Page 223 - Artificial Intelligence for Computational Modeling of the Heart

196 Chapter 6 Additional clinical applications

Figure 6.8. Examples of synthetically generated CoA anatomical models.

mined for the patient-specific cases. Eq. (6.6)isemployedtogen-
erate centerline points in Cartesian coordinates, while Eq. (6.3)is
used to generate surface points in cylindrical (r,z,φ) coordinates.
Unreported experiments suggest that best results are achieved
when parameter sampling is conducted following a normal dis-
tribution. Since the model is formulated as a set of continuous
functions, the surface can be generated with an arbitrary number
of points. For generating a synthetic anatomy, the surface func-
tion is evaluated at a finite number of uniformly distributed points
based on which a polygonal mesh is then defined. To increase the
anatomical fidelity of the resulting surface, some additional con-
straints are defined for:
1. The ratio between inlet and outlet radius (0.8–2).
2. The ratio between the healthy radius (upstream from the CoA
segment) and the CoA minimum radius (0.2–0.8).
Finally, 100 points along the centerline, and 50 points along
each cross section are generated and transformed from cylindrical
to Cartesian coordinates, obtaining thus the actual surface points
used to generate the final surface mesh. (See Fig. 6.8.)

6.2.2.2 Three-dimensional flow computations
The 3D flow model is based on the Lattice Boltzmann Method
(LBM), which describes physics of fluid flow at a mesoscopic
scale by taking into account molecular interactions between flow
particles. The LBM provides ultimately the same solution as the
Navier–Stokes based solvers [214], but it is inherently highly paral-
lelizable, which is a necessary feature to enable fast computation
for the large database of synthetic geometries.
Aortic flow typically has a high Reynolds number (up to 5000
at peak systole); to simulate this flow regime with LBM without
producing numerical instabilities, the spatial resolution needs to