the health
condition and general fitness of patients which differ from patient to patient [3].
This paper describes the development of an effective procedure and platform
to assess the effectiveness of surgical repair in vitro. This is performed using a
designed and fabricated transparent tube model. Computational fluid dynamic,
CFD simulations of the flow through the mitral valve at steady state, using 2D
simulations was also carried out.
2. Methodology
The study of the mitral valve has been carried out experimentally and
numerically. Experimental studies can be carried out either in vivo (inside the
body) or in vitro (in the lab). Numerical simulations have been carried out using
computational fluid dynamics software.
Experimental in vitro studies are more commonly carried out as compared to
in vivo studies as it is more ethical compared to using a live specimen. Various
experimental studies have been carried out in vitro for various purposes. Among
which is the study of the effect of formation of vortices in the ventricle [4]; the
pressure to cause mitral valve failure and the effect of surgical repair used on
pressure to cause mitral valve failure [1,5]; and the flow visualisation of flow
through the mitral valve using streak photography [6]. All the mentioned studies
except the study carried out by Al-Atabi et al. [6], which uses a plastic model;
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Y. Lim and M. Al-Atabi
utilised a mitral valve specimen obtained from either a porcine or bovine heart.
Although in vitro experiments have been widely used to study the mitral valve,
there are many challenges associated with in vitro studies. Uncertainties arising
from using the real mitral valve are attributed by the variation of size, physical
condition and health of the animal which the specimen originated from. These
discrepancies may contribute to the uncertainties in the results obtained.
Furthermore, the dissection of the heart to obtain the mitral valve specimen is
tedious and requires specialised knowledge on the heart anatomy to ensure that
the specimen removed is intact.
Numerical studies have emerged recently as a tool to study the flow
mechanics through the mitral valve. It is also carried out as a means to idealise the
structure of the mitral valve to obtain a more accurate result and to reduce
discrepancies. Numerical simulations in the form of computational fluid dynamics
have been widely used in the study of the mitral valve. Studies have been carried
out, for example, to study the filling phase of the ventricle in a 2-dimensional
model to detect early heart valve failure [7] and also to study the biomechanics of
the left heart chambers using a 2-dimensional idealised structure with fluidstructure interaction using an arbitrary Lagrangian-Eulerian mesh. However, there
are challenges associated with the use of numerical studies for mitral valve
research as well. The mitral valve structure is difficult to define, as is its motion,
therefore assumptions are used in the simulations to simplify the study, which
may reduce its accuracy.
Hence, both experimental in vitro experimental studies and numerical studies
are both carried out in this study. The experimental study was carried out using a
porcine mitral valve specimen and a numerical study of the experimental design
was carried out.
2.1. Experimental study
2.1.1. Experimental design
The experiment was carried out in a closed loop system, Fig. 1. A porcine mitral
valve specimen was used; the attachment of the specimen is described in the
section below. The mitral valve specimen was set in a fixed open position. The
atrial chamber was a PVC pipe of length 1 m and a diameter of 4.5 cm and flow
straighteners were positioned inside the tube to produce a fully developed flow.
The left ventricular chamber was a transparent tube with the same diameter and a
length of 0.3 m. The mitral valve was placed 4 cm from the opening of the
chamber to allow the flow visualisation photography. The atrial and ventricular
chambers were secured together with nuts and bolts along the flange. The
diameter and length of the bolts used were 2 mm and the 1 cm respectively. Water
was used as the fluid in the experiment. Due to the non-pulsatile nature of the
experiment, the non-Newtonian effect of blood is not considered and therefore
water was used as the fluid [3]. The fluid was placed in a 1 L reservoir. A
peristaltic pump was used to generate the flow in the system. The Reynolds
number of the flowing water was 845.
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Fig. 1. Experimental Set-up.
2.1.2. Mitral valve specimen
The mitral valve specimens were obtained from porcine hearts. Porcine
hearts were used as the anatomy is closest to the human heart [8]. The
porcine hearts were dissected carefully to remove a circular annulus of the
mitral valve and papillary muscles with chordae attached to the valve
leaflets removed. The annulus of the specimen was sutured onto a ring.
A transparent plastic valve holder was used to hold the mitral valve
specimen. The ring holding the specimen annulus was sutured onto the
valve holder and the papillary muscles were sutured onto the valve holder
approximately 3 cm from the annulus. This is shown in Fig. 2.
Fig. 2. Mitral Valve Specimen in Inner Circular Tube.
2.1.3. Flow visualisation
The flow was seeded using silver coated hollow glass beads of 1 µm diameter.
The glass beads were added to the fluid reservoir after the system was completely
filled. The hollow glass beads were illuminated by a scattered laser beam. This
was achieved by passing the laser beam through a glass rod place perpendicularly
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above the ventricular chamber. The room was blacked out in order to carry out the
flow visualisation experiments. A Nikon D7000 DSLR camera with a shutter
speed of 1/6 s, an ISO of 100 and an aperture of f/16 was used to capture the flow
structure [3].
