Abstract
In this paper a combined arbitrary Lagrange-Euler fictitious domain (ALE-FD) method for fluid-structure interaction problems in cardiovascular biomechanics is derived in terms of a weighted residual finite-element formulation. For both fluid flow of blood and solid mechanics of vascular tissue, the performance of tetrahedral and hexahedral Crouzeix-Raviart elements are evaluated. Comparable convergence results are found, although for the test cases considered the hexahedral elements are more accurate. The possibilities that are offered by the ALE-FD method are illustrated by means of a simulation of valve dynamics in a simplified left ventricular flow model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C.A. Taylor, Predictive medicine: computational techniques in therapeutic decision-making. Computer Aided Surgery 4 (1999) 231–247.
F.J.H. Gijsen, E. Allanic, F.N. van de Vosse and J. D. Janssen, The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90° curved tube, J. Biomech. 32 (1999) 705–713.
F.J.H. Gijsen, F.N. van de Vosse and J.D. Janssen, The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. J. Biomech. 32 (1999) 601–608.
G.A. Holzapfel, A new constitutive framework for arterial wall mechanics and a comparative study of material models. Elasticity 61 (2000) 1–48.
M. Fortin, Old and new finite-elements for incompressible flow. Int. J. Num. Meth. Fluids 1 (1981) 347–354.
M.P. Robichaud and P.A. Tanguy, Comparison of 3-D finite-elements for fluid flow. Commun. Appl. Num. Meth. 22 (1987) 1251–1267.
J. Donea, S. Giuliani and J.P. Halleux, An arbitrary Langragian-Eulerian finite-element method for transient dynamic fluid structure interactions. Comp. Meth. Appl. Mech. Engng. 33 (1982) 689–723.
P.J.G. Schreurs, Numerical Simulation of Forming Processes: the use of the Arbitrary-Eulerian-Langrangian (AEL) Formulation and the Finite Element Method. PhD thesis, University of Technology, Eindhoven (1983) 136 pp.
A.A. Johnson and T.E. Tezduyar, Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comp. Meth. Appl. Mech. Engng. 119 (1994) 73–94.
P.J.R. Reuderink, Analysis of the Flow in a 3D Distendible Model of the Carotid Artery Bifurcation. PhD thesis, University of Technology, Eindhoven (1991) 138 pp.
K. Perktold and G. Rappitsch, Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J. Biomech. 28 (1995) 845–856.
M.C.M. Rutten, Fluid Solid Interaction in Large Arteries. PhD thesis, University of Technology, Eindhoven (1998) 124 pp.
F. Bertrand, P.A. Tanguy and F. Thibault, A three-dimensional ficticious domain method for incompressible flow problems. Int. J. Num. Meth. Fluids 25 (1997) 719–736.
R. Glowinski, T.W. Pan and J. Periaux, Distributed Lagrange multiplier methods for incompressible viscous flow around moving rigid bodies. Comp. Meth. Appl. Mech. Engng. 151 (1998) 181–194.
N.A. Patankar, P. singh, D.D. Joseph, R. Glowinski and T.-W. Pan, A new formulation of the distributed Lagrange multiplier/ficticious domain method for particulate flows. Int. J. Multiphase Flows 26 (2000) 1509–1524.
C.S. Peskin and D.M. McQueen, A general method for the computer simulation of biological systems interacting with fluids. Symposia Soc. Experimantal Biology 49 (1995) 265–276.
F.P.T. Baaijens, A fictitious domain/mortar element method for fluid-structure interaction. Int. J. Num. Meth. Fluids 35 (2001) 743–761.
J. de Hart, G.W.M. Peters, P.J.G. Schreurs and F.P.T. Baaijens, A two-dimensional fluid-structure interaction model of the aortic valve. J. Biomech. 33 (2000) 1079–1088.
J. de Hart, Fluid-Structure Interaction in the Aortic Heart Valve: A Three-Dimensional Computational Analysis. PhD thesis, University of Technology, Eindhoven (2002) 127 pp.
R. Temam, Navier-Stokes Equations. Amsterdam: North-Holland (1977) 526 pp.
J.D. Humphrey, Mechanics of the arterial wall: review and directions. Crit. Rev. Biomed. Engng. 23 (1995) 1–162.
C.H.G.A. Oijen, Mechanics and Design of Fibre Reinforced Vascular Prosthesis. PhD thesis, University of Technology, Eindhoven (2003) 89 pp.
R. Glowinski, T.W. Pan and J. Periaux, A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bidies: (i) case where the rigid body motions are known a priori. C.R. Acad. Sci. Paris 25 (1997) 361–369.
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. New York: Springer-Verlag (1981) 350 pp.
A. Segal, SEPRAN Manual. Leidschendam (Netherlands): Ingenieursbureau SEPRA (2000).
C.R. Ethier and D.A. Steinman, Exact fully 3D Navier-Stokes solutions for benchmarking. Int. J. Num. Meth. Fluids 19 (1994) 369–375.
R.M. Berne and M.N. Levy, Cardiovascular Physiology. St. Louis: Mosby (1967) 312 pp.
F. Bertrand, M.R. Gadbois and P.A. Tanguy, Tetrahedral elements for fluid flow. Int. J. Num. Meth. Engng. 33 (1992) 1251–1267.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van de Vosse, F., de Hart, J., van Oijen, C. et al. Finite-element-based computational methods for cardiovascular fluid-structure interaction. Journal of Engineering Mathematics 47, 335–368 (2003). https://doi.org/10.1023/B:ENGI.0000007985.17625.43
Issue Date:
DOI: https://doi.org/10.1023/B:ENGI.0000007985.17625.43