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By Luca Antiga, Bogdan Ene-Iordache, and Andrea Remuzzi,
Mario Negri Institute for Pharmacological Research, Bergamo, Italy
View the pdf of this article
Cardiovascular diseases represent the main cause of death in Western
countries. Among them, atherosclerosis has the greatest mortality rate.
Evidence that atherosclerotic plaques form near bifurcations, or branch
points, has led to the hypothesis that irregular hemodynamic conditions
play a role in the initiation and progression of vascular wall lesions.
Both in vitro and in vivo studies have confirmed these observations, identifying
wall shear stress as a major factor influencing endothelial cell dysfunction.
In years past, several research groups have investigated blood flow
in large arteries using CFD. The models were initially idealized, generated
with classic CAD tools on the basis of averaged ex vivo measurements.
More recently, the problem of modeling realistic vascular segments at
a patient-specific level has been addressed, taking advantage of the latest
3D angiographic techniques, such as computerized tomography (CT) and magnetic
resonance (MR), which allow non-invasive acquisition of detailed anatomic
information about vascular segments. At the Mario Negri Institute, GAMBIT
and FiDAP have been integrated with in-house software and VTK, a free
visualization library1, to generate realistic geometric models from medical
images .
Hexahedral mesh generation for a bifurcating blood vessel
The images are first acquired in DICOM format from contrast-enhanced
CT or MR scans. The 3D surface of the vascular wall is then extracted
from the images by finding the ridges of image gradient at the interface
between the contrast medium and surrounding tissue2. The resulting surface
is semi-automatically edited to add flow extensions with controlled surface
curvature at inlets and outlets.
Generation of hybrid meshes of quadratic elements with adaptive boundary
layer thickness for complex vascular tracts
Time-dependent streamlines and wall shear stress distribution in a realistic
model of an abdominal aorta
In order to generate volume meshes from
the extracted 3D surfaces, two different
approaches have been developed for vascular
tracts of differing complexity. In the
first approach2, single (e.g. carotid and iliac)
bifurcations are automatically decomposed
into their branches, taking care to avoid sharp
corners in the bifurcation region. The split
surface is then exported as a neutral file,
loaded into GAMBIT, and rejoined into separate
surface entities. Continuous boundary
layers are defined and vessel volumes
are meshed with hexahedral elements using
the Cooper scheme.
For more complex vascular segments (e.g.
the abdominal aorta), a second approach3
is employed, which leads to the generation
of hybrid meshes of wedges and tetrahedra.
Models are imported into GAMBIT for
surface remeshing using well-shaped linear
triangles. The mesh is then exported into
the in-house geometric analysis software,
where surface triangles are optimally
warped normal to the medial axis, creating
boundary layers of wedges whose
thickness smoothly adapts to the local vessel
size. The linear triangles and wedges are
then converted to 6- and 18-noded quadratic
elements, respectively. The remaining
volume is meshed with GAMBIT using 10-
noded quadratic tetrahedral elements conforming
to the boundary layer wedges.
Blood flow simulations are carried out
using FiDAP, with careful attention taken
when setting boundary conditions in order
to achieve representative clinical conclusions.
Specific boundary conditions are derived from
the patient’s echo-Doppler examination, and
imposed as fully-developed pulsatile velocity
profiles4. Carreau’s shear-thinning model
is employed for blood viscosity, with
parameters correlated to the patient’s
hematocrit and plasma protein concentration.
CFD is now ready for patient-specific investigations
of blood flow in the clinical context,
where it will provide invaluable help
for physicians toward a deeper understanding
of the pathophysiology of cardiovascular
disorders.
References:
- The Visualization Toolkit (VTK), www.vtk.org
- 2 L. Antiga, B. Ene-Iordache, L. Caverni, G.P. Cornalba and A. Remuzzi,
Comput Med Imaging Graph 26(4), p. 227-235, 2002.
- L. Antiga, B. Ene-Iordache and A. Remuzzi, IEEE Trans Med Imaging
22(5) p. 674-678, 2003.
- B. Ene-Iordache, L. Mosconi, G. Remuzzi, A. Remuzzi, J Biomech Eng
123(3), p. 284-292, 2001.
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