Abstract
Fluid–structure interaction (FSI) problems in modeling flexible structures and moving boundaries can be simulated by combining the immersed boundary (IB) method and the Lattice–Boltzmann (LB) method. In this paper, we propose an FSI model of mitral valve leaflets and the left ventricle to simulate the flow field in the left ventricle during diastolic filling based on an IB–LB coupling scheme. Changes in the flow field and mitral valve leaflets in the FSI model are simulated with the IB–LB method, in which two arc-shaped flexible fibers simulate mitral valve leaflets immersed in the flow field. At the same time, a semi-elliptical model is used to simulate the left ventricle, which is simplified as a rigid boundary. The LB method is used to solve the Newtonian flow field, and the IB method is used to simulate the deformation of the flexible fiber interacting with the flow. In this paper, we introduce the basic principles underlying the combination of the LB and the IB methods and elucidate the coupling frame and the left ventricular flow model in detail. Finally, we verify the effectiveness of the coupled models by simulating the effects of diastolic jet flow on the motion of the mitral leaflets in the simplified left ventricular flow model.
Highlights
Cardiology is a bioscience of fluid dynamics, and the primary function of the cardiovascular system is to facilitate the perfusion of blood to the many and varied tissues and organs in the human circulatory system.1 The anatomy of the heart is complex, functioning as a pump to direct blood flow
The immersed boundary (IB) method is an effective scheme for simulating the Fluid–structure interaction (FSI) and has been widely applied to different problems related to the mechanical interactions of biological fluids with solid structures
The left ventricular wall was set as a fixed rigid boundary, and the mitral valve was immersed in a flow field
Summary
Cardiology is a bioscience of fluid dynamics, and the primary function of the cardiovascular system is to facilitate the perfusion of blood to the many and varied tissues and organs in the human circulatory system. The anatomy of the heart is complex, functioning as a pump to direct blood flow. A principal challenge of numerical simulation is accurately modeling complex solid–fluid boundary conditions and movements. In 1972, Peskin proposed a numerical method for addressing problems of the fluid–structure interaction (FSI) called the “immersed boundary” (IB) method; it was applied to the mitral valve motion, simulating the change in the flow field in the heart.. The IB method has since been widely used for numerical simulation in the study of biological system–fluid interactions This technique has been successfully used to simulate the deformability and aggregation of red blood cells, the deformation and detachment of biofilms, insect flight, aquatic animal locomotion, and change in the flow field in a three-dimensional human heart.. The modeling of IBs as a force source rather than a boundary condition in the flow field enables the use of Cartesian grids for calculations. The IB–LB method is introduced and described in detail, with the numerical results for the flow field in a two-dimensional left ventricle
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