ADVANCED PATIENT-SPECIFIC MODELING AND ANALYSIS OF COMPLEX AORTIC STRUCTURES BY MEANS OF ISOGEOMETRIC ANALYSIS

Isogeometric Analysis (IgA) is an approach steadily consolidating in the field of computational mechanics and based on high-continuity functions, generally used in computer graphics for generating and representing curves and surfaces. The ultimate goal of this doctoral research, is the creation of a set of computational tools based on IgA to provide support to vascular surgeons during the pre-operative planning phase. In particular, one of the major innovation of our work is the use of IgA for structural isogeometric analysis performed on healthy and pathological thoracic aortas as well as the use of a particular type of knot vectors, essential ingredients of IgA, for the construction and analysis of the patient-specific models. In Chapter 2, pathologies of the aorta will be described in deep in order to understand which are the current medical needs. Subsequently, a review of the computational tools mostly used in cardiovascular biomechanics will be provided. Chapter 3 focuses on describing IgA basic ingredients. In particular, a detailed explanation of B-splines, NURBS and T-splines basis functions will be provided. Particular attention will be given to the so-called and not so used in the IgA community "unclamped" concept, for the construction of closed and periodic curves and surfaces. The unclamped concept is the key for the creation of a semi-automatic pipeline for the generation and analysis of reliable patient-specific isogeometric models of Thoracic Aortic Aneurysms, starting from DICOM images. The pipeline that will be presented in Chapter 4 is tested on a bigger cohort of patients, belonging to the "iCardioCloud project", a database of CFD on patients with thoracic aortic diseases. The ultimate goal of the pipeline is the identification of patients potentially at risk of aneurysm enlargement and rupture. A more advanced pipeline based on the T-spline technology for the generation of complex bifurcated aortic geometries characterized by an arbitrary topology will be approached in Chapter 5. This framework was born as an attempt to overcome the limitation of the rigid tensor-product structure of B-splines and NURBS basis functions, applied to the creation of branched geometries. Two real-life applications of NURBS-based IgA to 3D frictionless contact problems between stent devices (for Carotid Artery Stenting - CAS) and deformable surfaces undergoing large deformations will be described in Chapter 6. Performance comparison between IgA and linear (h-FEA) and higher-order FEA (p-FEA) with respect to solution accuracy and computational efficiency willbe shown. Open collaborations with physicians from IRCCS Policlinico San Donato, mainly employing the pipeline described in Chapter 4, will be approached in Chapter 7. In particular, the application on a case study of thoracic aorta showing a retrograde type A dissection will be presented together with a new algorithm for the application of the real patient-specific pressure distribution derived from CFD analyses on the control points of the Isogeometric model representing the thoracic aorta, to check how the stress distribution at the vessel wall changes with respect to the application of a constant pressure value. We conclude that we are able to provide physicians of computational tools based on IgA to be used in the pre-operative planning phase and in clinical practice, for reliably simulating big cohorts of patients in a short time, and extracting both single-patient and population-based results.