2.2. Numerical simulation
2.2.1. Numerical simulation of experimental design
A two-dimensional, 2D model of the experimental design was simulated using
ANSYS FLUENT ©. A two-dimensional simulation was chosen because from a
previous simulation of an experimental study by Hwang et al. [9], the 2D
simulation sufficiently mimics the experimental results [10]. Furthermore, 2D
simulations are easier and require less computational resources.
The geometry of the simulation is shown in Fig. 3. The geometry was generated
with a fixed opened valve. The geometry was designed as half of the experimental
chamber with the bottom axis as the axis to reflect the geometry. The walls were
assumed to be rigid with no-slip condition specified. The valve leaflet is assumed to
have uniform thickness of 10 mm. The left wall of the geometry was specified as
the inlet, the right wall was specified as the outlet. Water with a density of 1000
kg/m3 and a viscosity of 0.89 mPa.s was used as the fluid. The turbulence model
used was the realizable k-ε model. The simulation was done at steady-state.
Fig. 3. CFD Geometry of Experimental Chamber.
2.2.2. Numerical simulation of idealised left heart chambers
Simulation of idealised left heart chamber was carried out to compare the
experimental results to the actual flow within the mitral valve. It also explores the
potential of the CFD simulation to be used as a diagnostic tool. The CFD was
performed using ANSYS FLUENT ©.
Two-dimensional idealised geometries of the left atrium and ventricle with
opened and closed mitral valve were generated using echocardiographic
measurements of the left heart chambers [11]. The left ventricular quantification
data is obtained by measuring the major and minor axis of the left ventricle in the
apical four chamber view. The dimension of the left atrium is obtained from the
parasternal long axis view (echocardiographic view showing the left atrium and
ventricle, the right ventricle, the aortic and mitral valve) and apical two chamber
view (echocardiographic view showing the left atrium and ventricle). The mitral
valve annulus diameter was obtained from the apical four chamber view. The left
ventricular outflow tract is the channel in which the blood exits the left ventricle
when the ventricle contracts. It is diameter is obtained from the parasternal long
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axis view of the left ventricle. Table 1 shows the summary of the quantification
data obtained from the echocardiographic measurement as compiled by Anderson
[11]. The average values were used to generate the geometries as shown in Fig. 4.
Table 1. Left Heart Chamber Measurements.
Measured Range
(cm)
Left Ventricle:
Major Axis
Minor Axis
Left Atrium:
Major Axis
Minor Axis
Mitral Valve Annulus
Left Ventricular Outflow
Tract
Mean Value
(cm)
6.9 – 10.3
3.3 – 6.1
8.6
4.7
4.1 – 6.1
2.6 – 4.5
2.6 – 2.9 (Women)
2.9 – 3.2 (Men)
1.8 – 2.5 (Women)
1.9 – 2.7 (Men)
5.1
3.6
2.8
3.1
2.2
2.4
(a) Fixed Open Mitral Valve.
(b) Fixed Closed Mitral Valve.
Fig. 4. Geometry of Left Heart Chamber.
The open valve for the idealized geometry was simulated with the inlet at the
left atrium and no outlet. The closed valve for the idealized geometry was
simulated with the inlet at the apex and the outlet at the left ventricular outflow
tract. The walls were assumed to be rigid. No-slip conditions were used for the
walls; this includes the walls of the valves. For the heart chamber geometry
simulations, the fluid used was specified to be glycerine. This is because a
solution of glycerin has similar properties as blood. The density and viscosity of
glycerin used is 1060 kg/m3 and 0.0027 Pa.s respectively [12]. Using glycerine as
the blood analogue assumes the blood to be non-Newtonian. The velocity of the
fluid flow is 0.5 m/s, representing blood flow through the mitral valve into the left
ventricle [13]. The turbulence model used for all simulations was the realizable kε turbulence model. The numerical simulations were performed in steady-state.
2.2.3. Assumptions
The fluids used in the simulations are assumed to be Newtonian. Newtonians
fluids are incompressible and therefore the flow is governed by the Navier-Stokes
equation. This assumption has been made as it is found that for large diameters
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and for steady flow, the non-Newtonian effects are not prominent [14,15]. In
actual fact, blood is a non-Newtonian fluid.
The walls and the leaflets in the simulations were assumed to be rigid. And
therefore, the flow for the opened valve only models the flow at a particular
instant during diastole and the flow of a closed valve only models the flow at a
particular instant during systole. The walls of a real heart are not rigid and their
structure changes as the ventricle contracts and relaxes closing and opening the
mitral valve.
