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

Laura M. Sangalli Laura M. Sangalli is Post-Doctoral Fellow , Piercesare Secchi is Professor , and Simone Vantini is Post-Doctoral Fellow , MOX—Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy; Alessandro Veneziani is Associate Professor, Department of Mathematics and Computer Sciences, Emory University, 1131-002-1AC, Atlanta, GA 30322, USA . This research has been carried out within the AneuRisk Project, a joint research program involving MOX Laboratory for Modeling and Scientific Computing (Dipartimento di Matematica, Politecnico di Milano), Laboratory of Biological Structures (Dipartimento di Ingegneria Strutturale, Politecnico di Milano), Istituto Mario Negri (Ranica), Ospedale Niguarda Ca' Granda (Milano), and Ospedale Maggiore Policlinico (Milano). The Project is supported by Fondazione Politecnico di Milano and Siemens Medical Solutions Italia, and supported in part by Ministero dell'Istruzione dell'Università e della Ricerca (research project “Metodi numerici avanzati per il calcolo scientifico” PRIN2006). The authors are especially grateful to Edoardo Boccardi (Ospedale Niguarda Ca' Granda), who provided the three-dimensional angiographies and motivated their research by posing fascinating medical questions; and to Luca Antiga and Marina Piccinelli (Istituto Mario Negri), who performed the image reconstructions. Last, they also thank the editor and three anonymous reviewers for their constructive comments.

Piercesare Secchi Laura M. Sangalli is Post-Doctoral Fellow , Piercesare Secchi is Professor , and Simone Vantini is Post-Doctoral Fellow , MOX—Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy; Alessandro Veneziani is Associate Professor, Department of Mathematics and Computer Sciences, Emory University, 1131-002-1AC, Atlanta, GA 30322, USA . This research has been carried out within the AneuRisk Project, a joint research program involving MOX Laboratory for Modeling and Scientific Computing (Dipartimento di Matematica, Politecnico di Milano), Laboratory of Biological Structures (Dipartimento di Ingegneria Strutturale, Politecnico di Milano), Istituto Mario Negri (Ranica), Ospedale Niguarda Ca' Granda (Milano), and Ospedale Maggiore Policlinico (Milano). The Project is supported by Fondazione Politecnico di Milano and Siemens Medical Solutions Italia, and supported in part by Ministero dell'Istruzione dell'Università e della Ricerca (research project “Metodi numerici avanzati per il calcolo scientifico” PRIN2006). The authors are especially grateful to Edoardo Boccardi (Ospedale Niguarda Ca' Granda), who provided the three-dimensional angiographies and motivated their research by posing fascinating medical questions; and to Luca Antiga and Marina Piccinelli (Istituto Mario Negri), who performed the image reconstructions. Last, they also thank the editor and three anonymous reviewers for their constructive comments.

Simone Vantini Laura M. Sangalli is Post-Doctoral Fellow , Piercesare Secchi is Professor , and Simone Vantini is Post-Doctoral Fellow , MOX—Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy; Alessandro Veneziani is Associate Professor, Department of Mathematics and Computer Sciences, Emory University, 1131-002-1AC, Atlanta, GA 30322, USA . This research has been carried out within the AneuRisk Project, a joint research program involving MOX Laboratory for Modeling and Scientific Computing (Dipartimento di Matematica, Politecnico di Milano), Laboratory of Biological Structures (Dipartimento di Ingegneria Strutturale, Politecnico di Milano), Istituto Mario Negri (Ranica), Ospedale Niguarda Ca' Granda (Milano), and Ospedale Maggiore Policlinico (Milano). The Project is supported by Fondazione Politecnico di Milano and Siemens Medical Solutions Italia, and supported in part by Ministero dell'Istruzione dell'Università e della Ricerca (research project “Metodi numerici avanzati per il calcolo scientifico” PRIN2006). The authors are especially grateful to Edoardo Boccardi (Ospedale Niguarda Ca' Granda), who provided the three-dimensional angiographies and motivated their research by posing fascinating medical questions; and to Luca Antiga and Marina Piccinelli (Istituto Mario Negri), who performed the image reconstructions. Last, they also thank the editor and three anonymous reviewers for their constructive comments.

Alessandro Veneziani Laura M. Sangalli is Post-Doctoral Fellow , Piercesare Secchi is Professor , and Simone Vantini is Post-Doctoral Fellow , MOX—Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy; Alessandro Veneziani is Associate Professor, Department of Mathematics and Computer Sciences, Emory University, 1131-002-1AC, Atlanta, GA 30322, USA . This research has been carried out within the AneuRisk Project, a joint research program involving MOX Laboratory for Modeling and Scientific Computing (Dipartimento di Matematica, Politecnico di Milano), Laboratory of Biological Structures (Dipartimento di Ingegneria Strutturale, Politecnico di Milano), Istituto Mario Negri (Ranica), Ospedale Niguarda Ca' Granda (Milano), and Ospedale Maggiore Policlinico (Milano). The Project is supported by Fondazione Politecnico di Milano and Siemens Medical Solutions Italia, and supported in part by Ministero dell'Istruzione dell'Università e della Ricerca (research project “Metodi numerici avanzati per il calcolo scientifico” PRIN2006). The authors are especially grateful to Edoardo Boccardi (Ospedale Niguarda Ca' Granda), who provided the three-dimensional angiographies and motivated their research by posing fascinating medical questions; and to Luca Antiga and Marina Piccinelli (Istituto Mario Negri), who performed the image reconstructions. Last, they also thank the editor and three anonymous reviewers for their constructive comments.

Abstract

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.

KEY WORDS:

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

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

Related Research Data

Information for

Open access

Opportunities

Help and information

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

Abstract

Reprints and Corporate Permissions

Academic Permissions

Related Research Data

Related research

To cite this article:

Download citation

Information for

Open access

Opportunities

Help and information

Keep up to date

Your download is now in progress and you may close this window

Login or register to access this feature