  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 models and 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 model, point correspondence can be defined among different samples of a
cohort, allowing data transfer, quantitative comparison, shape coregistration
or population analysis. Furthermore, the VCS model allows for the generation of
specific meshes (e.g. cylindrical grids, ogrids) necessary for an accurate
reconstruction of the geometries used in fluid simulations. We provide the
technical details for coordinates computation and discuss the assumptions taken
to guarantee that they are well defined. The VCS model 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. The atlas originates from
fluid simulations (Navier-Stokes with Finite Volume Method) conducted using
OpenFOAMv10. We finally present a relevant discussion on the VCS model, which
covers its impact in important areas such as shape modeling and computer fluids
dynamics (CFD).