3. Results
3.1. Experimental results
As the water emerges from the mitral valve annulus, two vortices are formed. The
vortices appear right after the water emerges from the mitral valve leaflets.
Figures 5 and 6 show the vortices formed behind the mitral valve leaflets.
Fig. 5. Flow through a Healthy Mitral Valve Producing Two Vortices.
Fig. 6. Flow through a Healthy Mitral Valve with Path of Vortices Drawn.
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3.2. Numerical results
3.2.1. Numerical simulation of experimental design
Figure 7 is the generated image of velocity vectors reflected upon its axis of
symmetry. The velocity vector shows the formation of two vortices behind the
mitral valve leaflets.
The numerical simulation of the experimental chamber generated velocity
vectors which are comparable with the experimental results (Fig. 5).
Fig. 7. Velocity Vector of Simulated Flow through
a Mitral Valve in the Experimental Set-up.
3.2.2. Numerical simulation of Idealised Left Heart Chambers
Figure 8 shows the idealized left heart chamber with the opened mitral valve
simulation generated results. The figure shows two vortices formed behind the
mitral valve leaflets. The cardiographic magnetic resonance, CMR image of the
left ventricle during diastasis, the mid stage of ventricular relaxation shows two
vortices behind the mitral valve leaflets [16]. The numerical simulation of the
open mitral valve is similar to the CMR image, and therefore is validated.
(a) Velocity Vector of the
Simulated Flow through the
Opened Mitral Valve.
(b) Pathline Visualisation of
Blood Flow during Left
Ventricular Diastasis [16].
Fig. 8. Flow through Open Mitral Valve.
The generated results from the simulation of closed mitral valve shows the
flow from the apex of the ventricle and out though the left ventricular outflow
tract. There are no vortices formed inside the ventricle during this stage.The
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generated velocity vectors of the closed mitral valve simulation closely resembles
the CMR image of a ventricle during peak systole as seen in Fig. 9.
(a) Velocity Vector of the
Simulated Flow through the
Closed Mitral Valve.
(b) Pathline Visualisation of
Blood Flow during Peak Systole [16].
Fig. 9. Flow through Ventricle when Mitral Valve is Closed.
4. Discussion
As mentioned above, the porcine valve closely resembles the human heart structure,
and therefore the flow obtained may be considered similar to a human mitral valve.
In the experimental study, it can be seen that two vortices formed behind the mitral
valve leaflets. Vortices are areas where the vorticity of the region is compact and is
due to the no-slip condition of the valve walls. The water flowing before the test
region flowed in a fully developed velocity profile. When water passes through the
mitral valve annulus, the velocity increases because the same amount of water has
to pass through the smaller cross-sectional area as compared to the cross-sectional
area of the tube. The flow decelerates as the water emerges from the mitral valve
annulus, as the cross sectional area increases. As the flow of water pass the leaflets,
the boundary layer separates causing flow in opposite directions, causing the
formation of a vortex [17].
The formation of vortices is an important aspect in the blood flow in the heart.
Vortices are energy containing eddies [18]. The energy generated by the motion of
the vortices help propel the flow out of the ventricle when the ventricle contracts.
The formation of vortices may be employed as a means of diagnosis of mitral
valve failures; a mitral valve with anomalies would present different vortices
structures. The structure of the vortices can be used as a baseline for the protocol to
determine the optimal mitral valve surgical repair method. The closeness of the
resemblance of the vortices of the mitral valve repaired using a particular repair
method to a healthy mitral valve will give an indication of how well is a repair
method. The experimental set-up can be used to test surgical repair methods. The
repaired mitral valve could be placed in the experimental set-up and flow
visualisation can be done to compare the baseline and the repaired valve.
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The computational fluid dynamics simulation of the open mitral valve, both the
experimental and the idealized geometry; generated results which show the
formation of vortices behind the mitral valve leaflets. This corresponds to the blood
flow inside the left heart chambers of a living person as seen in from the CMR
images. The simulation for the closed mitral valve in the idealized model also
corresponds to the outflow of blood from the left ventricle. This shows that CFD is
a powerful tool and the use of CFD to diagnose mitral valve failure and evaluate
surgical repair methods can be developed. The accurate assumptions to the
structure, dimensions, and physical properties of the mitral valve have to be first
defined in order to obtain accurate results.
5. Conclusion and Future Work
Flow through a healthy mitral valve produces two vortices. Vortices are important
as they help propel the flow from the ventricle. The absence and presence of the
vortices and the structure of the vortices can be used to identify possible mitral
valve anomalies. This can be used as the baseline for the protocol.
The simulated results of the experimental model and the idealised geometry
agree with the experimental result obtained as well as the CMR images. The
numerical results can therefore be further developed to numerically test surgical
repair methods.
