Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics
Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics
复制标题
血液动力学中流固耦合问题的降阶模型和全 3D 模型之间的比较
DOI：
10.1016/j.cam.2013.09.049
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Quarteroni
中科院分区：
文献类型：
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作者：
C. M. Colciago;S. Deparis;A. Quarteroni
在对心血管系统建模时，血管壁对血流的影响具有很大的相关性。动脉血管是复杂的活组织，已经提出了三维特定模型来表示它们的行为。三维-三维流固耦合问题的数值模拟在计算时间和存储空间方面具有很高的计算成本。即使已经探索了许多可能的解决方案来加速解决这一问题，我们也远远没有一个可以快速解决的3D-3D FSI模型。在3D-3D FSI模型中，复杂性的两个主要来源是域运动和流体与结构部件之间的耦合。然而，在许多情况下，我们感兴趣的是柔顺血管中的血流动力学，而区域的位移很小，结构动力学不太相关。在这些情况下，可以使用降低问题复杂性的技术。一是用流体模型的蒸腾条件代替壁面位移，从而使问题在一个固定的域上得到解决。另一种策略是在特定假设下将动脉壁建模为薄膜（Figueroa等人，2006年，Nobile和Vergara， 2008年），而不是使用更现实（但计算量更大）的3D弹性动力学模型。使用这种策略，血管运动的动力学嵌入到血流方程中。将蒸腾条件与膜模型假设相结合，我们得到了一个吸引人的公式，实际上，我们不是在两个移动的物理域中求解两个不同的模型，而是在一个固定的流体域中求解一个Navier-Stokes系统，其中结构模型作为一个广义的Robin条件集成。在本文中，我们提出了一个与时间离散方案的选择和容器壁结构所采用的应力-应变本构关系无关的边界条件的一般公式。我们的目标是，首先，为通用时间离散方案编写具有零阶蒸腾条件的降阶模型的公式，然后在两个实际的患者特定病例中比较3D-3D FSI模型和降阶FSI模型：股腘动脉旁路和主动脉。特别是，我们对壁剪切应力的比较很感兴趣，事实上，这个量可以作为一些病理如动脉粥样硬化或血栓形成的危险因素。更一般地说，我们希望评估使用基于降阶模型的更简单公式的准确性和计算便利性。特别是，我们表明，在小位移的情况下，使用3D-3D FSI线性弹性模型或相应的降阶一产生许多类似的结果。
When modelling the cardiovascular system, the effect of the vessel wall on the blood flow has great relevance. Arterial vessels are complex living tissues and three-dimensional specific models have been proposed to represent their behaviour. The numerical simulation of the 3D–3D Fluid–Structure Interaction (FSI) coupled problem has high computational costs in terms of required time and memory storage. Even if many possible solutions have been explored to speed up the resolution of such problem, we are far from having a 3D–3D FSI model that can be solved quickly.In 3D–3D FSI models two of the main sources of complexity are represented by the domain motion and the coupling between the fluid and the structural part. Nevertheless, in many cases, we are interested in the blood flow dynamics in compliant vessels, whereas the displacement of the domain is small and the structure dynamics is less relevant. In these situations, techniques to reduce the complexity of the problem can be used. One consists in using transpiration conditions for the fluid model as surrogate for the wall displacement, thus allowing problem’s solution on a fixed domain. Another strategy consists in modelling the arterial wall as a thin membrane under specific assumptions (Figueroa et al., 2006, Nobile and Vergara, 2008) instead of using a more realistic (but more computationally intensive) 3D elastodynamic model. Using this strategy the dynamics of the vessel motion is embedded in the equation for the blood flow. Combining the transpiration conditions with the membrane model assumption, we obtain an attractive formulation, in fact, instead of solving two different models on two moving physical domains, we solve only a Navier–Stokes system in a fixed fluid domain where the structure model is integrated as a generalized Robin condition. In this paper, we present a general formulation in the boundary conditions which is independent of the time discretization scheme choice and on the stress–strain constitutive relation adopted for the vessel wall structure.Our aim is, first, to write a formulation of a reduced order model with zero order transpiration conditions for a generic time discretization scheme, then to compare a 3D–3D FSI model and a reduced FSI one in two realistic patient-specific cases: a femoropopliteal bypass and an aorta. In particular, we are interested in comparing the wall shear stresses, in fact this quantity can be used as a risk factor for some pathologies such as atherosclerosis or thrombogenesis. More in general we want to assess the accuracy and the computational convenience to use simpler formulations based on reduced order models. In particular, we show that, in the case of small displacements, using a 3D–3D FSI linear elastic model or the correspondent reduced order one yields many similar results.