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

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，是增强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，从当前状态走向更现实的设置。这些包括血管壁在体内行为的高级建模，它的几何形状，血管壁的多层结构，以及边界条件。此外，我们将根据这些更现实的设置提高算法的鲁棒性，并分析算法的时间关键方面及其实现，以减少解决问题的时间。由于收敛所需的时间步长较小，在第一个周期中开发的求解器环境不能仅通过空间并行化进一步加速。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并行时间积分器，它们仍然可以与我们的空间并行化很好地结合起来。另一个算法方面是进一步提高前置条件的鲁棒性，以及进一步增加空间中的并行可扩展性。虽然我们不期望通过单独在空间中并行化来减少求解时间，但是改进的时间离散化（允许更大的时间步长）也将使我们能够从进一步改进的空间可伸缩性中获益。完全耦合的高度非线性流固相互作用问题将使用整体解决方案来解决，其中非线性以完全隐式的方式处理。关于壁组织的力学建模，在第一个阶段，实现了被动响应描述的发展，包括粘弹性模型，计算生物驱动纤维取向的算法，以及包含残余应力的方法。在第二阶段，我们计划建立模型来描述由平滑肌激活引起的主动反应，这对体内条件下的应激有重要贡献。此外，将开发一个各向异性壳单元公式，以将内膜纳入模拟。模拟时还需要考虑更现实的边界条件。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，考虑全球环流。敏感性分析将使用新方法来评估不同斑块成分对危险应力浓度的影响。

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.