Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms - Mathematical Methods and Models in Biomedicine - page 144

as from the inclusion or exclusion of the main side-branches in the geometry. The
geometries employed in this work consist of a patient-specific aneurysm, obtained
from medical imaging, and an idealization, for comparison purposes.
The outline of this chapter is as follows. Section 2 is dedicated to the geometry
reconstruction of the patient-specific medical image data. The idealization of the
anatomically realistic geometry will be also discussed. Section 3 is devoted to
the detailed description of the mathematical models. It includes the description of
the three-dimensional (3D) fluid model, as well as the reduced one-dimensional
(1D), and zero-dimensional (0D) models. The couplings of the reduced models
with the 3D one, that serve here as proper outflow boundary conditions, are also
discussed. The numerical methods, geometry specifications, and inflow boundary
conditions are introduced in Sect. 4 . In Sect. 5 the numerical results are presented
and discussed. Finally, in Sect. 6 conclusions are drawn.

2 Geometries Definition

The numerical simulations of hemodynamics are performed on both idealized ge-
ometries and an anatomically realistic geometry of a patient-specific aneurysm. The
patient-specific geometry is reconstructed from medical images obtained in vivo
from rotational computerized tomography angiography (CTA), with resulting voxel
resolution of 0.4 mm on a 512 3 grid. This volumetric data is segmented using a
constant threshold value. The surface triangulation of the vessel wall is extracted
using a marching tetrahedra algorithm and hence a linear interpolation. This
approach is computationally inexpensive but assumes that the image intensity of the
desired object is sufficiently different from the background to permit a constant gray
scale threshold choice. It furthermore requires that the medical image resolution
is fine enough and isotropic to perform marching tetrahedra directly, instead of
performing an interpolation as presented in [ 8 ] and references therein.
Several other segmentation methods exist for image data of cerebral aneurysms,
such as deformable models and region growing [ 2 , 4 , 23 ]; however these tend to
be sensitive to user defined parameter settings. Each segmentation approach will
yield a different geometry definition that depends on user-defined coefficients or
assumptions made in the approach [ 26 ]. Ultimately there is an inherent uncertainty
in the model definition limited by the acquisition modality, resolution, contrast, and
noise.
The resulting virtual model of the vasculature is then prepared for the numerical
simulations by identifying the regions of interest and removing secondary branches.
Successively surface smoothing is performed due to medical imaging noise and
limited resolution, taking care not to alter the object beyond the pixel size, since
this represents the inherent uncertainty size. Smoothing is performed using the
bi-Laplacian method, with a final inflation along the local normal by a constant
distance in order to minimize the volume alteration and surface distortion [ 8 ].