In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived. The proposed approach is highly flexible and suitable for studying the human cardiovascular system, which is composed of vessels with high morphological and mechanical variability. The resulting multiscale hyperbolic model of blood flow is solved using an asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method, which ensures the consistency of the numerical scheme with the different asymptotic limits of the mathematical model without affecting the choice of the time step by restrictions related to the smallness of the scaling parameters. Several numerical tests confirm the validity of the proposed methodology, including a case study investigating the hemodynamics of a thoracic aorta in the presence of a stent.

翻译：本文提出并讨论了一维血流建模的多尺度本构框架。通过分析所提出模型的渐近极限，表明通过适当选择与血管壁和血流之间流固耦合作用机制（弹性或粘弹性）的不同表征相关的尺度参数，可以描述动脉和静脉中不同类型的血液传播现象。在这些渐近极限下，可恢复文献中已知的血流模型。此外，通过分析系统局部弹性平衡的扰动，推导出一种新的粘弹性血流模型。所提出的方法高度灵活，适用于研究由形态和力学变异性较大的血管组成的人体心血管系统。采用一种渐近保持的隐式-显式龙格-库塔有限体积法求解得到的多尺度双曲血流模型，该方法确保了数值格式与数学模型不同渐近极限的一致性，且时间步长的选择不受尺度参数微小性的限制。多项数值测试验证了所提出方法的有效性，包括一项研究胸主动脉在支架存在下血流动力学的案例。