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Fluid-structure interaction simulations of cerebral arteries modeled by isotropic and anisotropic constitutive laws

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Abstract

This paper considers numerical simulations of fluid-structure interaction (FSI) problems in hemodynamics for idealized geometries of healthy cerebral arteries modeled by both nonlinear isotropic and anisotropic material constitutive laws. In particular, it focuses on an anisotropic model initially proposed for cerebral arteries to characterize the activation of collagen fibers at finite strains. In the current work, this constitutive model is implemented for the first time in the context of an FSI formulation. In this framework, we investigate the influence of the material model on the numerical results and, in the case of the anisotropic laws, the importance of the collagen fibers on the overall mechanical behavior of the tissue. With this aim, we compare our numerical results by analyzing fluid dynamic indicators, vessel wall displacement, Von Mises stress, and deformations of the collagen fibers. Specifically, for an anisotropic model with collagen fiber recruitment at finite strains, we highlight the progressive activation and deactivation processes of the fibrous component of the tissue throughout the wall thickness during the cardiac cycle. The inclusion of collagen recruitment is found to have a substantial impact on the intramural stress, which will in turn impact the biological response of the intramural cells. Hence, the methodology presented here will be particularly useful for studies of mechanobiological processes in the healthy and diseased vascular wall.

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Notes

  1. We remark that the numerical solution of the FSI problem with the (\(\text {EXP}1\), \(\text {EXP2-FS}\)) model is numerically challenging since it requires a suitable tuning and setting of the numerical parameters and discretization in order to be efficient.

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Acknowledgments

We acknowledge the support of the Swiss National Supercomputing Centre (CSCS) under the project ID s475 for providing the computational resources for the numerical simulations. P. Tricerri acknowledges the financial support of Fundação para Ciênca e a Tecnologia (FCT) of Portugal through the Research Center CEMAT-IST (under the grant SFRH/BD/51069/2010) and of the project EXCL/MAT-NAN/0114/2012. Prof. Quarteroni acknowledges the MATHCARD and the HP2C projects; Dr. Deparis thanks the HP2C project.

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Authors and Affiliations

  1. École Polytechnique Fédérale de Lausanne, Av. Piccard, Station 8, 1015, Lausanne, Switzerland

    Paolo Tricerri, Luca Dedè, Simone Deparis & Alfio Quarteroni

  2. Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal

    Paolo Tricerri & Adélia Sequeira

  3. MOX - Modeling and Scientific Computing, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, via Bonardi 9, 20133, Milano, Italy

    Alfio Quarteroni

  4. Department of Mechanical Engineering and Materials Science, Department of Bioengineering, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA, 15261, USA

    Anne M. Robertson

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  1. Paolo Tricerri
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Tricerri, P., Dedè, L., Deparis, S. et al. Fluid-structure interaction simulations of cerebral arteries modeled by isotropic and anisotropic constitutive laws. Comput Mech 55, 479–498 (2015). https://doi.org/10.1007/s00466-014-1117-y

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