Modeling and simulation of flow in cerebral aneurysms
Julia Mikhal · 2012
Outline.The organization of the thesis is as follows.In Chapter 2 we present the computational model, based on the Navier-Stokes equations, discuss skew-symmetric finite volume discretization and introduce the IB method for defining complex vessel and aneurysm geometries.We focus on the validation of the numerical method for the classical case of Poiseuille flow in a cylindrical pipe and for model vessels and aneurysm geometries.We establish firstorder convergence with grid refinement.Also, numerical shear stresses are computed and the simulations are validated also in this respect, i.e., with reference to the derivatives of the velocity, next to validation in terms of the velocity itself.The process of reconstruction of the geometry from medical imagery is presented in Chapter 3. We illustrate steady flow inside a realistic aneurysm geometry and discuss the sensitivity of flow predictions to the reconstruction steps.In Chapter 4 we present the inclusion of realistic pulsatile flow in the computational model.We consider different flow regimes, which correspond to physiologically relevant situations ranging from 'normal' to unhealthy, high Reynolds number flow conditions.We show a strong transition from simple laminar flow with a small relevant frequency content to complex flow with many high frequencies as the Reynolds number, i.e., the flow velocity or aneurysm size, increase sufficiently.Concluding remarks and an outlook for further research are given in the last chapter.