  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.
