Biomedical Engineering Reference
In-Depth Information
The presented algorithms include a remeshing strategy of an initial low-quality
triangulation and an advancing front boundary layer generation technique. The
remeshing strategy relies on the computation of a conformal mapping. We show
that the remeshing in the parametric space is then optimal with a two-dimensional
Frontal algorithm.
We have put to the fore the importance of the mesh quality and the mesh algorithm
upon the simulations. By comparing an important clinical indicator, the wall shear
stress, on different meshes,we have shown how the mesh quality, and in particular
wether accounting or not for the fluid boundary layer, affects the reliability of these
evaluations.
Acknowledgements.
Swiss National Science Foundation under grant 200020-117587 and the Eu-
ropean Research Council Advanced Grant ”Mathcard, Mathematical Modelling and Simulation of
the Cardiovascular System” Project ERC-2008-AdG 227058. The virtual pathological heart of the
virtual physiological human (VPH2) project and the Swiss Platform for High-Performance and
High-Productivity Computing (HP2C).
References
[1] Alliez P., Meyer M., Desbrun M.: Interactive geometry remeshing. Computer graphics (Pro-
ceedings of the SIGGRAPH 02) pp. 347-354, 2002.
[2] Antiga L., Piccinelli M., Botti L., Ene-Iordache B., Remuzzi A., Steinman D.: An image-
based modeling framework for patient-specific computational hemodynamics. Medical and
Biological Engineering and Computing
46
(11): 1097-1112, 2008.
[3] Antiga L., Steinman D.: The vascular modeling toolkit, http://www.vmtk.org
[4] Babuska I., Aziz A.: On the angle condition in the finite element method. SIAM Journal on
Numerical Analysis
13
: 214-226, 1976.
[5] Batdorf M., Freitag L., Ollivier-Gooch, C.: A computational study of the effect of unstructured
mesh quality on solution efficiency. In: Proc. 13th AIAA Computational Fluid Dynamics
Conf., 1997.
[6] Bechet E., Cuilliere J.C., Trochu F.: Generation of a finite element mesh from stereolithog-
raphy (stl) files. Computer-Aided Design
34
(1): 1-17, 2002.
[7] Borouchaki H., Laug P., George P.: Parametric surface meshing using a combined advancing-
front generalized delaunay approach. International Journal for Numerical Methods in Engi-
neering
49
: 223-259, 2000.
[8] Burleson A., Turitto V.: Identification of quantifiable hemody- namic factors in the assess-
ment of cerebral aneurysm behavior. Thromb. Haemost.
76
: 118-123, 1996.
[9] Compere G., Remacle J.F.: A mesh adaptation framework for large deformations. Interna-
tional Journal for Numerical Methods in Engineering
82
(7): 843-867, 2009.
[10] Connell S., Braaten M.: Semistructured mesh generation for three-dimensional navier-stokes
calculations. AIAA Journal
33
(6): 1017-1024, 1995.
[11] Crosetto P., Deparis S., Fourestey G., Quarteroni A.: Parallel Algorithms for Fluid-Structure
Interaction Problems in Haemodynamics. MATHICSE Technical Report
8
, 2010.
[12] Crosetto P., Reymond P., Deparis S., Kontaxakis D., Stergiopulos N., Quarteroni A.: Fluid
Structure Interaction simulations of aortic blood flow. Computers & Fluids, accepted, 2011.
[13] Eck M., DeRose T., Duchamp T., Hoppe H., Lounsbery M., Stuetzle W.: Multiresolution
analysis of arbitrary meshes. In: SIGGRAPH '95: Proceedings of the 22nd annual conference
on Computer graphics and interactive techniques, pp. 173-182, 1995.
[14] Floater M.S.: Parametrization and smooth approximation of surface triangulations. Computer
aided geometric design
14
: 231-250, 1997.
