We study the impact of anatomical and fluid dynamics factors on the development of cerebral aneurysms. The indications for the proper medical treatment of this pathology are still quite controversial. The site and the size of the aneurysmatic sack are the main morphological features considered in decision making (see ). In this study, called Aneurisk Project, supported by Fondazione Politecnico di Milano, Italy and Siemens Medical Solutions Italy, we present a morphological and haemodynamics analysis extended to the parent vessels and the vascular network hosting the aneurysm. We started from a data-base of about 70 patients collected at the Ca' Granda Hospital in Milan. Some of these patients did not present any pathology, others had an aneurysms in the Internal Carotid Artery, some others had an aneurysm downstream the carotid, in the Willis circle. After a level set-based 3D reconstruction of the vascular morphologies (with the code Vascular Modeling Toolkit (VMTK)) we!
computed the centerlines of the carotid arteries, their curvature, their torsion and the associated vessel radii. Analysis of these data has been associated with the presence, the position and the possible rupture of the aneurysms . More precisely, a Principal Component Analysis of the data set has been carried out for identifying the anatomical features statistically more relevant for the development of the pathology. A Quadratic Discrminant Analysis (QDA) has been then carried out for devising a proper classification of the patients . In order to corroborate the results obtained by the statistical analysis of the morphology, numerical simulations have been carried out for the computation of haemodynamics factors. In particular, we analyzed the wall shear stress on the carotid artery. This analysis seems to confirm the classification established by the QDA, providing some possible landmarks to be monitored for diagnostic and prognostic purposes. In the talk, we will!
address also some methodological aspects required in the development
of the Aneurisk Project, including the appropriate identification of the vessel centerlines (based on free knot regression splines) and the multiscale numerical simulation of the Willis Circle .
This is a joint work with: E. Boccardi (Ca' Granda Hospital, Milan, Italy), L.Antiga (Mario Negri Institute for Pharmacological Research, Bergamo, Italy), M.Piccinelli (Emory University and Mario Negri Institute for Pharmacological Research) P.Secchi, S.Vantini, L. Sangalli, S. Vele (MOX, Politecnico di Milano, Italy), T. Passerini (Emory University and MOX, Politecnico di Milano), S. Bacigaluppi (University of Milan, Neurosurgery Dept.).
 T. Hassan, et al., J. Neurosurg., 103:662-680
 M. Piccinelli, S. Bacigaluppi, E. Boccardi, B. Ene-Iordache, A. Remuzzi, A. Veneziani, L. Antiga Influence of Internal Carotid Artery Geometry on Aneurysm Location and Orientation: A Computational Geometry Study, TR-2007-021 Math&CS Department, Emory University
 L. M. Sangalli, P. Secchi, S. Vantini, A. Veneziani, Efficient estimation of 3-dimensional centerlines of inner carotid arteries and their curvature functions by free knot regression splines, TR-2007-026 Math&CS Department, Emory University
 L. M. Sangalli, P. Secchi, S. Vantini, A. Veneziani, A Case Study in Explorative Functional Data Analysis: Geometrical Features of the Internal Carotid Artery, TR-2007-027 Math&CS Department, Emory University, to appear in J Am Stat Ass (2008)