Modeling and simulation of flow in cerebral aneurysms

The formation of aneurysms in the human brain is an important cerebrovascular disorder, which affects a large number of people (estimates range from 2-6% of the population). A complex-shaped bulge may develop at a weak spot of the vessel wall. Over time this aneurysm may grow and even rupture. Diagnostic procedures available these days allow to visualize cerebral vessels and to detect aneurysms. Mathematical modeling and computational fluid dynamics can start from this patient-specific medical imagery and add important information. In fact, by computing flow and forces that develop in and near a particular cerebral aneurysm, it becomes possible to understand the intricate patterns of blood flow that develop. This can be used to support and extend the medical decision-making process. In this thesis a computational model of blood flow in the human brain was developed and applied to the simulation of pulsatile flow through a vessel segment containing a cerebral aneurysm. The simulation strategy was developed in three main steps: (i) formulation of the numerical method for incompressible flow and testing on model geometries, (ii) inclusion of realistic flow domains obtained from medical imagery and simulation of flow at physiologically realistic conditions and (iii) incorporation of realistic pulsatile variation of the flow-rate through the affected vessel segment. We developed a new immersed boundary method and extended this to not only predict the flow of blood in a vessel geometry, but also quantify the reliability of those predictions. We formulated a method to obtain practical bounding solutions, which can be used to indicate outcome-intervals for pressure and shear stresses. This idea can provide new and reliable insights for medical experts as part of the treatment of individual patients.