##
**Space-time finite element computation of arterial fluid-structure interactions with patient-specific data.**
*(English)*
Zbl 1180.92023

Summary: The stabilized space-time fluid-structure interaction (SSTFSI) technique developed by the team for advanced flow simulation and modeling is applied to the computation of arterial fluid-structure interactions (FSI) with patient-specific data. The SSTFSI technique is based on the deforming-spatial-domain/stabilized space-time formulation and is supplemented with a number of special techniques developed for arterial FSI. These include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, layers of refined fluid mechanics mesh near the arterial walls, and a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape. In the test computations we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images.

### MSC:

92C35 | Physiological flow |

92C50 | Medical applications (general) |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

### Keywords:

cardiovascular fluid mechanics; cerebral aneurysms; patient-specific data; fluid-structure interactions; hyperelastic material; space-time methods
PDF
BibTeX
XML
Cite

\textit{K. Takizawa} et al., Int. J. Numer. Methods Biomed. Eng. 26, No. 1, 101--116 (2010; Zbl 1180.92023)

Full Text:
DOI

### References:

[1] | Torii, Influence of wall elasticity on image-based blood flow simulation, Japan Society of Mechanical Engineers Journal Series A 70 pp 1224– (2004) |

[2] | Gerbeau, Fluid-structure interaction in blood flow on geometries based on medical images, Computers and Structures 83 pp 155– (2005) |

[3] | Torii, Computer modeling of cardiovascular fluid-structure interactions with the Deforming-Spatial-Domain/Stabilized Space-Time formulation, Computer Methods in Applied Mechanics and Engineering 195 pp 1885– (2006) · Zbl 1178.76241 |

[4] | Torii, Fluid-structure interaction modeling of aneurysmal conditions with high and normal blood pressures, Computational Mechanics 38 pp 482– (2006) · Zbl 1160.76061 |

[5] | Bazilevs, Isogeometric fluid-structure interaction analysis with applications to arterial blood flow, Computational Mechanics 38 pp 310– (2006) · Zbl 1161.74020 |

[6] | Torii, Influence of wall elasticity in patient-specific hemodynamic simulations, Computers and Fluids 36 pp 160– (2007) · Zbl 1113.76105 |

[7] | Tezduyar, Modeling of fluid-structure interactions with the space-time finite elements: arterial fluid mechanics, International Journal for Numerical Methods in Fluids 54 pp 901– (2007) · Zbl 1276.76043 |

[8] | Torii, Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm-dependence of the effect on the aneurysm shape, International Journal for Numerical Methods in Fluids 54 pp 995– (2007) · Zbl 1317.76107 |

[9] | Tezduyar, Arterial fluid mechanics modeling with the stabilized space-time fluid-structure interaction technique, International Journal for Numerical Methods in Fluids 57 pp 601– (2008) · Zbl 1230.76054 |

[10] | Bazilevs, Isogeometric fluid-structure interaction: theory, algorithms, and computations, Computational Mechanics 43 pp 3– (2008) · Zbl 1169.74015 |

[11] | Torii, Fluid-structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling, Computational Mechanics 43 pp 151– (2008) · Zbl 1169.74032 |

[12] | Tezduyar, Sequentially-coupled arterial fluid-s-structure interaction (SCAFSI) technique, Computer Methods in Applied Mechanics and Engineering (2008) · Zbl 1229.74100 |

[13] | Torii, Fluid-structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes, Computer Methods in Applied Mechanics and Engineering (2008) · Zbl 1229.74101 |

[14] | Tezduyar, Parallel finite-element computation of 3D flows, Computer 26 pp 27– (1993) |

[15] | Tezduyar, Massively parallel finite element simulation of compressible and incompressible flows, Computer Methods in Applied Mechanics and Engineering 119 pp 157– (1994) · Zbl 0848.76040 |

[16] | Mittal, Massively parallel finite element computation of incompressible flows involving fluid-body interactions, Computer Methods in Applied Mechanics and Engineering 112 pp 253– (1994) · Zbl 0846.76048 |

[17] | Mittal, Parallel finite element simulation of 3D incompressible flows-fluid-structure interactions, International Journal for Numerical Methods in Fluids 21 pp 933– (1995) · Zbl 0873.76047 |

[18] | Johnson, Advanced mesh generation and update methods for 3D flow simulations, Computational Mechanics 23 pp 130– (1999) · Zbl 0949.76049 |

[19] | Kalro, A parallel 3D computational method for fluid-structure interactions in parachute systems, Computer Methods in Applied Mechanics and Engineering 190 pp 321– (2000) · Zbl 0993.76044 |

[20] | Stein, Parachute fluid-structure interactions: 3-D computation, Computer Methods in Applied Mechanics and Engineering 190 pp 373– (2000) · Zbl 0973.76055 |

[21] | Tezduyar, Fluid-structure interactions of a parachute crossing the far wake of an aircraft, Computer Methods in Applied Mechanics and Engineering 191 pp 717– (2001) · Zbl 1113.76407 |

[22] | Ohayon, Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems, Computer Methods in Applied Mechanics and Engineering 190 pp 3009– (2001) · Zbl 0971.74032 |

[23] | Tezduyar TE, Sathe S, Keedy R, Stein K. Space-time techniques for finite element computation of flows with moving boundaries and interfaces. In Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Science, CD-ROM, Monterrey, Mexico, Gallegos S, Herrera I, Botello S, Zarate F, Ayala G (eds), 2004. |

