Statistical Shape Analysis of the Thoracic Aorta with supra-aortic vessels: development of a Non Rigid Registration Algorithm and correlation with CFD simulation results

The aorta is the major and most important artery in the human body. Due to an increase in the occurrence of cases of aortic pathologies, such as aneurysm or coarctation, the preventive diagnosis of these pathologies remains the main and most effective strategy to contrast them. Since the diagnosis is not a trivial thing, in the context of clinical research it is fundamental to be able to process, integrate and interpret large amounts of complex anatomical, functional and clinical data. In this panorama, the core tools used here to extract information and knowledge from the input data are Statistical Shape Models (SSMs). In this thesis, we have developed a computational framework for image-based statistical analysis of anatomical shapes in a populations made both of pathological and healthy patients. This population was tested by first applying geometric simplifications (removal of supra aortic vessels) and then with the full geometrical complexity. The fundamental issue in Statistical Shape Modeling is the “Correspondence Problem” between a source and a target object. To achieve this goal, it is necessary to find the point in the target that gives the best matching for each point of the source mesh. The correspondence problem is solved by searching for an optimal deformation between the two shapes, which is, in turn, a registration problem. In medical image analysis, registration involves finding a geometric transformation that maximizes the correspondence between the two objects without the need for landmarks and point correspondence. Many software have been developed trying to overcome this issue. In particular, we tested two available software for non-rigid registration. We then added in-house code to these software to achieve satisfactory results within our dataset. Finally, we implemented our own algorithm with a code completely written from scratch based on a resembling second order optimization scheme which implicitly brings regularization properties. In our knowledge, this is the first time that non rigid registration is applied to human aorta geometries with supra-aortic vessels by using a surface based representation. Principal Component Analysis (PCA) was then applied on the resulting meshes to break down the high-dimensional variability present in the dataset of shapes into a smaller set of independent variables, or modes, which describe the principal contributors to shape variability. Afterwards, a correlation study between the SSM most relevant mode for describing anatomy variations and the output of cardiac fluid dynamic simulations was carried out. We generated five geometries by selecting the mean shape from the SSM and by varying the first mode from -2 standard deviation (SD) to +2 SD. We have found a progression on the shapes of these meshes: starting from a tiny healthy aortic shape (-2 SD), we reached a shape that presents an aneurysmatic dilatation (+2 SD), particularly noticeable in the ascending part of the aorta. A relevant parameter which has been correlated in many studies to pathological aortic shapes is the Wall Shear Stress (WSS). We also investigate several indices based on Wall Shear Stress WSS and its temporal and spatial variations to capture various mechanobiological effects. These are the Oscillatory Shear Index (OSI), the Time Averaged Wall Shear Stress (TAWSS), the Relative Residence Time RRT and the Endothelial Cell Activation Potential (ECAP). One of the most widely used practices is to generate WSS data throughout Computational Fluid Dynamics (CFD) simulations which allow to solve numerically the fundamental fluid mechanic equations for complex geometries and various types of boundary conditions. For this very reason, CFD has become more and more common in the biomedical field as a tool to thoroughly investigate hemodynamics of human blood flow and arterial diseases. Therefore, five studies were performed to assess a correlation between shape, fluid dynamics and pathology