Biomedical Engineering Reference
In-Depth Information
centerlines using multi-scale medialness filters to model circular like cross-sections
of vessel geometries. As illustrated in Fig.
1
b the result of the centerline extraction is
an ordered set of points along the geometrical mean of the thoractic aortic lumen and
is performed within approximately 30 s.
2.2.2 Aorta Segmentation
The extracted centerline is uniformly sampled to extract orthogonal circular
structures of constant radius (
r
¼
20 mm) that provide positive samples for a
min-cut/max-flow segmentation algorithm [
13
]. Negative samples are generated
outside at the same locations along the centerline at a radius
r
75 mm. The
segmented image is undergoing a marching cubes isosurface [
14
] extraction to
produce a polygonal mesh of the lumen geometry. Further processing of the
unstructured mesh involves welding identical vertices, keeping the largest
connected component with surface smoothing constraints [
15
] to retain a manifold
triangular surface mesh. Figure
1
c illustrates the result of the aorta segmentation
performed within approximately 5 min.
¼
2.3 Estimation of the Patient-Specific Aorta Flow
Within this step the patient-specific flow profiles over the entire cardiac cycle are
extracted at the aortic inflow and outflow from the 2D PC-MRI cine images.
Typically, the PC-MRI sequence is easily registered with the anatomy image
and aortic segmentation using the MR machine coordinates. The intersection of
the PC-MRI image plane and the vessel geometry defines two 2D closed contours.
These planar patches are densely triangulated and treated as an inflow and outflow
profile, respectively. Inside each patch a uniform grid sampling of the PC-MRI
image is performed at the pixel center locations to obtain spatially constrained
velocity values over the entire cardiac cycle. It is important to note that depending
on the scanner type and vendor particular care must be taken for the correct
normalization of the flow velocity encoding.
2.4 Computational Fluid Dynamics of Aortic Blood Flow
We model the blood flow dynamics in the aorta using 3D incompressible
Navier-Stokes equations with viscous terms—the standard continuum mechanics
model for fluid flow. The equations are discretized and solved with the embedded
boundary method. We use both finite difference and finite volume techniques to
solve the fractional step combined with an approximate projection method for the
pressure. The blood is modeled as a Newtonian fluid, which is generally accepted as
