Computational Mechanics

, Volume 50, Issue 6, pp 789–804 | Cite as

Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves

  • Jianyao Yao
  • G. R. Liu
  • Daria A. Narmoneva
  • Robert B. Hinton
  • Zhi-Qian Zhang
Original Paper


This paper presents a novel numerical method for simulating the fluid–structure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/element method and the smoothed finite element method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed finite element method (or S-FEM). The FSI force is calculated on the Lagrangian fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.


Fluid–structure interaction Immersed smoothed finite element method Fictitious fluid Characteristic-based split Aortic valve 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Jianyao Yao
    • 1
  • G. R. Liu
    • 1
  • Daria A. Narmoneva
    • 2
  • Robert B. Hinton
    • 3
  • Zhi-Qian Zhang
    • 4
  1. 1.School of Aerospace Systems, College of Engineering and Applied ScienceUniversity of CincinnatiCincinnatiUSA
  2. 2.Department of Biomedical EngineeringUniversity of CincinnatiCincinnatiUSA
  3. 3.Division of Cardiology, The Heart InstituteCincinnati Children’s Hospital Medical CenterCincinnatiUSA
  4. 4.Singapore-MIT Alliance (SMA)National University of SingaporeSingaporeSingapore

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