A Case Study in Exploratory Functional Data Analysis: Geometrical Features of the Internal Carotid Artery

This pilot study is a product of the AneuRisk Project, a scientific program that aims at evaluating the role of vascular geometry and hemodynamics in the pathogenesis of cerebral aneurysms. By means of functional data analyses, we explore the AneuRisk dataset to highlight the relations between the geometric features of the internal carotid artery, expressed by its radius profile and centerline curvature. and the aneurysm location. After introducing a new similarity index for functional data, we eliminate ancillary variability of vessel radius and curvature profiles through an iterative registration procedure. We then reduce data dimension by means of functional principal components analysis. Last, a quadratic discriminant analysis of functional principal components scores allows us to discriminate patients with aneurysms in different districts.