Statistical Shape Modeling of Diseased Coronary Arteries

Coronary arteries are susceptible to atherosclerosis, a chronic inflammation characterized by progressive intimal thickening due to plaque accumulation, leading to lumen constriction. Arterial geometry significantly influences hemodynamics, which in turn is crucial in both the initiation and progression of the disease. Given the key role of vascular geometry, Statistical Shape Modeling (SSM) has emerged as a well-established method for anatomical characterization. This computational approach enables the quantification of anatomical variations and has gained prominence in cardiovascular research for capturing complex morphological features in cardiovascular districts. In this context, this thesis project is aimed at the application of SSM to derive the main pathological shape features of a cohort of diseased Left Anterior Descending (LAD) coronary arteries. A total of 233 patient-specific diseased LAD models reconstructed from three-dimensional (3D) quantitative coronary angiography were employed to build a statistical shape model based on Principal Component Analysis (PCA). More in detail, the overall analysis was carried out on models clipped to include the lesion segment, plus upstream and downstream segments, each three times the cross-sectional diameter at the lesion’s most proximal and distal points. To build the statistical shape model, a non-parametric approach based on the open-source code Deformetrica, able to handle non-isotopological meshes, was adopted starting from 3Dsurface meshes. Firstly, a data pre-processing phase was performed, including rigid registration to align models and a further non-rigid registration through Procrustes Analysis (PA). Then, Deformetrica was employed to extract a template, representing the anatomical average shape of the population, and vessel-specific sets of moment vectors mapping the template towards each vessel-specific shape. PCA was then applied to the moment vectors to retrieve the main shape modes among the population. Finally, Linear Discriminant Analysis (LDA) was performed on the PCA scores on a smaller subset (48 vessels, the only cases with available clinical outcomes) of the total cohort. In this case, LDA was employed to investigate the association between geometric features and the risk of myocardial infarction, through the generation of an hyperplane maximizing class separation and consequently a unique Z-score for each vessel in the subset by projecting each shape onto the LDA hyperplane. Reconstruction errors showed minimal discrepancies between reconstructed and original shapes, with maximum Euclidean and Hausdorff distances under 0.8 mm, confirming the SSM-based approach reliability in representing the original geometries. PCA revealed that 14 modes accounted for 90% of the total shape variation, yielding a reconstruction error with a mean Euclidean distance of 0.21 mm and a maximum Euclidean distance of 1.0132 mm. Likewise, 22 modes accounted for 95% of the total variance, decreasing the mean Euclidean distance to 0.190 mm and the maximum Euclidean distance to 0.8 mm. The ROC curves obtained with LDA Z-scores produced an AUC of 0.85 considering 14 modes to build the LDA hyperplane and of 0.92 considering 22 modes instead. In conclusion, the findings of this thesis underscore the feasibility of applying a SSM-based approach to capture the main morphological features of LAD lesions and their association with future myocardial infarction, thus offering valuable tools for both research and clinical practice in CAD management.