RESUMEN
Morphological variations in the left atrial appendage (LAA) are associated with different levels of ischemic stroke risk for patients with atrial fibrillation (AF). Studying LAA morphology can elucidate mechanisms behind this association and lead to the development of advanced stroke risk stratification tools. However, current categorical descriptions of LAA morphologies are qualitative and inconsistent across studies, which impedes advancements in our understanding of stroke pathogenesis in AF. To mitigate these issues, we introduce a quantitative pipeline that combines elastic shape analysis with unsupervised learning for the categorization of LAA morphology in AF patients. As part of our pipeline, we compute pairwise elastic distances between LAA meshes from a cohort of 20 AF patients, and leverage these distances to cluster our shape data. We demonstrate that our method clusters LAA morphologies based on distinctive shape features, overcoming the innate inconsistencies of current LAA categorization systems, and paving the way for improved stroke risk metrics using objective LAA shape groups.
RESUMEN
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic distances between parametrized or unparametrized immersed surfaces represented as 3D meshes. Building on this, we develop tools for the statistical shape analysis of sets of surfaces, including methods for estimating Karcher means and performing tangent PCA on shape populations, and for computing parallel transport along paths of surfaces. Our proposed approach fundamentally relies on a relaxed variational formulation for the geodesic matching problem via the use of varifold fidelity terms, which enable us to enforce reparametrization independence when computing geodesics between unparametrized surfaces, while also yielding versatile algorithms that allow us to compare surfaces with varying sampling or mesh structures. Importantly, we demonstrate how our relaxed variational framework can be extended to tackle partially observed data. The different benefits of our numerical pipeline are illustrated over various examples, synthetic and real. Supplementary Information: The online version contains supplementary material available at 10.1007/s11263-022-01743-0.
