Fast Isogeometric Method for Fluid–Structure Interaction Simulation of Heart Valves with GIFT Framework

Abstract

In order to improve the efficiency of heart valve simulation, we proposed a fast isogeometric simulation approach for time-dependent heart valve simulation algorithm with the idea of Geometric-Independent Field approximation (GIFT for short). For the solution of the blood flow field problem in a heart valve, the fluid background mesh is first simplified, then a Bézier tetrahedral mesh is generated based on the simplified mesh to maintain geometric precision, and finally, the fluid velocity field and pressure are solved. In addition, the GIFT idea is used to represent the geometry of computational domain geometry and approximate the physical field solution with different basis function spaces to obtain the numerical solution with the same precision as before simplification. In the structural mechanics simulation of valve leaflets, NURBS surfaces are used to represent the geometric model. To avoid degeneration on geometric boundary, a single leaflet geometric patch is subdivided into four patches. The immersion geometry strategy is adopted in solving the deformation problem of cardiac valve leaflets to achieve high simulation precision, and the dynamic augmented Lagrangian algorithm is used to couple fluid–structure control equations. For the time discretization, the generalized $\alpha $ method is used to control high-frequency dissipation. Numerical examples and comparisons with previous methods are also presented. The proposed algorithm can reduce the computing costs by about 54.3%, which proves the effectiveness of the proposed method.

Keywords

Isogeometric analysis / Fluid–structure Interaction / Heart valve simulation / Bézier tetrahedra / 65D17 / 68U07

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Funding

National Natural Science Foundation of China(U1909210)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature