The emerging field of mechanobiology, which examines the effect of mechanical stimuli on physiological processes on both cellular and tissue scale, has attracted rapidly increasing attention during the last two decades. An important application of this discipline is growth and remodeling of biological tissue especially in the vasculature. These play an important role not only during adolescence, but for example also in aneurysms, pathological local dilations of blood vessels, which often keep growing and finally rupture causing significant morbidity and mortality. So far the rupture risk of aneurysms is mainly estimated based on their diameter or the mechanical stresses in their walls, while future growth and remodeling is largely neglected despite its obviously high relevance. An important reason for this is certainly the still fairly limited accuracy of quantitative models developed in this field during the last decade.This research project thus pursues four main goals:First, significantly enhanced quantitative models for growth and remodeling in the vasculature will be developed by a sufficiently precise incorporation of the most important underlying microscopic processes and the derivation of a mathematically more rigorous foundation.Second, computer simulations based on these enhanced models will be conducted by means of the finite element method in order to examine so far only poorly understood phenomena in the growth of aneurysms such as the frequent occurrence of intracranial saccular aneurysms behind bifurcation points in the vasculature.Third, risk indices for aneurysms will be developed which allow for a diagnosis no longer almost exclusively on the basis of their diameter or wall stress, but rather based on mathematically well-founded models of their future growth and remodeling.Fourth, a new class of computer aided diagnosis methods for aneurysms will be developed which incorporate patient-specific physiological factors (beyond just the vessel geometry) as precisely as possible and utilize not only simple scalar risk indices, but rather complex decision making algorithms trained by machine learning.Generally, this research project is intended to contribute to the extension of the principles and methods of engineering mechanics - a discipline which is so far mainly employed in mechanical and civil engineering - in such a way that also the behavior of biological systems can be increasingly well understood and predicted.