Cardiovascular diseases (CVDs), a group of disorders impeding the blood supply to heart, brain, or arms and legs, represent the leading cause of death worldwide. The high number of deaths motivates the desire for minimally invasive procedures and accounts for the success of image-guided catheter-based treatment procedures such as balloon angioplasty and stent insertion. However, the risk of post-surgical complications and follow-up surgeries due to pathological tissue responses such as restenosis is relatively high. This motivates computational methods as a tool to enhance the understanding of the underlying causes and for the computer-aided design of new endovascular devices in order to prevent post-operative complications in the future. Especially because of their complex geometry, high slenderness, and large deformations during insertion, the efficient simulation of stent structures and the interaction with their surroundings still pose a challenge. Within this thesis, a reduced-dimensional model to represent the stent structure, based on geometrically exact beam theory, is adopted, and the applicability of a mixed-dimensional framework in the context of balloon angioplasty and stented arteries is investigated. In particular, a novel coupling of 1-dimensional (1D) geometrically exact beam equations to a 3-dimensional (3D) background fluid mesh is developed, and arising numerical and algorithmic challenges connected to its multi-physics nature and large dimensionality gap are addressed. The high efficiency gained by the employment of a reduced-dimensional model allows the design of an efficient mixed-dimensional model taking into account the interactions between all components of a stented artery, namely the blood flow, the stent structure, and the vessel wall, making it the first model of its kind. In the first part of this thesis, the computational framework for the embedding of geometrically exact beam theory in 3-dimensional fluid flow is presented. The consequently arising truly mixed-dimensional 1D-3D coupling scheme constitutes a novel numerical strategy that naturally necessitates consistent discretization methods and specifically tailored algorithmic solution schemes to ensure accurate and efficient computational treatment. Two state-of-the-art interface discretization methods, a Gauss-Point-to-Segment (GPTS) and a mortar-type method, as well as a specially-tailored strongly-coupled Quasi-Newton based partitioned solution algorithm for applications involving fibers with high slenderness ratios, are presented. The influence of all employed algorithmic and numerical parameters on efficiency and results of the solution procedure as well as the limit of the method's modeling assumptions are studied through appropriate examples. Finally, the convergence of the mixed-dimensional problem solution under uniform mesh refinement is demonstrated and the method's capabilities in capturing flow phenomena at large scale are illustrated. Further, an extension of the proposed fluid-beam interaction (FBI) method to a full fluid-beam-structure interaction (FBSI) framework, allowing the representation of additional effects in regard to the interaction of fluid flow with 3D continuum structures, is presented. Next, the focus lies on the mixed-dimensional modeling of balloon angioplasty based on state-of-the-art approaches to beam-to-solid-surface (BTSS) interactions and mortar finite element-based contact mechanics. The model is validated by chosen numerical examples and used as the foundation for the proposal of a novel patient-specific balloon-catheter technology for the stenting of curved or asymmetrically stenosed arteries. An optimization procedure for the automated adaptation of the proposed technology to patient-specific geometries is presented, and the benefit of the improved devices is demonstrated through numerical experiments. Eventually, the core capabilities of the newly developed solution algorithm for mixed-dimensional multi-physics problems and the mixed-dimensional structure model for balloon angioplasty are combined to form a novel fluid-beam-structure interaction framework that takes beam-to-solid-surface mesh tying into account, and the resulting procedure is applied to an idealized model of a stented artery. All in all, the results obtained in this thesis demonstrate the substantial potential of mixed-dimensional modeling not only in the context of balloon angioplasty but as a general-purpose tool for the interaction of slender structures with 3-dimensional continua. Possible extensions and exciting future application scenarios are outlined at the end of this thesis.    «

Cardiovascular diseases (CVDs), a group of disorders impeding the blood supply to heart, brain, or arms and legs, represent the leading cause of death worldwide. The high number of deaths motivates the desire for minimally invasive procedures and accounts for the success of image-guided catheter-based treatment procedures such as balloon angioplasty and stent insertion. However, the risk of post-surgical complications and follow-up surgeries due to pathological tissue responses such as restenosi...    »