In the cardiovascular system the continuous interaction between blood flow and the arterial wall plays a crucial role. Plaque or aneurysm rupture occurs when hemodynamic blood pressure and thus internal plaque stress exceed a threshold that cannot be compensated by vessel wall deformation. Diseases such as atherosclerosis significantly change the vessel wall composition by incorporation of lipids, smooth muscle cells, and extracellular matrix, thereby locally changing the material properties.
Magnetic resonance imaging (MRI) may help elucidating the interplay between blood flow and vessel wall stability by providing patient-specific data on regional blood flow, vessel wall geometry, and vessel wall deformability, but the resolution of these data, in particular of the vessel wall composition, is limited. Refined mathematical models of the blood flow wall interaction in combination with efficient and robust numerical simulation methods, on the other hand, have the potential to enhance these patient-specific MRI data so that changes in wall composition and stress peaks can be identified at early stages. In this way, a real medical impact is achievable.
The ingredients needed for such an approach are the best of medical imaging, arterial wall modeling and the most efficient, robust and reliable computational methods for fluid-structure interaction. With respect to the latter, we concentrate on partitioned methods and their stable and efficient realization as combined iterative processes that consist of up to three different iteration levels.