The set-up can be further developed to test various mitral valve repair methods
and implemented for more personalised healthcare. A patient’s mitral valve failure
can be evaluated through various medical imaging methods and the data obtained
may be used to simulate a physical model which can be used as an analogue to be
placed inside the chamber. Various repair methods may be tested on the damaged
mitral valve analogue. The method which yields the flow structure closest to a
healthy mitral valve will be chosen for the patient. This can lead to personalised
health care for each patient, reducing misdiagnosis and surgical errors, hence a tool
to provide better healthcare.
References
1.
2.
3.
4.
5.
Espino, D.M.; Hukins, D.W.L.; Shepherd, D.E.T.; Watson, M.A.; and
Buchan, K.G. (2006). Determination of pressure required to cause mitral
valve failure. Journal of Medical Engineering and Physics, 28(1), 36-41.
Miles, S.H. (2005) The hippocratic oath and the ethics of medicine. (1st Ed.)
New York: Oxford University Press.
Lim, Y.H.L.; and Al-Atabi, M. (2013). Investigation of blood flow through
the mitral valve. Proceedings of Engineering Undergraduate Research
Catalyst Conference (eureca 2013), School of Engineering, Taylor’s
University, Kuala Lumpur, Malaysia.
Carey, R.F.; and Herman, B.A. (1989). The effects of a glycerine-based
blood analog on the testing of bioprosthetic heart valves. Journal of
Biomechanics, 22(11-12), 1185-1192.
Espino, D.M.; Hukins, D.W.L.; Shepherd, D.E.T.; and Buchan, K.G. (2006).
Mitral valve repair: An in-vitro comparison of the effect of surgical repair on
Journal of Engineering Science and Technology
Special Issue 8/2014
78
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Y. Lim and M. Al-Atabi
the pressure required to cause mitral valve regurgitation. The Journal of
Heart Valve Disease, 15(3), 375-381.
Al-Atabi, M.; Espino, D.M.; and Hukins, D.W.L. (2010). Computer and
experimental modelling of blood flow through the mitral valve of the heart.
Journal of Biomedical Science and Engineering, 5(1), 78-83.
Baccani, B.; Domenichini, F.; and Pedrizzetti, G. (2003). Model and
influence of mitral valve opening during the left ventricular filling. Journal of
Biomechanics, 36(3), 355-361.
Kunzelmann, K.S.; Cochran, R.P.; Verrier, E.D.; and Eberhart, R.C. (1994)
Anatomical basis for mitral valve modelling. The Journal of Heart Valve
Disease, 3(5), 491-496.
Hwang, N.H.C.; Hussain, A.K.M.F.; Hui, P.W.; Stripling, T.; and Wieting,
D.W. (1977). Turbulent Flow through a Natural Human Mitral Valve.
Journal of Biomechanics, 10(1), 59-67.
Lim, Y.H.L.; and Al-Atabi, M. (2013). Investigation of blood flow through
the mitral valve: A numerical approach. Proceeding of The Seventh MIT
Conference on Solid and Fluid Mechanics, Cambridge, Massachusetts.
Anderson, B. (2007). Echocardiography: The normal examination and
echocardiographic measurement (2nd Ed.). Queensland, Australia: MGA graphics.
Espino, D.M.; Hukins, D.W.L.; Shepherd, D.E.T.; Watson, M.A.; and
Buchan, K.G. (2006). Simulation of blood flow through the mitral valve of
the heart: A fluid structure interaction model. Proceedings of the COMSOL
Users Conference, Birmingham, UK.
Pozzoli, M.; Selva, A.; Skouse, D.; Traversi, E.; Mancini, R.; Bana, G.;
Rossi, A.; and Bossi, M. (2002). Visualization of left atrial appendage and
assessment of its function by transthoracic second harmonic imaging and
contrast enhanced pulsed Doppler. European Journal of Echocardiography,
3(1), 13-23.
Weiting, D.W. (1969) Dynamic flow characteristics of heart valves. Ph.D.
thesis, University of Austin, USA.
Nguyen, T.T. (2004) Development of blood analog for flow visualization and
hemolysis investigations. Master’s thesis, McGill University, Canada.
Markl, M.; Kilner, P.J.; and Ebbers, T. (2011). Comprehensive 4D velocity
mapping of the heart and the great vessels by cardiovascular magnetic
resonance. Journal of Cardiovascular Magnetic Resonance, 13:7, 22 pages.
Sengupta, P.P.; Pedrizzetti, G.; Kilner, P.J.; Kheradvar, A.; Ebbers, T.; Tonti,
G.; Fraser, A.G.; and Narula, J. (2012). Emerging trends in CV flow
visualization. JACC: Cardiovascular Imaging, 5(3), 305-316.
Versteeg, H.K.; and Malalasekera, W. (2007). An introduction to computational
fluid dynamics: The finite volume method. (2nd Ed.) Prentice Hall.
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