Medical image - based computational model of pulsatile flow in saccular aneurisms
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 4, p. 663-679

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical variability of the diseased vessel segment. The 3D reconstruction is associated with a faceted surface. A geometrical model is then obtained to be finally meshed for a finite element use. The pulsatile flow of incompressible newtonian blood is illustrated by numerical simulations carried out in two saccular aneurism types, a side- and a terminal-aneurism. High pressure zones are observed in the aneurism cavity, especially in the terminal one.

DOI : https://doi.org/10.1051/m2an:2003053
Classification:  68U05,  68U10,  76D05,  35Q30,  65N30
Keywords: 3D surface reconstruction, finite element method, medical images, mesh generation, Navier-Stokes equations
@article{M2AN_2003__37_4_663_0,
     author = {Salmon, St\'ephanie and Thiriet, Marc and Gerbeau, Jean-Fr\'ed\'eric},
     title = {Medical image - based computational model of pulsatile flow in saccular aneurisms},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {4},
     year = {2003},
     pages = {663-679},
     doi = {10.1051/m2an:2003053},
     zbl = {1065.92029},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2003__37_4_663_0}
}
Salmon, Stéphanie; Thiriet, Marc; Gerbeau, Jean-Frédéric. Medical image - based computational model of pulsatile flow in saccular aneurisms. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 4, pp. 663-679. doi : 10.1051/m2an:2003053. http://www.numdam.org/item/M2AN_2003__37_4_663_0/

[1] D.N. Arnold, F. Brezzi and M. Fortin, A stable finite element for the Stokes equations. Calcolo 21 (1984) 337-344. | Zbl 0593.76039

[2] J.-D. Boissonnat and M. Yvinec, Algorithmic Geometry. Cambridge University Press, UK (1998). | MR 1631175 | Zbl 0917.68212

[3] J.-D. Boissonat, R. Chaine, P. Frey, J.F. Gerbeau, G. Malandain, F. Nicoud, S. Salmon, E. Saltel and M. Thiriet, From medical images to computational blood flow models. INRIA Research Report (2003).

[4] V.D. Butty, K. Gudjonsson, P. Buchel, V.B. Makhijani, Y. Ventikos and D. Polikakos, Residence time and basins of attraction for a realistic right internal carotid artery with two aneurysms. Biorheology 39 (2002) 387-393.

[5] S. Chien, Shear dependence of effective cell volume as a determinant of blood viscosity. Science 168 (1970) 977-978.

[6] S. Chien, Biophysical behavior in suspensions, in The Red Blod Cell, D. Surgenor Ed., Academic Press, New York (1975).

[7] P.G. Ciarlet, The finite element method for elliptic problems. Stud. Math. Appl. 4 (1978). | MR 520174 | Zbl 0383.65058

[8] G.G. Ferguson, Physical factors in the initiation, growth and rupture of human intracranial saccular aneurysms. J. Neurosurg. 37 (1972) 666-677.

[9] P. Frey, A fully automatic adaptive isotropic surface remeshing procedure. INRIA Research Report 0252 (2001).

[10] J.-F. Gerbeau and M. Vidrascu, A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows. INRIA Research Report 4691 (2001).

[11] P.L. George, F. Hecht and E. Saltel, TetMesh (distributed by SIMULOG).

[12] R. Glowinski, Numerical methods for nonlinear variational problems. Springer Ser. Comput. Phys. (1984). | MR 737005 | Zbl 0575.65123 | Zbl 0536.65054

[13] F. Hecht and C. Parès, NSP1B3 : un logiciel pour résoudre les équations de Navier Stokes incompressible 3D. INRIA Research Report 1449 (1991).

[14] T.M. Liou and S.N. Liou, A review on in vitro studies of hemodynamic characteristics in terminal and lateral aneurysm models. Proc. Natl. Sci. Counc. ROC(B) 4 (1999) 133-148.

[15] W.E. Lorensen and H.E. Cline, Marching cubes: A high resolution 3D surface construction algorithm. Comput. Graphics 21 (1987) 163-169.

[16] J.-B. Mossa, Simulation d'une bifurcation artérielle. CERFACS Report (2001).

[17] K. Perktold, R. Peter and M. Resch, Pulsatile non-newtonian blood flow simulation through a bifurcation with an aneurysm. Biorheology 26 (1989) 1011-1030.

[18] O. Pironneau, On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numerische Mathematik 38 (1982) 309-332. | Zbl 0505.76100

[19] H.J. Steiger, D.W. Liepsch, A. Poll and H.J. Reulen, Hemodynamic stress in terminal saccular aneurysms: a laser-Doppler study. Heart Vessels 4 (1988) 162-169.

[20] D.A. Steinman, J.S. Milner, C.J. Norley, S.P. Lownie and D.W. Holdsworth, Image-based computational simulation of flow dynamics in a giant intracranial aneurysm. AJNR Am. J. Neuroradiol. 24 (2003) 559-566

[21] G. Taubin, Curve and surface smoothing without shrinkage, in 5th Int. Conf. on Computer Vision Proc. (1995) 852-857.

[22] M. Thiriet, G. Martin-Borret and F. Hecht, Ecoulement rhéofluidifiant dans un coude et une bifurcation plane symétrique. Application à l'écoulement sanguin dans la grande circulation. J. Phys. III France 6 (1996) 529-542.

[23] M. Thiriet et al., Apports et limitations de la vélocimétrie par résonance magnétique nucléaire en biomécanique. Mesures dans un embranchement plan symétrique. J. Phys. III France 7 (1997) 771-787.

[24] M. Thiriet, P. Brugières, J. Bittoun and A. Gaston, Computational flow models in cerebral congenital aneurisms: I. Steady flow. Méca. Ind. 2 (2001) 107-118.

[25] M. Thiriet, S. Naili and C. Ribreau, Entry length and wall shear stress in uniformly collapsed-pipe flow. Comput. Model. Engrg. Sci. 4 (2003) No. 3 and 4. | Zbl 1048.76533