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

• Applicants: Professor Dr.-Ing. Daniel Balzani; Professor Dr. Axel Klawonn; Professor Dr. Oliver Rheinbach; Professor Dr.-Ing. Jörg Schröder
• Subject Area: Mathematics ; Applied Mechanics, Statics and Dynamics
• Term: from 2012 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 214421492

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.

• DFG Programme: Research Grants
• International Connection: Switzerland
• Partner Organisation: Schweizerischer Nationalfonds (SNF)
• Co-Investigators: Professor Dr. Simone Deparis; Professor Dr. Alfio Quarteroni