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A design-based model of the aortic valve for fluid-structure interaction
Biomechanics and Modeling in Mechanobiology ( IF 3.5 ) Pub Date : 2021-09-21 , DOI: 10.1007/s10237-021-01516-7
Alexander D Kaiser 1, 2, 3 , Rohan Shad 3, 4 , William Hiesinger 3, 4 , Alison L Marsden 1, 2, 3, 5
Affiliation  

This paper presents a new method for modeling the mechanics of the aortic valve and simulates its interaction with blood. As much as possible, the model construction is based on first principles, but such that the model is consistent with experimental observations. We require that tension in the leaflets must support a pressure, then derive a system of partial differential equations governing its mechanical equilibrium. The solution to these differential equations is referred to as the predicted loaded configuration; it includes the loaded leaflet geometry, fiber orientations and tensions needed to support the prescribed load. From this configuration, we derive a reference configuration and constitutive law. In fluid-structure interaction simulations with the immersed boundary method, the model seals reliably under physiological pressures and opens freely over multiple cardiac cycles. Further, model closure is robust to extreme hypo- and hypertensive pressures. Then, exploiting the unique features of this model construction, we conduct experiments on reference configurations, constitutive laws and gross morphology. These experiments suggest the following conclusions: (1) The loaded geometry, tensions and tangent moduli primarily determine model function. (2) Alterations to the reference configuration have little effect if the predicted loaded configuration is identical. (3) The leaflets must have sufficiently nonlinear material response to function over a variety of pressures. (4) Valve performance is highly sensitive to free edge length and leaflet height. These conclusions suggest appropriate gross morphology and material properties for the design of prosthetic aortic valves. In future studies, our aortic valve modeling framework can be used with patient-specific models of vascular or cardiac flow.



中文翻译:

基于设计的主动脉瓣流固耦合模型

本文提出了一种对主动脉瓣力学进行建模并模拟其与血液相互作用的新方法。模型构建尽可能基于第一原理,但模型与实验观察结果一致。我们要求小叶中的张力必须支持压力,然后导出控制其机械平衡的偏微分方程组。这些微分方程的解被称为预测负载配置;它包括负载的小叶几何形状、纤维方向和支撑规定负载所需的张力。从这个配置中,我们推导出参考配置和本构定律。在采用浸入边界法的流固耦合模拟中,模型在生理压力下可靠密封,并在多个心动周期内自由打开。此外,模型闭合对极端低血压和高血压具有鲁棒性。然后,利用该模型构建的独特特征,我们对参考构型、本构定律和总体形态进行了实验。这些实验得出以下结论: (1) 加载的几何形状、张力和切线模量主要决定模型函数。(2) 如果预测的加载配置相同,则对参考配置的更改几乎没有影响。(3) 小叶必须具有足够的非线性材料响应,以在各种压力下发挥作用。(4) 瓣膜性能对自由边长度和瓣叶高度高度敏感。这些结论为人工主动脉瓣的设计提供了适当的总体形态和材料特性。在未来的研究中,我们的主动脉瓣建模框架可以与患者特定的血管或心脏流量模型一起使用。

更新日期:2021-11-18
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