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：心血管系统数字孪生技术的实现将为科研与临床实践提供具有深刻洞察力的计算工具。然而，这要求为该流程中的各个环节建立稳健且定义明确的模型与方法。本文提出一种血管坐标系（VCS），通过将柱坐标系概念适配于血管几何形态，实现了血管截面内位置的明确界定。利用VCS模型，可在队列的不同样本间建立点对应关系，从而支持数据传输、定量比较、形状协同配准或群体分析。此外，VCS模型能够生成流体模拟所需特定网格（如柱面网格、O型网格），这对于几何重建的精确性至关重要。我们提供了坐标计算的技术细节，并讨论了为确保其明确定义所作的基本假设。通过系列应用验证了VCS模型的效能：首先构建了稳健的低维患者特异性血管模型，并用于研究患者队列中胸主动脉的表型变异分析；继而利用点对应关系为同队列构建主动脉血流动力学图谱，该图谱源自使用OpenFOAMv10进行的流体模拟（基于有限体积法的Navier-Stokes方程）。最后对VCS模型进行了深入探讨，涵盖其在形状建模与计算流体动力学（CFD）等重要领域的影响。