Mechanical properties of blood flow are commonly correlated to a wide range of cardiovascular diseases. In this work means to describe and characterise the flow field in the free-slip and no-slip domains are discussed in the context of cerebral aneurysms, reconstructed from in vivo medical imaging. The approaches rely on a Taylor series expansion of the velocity field to first order terms that leads to a system of ODEs, the solution to which locally describes the motion of the flow. On performing the expansion on the vessel wall using the wall shear stress, the critical points can be identified and the near-wall flow field parallel to the wall can be concisely described and visualised. Furthermore the near-wall expansion can be expressed in terms of relative motion, and the near-wall convective transport normal and parallel to the wall can be accurately derived on the no-slip domain. Together, these approaches give a viable and robust means to identify and describe fluid mechanic phenomena both qualitatively and quantitatively, leading to feasible practical use in biomedical applications.

From analysis of steady and unsteady flow simulations in two anatomically accurate cerebral saccular aneurysm cases, a set of measures can be readily obtained at all time intervals, including the impingement region, separation lines, convective transport near the wall and vortex core lines or structures, which have all been related to diseased states. Other fluid mechanic measures are also discussed in order to give further detail and insight during post-processing, and may play an important role in the growth and rupture of the aneurysm.

CEMAT - Center for Computational and Stochastic Mathematics