Biomedical Engineering Reference
In-Depth Information
In the context of cardiovascular flow simulations, another important point con-
cerns the generation of a mesh boundary layer that is able to capture at the vicinity
of the wall derived quantities of clinical interest. While many authors still use fully
unstructured isotropic tetrahedral meshes, these meshes are not efficient in terms
of computational time. Indeed, they require a huge number of elements in order to
have sufficiently small elements near the wall to resolve the boundary layer and
to be able to capture accurately derived quantities such as WSS. Moreover, some
authors have reported that these meshes can produce spurious fluctuations for the
WSS [36, 38]. Boundary layer meshes permit to capture those derived quantities
accurately while keeping for efficiency purposes a reasonable number of mesh el-
ements. Those meshes can be built with an advancing layer method [10, 17, 24]
that extrudes the lumen surface mesh in the inward direction. The extruded prisms
are then subsequently split into tetrahedra and the remaining of the lumen volume
filled with tetrahedra. For blood flow simulations with compliant walls, one has to
build also the vascular wall. Using the presented mesh boundary layer technique,
the vascular wall can be built by extruding the lumen surface mesh in the outward
direction with a given wall thickness. For arteries, the ratio of this wall thickness
h
to the inside radius is typically between 0
15.
Sect. 13.2 presents two meshing algorithms for cardiovascular simulations. The
first algorithm is a surface remeshing method based on a finite element conformal
parametrization and the second is volume meshing algorithm with a mesh boundary
layer generation technique. Sect. 13.3 shows mesh quality statistics for cardiovas-
cular meshes generated with the presented algorithms. Finally simulation results are
given in Sect. 13.4 that show the impact of tetrahedral mesh quality for cardiovas-
cular flow simulations.
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1and0
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13.2 Methods
In this section, we present the algorithms for the generation of high quality meshes of
cardiovascular districts. Our proposed meshing pipeline consists mainly in two steps,
which are described in the following subsections: (i) From a given triangulation of
the lumen surface, use finite element conformal parametrizations to create a new
surface mesh with a higher quality and a computational mesh size field (ii) extrude
the lumen surface mesh outward and inward in order to build the vascular wall and
the viscous boundary layer mesh for the blood flow.
The last meshing step involves the use of a tetrahedral mesh generator to mesh
the two extruded volumes as well as the remaining volume of the lumen. All the
presented algorithms are implemented in the open-source mesh generator Gmsh [19]
and examples can be found on the Gmsh wiki
1
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1
Gmsh's wiki:
https://geuz.org/trac/gmsh
(username: gmsh, password: gmsh).
