Functional Data Analysis of CFD Simulations: the Systolic Wall Shear Stress Map of the Internal Carotid Artery
Monday 20th December 2010
In this work, situated in the context of the AneuRisk project, we investigate possible relationships between Wall Shear Stress on Internal Carotid Artery wall and the origin of cerebral aneurysms. Our data come from ﬂuidynamics numerical simulations performed by the Mathematics and Computer Science Department of Emory University. We decided to analyze CFD simulations by means of a very innovative approach that is Functional Data Analysis. At our knowledge, this the very ﬁrst time that this kind of data is statistically analyzed. Simulations provide us Wall Shear Stress values for every point of ICA wall, which is represented as a two dimensional surface. In this work the techniques and results obtained by using Functional Data Approach on Wall Shear Stress surfaces are presented. In Chapter 1, purposes of the present work, with respect to the scientiﬁc literature, are outlined and the process of collection and elicitation of raw data from medical imagery is described. A ﬁrst exploratory analysis about the composition of patients’ set is presented. In Section 2.1, a brief introduction to Functional Data Analysis is presented, underlying its peculiarities with rapport to the classical approach. In Chapter 2, we describe the smoothing procedure, i.e. in this step discrete data are transformed into continuous ones, focusing on the choice of the bandwidth. In Chapter 3, the registration problem is treated, showing the transition from continuous to continuous and aligned data, ready to be analyzed. In Chapter 4, the statistical analysis on continuous, aligned, reduced data is performed by means of the Functional Principal Component Analysis. Finally, in Chapter 5, conclusions of this work are exposed, keeping into considerations also all the results previously found in the AneuRisk project, suggesting other research directions suitable for possible future developments of the program.