心脏模型构建及应用

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改善心脏瓣膜力学模型的有限元结果

Improving finite element results in modeling heart valve mechanics.

Earl E, Mohammadi H. Improving finite element results in modeling heart valve mechanics. Proc Inst Mech Eng H. 2018;232(7):718-725. doi:10.1177/0954411918780150

Abstract

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

Keywords: Finite element method; continuum mechanics; finite difference method; least square algorithm; numerical methods.

摘要有限元分析是一种成熟的计算工具，可用于软组织力学分析。由于心脏瓣膜瓣叶组织结构的复杂性，现有的有限元模型不能很好地描述瓣叶组织。解决这一问题的一种方法是实现计算昂贵的有限元模型，其特征是包括高阶和高密度网格技术在内的精确本构模型。在这项研究中，我们引入了一种新的数值技术，它增强了粗网格有限元模型的结果，以提供与细网格有限元模型相当的精度，同时保持相对较低的计算成本。本研究介绍了一种方法，通过该方法，在继续考虑大变形和无穷小变形的同时，减少了求解心脏瓣膜力学模拟中常用的线性和非线性本构模型所需的计算费用。该连续体模型是基于最小二乘算法和有限差分法相结合的过程，并假定应变张量的分量在有限元网格模型的所有节点上都是有效的。与现有的商业有限元软件如ANSYS和/或ABAQUS相比，所建议的数值技术易于实现，实用有效，所需的计算时间更少。

关键字：有限元法；连续介质力学；有限差分法；最小二乘算法；数值方法。