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Domain-Decomposition-Based Fluid Structure Interaction Algorithms for Highly Nonlinear and Anisotropic Elastic Arterial Wall Models in 3 D

基于域分解的 3D 高度非线性和各向异性弹性动脉壁模型的流固耦合算法

基本信息

批准号：
214421492
负责人：
Professor Dr.-Ing. Daniel Balzani
金额：
--
依托单位：
Lehrstuhl für Numerische Mathematik und Wissenschaftliches Rechnen
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/214421492?language=en
关键词：
Domain Decomposition Based Fluid Structure

项目摘要

The reliable prediction of stress distributions in arterial walls is the basis for a quantitative estimation of rupture probabilities in diseased arteries as part of a simulation-based framework for enhanced medical therapeutics. In this extension project, we plan to further enhance our algorithms, models, and software from the current state towards more realistic settings. These include an advanced modeling of the in-vivo behavior of the vessel wall, its geometry, the multi-layered structure of the wall, as well as the boundary conditions. Additionally, we will improve the robustness of our algorithms with respect to these more realistic settings and also analyze time-critical aspects of our algorithms and their implementations in order to reduce the time to solution. The solver environment developed in the first period could not be further accelerated by parallelization in space alone due to small time steps necessary for the convergence. Thus, we have to improve the time-critical aspects of our algorithmic approach. This will include adaptive time stepping, robust fully implicit methods, and parallel-in-time integrators, which can be still combined well with our parallelization in space. Another algorithmic aspect is to further improve the robustness of the preconditioners as well as to even further increase the parallel scalability in space. Although we do not expect to decrease the time to solution by parallelization in space alone, the improved time discretization, allowing for larger time steps, will also enable us to profit from further improved scalability in space. The fully coupled highly-nonlinear fluid-structure interaction problem will be solved using a monolithic solution scheme wherein the nonlinearities are treated in a fully-implicit manner. With respect to the mechanical modeling of the wall tissue, in the first period, developments were achieved for the description of the passive response including a visco-elastic model, an algorithm for computing a biologically motivated fiber orientation, and a method to incorporate residual stresses. In the second period, we plan to include models to describe the active response resulting from smooth muscle activation, which contributes significantly to the stresses under in-vivo conditions. Furthermore, an anisotropic shell element formulation will be developed to include the intima into the simulation. More realistic boundary conditions for the simulations need to be taken into account as well. In FSI simulations of arterial walls, often the boundary conditions of the structural part are not well determined. In the second period, we will investigate an artery embedded in surrounding tissue to devise more realistic boundary conditions. We also plan to include a geometric multiscale model, accounting for the global circulation. Sensitivity analyses will be performed using the new methods to estimate the influence of different plaque compositions on hazardous stress concentrations.

动脉壁应力分布的可靠预测是定量估计病变动脉破裂概率的基础，这是基于模拟的增强医学治疗框架的一部分。在这个扩展项目中，我们计划进一步增强我们的算法、模型和软件，从当前的状态转向更现实的设置。其中包括对血管壁的体内行为、其几何形状、管壁的多层结构以及边界条件的高级建模。此外，我们将提高我们的算法相对于这些更现实的设置的健壮性，并分析我们的算法及其实现的时间关键方面，以减少解决问题的时间。由于收敛所需的时间步长较小，仅靠空间并行化不能进一步加速第一阶段开发的求解器环境。因此，我们必须改进算法方法中对时间至关重要的方面。这将包括自适应时间推进、稳健的全隐式方法和时间并行积分器，它们仍然可以很好地与我们的空间并行化相结合。算法的另一个方面是进一步提高预条件的健壮性，以及进一步增加空间上的并行可伸缩性。虽然我们不希望仅通过空间并行化来减少求解时间，但改进的时间离散化允许更大的时间步长，也将使我们能够从进一步改善的空间可伸缩性中受益。完全耦合的高度非线性流固耦合问题将使用整体解格式来求解，其中以完全隐式的方式处理非线性。关于壁组织的力学模型，在第一阶段，在描述被动响应方面取得了进展，包括粘弹性模型、计算生物激励的纤维取向的算法以及考虑残余应力的方法。在第二阶段，我们计划包括模型来描述由平滑肌激活引起的主动反应，这对活体条件下的压力有很大的贡献。此外，还将开发一种各向异性壳单元，以将内膜包含在模拟中。还需要考虑模拟的更真实的边界条件。在动脉壁的FSI模拟中，结构部分的边界条件往往不能很好地确定。在第二阶段，我们将研究嵌入周围组织的动脉，以设计更现实的边界条件。我们还计划包括一个几何多尺度模型，以考虑全球环流。将使用新方法进行敏感性分析，以估计不同斑块成分对危险应力集中的影响。