[24] | van Brummelen, On the nonnormality of subiteration for a fluid-structure interaction problem, SIAM Journal on Scientific Computing 27 pp 599– (2005) · Zbl 1136.65334 |

[25] | Michler, An interface Newton-Krylov solver for fluid-structure interaction, International Journal for Numerical Methods in Fluids 47 pp 1189– (2005) · Zbl 1069.76033 |

[26] | Tezduyar, Space-time finite element techniques for computation of fluid-structure interactions, Computer Methods in Applied Mechanics and Engineering 195 pp 2002– (2006) |

[27] | Tezduyar, Solution techniques for the fully-discretized equations in computation of fluid-structure interactions with the space-time formulations, Computer Methods in Applied Mechanics and Engineering 195 pp 5743– (2006) · Zbl 1123.76035 |

[28] | Tezduyar, Fluid-Structure Interaction pp 50– (2006) |

[29] | Dettmer, A computational framework for fluid-structure interaction: finite element formulation and applications, Computer Methods in Applied Mechanics and Engineering 195 pp 5754– (2006) |

[30] | Khurram, A multiscale/stabilized formulation of the incompressible Navier-Stokes equations for moving boundary flows and fluid-structure interaction, Computational Mechanics 38 pp 403– (2006) · Zbl 1184.76720 |

[31] | Kuttler, A solution for the incompressibility dilemma in partitioned fluid-structure interaction with pure Dirichlet fluid domains, Computational Mechanics 38 pp 417– (2006) |

[32] | Lohner, Fluid-Structure Interaction pp 82– (2006) |

[33] | Bletzinger, Fluid-Structure Interaction pp 336– (2006) |

[34] | Masud, An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction, Computers and Fluids 36 pp 77– (2007) · Zbl 1181.76108 |

[35] | Sawada, Fluid-structure interaction analysis of the two dimensional flag-in-wind problem by an interface tracking ALE finite element method, Computers and Fluids 36 pp 136– (2007) · Zbl 1181.76099 |

[36] | Wall, A strong coupling partitioned approach for fluid-structure interaction with free surfaces, Computers and Fluids 36 pp 169– (2007) |

[37] | Tezduyar, Modeling of fluid-structure interactions with the space-time finite elements: solution techniques, International Journal for Numerical Methods in Fluids 54 pp 855– (2007) · Zbl 1144.74044 |

[38] | Kuttler, Fixed-point fluid-structure interaction solvers with dynamic relaxation, Computational Mechanics 43 pp 61– (2008) |

[39] | Dettmer, On the coupling between fluid flow and mesh motion in the modelling of fluid-structure interaction, Computational Mechanics 43 pp 81– (2008) · Zbl 1235.74272 |

[40] | Tezduyar, Stabilized finite element formulations for incompressible flow computations, Advances in Applied Mechanics 28 pp 1– (1992) · Zbl 0747.76069 |

[41] | Tezduyar, A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests, Computer Methods in Applied Mechanics and Engineering 94 pp 339– (1992) · Zbl 0745.76044 |

[42] | Tezduyar, A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows two-liquid flows and flows with drifting cylinders, Computer Methods in Applied Mechanics and Engineering 94 pp 353– (1992) · Zbl 0745.76045 |

[43] | Tezduyar, Computation of moving boundaries and interfaces and stabilization parameters, International Journal for Numerical Methods in Fluids 43 pp 555– (2003) · Zbl 1201.76123 |

[44] | Hughes, Finite Element Methods for Convection Dominated Flows 34 pp 19– (1979) |

[45] | Brooks, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering 32 pp 199– (1982) · Zbl 0497.76041 |

[46] | Tezduyar, Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements, Computer Methods in Applied Mechanics and Engineering 95 pp 221– (1992) · Zbl 0756.76048 |

[47] | Hughes, A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations, Computer Methods in Applied Mechanics and Engineering 59 pp 85– (1986) · Zbl 0622.76077 |

[48] | Tezduyar, New Methods in Transient Analysis 246/AMD pp 7– (1992) |

[49] | Johnson, Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces, Computer Methods in Applied Mechanics and Engineering 119 pp 73– (1994) · Zbl 0848.76036 |

[50] | Tezduyar, Finite element methods for flow problems with moving boundaries and interfaces, Archives of Computational Methods in Engineering 8 pp 83– (2001) |

[51] | Tezduyar, Encyclopedia of Computational Mechanics, Volume 3: Fluids (2004) |

[52] | Tezduyar TE, Cragin T, Sathe S, Nanna B. FSI computations in arterial fluid mechanics with estimated zero-pressure arterial geometry, In Marine 2007, CIMNE, Barcelona, Spain, Onate E, Garcia J, Bergan P, Kvamsdal T (eds), 2007. |

[53] | Tezduyar TE, Schwaab M, Sathe S. Arterial fluid mechanics with the sequentially-coupled arterial FSI technique. In Coupled Problems 2007, CIMNE, Barcelona, Spain, Onate E, Papadrakakis M, Schrefler B (eds), 2007. · Zbl 1229.74100 |

[54] | Womersley, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, Journal of Physiology 127 pp 553– (1955) |

[55] | Saad, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing 7 pp 856– (1986) · Zbl 0599.65018 |

[56] | Huang, The impact of calcification on the biomechanical stability of atherosclerotic plaques, Circulation 103 pp 1051– (2001) |

[57] | Otto, Die grundform des arteriellen pulses, Zeitung fur Biologie 37 pp 483– (1899) |

[58] | Hilber, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engineering and Structural Dynamics 5 pp 283– (1977) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.