Harmonic Mapping of Intracranial Aneurysm Surfaces

We describe an approach for harmonic surface mapping of blood vessel aneurysms into a topologically equivalent canonical space. We use this approach to map and visualize local hemodynamic variables associated with the surface of sidewall internal carotid artery aneurysms (ICA) imaged by 3D X-ray angiography. These variables are derived from steady-state computational fluid dynamic simulations. An invertible harmonic map of the aneurysm surface onto the unit disc allows visual inspection of the entire surface and associated quantities at once, unobscured by shape irregularities. Results indicate that the developed approach is close to being conformal, thereby preserving local shape. This approach has applications in the generation of statistical atlases of aneurysms and in quantitative group studies of aneurysm development, growth, rupture, and treatment.