A partitioned solution approach for fluid-structure interaction problems in the arterial system

Abstract

Die vorliegende Arbeit beschäftigt sich mit der partitionierten Lösung von Mehrfeldproblemen, die aus einer hierarchischen Modellierung kardiovaskulärer Fluid-Struktur-Interaktion folgen. Verschiedene Strategien zur Kopplung der beteiligten Feldlöser werden im Detail untersucht. Dies beinhaltet die Untersuchung von sequenziellen und parallelen Kopplungsalgorithmen sowie Methoden zur Konvergenzbeschleunigung, zur räumlicher Interpolation und zeitlicher Extrapolation von Kopplungsgrößen und Konvergenzkriterien. In dem entwickelten Lösungsansatz wird ein vollaufgelöstes Modell eines Segments des arteriellen Netzwerks mit reduzierten Modellen gekoppelt, um den Einfluss der Umgebung zu berücksichtigen.

The present work is concerned with the partitioned solution of the multifield problem arising from a hierarchical modeling approach to cardiovascular fluid-structure interaction. Different strategies to couple the participating field solvers are investigated in detail. This includes staggered and parallel coupling algorithms as well as different methods for convergence acceleration, spatial interpolation and temporal extrapolation of coupling quantities as well as convergence criteria. In the developed modeling and simulation approach, a fully resolved model of a segment of the arterial network is coupled to reduced order models in order to account for the in uence of the surrounding. The resulting problem is solved using five specialized field solvers, namely a fluid and a structural solver for the three-dimensional fluid-structure interaction problem, a one-dimensional blood flow solver for the surrounding vessel network, a solver for diffrent types of windkessel models used to obtain physiological boundary conditions at the distal ends of the one- and three-dimensional models, and a solver for an elastic foundation that describes the surrounding tissue. The applicability of the solution approach is demonstrated in terms of several exemplary applications including studies of idealized and patient specific end-to-side anastomoses of bypass grafts. They are known to be prone to the development of intimal hyperplasia, i.e. a thickening of the vessel wall that may lead to occlusions in the anastomosis region. There is experimental evidence that hemodynamic quantities such as the wall shear stress promote the progression of this secondary disease. Cardiovascular FSI simulation are therefore of great interest and can aid in surgical planning and optimization of anastomoses shapes and graft materials.