Vortex Dynamics in Cerebral Aneurysms

We use an autonomous three-dimensional dynamical system to study embedded vortex structures that are observed to form in computational fluid dynamic simulations of patient-specific cerebral aneurysm geometries. These structures, described by a vortex which is enclosed within a larger vortex flowing in the opposite direction, are created and destroyed in phase space as fixed points undergo saddle-node bifurcations along vortex core lines. We illustrate how saddle-node bifurcations along vortex core lines also govern the formation and evolution of embedded vortices in cerebral aneurysms under variable inflow rates during the cardiac cycle.