Griffith Boyce E
Leon H. Charney Division of Cardiology, Department of Medicine, New York University School of Medicin, New York, NY 10016, U.S.A.
Int J Numer Method Biomed Eng. 2012 Mar;28(3):317-45. doi: 10.1002/cnm.1445.
The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid–structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB approach to such problems is to describe the elasticity of the immersed structure in Lagrangian form, and to describe the momentum, viscosity, and incompressibility of the coupled fluid–structure system in Eulerian form. Interaction between Lagrangian and Eulerian variables is mediated by integral equations with Dirac delta function kernels. The IB method provides a unified formulation for fluid–structure interaction models involving both thin elastic boundaries and also thick viscoelastic bodies. In this work, we describe the application of an adaptive, staggered-grid version of the IB method to the three-dimensional simulation of the fluid dynamics of the aortic heart valve. Our model describes the thin leaflets of the aortic valve as immersed elastic boundaries, and describes the wall of the aortic root as a thick, semi-rigid elastic structure. A physiological left-ventricular pressure waveform is used to drive flow through the model valve, and dynamic pressure loading conditions are provided by a reduced (zero-dimensional) circulation model that has been fit to clinical data. We use this model and method to simulate aortic valve dynamics over multiple cardiac cycles. The model is shown to approach rapidly a periodic steady state in which physiological cardiac output is obtained at physiological pressures. These realistic flow rates are not specified in the model, however. Instead, they emerge from the fluid–structure interaction simulation.
浸入边界（IB）方法是一种用于解决流固耦合问题的数学和数值框架，用于处理弹性结构浸入粘性不可压缩流体的特殊情况。处理此类问题的IB方法是用拉格朗日形式描述浸入结构的弹性，并用欧拉形式描述耦合流固系统的动量、粘性和不可压缩性。拉格朗日变量和欧拉变量之间的相互作用由具有狄拉克δ函数核的积分方程介导。IB方法为涉及薄弹性边界和厚粘弹性体的流固耦合模型提供了统一的公式。在这项工作中，我们描述了IB方法的自适应交错网格版本在主动脉心脏瓣膜流体动力学三维模拟中的应用。我们的模型将主动脉瓣的薄瓣叶描述为浸入弹性边界，并将主动脉根部的壁描述为厚的半刚性弹性结构。使用生理左心室压力波形来驱动通过模型瓣膜的血流，并通过已拟合临床数据的简化（零维）循环模型提供动态压力加载条件。我们使用此模型和方法来模拟多个心动周期内的主动脉瓣动力学。结果表明，该模型迅速接近周期性稳态，在生理压力下可获得生理心输出量。然而，模型中并未指定这些实际流速。相反，它们是从流固耦合模拟中得出的。
