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

动脉壁中应力分布的可靠预测是定量估计患病动脉中破裂概率的基础，作为增强的医学治疗的基于模拟的框架的一部分。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，从当前状态到更现实的设置。这些包括血管壁的体内行为、其几何形状、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鲁棒性，并分析我们的算法及其实现的时间关键方面，以减少解决方案的时间。由于收敛所需的时间步长很小，因此在第一阶段开发的求解器环境无法单独通过空间中的并行化来进一步加速。因此，我们必须改进算法方法的时间关键方面。这将包括自适应时间步进，鲁棒的全隐式方法和时间并行积分器，它们仍然可以与我们的空间并行化很好地结合在一起。另一个算法方面是进一步提高预处理器的鲁棒性以及甚至进一步增加空间上的并行可扩展性。虽然我们不希望通过空间上的并行化来减少解决方案的时间，但改进的时间离散化允许更大的时间步长，也将使我们能够从空间上进一步改进的可扩展性中获益。完全耦合的高度非线性流体-结构相互作用问题将使用整体解决方案来解决，其中非线性以全隐式方式处理。关于壁组织的机械建模，在第一阶段，实现了用于描述被动响应的发展，包括粘弹性模型、用于计算生物学激发的纤维取向的算法以及并入残余应力的方法。在第二阶段，我们计划包括模型来描述平滑肌激活产生的主动反应，这对体内条件下的应力有显着贡献。此外，将开发各向异性壳单元公式，以将内膜纳入模拟中。还需要考虑模拟的更现实的边界条件。在动脉壁的流固耦合模拟中，结构部分的边界条件往往不能很好地确定。在第二节课中，我们将研究嵌入周围组织中的动脉，以设计更真实的边界条件。我们还计划包括一个几何多尺度模型，占全球流通。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。

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.