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By Kris Dumont and Pascal Verdonck, Institute of Biomedical Technology (IbiTech);
and Jan Vierendeels, Dept. of Flow, Heat, and Combustion Mechanics; Ghent University, Ghent, Belgium
View the pdf of this Supplement
The interaction between blood and the structures that transport it
plays an important role in many biofluid dynamic flow problems,
such as blood flow in the heart and vessels, through heart valves,
in cardiac assist devices, and in artificial organ design. Different numerical
techniques have been used to tackle this fluid-structure interaction
(FSI) problem. At Ghent University, a new fluid-structure
interaction model has been developed that is based on the dynamic
mesh model in FLUENT. The model has been used to simulate a prosthetic
aortic valve, and the results have been helpful for visualizing the
blood flow in the region of the valve throughout a cardiac cycle.
Inlet velocity, pressure
drop, and leaflet angle
during the cardiac cycle
(left); the resulting flow
through the valve is
shown right three
times
The FSI technique was implemented in FLUENT using journal files
and user-defined functions (UDFs). An external FSI code (written in C++)
drives the transient calculation. This code runs a subiteration loop for
every timestep in order to solve the fluid-structure interaction problem.
During every subiteration a journal file with FLUENT commands
is produced by the FSI code and executed by FLUENT. In this journal
file an estimation of the position of the valve is calculated in a “Define
on Demand” UDF. This valve position is used in the “Define Grid Motion”
UDF for the dynamic mesh model, and the corresponding flow field
is computed. Once the solution converges, the forces on the leaflet
are calculated using another “Define on Demand” UDF. When the first
subiteration finishes, the external FSI code checks the convergence criteria
for the fluid-structure interaction problem. If certain criteria are
not met, a new subitertion is started. The valve position is adjusted
using a stabilizing subiteration scheme that uses a numerical derivative
of the moment on the leaflet1, and a new flow solution is computed,
starting from the results at the previous time. This process continues
until the prescribed conditions are satisfied, at which point the time
is incremented by the FSI code, and a new valve position for a new
time is computed. Using between three and four subiteration loops,
the FSI problem typically converges to within 3 or 4 orders of magnitude
before the next time step is started. A fully implicit coupling procedure
is therefore achieved by using a separate solver for the fluid
problem (FLUENT) and for the structural problem (the FSI code).
Initial tests of the model were performed on a 2D case that illustrated
the dramatic change in the flow in the aortic sinus during a
cardiac cycle (http://navier.ugent.be/~kris). More recently, a 3D simulation
involving 500,000 cells has been performed to track the blood
flow and motion of one leaflet of a bi-leaflet heart valve for a complete
cardiac cycle. Clinical and in vitro studies show different dynamic
behavior under different physiological conditions, such as aortic versus
mitral position, and the expected flow patterns and leaflet movement
can be predicted by the FSI results. The FSI model could therefore be
an important means of better understanding the phenomena that drive
the coupled behavior of blood flow and artificial heart valve leaflets.
This new FSI algorithm has promise as a major engineering tool for
unraveling the hemodynamics associated with thrombolitic and hemolytic
events of existing and new mechanical heart valves.
Reference:
- J. Vierendeels, K. Dumont, and P. Verdonck, 33rd AIAA Fluid Dynamics
Conference and Exhibit AIAA–2003–3720, pp.23-26, June 2003.
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