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A fluid-structure interaction model of
the mechanical heart valves’ closure
D. Rafiroiu*, C. Giurgea*, C. Popa**
*Technical University of Cluj-Napoca, **University of Medicine and Pharmacy “Iuliu Hatieganu”
15 C. Daicoviciu str., 400020, Cluj-Napoca, Romania,
[email protected]
Abstract— A 2D finite element model of blood flow through a
mechanical heart valve (MHV), incorporating the fluid-structure
interaction, was build. The coupled model was used to simulate
the closure dynamics of two mono-leaflet MHVs, Medtronic-Hall
(MH) and Omniscience (OS), mounted in mitral position. The
obtained results were in good agreement with the experimental
findings and other similar results reported in the literature.
Keywords— fluid-structure interaction, mechanical heart
valves, cavitation
I.
INTRODUCTION
One subject area requiring careful attention is artificial
heart valve cavitation. Structural failure of the valves, with
pitting and erosion on the surface of the leaflets, and blood
damage determined by the exposure to relatively high shear
stresses in the clearance region during the closing phase are
the two devastating consequences of artificial heart valve
cavitation. In-vitro experimental tests performed at
Aerodynamisches Institut in Aachen [1] proved cavitation
occurrence in MH and OS mechanical heart valves.
Fig. 2 . The computational domain and the geometry of the generic valve.
B. Governing equations
An unsteady, laminar, incompressible and Newtonian flow
was considered. The mathematical model of the fluid dynamics
consists of the continuity equation
u  0
(1)
and the momentum equation
 u 
   u   u  p  u
 t 

(2)
The governing equation for the motion of the occluder is
expressed as follows:
MH 27
OS 27
Fig. 1. Cavitating MHVs.
Prosthetic heart valve behaviour at closure is determined
by its geometrical and structural characteristics. The most
effective way to study this behaviour is by numerical
simulation.
II.
NUMERICAL MODEL
A. Computational domain
The geometry of a typical mono-disk valve was reduced to a
generic one, having a hydrodynamic profile, which may be
particularized for the MH valve by establishing the curvature R
= 0 (generic flat valve), and for the OS valve with R = 0.04545
(lens form valve), the diameter of both valves being 0.022 m
corresponding to that of OS 27 and MH 27 valves, used in our
experiments. For the sake of economy, in fig. 2 we provide
only the geometry of the model corresponding to the OS valve,
although we simulated the closure for both valves [2].
d 2 M V  M h

dt 2
J 0  J ad
(3)
MV is the momentum resulting from the buoyancy and the
gravitational force. Mh is momentum resulting from the drag
FD and the lift FL forces. The drag and lift forces can be
calculated by integrating, over the complete occluder surface,
the elemental drag dFD and lift dFL, which are expressed as

 u u  
u 
dFD    p  2 x  nx    y  x  n y  i (4)
x 
y  
 x


u 
 u u  
dFL    p  2 y  n y    y  x  nx  j (5)
y 
y  
 x

where, nx  sin( ) and n y  cos( ) .
The moment of inertia of the system includes the occluder’s
Jo = 22x10-9 Kgm2 and the additional mass’s Jad = 5.937x10-7
Kgm2. Further details about the governing equations can be
found in [2, 3].
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C. Boundary conditions
The boundary conditions for the flow problem were the
followings: no-slip for the fixed boundaries, zero pressure at
the outlet and variable pressure at the inlet. According to [4],
the ventricular pressure rate during the closing phase is about
2000 mmHg/s. At the moving boundary (the occluder’s), the
numerical continuity of the velocity was ensured. Stress is also
automatically continuous across the interface.
D. Numerical procedure
Solution of the valve’s motion is based on the use of
commercial CFD software, Fastflo 3.0. A FSI algorithm
implemented by Nick Stokes [5] was used. The algorithm uses
ALE method and an intermediate-level CFD solver. The CFD
model iteratively solves the equations of a laminar,
incompressible unsteady flow. At every time step of the
iterative procedure, the inlet pressure boundary condition is
converted into a velocity one, according to a simple
methodology proposed by the authors,
EDV  EDV 2 
uin (t ) 
A(t ) 
2 A t  t
2 A2 (t ) K

 L2
t3
cos 2 0   cos 2   t   
4
(6)
(7)
where, EDV is the end-diastolic volume of the ventricle, A (t)
is the time-varying flowing section of the valve, K is the
pressure rate and  the density of the fluid.
III.
Fig. 4. The pressure field around the occluder, after its first rebound. Values
below the vaporisation threshold indicate cavitation inception on the atrial
side of the valve.
RESULTS AND DISCUSSIONS
The proposed FSI model successfully simulates the
occluder’s motion, relying only on upstream boundary
condition (pressure rate) as input. Further experiments are
currently undertaken with the Sheffield pulse duplicator for
accurate measurement of model’s input (velocity).
The model faithfully predicts the valve’s dynamics (fig. 3),
the negative pressure transient (fig. 4) and vortices in the flow
(fig. 5). These indicate the preferential location of cavitation
inception, thus confirming the experimental findings.
Fig. 5. Stream function indicating the vortex formation .
For both the MH and OS valve, the same qualitative results
were found. Yet quantitatively, lower negative pressures were
found for MH, indicating a lower caviational potential. As fig.
1 shows, the peripheral cavitational cloud generated by MH
valve is smaller then the other.
A 3D model would be useful to capture the other
cavitational clouds produced by the rest of its structural
elements (e.g. the strut).
ACKNOWLEDGEMENT
Professors Rod Hose and Pat Lawford from the University
of Sheffield generously provided their support in establishing
the correct boundary conditions and explaining the results.
IV.
[1]
[2]
[3]
[4]
[5]
Fig. 3. Inlet velocity and position histories.
REFERENCES
C. Giurgea, R. Wirtz, C. Koehler, ‘Vizualizarea in-vitro a fenomenului
cavitatie in protezele valvulare cardiace’, HERVEX, noiembrie, 2001.
C. Giurgea, D. Rafiroiu. L. Nascutiu, „Numerical simulation of
mechanical heart valve closure dynamics. Observations of the
occurrence of vortices.”, Workshop of vortex dominated flows –
Acievements and open problems. Timisoara, Romania, June, 10-11,
2005, Tom 50<64> Special Issue, pp. 161-168.
D. Rafiroiu, C. Giurgea, A. Vlad, M. Munteanu, C. Popa, P. Manea, R.
Ciupa, “Numerical Modelling of Mechanical Heart Valve Closure
Dynamics. The Cavitational Potential of Medtronic-Hall and
Omniscience MHV’s.”, in Proc. ICMP 2005, 14th-17th September 2005,
Nuremberg, Germany, pp: 1581-1582.
Cheng R., Lai Y.G., Chandran, K.B. (2003): Two-dimensional fluidstructure interaction simulation of bileaflet mechanical heart valves, J
Heart Dis. Vol. 12. No. 6:772-780
Nick Stokes, A heart-valve model-fluid-structure interaction,
www.cmis.csiro.au/cfd/fem/valve/index.htm