  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.
