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).

翻译：心血管系统的数字孪生技术将为研究和临床实践提供强大的计算工具。然而，这要求在该过程涉及的各个环节中具备鲁棒且定义明确的模型与方法。我们提出了一种血管坐标系（VCS），通过将柱坐标的概念适配于血管几何结构，能够对血管截面内的位置进行明确无歧义的定义。利用VCS模型，可以在群体不同样本间建立点对应关系，从而实现数据传输、定量比较、形状共配准或群体分析。此外，VCS模型还可生成流体模拟中精确重建几何结构所需的特定网格（如圆柱网格、O型网格）。我们提供了坐标计算的技术细节，并讨论了确保其定义明确所采用的假设条件。该VCS模型在一系列应用中得到了验证。我们提出了一种鲁棒、低维度的患者特定血管模型，并将其用于研究某患者群体中胸主动脉的表型变异性分析。利用点对应关系，我们为同一群体构建了主动脉血流动力学图谱。该图谱基于使用OpenFOAMv10进行的流体模拟（采用有限体积法的纳维-斯托克斯方程）。最后，我们围绕VCS模型在形状建模和计算流体动力学（CFD）等重要领域的影响展开了深入讨论。