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Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling

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Abstract

This is an extensive overview of the core and special space–time and Arbitrary Lagrangian–Eulerian (ALE) techniques developed by the authors’ research teams for patient-specific cardiovascular fluid–structure interaction (FSI) modeling. The core techniques are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized Space–Time formulation, and the stabilized space–time FSI technique. The special techniques include methods for calculating an estimated zero-pressure arterial geometry, prestressing of the blood vessel wall, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, the Sequentially-Coupled Arterial FSI technique and its multiscale versions, techniques for the projection of fluid–structure interface stresses, calculation of the wall shear stress and oscillatory shear index, arterial-surface extraction and boundary condition techniques, and a scaling technique for specifying a more realistic volumetric flow rate. With results from earlier computations, we show how these core and special FSI techniques work in patient-specific cardiovascular simulations.

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Notes

  1. In some cases where the outflow diameters significantly differ, the solution obtained from the Laplace’s equation for shrinking amount and wall thickness for the aneurysm/bifurcation area could have an undesirable distribution. The need for specifying values at a set of inter-patch points comes from seeking a better distribution in that area.

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Acknowledgements

This work was supported in part by a seed grant from the Gulf Coast Center for Computational Cancer Research funded by John & Ann Doerr Fund for Computational Biomedicine. It was also supported in part by the Rice Computational Research Cluster funded by NSF Grant CNS-0821727. This work was also partially supported by the UC San Diego Chancellor’s grant. We thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources that have contributed to the research reported. We also thank SINTEF, ICT for partially supporting this work. Prof. Tor Ingebrigtsen and Dr. Jorgen Isaksen of the Institute for Clinical Medicine, University of Tromsø, Norway and the Department of Neurosurgery, the University Hospital of Northern Norway provided us with patient-specific cerebral aneurysm data. Prof. Jessica Zhang and Wenyan Wang at Carnegie Mellon University provided us with meshes of the aneurysm models employed in this work. We would like to thank Fred Nugen for segmenting the thoracic aorta model. We would also like to thank Rebecca Boon of TACC for her help with visualization. Finally, we thank Dr. Ryo Torii (Imperial College) for the inflow velocity waveform used in the computations and the arterial geometry used in Sects. 11.1–11.3.

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Authors and Affiliations

  1. Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Kenji Takizawa

  2. Structural Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

    Yuri Bazilevs

  3. Mechanical Engineering, Rice University—MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Tayfun E. Tezduyar

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  1. Kenji Takizawa
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Correspondence to Kenji Takizawa.

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Takizawa, K., Bazilevs, Y. & Tezduyar, T.E. Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling. Arch Computat Methods Eng 19, 171–225 (2012). https://doi.org/10.1007/s11831-012-9071-3

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