Computational analysis and the geometry of intracranial saccular aneurysms

Abstract

Intracranial saccular aneurysms present a very challenging problem both clinically and for the bioengineer. As long as a complete understanding of their material properties is unavailable, other ways to gain insight into their potential for rupture must be sought. Because aneurysms do not present in nature as simple, easily describable entities, a thorough analysis of their geometry is a necessary first step. This thesis attempts to further the body of knowledge available on this vital issue by applying surface patch methods for the computation of local curvatures, previously used in the analysis of abdominal aortic aneurysms, to the study of intracranial saccular aneurysms. This thesis also examines preliminary stress resultant calculations based on these calculated curvatures. Finally, a class of equations, Legendre functions of the first kind, are introduced and shown to provide a more accurate description of aneurysm geometry than the commonly used spherical geometry.