Robust inter-patient comparison and analysis of blood vessels through the univocal definition of point coordinates

The availability of digital twins for the cardiovascular system will enable insightful computational tools both for research and clinical practice. This, however, demands robust and well defined methods for the different steps involved in the process. We present a vessel coordinate system (VCS) that enables the unanbiguous definition of locations in a vessel section, by adapting the idea of cylindrical coordinates to the vessel geometry. Using the VCS, point correspondence can be defined among different samples of a cohort, allowing data transfer, quantitative comparison, shape coregistration or population analysis. We provide the technical details for coordinates computation and discuss the assumptions taken to guarantee that they are well defined. The VCS is tested in a series of applications. We present a robust, low dimensional, patient specific vascular model and use it to study phenotype variability analysis of the thoracic aorta within a cohort of patients. Point correspondence is exploited to build an haemodynamics atlas of the aorta for the same cohort. Across the paper, we also show how VCS can be used for visualization of different types of data on the anatomy.